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Thermodynamics, Transport, and Fluid Mechanics

Phase Behavior Measurements and Modeling for N2/ CO2/Extra-Heavy-Oil Mixtures at Elevated Temperatures Qianhui Zhao, Zhiping Li, Shuoliang Wang, Fengpeng Lai, and Huazhou Andy Li Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b03945 • Publication Date (Web): 04 Dec 2018 Downloaded from http://pubs.acs.org on December 5, 2018

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Industrial & Engineering Chemistry Research

Manuscript Submitted to Industrial & Engineering Chemistry Research

Phase Behavior Measurements and Modeling for N2/CO2/Extra-Heavy-Oil Mixtures at Elevated Temperatures

Qianhui Zhao1, 2, Zhiping Li1, 3*, Shuoliang Wang1, 3, Fengpeng Lai1, 3, Huazhou Li4*, of Energy Resources, China University of Geosciences, Beijing 100083, PR China 2Key Laboratory of Strategy Evaluation for Shale Gas, Ministry of Land and Resources, Beijing 100083, PR China 3Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, Beijing 100083, PR China 4School of Mining and Petroleum Engineering, Faculty of Engineering, University of Alberta, Edmonton, Canada T6G 1H9 1 School

*Corresponding Authors: Dr. Zhiping Li Professor, Petroleum Engineering China University of Geosciences Phone: 86-15300153581 Email: [email protected] Dr. Huazhou Andy Li Assistant Professor, Petroleum Engineering University of Alberta Phone: 1-780-492-1738 Email: [email protected] 1 ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Abstract

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Recently, a new technology, the so-called multi-thermal fluids huff and puff, to exploit extra

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heavy oil reservoirs has been applied successfully in several shallow heavy oil reservoirs in

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China. However, the use of this technology in deep extra heavy oil reservoirs is rare. Successful

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application of this technique in deep extra heavy oil reservoirs requires a good knowledge of the

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phase behavior and physical properties of multi-thermal fluids and extra heavy oil mixture. The

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major components of multi-thermal fluids mixtures are steam, N2, and CO2. In this work,

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targeting the application of multi-thermal fluids injection in heavy oil reservoirs, we conduct

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PVT experiments on the N2/CO2/heavy-oil mixtures under deep reservoir conditions and develop

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equation of state models for representing these PVT data. Experimentally, it is found that CO2

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solubility in extra heavy oil decreases with an increasing temperature at given pressure. Contrary

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to CO2, N2 solubility in extra heavy oil increases with an increasing temperature at given

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pressure. Theoretically, the extra heavy oil is split and lumped into 8 pseudo-components to

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characterize the critical temperatures, critical pressures, acentric factors and other properties by

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using the Kesler-Lee formulae. To match the solubility obtained in the experiments, two binary

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interaction parameter (BIP) correlations in Peng and Robinson equation of state (PR EOS) are

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selected to calculate the solubility of both N2 and CO2 in extra heavy oil (Peng and Robinson,

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1976). At a given temperature, the exponent in each BIP correlation is optimized to match the

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measured solubility of N2 or CO2 in extra heavy oil. We validate the optimized BIP exponents in

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PR EOS model by using them to reproduce the measured saturation pressures and swelling

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factors of the ternary N2/CO2/heavy-oil mixtures. The validation results show that the BIP

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correlations with the optimized exponents can reproduce the measured swelling factors and

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saturation pressures of N2/CO2/heavy-oil mixtures with a good accuracy. In addition, by carrying

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out example calculations using the tuned PR-EOS model, we discuss the possible multiphase

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equilibria that can be encountered under reservoir conditions when the multi-thermal fluids

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(N2/CO2/H2O) are injected into an extra heavy oil reservoir.

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Keywords: Multi-thermal fluids, Phase behavior, Binary interaction parameter, Extra heavy oil

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recovery

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1. Introduction

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Heavy oil is one of the most abundant oil resources in the world, but challenging to be exploited

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due to its high viscosity. Several techniques have been proposed to recover heavy oil, among

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which the most effective ones are steam flooding, cyclic steam stimulation, and steam-assisted

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gravity drainage (SAGD).1 Multi-thermal fluids stimulation using a huff and puff manner is a

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new thermal technology for recovering heavy oil that is initially proposed to recover offshore

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heavy oil resources in China.2 It enhances oil recovery by burning fuel and water to generate a

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flue gas mixture comprising of flue gas (mainly N2 and CO2) and steam, and then injecting it into

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reservoir. In essence, the mechanism of multi-thermal fluids generator is similar to the working

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mechanism of a rocket engine. The diesel oil will be mixed with air in an injection pump. After

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gas mixture is burned in the generator, the principal combustion effluents containing flue gas

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(mainly N2 and CO2) and steam will be injected through the tubing into the formation.3 Its major

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advantages include that: the burning setup occupies a small space and its construction cost is low.

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More importantly, the recovery efficiency is higher than the pure steam injection due to the

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additional heavy oil diluting effect provided by flue-gas dissolution and pressure maintenance

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effect provided by the high-pressure flue gas.4-5

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Multi-thermal fluids stimulation technology has been applied in several oil fields in China. In

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2009, the first field pilot test was carried out in the Cao 20 Block, Shengli Oilfield.6 The

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productivity turned out to be 1.6 to 2 times of the original production rate. Another pilot test in

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the Bohai Nanpu oilfield showed that the implementation of this technique led to a recovery

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efficiency significantly higher than the conventional steam stimulation.7 Laboratory simulation



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tests showed that the recovery rate of using multi-thermal fluids injection in SAGD was 4.7%

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higher than that provided by the conventional SAGD process.8 But it is noted that all these

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existing studies have been focused on the application of this technique in shallow heavy oil

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reservoirs, while few studies have explored its potential application in deep extra heavy oil

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reservoirs. One difficulty encountered when applying this technique to deep reservoirs is that the

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excessive heat loss along the tubing can result in a much smaller steam quality at the bottomhole.

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This could lead to a larger volume of condensed water, a lower injectivity of the multi-thermal

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fluids into the reservoir, and eventually a lower thermal efficiency of the process. How to

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address this difficulty relies on the good understanding of the multiphase equilibria in the

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wellbore as well as in the reservoir as they could exert significant effects on the process

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performance.

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Several experimental studies were conducted to measure the phase behavior of non-condensable

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gas (N2 and CO2) and heavy oil systems. Sayegh et al. tested the CO2 solubility in Lindbergh

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heavy oil at conditions up to 140oC and 15 MPa.9 Svrcek and Mehrotra measured the CO2

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solubility in Athabasca bitumen at conditions up to 100oC and 10 MPa.10 Varet et al. tested the

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solubility of CO2 in Athabasca bitumen and Venezuelan heavy oil up to 80oC and 12 MPa.11 All

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of the above experiments demonstrate a consistent result that the CO2 solubility in heavy oil

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decreases with an increasing temperature at a fixed pressure, but increases with an increasing

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pressure at a fixed temperature. However, divergent viewpoints appear regarding the variation of

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N2 solubility in heavy oil with changing temperatures at a fixed pressure. Svrcek and Mehrotra

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measured N2 solubility in bitumen up to 100oC and 8.79 MPa.10 Gao et al. measured N2

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solubility in a heavy oil sample at pressures up to 4 MPa and temperatures up to 280oC.12 Their

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experimental results indicated that N2 solubility in heavy oil decreases with an increasing 4 ACS Paragon Plus Environment

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temperature at a fixed pressure. Contrary to above, the experimental results given by Haddadnia

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et al., who measured N2 solubility in bitumen up to 190oC and 8 MPa, indicated that, at a given

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pressure, N2 solubility in Athabasca bitumen increases with an increasing temperature.13 As for

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the variation of N2 solubility in heavy oil with changing pressure, all of the experimental results

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showed an increasing tendency with an increasing pressure at a fixed temperature.9-13 But there is

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no sufficient experimental test dedicated to the measurement of the non-condensable gas (N2 and

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CO2) solubility at high reservoir pressure around 20 MPa and elevated temperature up to 280oC;

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these elevated conditions can be encountered in deep extra heavy oil reservoirs.

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Both laboratory experiments and numerical simulations are conducted to study the mechanisms

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of enhancing the heavy oil recovery by injecting the multi-thermal fluids. Mohsenzadeh et al.

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conducted laboratory experiments to study the injection of different mixtures (including N2-

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steam system, CO2-steam system, and synthetic flue gas-steam system) into authentic core at 750

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psia and 80oC.14 The results showed that before the gas breakthrough, flue gas-steam injection

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had the highest recovery efficiency. But after the breakthrough, CO2-steam injection achieved

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the highest recovery efficiency. Dong et al. measured CO2 and the flue gas solubility in heavy oil

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at the temperature up to 120oC and 12 MPa.3 Their results showed that, the flue gas solubility in

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heavy oil decreased with an increasing temperature at a given pressure. In the same work, they

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also conducted 2D and 3D steam-flooding experiments examining the oil-recovery performance

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of different injection fluids. Their results showed that the displacement efficiency of different

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injection fluids followed the order of: CO2-steam injection> multi-thermal fluids injection>steam

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injection>N2-steam injection.3 A simulation model was established to simulate these four

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injection processes, and a good match between the experimental results and simulated results

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could be obtained. However, the number of phases and compositions of each phases have 5 ACS Paragon Plus Environment


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significant variations in the multi-thermal-fluids-assisted SAGD process due to the injection of

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multi-thermal fluids (mainly comprised of steam, N2 and CO2) and the varied

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temperature/pressure conditions. To accurately capture the behavior of multi-thermal fluids

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during injection, it is necessary to have a profound understanding of the phase behavior of multi-

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thermal fluids at varied temperature/pressure conditions. It becomes even more important when

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this technology is applied in deep extra heavy oil reservoirs. In the reservoir, the presence of

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extra heavy oil can make the phase behavior become much more complex, justifying the need for

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conducting phase behavior measurements on the multi-thermal fluids and extra heavy oil

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mixtures.

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This research conducts a series of laboratory experiments to measure the phase behavior of

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multi-thermal fluids and extra heavy oil mixtures at high pressure and elevated temperature

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conditions. Modeling efforts using Peng-Robinson Equation of State (PR EOS) together with

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two binary interaction parameter (BIP) correlations are also made to represent the measured

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phase behavior data. Optimized exponent in each BIP correlation is developed to match the

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measured solubility of N2 or CO2 in extra heavy oil at each given temperature.15 A good

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accuracy can be found when using the optimized BIP exponents to reproduce the measured

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saturation pressures and swelling factors of the N2/CO2/heavy-oil mixtures.

161 162

2. Experimental Section

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Experiments are conducted to measure the basic properties of extra heavy oil sample such as

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density, viscosity, and molecular weight. We also measure the solubility (equivalent to saturation

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pressure measurements) of non-condensate gas (N2 and CO2) in extra heavy oil sample at

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different temperatures and pressures. 6 ACS Paragon Plus Environment

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2.1 Materials

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The extra heavy oil samples are collected from one block in Xinjiang oil field in China. The

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reservoir temperature and pressure are 80oC and 200 bar, respectively. The viscosity of the crude

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oil is 2379 mPa·s at reservoir temperature (Haake Mars, Thermo Fisher Corporation, Germany).

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When the temperature increases from 54oC to 180oC, the viscosity of extra heavy oil decreases

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from 21090 mPa·s to 20.1 mPa·s (Fig. 1). The molecular weight and specific gravity are 574.5

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g/mol and 1.0352 g/cm3, respectively. The molecular weight of the extra heavy oil is measured

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by the vapor pressure osmometry method. The instrument model is JI833-100-00 (UIC, Inc.).

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Distilled water is used in the experiments. The CO2 and N2 used in the experiments have purities

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of 99.999 mol% and 99.998 mol%, respectively.

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Fig. 1. Measured viscosity of the extra heavy oil at different temperatures

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2.2 Experimental Setup

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The major experimental setup used in this work is a high pressure PVT cell (1500FV-240, ST

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Corporation, France). Its core component is a visual PVT cell, while its peripheral components 7 ACS Paragon Plus Environment


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include high pressure metering pump, digital gas meter, ultrahigh-temperature electronic

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pressure gauge et al. This system can be used to measure some essential PVT properties, such as

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saturation pressure and swelling factor. The operating temperature range of the PVT cell is from

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20oC to 300oC. The PVT cell can sustain pressure as high as 100 MPa. The total pump volume is

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300 ml. The accuracies of the pressure, temperature and volume measurement are 0.001 MPa,

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0.1oC and 0.01 ml, respectively. A gas chromatograph (GC) apparatus (7890B, Agilent, US) is

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used to measure the crude oil composition. The standard GB/T 30430-2013, a Chinese official

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standard, is applied for the GC analysis. Fig. 2 presents the schematic diagram of the

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experimental setup for conducting PVT measurements. Table 1 shows the carbon number

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distribution of extra heavy oil sample measured with the GC apparatus.

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Table 1 Compositional analysis results of the extra heavy oil. Carbon No. C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16

wt% 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.73 0.49 0.87 1.00 1.21 1.10 1.26

mol% 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2.5534 1.5624 2.5328 2.6784 2.9850 2.5028 2.6603

Carbon No. C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 8

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wt% 1.13 0.93 0.87 0.85 0.83 0.84 0.87 0.97 1.08 1.37 1.64 1.82 1.52 1.15 0.90 0.77 0.86 1.20

mol% 2.1101 1.6574 1.4828 1.3691 1.2755 1.2381 1.2320 1.3178 1.4101 1.7169 1.9812 2.1220 1.7126 1.2535 0.9501 0.7880 0.8540 1.1573

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C17

1.37

2.7094

C36+

72.37

54.1870

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194 195 196 197 198

Fig. 2. Schematic diagram of the experimental setup for conducting PVT measurements for the N2/CO2/extra heavy oil mixtures

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Two types of experiments are conducted: solubility measurements for pure N2, pure CO2 and (85

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mol% CO2, 15 mol% N2) mixture in extra heavy oil (Exp Groups #1, #2, and #3) and saturation

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pressure measurements for one N2/CO2/H2O-extra heavy oil mixture (Exp Group #4). Table 2

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lists the conditions used in the PVT experiments on multi-thermal fluids and extra heavy oil

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mixtures.

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Firstly, the solubility of pure N2, pure CO2 and CO2-N2 mixture in extra heavy oil is measured at

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different temperature/pressure conditions. The degassing experiments are conducted to measure

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the solubility. The procedure for conducting the degassing experiments is briefly explained here.

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At a given temperature, the extra heavy oil is first loaded into the PVT cell. The non-condensable

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gas is then injected to the PVT cell. After gas injection, the PVT cell volume is then adjusted so

2.3 Experimental Procedure



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as to reach the predetermined pressure. A single liquid phase should be observed during the non-

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condensable gas injection if the heavy oil can still dissolve more gas. When a vapor phase

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appears at a given temperature and a fixed pressure, the liquid phase cannot dissolve more gas,

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and then gas supply should be cut off. The dissolution process has been done in a stepwise

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manner, and at each step the mixture is being stirred and maintained at the preset temperature

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and pressure for more than 12 hours. When the dissolution capacity is reached, we flash the

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single-phase fluid to standard conditions, and record the volume of non-condensable gas released

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as well as the volume of the remaining heavy oil.

Table 2 Conditions used in the mixtures. Exp Experimental Group Type CO2 No. To be 1 measured Solubility 2 0.0 Measurements To be 3 measured CCE 4 0.3 Experiments

217 218

PVT experiments on multi-thermal fluids and extra heavy oil Composition, mol% Extra Heavy N2 H2O oil To be 0.0 0.0 measured To be To be 0.0 measured measured To be To be 0.0 measured measured 1.6

48.1

50.0

Temperature, oC 80, 150, 280 80, 150, 280 80, 150, 280 80, 150, 280

Pressure, bar 50, 100, 150, 200 50, 100, 150, 200 50, 100, 150, 200 To be measured

219 220

Secondly, the constant composition expansion (CCE) experiment is conducted to measure the

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saturation pressure and swelling factor of the N2/CO2/H2O-extra heavy oil mixture (Exp Group

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#4). The PVT cell should be cleaned and vacuumed before the experiments. After cleaning and

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vacuuming, a certain amount of multi-thermal fluids and extra heavy oil sample is first

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transferred into the PVT cell at a given temperature. At each temperature, the CCE experiment is

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initiated starting from a single liquid phase. The initial pressure is kept higher than 200 bar in

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order to maintain the mixture as one single liquid phase. The mixture is being stirred and 10 ACS Paragon Plus Environment

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maintained at the preset temperature for more than 12 hours. Then the pressure is gradually

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decreased in a continuous manner (i.e., a slow withdrawal rate of 3 cm3/hr is applied). The

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mixture should be stirred rigorously during the measurements. When volume reading is needed,

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the stirrer is temporarily shut off to enable the volume reading on the sample. The saturation

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pressure (i.e., the two-phase/three-phase boundary) and saturation volume can be determined by

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pinpointing the inflection point of the pressure-volume relationship curves. After the test at 80oC

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is finished, the CCE experiments are repeated at higher temperatures of 150oC and 280oC.

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3. Modeling Methodology

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In this section, we describe how to characterize the extra heavy oil as well as how to model the

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phase behavior of N2/CO2/heavy-oil mixtures. The C7+ fraction is firstly split into single carbon

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numbers (SCNs) and then lumped into several pseudo-components. The thermodynamic

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properties of each SCN should be calculated by using correlations, while the thermodynamic

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properties of each pseudo-component should be estimated with a particular mixing rule. The

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detailed equations used can be referred to Appendix B. After C7+ characterization is completed,

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two correlations used to calculate the BIPs between the non-condensable gas (N2 or CO2) and

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pseudo-components are implemented in PR EOS. The exponents in the two BIP correlations are

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tuned to match the measured solubility of either N2 or CO2 in extra heavy oil at different

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temperatures. Finally, the optimized indices in the BIP correlations are validated with the

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measured saturation pressures and swelling factors of ternary N2/CO2/heavy-oil mixtures.

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3.1 Heavy Oil Characterization

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3.1.1 Splitting of C7+ Fraction and Determination of Critical Properties of Each SCN



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To characterize the extra heavy oil sample with EOS parameters, the C7+ fraction needs to be

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split first. Pedersen et al. gives a relationship between a given carbon number and the logarithm

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of its corresponding mole fraction for the carbon numbers starting at C11;16 this relationship is

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expressed below,

ln zi  A  BN i

252

(1)

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where zi is mole fraction, Ni is carbon number, while A and B are coefficients. The molecular

254

weight of SCN can be calculated based on the carbon number as follows,

M i  14 N i  

255

(2)

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where Mi is the molecular weight of each SCN, while  is a constant depending on the

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hydrocarbon type. The Watson factor Kw can be used to determine the component classes: 1) Kw

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of aromatic hydrocarbons is between 8.5 to 11.0; 2) Kw of naphthenic hydrocarbons is between

259

11.0 and 12.5; and 3) Kw of n-alkanes is between 12.5 and 13.5.17 In this study, we assume that

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the Watson factor is a constant for the extra heavy oil under study.

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The specific gravity of each SCN can be calculated based on Kw using the formula presented in

262

Appendix B. After determining the molecular weight and specific gravity for each SCN, the

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boiling point of each SCN can be calculated by the correlation given by Soreide.18 Then, the Lee-

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Kesler correlations are used to determine the critical temperature, critical pressure, and acentric

265

factor of each SCN, while the correlations proposed by Hall-Yarborough et al. are used to

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determine the critical volume of each SCN.19-21 Refer to Appendix B for more details about the

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equations used to calculate the aforementioned properties of each SCN.

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3.1.2 Lumping Scheme


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Due to the large number of SCNs split in the last step, the SCNs should be lumped before

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performing phase equilibrium calculations in order to reduce the computational cost. In this

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study, the number of lumped pseudo-components is estimated by the following equation

272

proposed by Whitson, 22 N H  1  3.3log  imax  7 

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(3)

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where NH is the number of lumped pseudo-components, and imax is the maximum carbon number

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of the reservoir fluid. The determination of the composition of each group should satisfy the two

276

principles: 1) the term

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the lumped pseudo-components should have a consistent thermodynamic behavior with the

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original one.23-24 After lumping, Hong’s mixing rule listed in Appendix B is applied to estimate

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the critical properties of the pseudo-components.25

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3.2 BIP Models

281

3.2.1 BIP Correlations

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BIP plays an important role in ensuring the accuracy of PR EOS in describing the

283

thermodynamic behavior of mixtures. The PR EOS model is listed in Appendix A. Generally, the

284

BIP between pseudo-components and the IP between N2 and CO2 are both regarded as zero.17 To

285

estimate the BIP values between non-condensable gas (N2 or CO2) and pseudo-components, two

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commonly used correlations are used: the critical volume method and the critical temperature

287

method.26-27 The critical volume method calculates the BIP with the following expression,26

  z ln M  should be consistent for different pseudo-components; and 2) i

i



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 2v1/6 v1/6  kij  1   1/3ci cj1/3  v v  cj   ci


(4)


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where kij is the BIP between the ith component and the jth component, vci and vcj are the critical

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volume of the ith component and the jth component, respectively, and  is the exponent constant

291

for this critical volume method. The critical temperature method calculates the BIP with the

292

following expression,27 

293

 2Tci1/2Tcj1/2  kij  1    T  T   ci cj 

(5)

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where Tci and Tcj are the critical temperature of the ith component and the jth component,

295

respectively, and  is the exponent constant in this correlation.

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BIP can be temperature dependent. We optimize the exponents in these BIP correlations at

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different temperatures. Fig. 3 shows the flowchart used to optimize the BIP correlation used for

298

modeling the phase behavior of CO2-extra heavy oil mixtures.

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300 301 302 303 304 305

Fig. 3. Flowchart used to optimize the BIP correlation used for modeling the phase behavior of CO2-extra heavy oil mixtures. The absolute average relative deviation (AARD) in Fig. 3 is calculated as per,

AARD 

1 n X ical  X iexp  X exp n i 1 i

(6)

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where X ical is the calculated CO2 (or N2) solubility in extra heavy oil, X iexp is the measured CO2

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(or N2) solubility in extra heavy oil, and n is the number of data points. 15 ACS Paragon Plus Environment


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308 309

3.2.2 Swelling Factor Calculation

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Viscosity reduction and swelling of extra heavy oil are the two important mechanisms

311

contributing to the recovery of heavy oil. Swelling factor can be used to quantify how much

312

swelling occurs to extra heavy oil. The swelling factor of a gas-dissolved heavy oil sample can

313

be calculated by,28

SF =

314

V2 V1 1  S 

(7)

315

where SF is swelling factor, V1 is molar volume under saturation temperature and atmospheric

316

pressure (101.3 kPa), V2 is molar volume under saturation temperature/pressure conditions, and S

317

stands for the mole fraction of gas in the heavy oil.

318

4. Results and Discussion

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4.1 Heavy Oil Characterization

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Fig. 4 shows the mole fraction of each SCN. In this figure, the mole fractions of C10-C35 are

321

measured by GC, while the mole fractions of C36-C100 are estimated by Equation (1). In this

322

study, the heaviest component of extra heavy oil is C101+. The Kw value of extra heavy oil is

323

11.65, which indicates that the hydrocarbons contained in the extra heavy oil are predominantly

324

naphthenic.


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325 326

Fig. 4. Carbon number distributions of extra heavy oil used in this study.

327

4.2 Lumping

328

In the study by Li’s et al., 6 to 8 pseudo-components are found to be more accurate in describe

329

the phase behavior of solvent(s)/heavy-oil mixtures.29 Following the work by Li et al., in this

330

study, the heavy oil is divided into 8 pseudo-components based on Equation (3).29 We determine

331

the composition of each pseudo-component by satisfying the two aforementioned principles

332

introduced in Section 3.1.2. Table 3 shows the properties of lumped pseudo-components which

333

have been calculated by the equations listed in Appendix B.

334

Table 3 Properties of lumped pseudo-components. Group No.

Carbon No.

z, mol%

Ml-i

Pc, psi

Tc, K

ω

γ

Group 1

C10-C13

13.31

164.0

332.26

674.07

0.508

0.8238

Vc， ft3/mol 10.2618

Group 2

C14-C16

13.43

209.8

281.30

732.93

0.621

0.8607

13.1724

Group 3

C17-C20

14.49

256.9

247.27

782.65

0.721

0.8925

15.7792



Page 18 of 87

Group 4

C21-C26

13.60

326.3

215.92

841.42

0.836

0.9318

19.2124

Group 5

C27-C35

12.50

426.7

191.22

905.77

0.951

0.9779

24.4443

Group 6

C36-C50

11.71

592.4

174.39

980.36

1.038

1.0374

32.3774

Group 7

C51-C82

10.92

887.7

172.04

1063.10

1.062

1.1163

44.7466

Group 8

C83-C101+

10.04

1443.5

193.31

1143.31

0.986

1.2168

113.3248

335 336

4.3 Solubility Matching

337

Fig. 5 shows the experimental results on the solubility of non-condensable gas in extra heavy oil.

338

As shown in Fig. 5a, the CO2 solubility in extra heavy oil decreases as temperature increases at a

339

given pressure. In contrast, Fig. 5b shows that the N2 solubility in extra heavy oil increases as

340

temperature increases at a given pressure; such trend is becoming more obvious at a higher

341

pressure. By comparing Fig. 5a and Fig. 5b, one can find a larger amount of CO2 can be

342

dissolved in extra heavy oil than N2 under the same condition. At a given temperature, both the

343

two figures show that the gas solubility in the extra heavy oil increases as pressure increases.

344 345

(a) 18 ACS Paragon Plus Environment

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346

(b)

347 348 349 350

Fig. 5. The solubility of non-condensable gas in extra heavy oil: (a) CO2 solubility in extra heavy oil at 80oC, 150oC, and 280oC; (b) N2 solubility in extra heavy oil at 80oC, 150oC, and 280oC.

351

Table 4 shows the optimized exponents in the two BIP correlations at different temperatures.

352

These exponents are optimized with the procedures listed in Section 3.2.2. It is noted that the

353

optimized exponents between CO2 and extra heavy oil are positive, while the optimized

354

exponents between N2 and extra heavy oil are negative. Moreover, the exponents between the

355

non-condensable gas and extra heavy oil tend to decrease with an increasing temperature.

356

Table 4 Optimized exponents in the two BIP correlations at different temperatures. Exponent

 in Equation (10)



in Equation (11)

Temperature (oC)

80

150

280

CO2- Extra Heavy oil

0.562

0.398

0.141

N2- Extra Heavy oil

-1.471

-2.157

-2.695

CO2- Extra Heavy oil

0.435

0.235

0.095

N2- Extra Heavy oil

-0.487

-0.852

-1.252



357

Fig. 6 depicts the comparison between the measured and calculated CO2 solubility in extra heavy

358

oil at different conditions for Feed #1. As shown in Fig. 6, both BIP correlations with the

359

optimized exponents can provide good match to the measured CO2 solubility in extra heavy oil.

360 361

(a)

362 363

(b)


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364 365 366 367

(c) Fig. 6. Measured and calculated CO2 solubility in extra heavy oil at (a) 80oC, (b) 150oC, and (c) 280oC.

368

Fig. 7 describes the comparison between the measured and calculated N2 solubility in extra

369

heavy oil at different conditions for Feed #2. A good agreement can be seen between the

370

predicted N2 solubility in extra heavy oil and the measured one. Nevertheless, the discrepancy

371

between the calculated N2 solubility in extra heavy oil and the measured one become enlarged as

372

temperature and pressure increases.

373



374 375

(a)

376 377

(b) 22 ACS Paragon Plus Environment

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378 379

(c)

380 381

Fig. 7. Measured and calculated N2 solubility in extra heavy oil (a) 80oC, (b) 150oC, and (c) 280oC.

382

Fig. 8 shows the AARDs of the solubility prediction for Feed #1 and Feed #2 by using the two

383

BIP correlations. As shown in Fig. 8, the largest AARD is smaller than 8%, indicating that the

384

two BIP correlations can both have a good prediction of the solubility of non-condensable gas in

385

extra heavy oil. The AARDs at 280oC are larger than those obtained at 80oC and 150oC for both

386

Feed #1 and Feed #2. It can be noted that AARDs obtained by the critical volume correlation are

387

smaller than those obtained by the critical temperature correlation at the same condition. It

388

indicates that the critical volume correlation provides more accurate BIPs to describe the

389

solubility of non-condensable gas in extra heavy oil, although this might be only specifically true

390

for the fluid mixtures studied in this work. In the following predictions, the BIPs calculated by

391

the critical volume correlation are applied.



392 393

(a)

394 395

(b)


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396 397

Fig. 8. AARD of the solubility prediction for (a) CO2-extra heavy oil mixtures and (b) N2-extra heavy oil mixtures using the two BIP correlations

398

Fig. 9 presents the BIPs between CO2 and pseudo-components obtained by the critical volume

399

correlation at different temperatures, while Fig. 10 shows the BIPs between N2 and pseudo-

400

components obtained by the critical volume correlation at different temperatures. As shown in

401

these two figures, the BIPs between non-condensable gas and pseudo-components decrease as

402

temperature increases at a given pressure. At a given temperature, the BIPs between CO2 and

403

pseudo-components increase with an increasing molecular weight of pseudo-component, while

404

the BIPs between N2 and pseudo-components decrease with an increasing molecular weight of

405

pseudo-component.

406 407 408

Fig. 9. BIPs between CO2 and pseudo-components at 80oC, 150oC and 280oC predicted by using the critical volume BIP correlation



409 410 411

Fig. 10. BIP between N2 and pseudo-components at 80oC, 150oC and 280oC predicted by using the critical volume BIP correlation

412

Fig. 11 describes the comparison between measured and predicted mole fraction of gas mixture

413

(85 mol% N2 +15 mol% CO2) in extra heavy oil at different conditions for Feed #3. The BIPs

414

between non-condensable gas and pseudo-components used in the predictions are shown in Figs.

415

9 and 10. As shown in Figure 11, at 50 bar and 100 bar, the mole fraction of N2-CO2 mixture in

416

extra heavy oil at 280oC is smaller than those at 80oC and 150oC. However, the mole fraction of

417

N2-CO2 mixture in extra heavy oil follows the order of 280oC>80oC>150oC at both 150 bar and

418

200 bar. A good agreement can be found between the measured and predicted solubility of N2-

419

CO2 mixture in extra heavy oil, indicating that the tuned BIPs are able to provide a satisfactory

420

description of the mole fraction of N2-CO2 mixture in extra heavy oil. However, a larger

421

discrepancy between the measured and predicted mole fraction of N2-CO2 mixture in extra heavy

422

oil appears at 280oC. The possible reason leading to such larger error can be that the extra heavy 26 ACS Paragon Plus Environment

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423

oil might experience thermal cracking under such higher temperature, which could generate

424

additional hydrocarbon components in the mixture. This will result in a change in extra heavy oil

425

properties, leading to inaccurate description of the extra heavy oil by the original characterization

426

scheme described above as well as shifting in the phase equilibrium.34

427 428 429

Fig. 11. Comparison of measured and predicted mole fraction of gas mixture (85 mol% N2 +15 mol% CO2) in extra heavy oil at 80oC, 150oC, and 280oC.

430

4.4 Prediction of Upper Three-Phase Boundary of N2/CO2/H2O/Heavy-Oil Mixtures

431

Next, to further validate the predictive capability of the EOS model developed above, we show

432

its prediction results on the upper three-phase boundary of N2/CO2/H2O/heavy-oil mixtures. Fig.

433

12 shows the comparison between the measured and predicted swelling factors for Feed #4 at

434

different temperatures, while it also depicts the comparison between the measured and predicted

435

saturation pressures for Feed #4 at different temperatures. The BIPs between non-condensable

436

gas and pseudo-components applied in the prediction of the swelling factor are shown in Fig. 9

437

and Fig. 10. The BIPs between water and pseudo-components are 0.5, while the BIPs for CO227 ACS Paragon Plus Environment


438

H2O pair and N2-H2O pair are set as 0.2 and 0.275, separately. Again, a reasonably good

439

agreement can be found between the predicted and measured swelling factors and saturation

440

pressures. However, larger deviations appear again at high temperatures.

441 442 443 444

Fig. 12. Comparison of measured and predicted upper three-phase boundary (boundary between aqueous-oleic two phases and vapor-oleic-aqueous three phases) for the Feed #4 mixture (1.6 mol% N2 +0.3 mol% CO2+48.1 mol% H2O+50 mol% extra heavy oil) at 80oC, 150oC and 280oC.

445

To check if thermal degradation occurs at 280oC, we measured the composition of the extra

446

heavy oil sample after the experiment. Table 5 compares the compositions of the extra heavy oil

447

sample measured before and after the experiment at 280oC. After the high-temperature

448

experiments, we can see that the components lighter than C10 appear in the oil sample and the

449

mole fraction of C36+ decreases. The emergence of C6-C9 illustrates that thermal degradation

450

indeed happens at 280oC. As such, due to the compositional change in the extra heavy oil sample,

451

the static EOS model described above cannot fully capture the true thermodynamic behavior of

452

the gas/heavy-oil mixtures at 280oC.


Page 28 of 87

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453 454


Table 5 Comparison of the compositions of the extra heavy oil sample measured before and after the phase-behavior experiment at 280oC Carbon No.

Before experiment at 280oC

After experiment at 280oC

C1

wt% 0

mol% 0

wt% 0

mol% 0

C2

0

0

0

0

C3

0

0

0

0

iC4

0

0

0

0

nC4

0

0

0

0

iC5

0

0

0

0

nC5

0

0

0

0

C6

0

0

1.01

0.1984

C7

0

0

1.55

0.3478

C8

0

0

0.82

0.2043

C9

0

0

1.54

0.4370

C10

0.73

2.5534

2.20

0.6907

C11

0.49

1.5624

4.56

1.5686

C12

0.87

2.5328

2.53

0.9537

C13

1.00

2.6784

2.67

1.0921

C14

1.21

2.9850

3.89

1.7264

C15

1.10

2.5028

2.50

1.2058

C16

1.26

2.6603

2.56

1.3293

C17

1.37

2.7094

2.61

1.4464

C18

1.13

2.1101

2.11

1.2387

C19

0.93

1.6574

1.61

0.9887

C20

0.87

1.4828

1.48

0.9537

C21

0.85

1.3691

1.36

0.9276

C22

0.83

1.2755

1.27

0.9084

C23

0.84

1.2381

1.24

0.9207

C24

0.87

1.2320

1.23

0.9522

C25

0.97

1.3178

1.32

1.0627

C26

1.08

1.4101

1.41

1.1839

C27

1.37

1.7169

1.72

1.5010



Page 30 of 87

C28

1.64

1.9812

1.98

1.7977

C29

1.82

2.1220

2.08

1.9565

C30

1.52

1.7126

1.71

1.6657

C31

1.15

1.2535

1.25

1.2601

C32

0.90

0.9501

0.95

0.9865

C33

0.77

0.7880

0.79

0.8441

C34

0.86

0.8540

0.85

0.9427

C35

1.20

1.1573

1.16

1.3154

C36+

72.37

54.1870

46.04

67.3932

455 456

To gain further insight into the multiphase equilibria that can possibly take place under actual

457

reservoir conditions, we calculate the two-phase and three-phase envelopes for Feed #4 mixture

458

by using PR EOS with the critical-volume BIP correlation. Fig. 13 shows the calculation results.

459

It can be seen from Fig. 13 that three-phase equilibria (vapor+HC liquid+water) or two-phase

460

equilibria (HC liquid+water or vapor+HC liquid) can possibly take place under normal heavy-oil

461

reservoir conditions. Such complex phase equilibria would exert significant impact on the oil

462

recovery performance of the multi-thermal fluids injection process. For example, the

463

N2/CO2/H2O mixture should ideally stay in the single phase before being injected into the

464

reservoir because overheated N2/CO2/H2O mixture carries more heat than that carried by a two-

465

phase mixture. Future wellbore flow simulation and reservoir simulation works need to be

466

conducted to elucidate how such complex phase behavior would affect the flow behavior of the

467

multi-phases across the reservoir as well as the final recovery performance. It is suggested that

468

comprehensive phase behavior measurements and modeling should be conducted and considered

469

in the field implementation of multi-thermal fluid injection.


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470 471 472 473

Fig. 13. Predicted three-phase and two-phase boundaries for Feed #4 mixture (1.6 mol% N2 +0.3 mol% CO2+48.1 mol% H2O+50 mol% extra heavy oil) by using PR EOS coupled with the critical-volume BIP correlation.

474 475

5. Conclusions

476

In this work, extensive experiments have been conducted to quantify the phase behavior of

477

N2/CO2/heavy-oil mixtures at temperatures up to 280oC and pressures up to 200 bar.

478

Experimental results indicate that the CO2 solubility in extra heavy oil decreases as temperature

479

increases at a given pressure, while the N2 solubility in extra heavy oil increases as temperature

480

increases at a given pressure. At pressures of 150 bar and 200 bar, the solubility of N2/CO2

481

mixture (85 mol% N2 and 15 mol% CO2) in extra heavy oil follows the order of: 280oC>

482

80oC >150oC, indicating that the best viscosity reduction effect appears at 280oC. At a given

483

temperature, the solubility of all of the aforementioned gases in the extra heavy oil increases as 31 ACS Paragon Plus Environment


484

pressure increases. PR EOS model with two BIP correlations (i.e., the critical volume method

485

and critical temperature method) has been applied to reproduce the measured phase behavior

486

data; at a given temperature, the exponent in each BIP correlation is tuned to match the measured

487

saturation pressure of N2 (or CO2) and extra heavy oil mixture. Comparison of the AARDs

488

calculated by these two BIP correlations indicates that the BIPs obtained by the critical volume

489

method are more accurate in reproducing the measured saturation pressures. PR EOS coupled

490

with the BIPs calculated by the critical volume BIP correlations is then applied to predict the

491

saturation pressures and swelling factors of Feed #3 (N2/CO2/heavy-oil mixture) and Feed #4

492

(N2/CO2/H2O/heavy-oil mixture); the calculated results agree reasonably well with the measured

493

data, which verifies the accuracy of the BIPs obtained. However, the discrepancy between the

494

measured and predicted phase behavior for Feeds #3 and #4 is relatively large at 280oC, possibly

495

due to the fact that the extra heavy oil experiences thermal cracking at such high temperature.

496 497

Nomenclature

498

a = EOS constant in Equation 4

499

A = coefficient in Equation 1

500

AARD = absolute average relative deviation

501

b = EOS constant in Equation 4

502

B = coefficient in Equation 1

503

i = carbon number

504

imax = maximum carbon number of the reservoir fluid

505

Kw = Watson factor

506

kij = BIP between the ith component and the jth component 32 ACS Paragon Plus Environment

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507

Mi = molecular weight of ith component

508

Ni = carbon number

509

NH = number of lumped pseudo-components

510

P = pressure, bar

511

Pc = critical pressure, bar

512

R = universal gas constant

513

S = mole fraction of gas in the heavy oil

514

SF = swelling factor

515

T = temperature, oC

516

TbR = normal boiling temperature at 1 atm, oR

517

Tc = critical temperature, K

518

Tr = reduced temperature

519

Tci = critical temperature of the ith component

520

Tcj = critical temperature of the jth component

521

vc = critical volume, ft3/mol

522

vcl = critical volume of lumped component

523

vci = critical volume of the ith component

524

vcj = critical volume of the jth component

525

V = molar volume

526

V1 = molar volume under saturation temperature and atmospheric pressure (101.3 kPa)

527

V2 = molar volume under saturation temperature/pressure conditions

528

xi = molar fraction of ith component in the liquid phase

529

Xi cal = calculated CO2 (or N2) solubility in heavy oil



530

Xi exp = measured CO2 (or N2) solubility in heavy oil

531

yi = molar fraction of ith component in the vapor phase

532

zi = molar fraction of ith component in the feed (i=1……l)

533

 = a constant depending on the hydrocarbon type

534

 = exponent constant in critical volume BIP correlation

535

 = exponent constant in critical temperature BIP correlation

536

 = acentric factor

537

 = component-dependent correlation term in Equation 6

538

i = critical properties (Tc, Pc,  , or M) of ith component

539

l = critical properties (Tc, Pc,  , or M) of lumped components

540

 i = specific gravity of ith component

541

 l = specific gravity of lumped components

542 543

Acknowledgments

544

Q. Zhao greatly acknowledges a Discovery Grant from the National Natural Science Foundation

545

of China (NO.51504223) and National Science and Technology Major Project (Grant No.

546

2017ZX05009001 and 2017ZX05009-005) and a Visiting PhD Scholarship from the China

547

Scholarship Council (CSC) (201606400036) for the financial support. H. Li acknowledges the

548

financial support provided by one Discovery Grant from the Natural Sciences and Engineering

549

Research Council of Canada (NSERC) and the Open Science Fund provided by the Key

550

Laboratory of Strategy Evaluation for Shale Gas, Ministry of Land and Resources (China

551

University of Geosciences, Beijing).


Page 34 of 87

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552 553

References

554

(1) Butler, R. M. Steam-assisted gravity drainage: concept, development, performance and

555

future. J. Can. Pet. Tech. 1994, 33(02), 44-50.

556

(2) Zhong, L.; Jiang, Y.; Ma, S. Physical and numerical simulation of multi-component-thermal-

557

fluid-assisted gravity drainage in deep and extra-heavy oil reservoirs offshore. China

558

Offshore Oil and Gas 2015, 27(1), 68-73. (In Chinese)

559

(3) Dong, X.; Liu, H.; Hou, J. Multi-thermal fluid assisted gravity drainage process: A new

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improved-oil-recovery technique for thick heavy oil reservoir. J. Pet. Sci. Eng. 2015, 133, 1-

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11.

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(4) Zhang, W.; Sun, Y.; Lin, T. Experimental study on mechanisms of the multi-fluid thermal

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recovery on offshore heavy oil. J. Petrochem. Ind. App. 2013, 32(1), 34-36. (In Chinese)

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(5) Zhang, F.; Xu, W.; Wu, T. Study on improving recovery mechanism and reservoir

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adaptability of multi-thermal fluid huff and puff offshore. Petro. Geo. and Rec. Efficiency

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(10)Svrcek, W. Y.; Mehrotra, A. K. Gas solubility, viscosity and density measurements for Athabasca bitumen. J. Can. Pet. Tech. 1982, 21(04), 31-38.

577

(11)Varet, G.; Montel, F.; Nasri, D.; Daridon, J. L. Gas solubility measurement in heavy oil and

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(12)Gao, Y.; Liu, S. Improving oil recovery by adding N2 in SAGD process for super-heavy

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crude reservoir with top-water. In: SPE Russian Oil and Gas Technical Conference and

582

Exhibition, 28-30 October, Moscow, Russia: SPE-114590-MS; 2008.

583

(13)Haddadnia, A.; Zirrahi, M.; Hassanzadeh, H.; Abedi, J. Solubility and thermo-physical

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properties measurement of CO2-and N2-Athabasca bitumen systems. J. Pet. Sci. Eng. 2017,

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(14)Mohsenzadeh, A.; Escrochi, M.; Afraz, M. V.; Al-wahaibi, Y. M.; Ayatollahi, S.

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588

steam-gas assisted gravity drainage. In: SPE Heavy Oil Conference, 12-14 June, Calgary,

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Alberta, Canada: SPE-157202-MS; 2012.

590 591

(15)Peng, D. Y.; Robinson, D. B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15(1), 59-64.

592

(16)Pedersen, K. S.; Thomassen, P.; Fredenslund, A. Thermodynamics of petroleum mixtures

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containing heavy hydrocarbons. 2. Flash and PVT calculations with the SRK equation of

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(17)Whitson, C. H.; Brulé, M. R. Phase behavior. Richardson. Richardson, Texas; 2000.


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(18)Soreide, I. Improved phase behavior predictions of petroleum reservoir fluids from a cubic

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equation of state. [PH.D. dissertation]. Norwegian Institute of Technology (NTH),

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Trondheim, Norway, 1989.

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(19)Kesler, M. G.; Lee, B. I. Improve predictions of enthalpy of factions. Hydro. Proc. 1976, 55: 153-158. (20)Lee, B. I.; Kesler, M. G. A generalized thermodynamic correlation based on three-parameter corresponding states. AIChE J. 1975, 21(3), 510-527. (21)Hall, K. R; YARBOROU, L. New, simple correlation for predicting critical volume. Chem. Eng. 1971, 78 (25), 76.

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(22)Whitson, C. H. Characterizing hydrocarbon plus fractions. SPE J. 1983, 23(4), 683-694.

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(23)Danesh, A.; Xu, D.; Todd, A. C. A grouping method to optimize oil description for

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compositional simulation of gas-injection processes. SPE Res. Eng. 1992, 7(3), 343-348.

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(24)Leibovici, C. F. A consistent procedure for the estimation of properties associated to lumped

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systems. Fluid Phase Equilib. 1993, 87(2), 189-197.

610

(25)Hong, K. C. Lumped-component characterization of crude oils for compositional simulation.

611

In: SPE/DOE Enhanced Oil Recovery Symposium, 4-7 April, Tulsa, Oklahoma, America:

612

SPE 10691; 1982.

613

(26)Chueh, P. L.; Prausnitz, J. M. Vapor-liquid equilibria at high pressures: Calculation of

614

critical temperatures, volumes, and pressures of nonpolar mixtures. AIChE J. 1967, 13(6):

615

1107-1111.

616

(27)Gao, G.; Daridon, J. L.; Saint-Guirons, H.; Xans, P.; Montel, F. A simple correlation to

617

evaluate binary interaction parameters of the Peng-Robinson equation of state: binary light

618

hydrocarbon systems. Fluid Phase Equilib. 1992, 74, 85-93.



619

(28)Teja, A. S.; Sandler, S. I.; A Corresponding states equation for saturated liquid densities. II.

620

Applications to the calculation of swelling factors of CO2-crude oil systems. AIChE J. 1980,

621

26(3), 341-345.

622

(29)Li, X.; Li, H.; Yang, D. Determination of multiphase boundaries and swelling factors of

623

solvent (s)-CO2-heavy oil systems at high pressures and elevated temperatures. Energy Fuels

624

2013, 27(3), 1293-1306.

625 626 627 628 629 630

(30)Henderson, J. H.; Weber, L. Physical upgrading of heavy crude oils by the application of heat. J. Can. Pet. Tech. 1965, 4(04), 206-212. (31)Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 27(6), 1197-1203. (32)Robinson, D. B.; Peng, D. Y.; Ng, H. J. Capabilities of the Peng-Robinson programs. Part Ⅱ. Three-phase and hydrate calculations. Hydro. Proc. 1979, 58(9), 269-273.

631

(33)Robinson, D. B.; Peng, D. Y. The characterization of the heptanes and heavier fractions for

632

the GPA Peng-Robinson programs. Research report. Tulsa, Oklahoma. Gas processors

633

association 1978.

634 635 636 637

(34)Edmister, W. C.; Lee, B. I. Applied hydrocarbon thermodynamics: Volume Ⅰ . Houston; 1988. (35)Watson, K. M.; Nelson, E. F. Improved methods for approximating critical and thermal properties of petroleum fractions. Ind. & Eng. Chem. 1933, 25(8), 880-887.

638


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639

Appendix A: PR-EOS and van der Waals’ Mixing Rule

640

The following PR EOS is used as the thermodynamic model in this study,15

641

642

P

RT a  V  b V (V  b)  b(V  b)

(A1)

where   a R 2Tc2 a   Tr  ,  a  0.457235  Pc   b   a RTc ,   0.077796 b  Pc

643

(A2)

644

where P is pressure, T is temperature, V is molar volume, Pc is critical pressure, Tc is critical

645

temperature, R is universal gas constant, and Tr is reduced temperature. The Soave alpha function

646

is given as,31  Tr   1  m 1  Tr0.5  

647

648

(A3)

If the acentric factor is below 0.49,15

m  0.37464  1.54226  0.26992 2

649 650

2

(A4)

If the acentric factor is above 0.49,32-33

m  0.3796  1.485  0.1644 2 +0.01667 3

651 652

For mixtures, the van der Waals’ mixing rule is applied to calculate the parameter a and b as

653

follows,34


(A5)


a   xi x j aij  i j  b   yi bi i  a  a a 1  k  i j ij  ij

654

655

where kij is the BIP between each two components.

656

Appendix B: Correlations Used for Estimating SCN Properties

657

(1) Specific Gravity 17, 35

658

659

660

661

662

Page 40 of 87

(A6)

 i  6.0108M i 0.17947 K w1.18241   n 0.82053    0.16637 C7+   zi M i    i 1  Kw     zC7+ M C7+    

(B1) 0.84573

(B2)

(2) Boiling Point Temperature (Soreide) 18

Tb  1928.3  1.695 105  M i 0.03522 i3.266  exp    4.922 103  M i  4.7658 i   3.462 103  M i i   

(B3)

(3) Critical Temperature and Pressure (Kesler-Lee) 19

Tc  341.7  811 +  0.4244+0.1174  Tb 663

  0.4699  3.2623  105 Tb1


(B4)

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ln pc  8.3634 

0.0566



 2.2898 0.11857  3    0.24244    10  Tb 2     

664

 3.648 0.47227  7  2  1.4685    10  Tb  2     

(B5)

 1.6977  10  3   0.42019   10  Tb 2     665 666

(4) Acentric Factor (Kesler-Lee) 20 If Tbr  Tb / Tc  0.8 ,



667

668

669

670

671

672

675

(B6)

where

 A1  5.92714, A2  6.09648, A3  1.28862, A4  0.169347   A5  15.2518, A6  15.6875, A7  13.4721, and A8  0.43577

(B7)

If Tbr  Tb / Tc  0.8 ,

  7.904  0.1352 K w  0.007465K w2  8.359Tbr  1.408  0.01063K w  Tbr1

(B8)

(5) Critical Volume (Hall-Yarborough) 21

vc  0.025M 1.15 0.7935

673

674

 ln  pc /14.7   A1  A2Tbr 1  A3 ln Tbr  A4Tbr 6 A5  A6Tbr 1  A7 ln Tbr  A8Tbr 6

(B9)

(6) Hong’s Mixing Rule 25

l

z  z il

il

i i

i


(B10)


676

l 

z M il

z M il

677

i

i

l i

Page 42 of 87

l i

(B11)

/  l i 

1 3   vcl    zi z j  vci1/3  vc j1/3   /   zi   8 il jl   il 

678


2

(B12)

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679


Table of Contents Graphic

680



Manuscript Submitted to Industrial & Engineering Chemistry Research

Phase Behavior Measurements and Modeling for N2/CO2/Extra-Heavy-Oil Mixtures at Elevated Temperatures

Qianhui Zhao1, 2, Zhiping Li1, 3*, Shuoliang Wang1, 3, Fengpeng Lai1, 3, Huazhou Li4*, 1 School of Energy Resources, China University of Geosciences, Beijing 100083, PR China 2 Key Laboratory of Strategy Evaluation for Shale Gas, Ministry of Land and Resources, Beijing 100083, PR China 3 Beijing Key Laboratory of Unconventional Natural Gas Geological Evaluation and Development Engineering, Beijing 100083, PR China 4 School of Mining and Petroleum Engineering, Faculty of Engineering, University of Alberta, Edmonton, Canada T6G 1H9

*Corresponding Authors: Dr. Zhiping Li Professor, Petroleum Engineering China University of Geosciences Phone: 86-15300153581 Email: [email protected] Dr. Huazhou Andy Li Assistant Professor, Petroleum Engineering University of Alberta Phone: 1-780-492-1738 Email: [email protected] 1 ACS Paragon Plus Environment

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Abstract Recently, a new technology, the so-called multi-thermal fluids huff and puff, to exploit extra heavy oil reservoirs has been applied successfully in several shallow heavy oil reservoirs in China. However, the use of this technology in deep extra heavy oil reservoirs is rare. Successful application of this technique in deep extra heavy oil reservoirs requires a good knowledge of the phase behavior and physical properties of multi-thermal fluids and extra heavy oil mixture. The major components of multi-thermal fluids mixtures are steam, N2, and CO2. In this work, targeting the application of multi-thermal fluids injection in heavy oil reservoirs, we conduct PVT experiments on the N2/CO2/heavy-oil mixtures under deep reservoir conditions and develop equation of state models for representing these PVT data. Experimentally, it is found that CO2 solubility in extra heavy oil decreases with an increasing temperature at given pressure. Contrary to CO2, N2 solubility in extra heavy oil increases with an increasing temperature at given pressure. Theoretically, the extra heavy oil is split and lumped into 8 pseudo-components to characterize the critical temperatures, critical pressures, acentric factors and other properties by using the Kesler-Lee formulae. To match the solubility obtained in the experiments, two binary interaction parameter (BIP) correlations in Peng and Robinson equation of state (PR EOS) are selected to calculate the solubility of both N2 and CO2 in extra heavy oil (Peng and Robinson, 1976). At a given temperature, the exponent in each BIP correlation is optimized to match the measured solubility of N2 or CO2 in extra heavy oil. We validate the optimized BIP exponents in PR EOS model by using them to reproduce the measured saturation pressures and swelling factors of the ternary N2/CO2/heavy-oil mixtures. The validation results show that the BIP correlations with the optimized exponents can reproduce the measured swelling factors and saturation pressures of N2/CO2/heavy-oil mixtures with a good accuracy. In addition, by carrying out example calculations using the tuned PR-EOS model, we discuss the possible multiphase equilibria that can be encountered under reservoir conditions when the multi-thermal fluids (N2/CO2/H2O) are injected into an extra heavy oil reservoir. Keywords: Multi-thermal fluids, Phase behavior, Binary interaction parameter, Extra heavy oil recovery



1. Introduction Heavy oil is one of the most abundant oil resources in the world, but challenging to be exploited due to its high viscosity. Several techniques have been proposed to recover heavy oil, among which the most effective ones are steam flooding, cyclic steam stimulation, and steam-assisted gravity drainage (SAGD).1 Multi-thermal fluids stimulation using a huff and puff manner is a new thermal technology for recovering heavy oil that is initially proposed to recover offshore heavy oil resources in China.2 It enhances oil recovery by burning fuel and water to generate a flue gas mixture comprising of flue gas (mainly N2 and CO2) and steam, and then injecting it into reservoir. In essence, the mechanism of multi-thermal fluids generator is similar to the working mechanism of a rocket engine. The diesel oil will be mixed with air in an injection pump. After gas mixture is burned in the generator, the principal combustion effluents containing flue gas (mainly N2 and CO2) and steam will be injected through the tubing into the formation.3 Its major advantages include that: the burning setup occupies a small space and its construction cost is low. More importantly, the recovery efficiency is higher than the pure steam injection due to the additional heavy oil diluting effect provided by flue-gas dissolution and pressure maintenance effect provided by the high-pressure flue gas.4-5 Multi-thermal fluids stimulation technology has been applied in several oil fields in China. In 2009, the first field pilot test was carried out in the Cao 20 Block, Shengli Oilfield.6 The productivity turned out to be 1.6 to 2 times of the original production rate. Another pilot test in the Bohai Nanpu oilfield showed that the implementation of this technique led to a recovery efficiency significantly higher than the conventional steam stimulation.7 Laboratory simulation


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tests showed that the recovery rate of using multi-thermal fluids injection in SAGD was 4.7% higher than that provided by the conventional SAGD process.8 But it is noted that all these existing studies have been focused on the application of this technique in shallow heavy oil reservoirs, while few studies have explored its potential application in deep extra heavy oil reservoirs. One difficulty encountered when applying this technique to deep reservoirs is that the excessive heat loss along the tubing can result in a much smaller steam quality at the bottomhole. This could lead to a larger volume of condensed water, a lower injectivity of the multi-thermal fluids into the reservoir, and eventually a lower thermal efficiency of the process. How to address this difficulty relies on the good understanding of the multiphase equilibria in the wellbore as well as in the reservoir as they could exert significant effects on the process performance. Several experimental studies were conducted to measure the phase behavior of non-condensable gas (N2 and CO2) and heavy oil systems. Sayegh et al. tested the CO2 solubility in Lindbergh heavy oil at conditions up to 140oC and 15 MPa.9 Svrcek and Mehrotra measured the CO2 solubility in Athabasca bitumen at conditions up to 100oC and 10 MPa.10 Varet et al. tested the solubility of CO2 in Athabasca bitumen and Venezuelan heavy oil up to 80oC and 12 MPa.11 All of the above experiments demonstrate a consistent result that the CO2 solubility in heavy oil decreases with an increasing temperature at a fixed pressure, but increases with an increasing pressure at a fixed temperature. However, divergent viewpoints appear regarding the variation of N2 solubility in heavy oil with changing temperatures at a fixed pressure. Svrcek and Mehrotra measured N2 solubility in bitumen up to 100oC and 8.79 MPa.10 Gao et al. measured N2 solubility in a heavy oil sample at pressures up to 4 MPa and temperatures up to 280oC.12 Their experimental results indicated that N2 solubility in heavy oil decreases with an increasing 4 ACS Paragon Plus Environment


temperature at a fixed pressure. Contrary to above, the experimental results given by Haddadnia et al., who measured N2 solubility in bitumen up to 190oC and 8 MPa, indicated that, at a given pressure, N2 solubility in Athabasca bitumen increases with an increasing temperature.13 As for the variation of N2 solubility in heavy oil with changing pressure, all of the experimental results showed an increasing tendency with an increasing pressure at a fixed temperature.9-13 But there is no sufficient experimental test dedicated to the measurement of the non-condensable gas (N2 and CO2) solubility at high reservoir pressure around 20 MPa and elevated temperature up to 280oC; these elevated conditions can be encountered in deep extra heavy oil reservoirs. Both laboratory experiments and numerical simulations are conducted to study the mechanisms of enhancing the heavy oil recovery by injecting the multi-thermal fluids. Mohsenzadeh et al. conducted laboratory experiments to study the injection of different mixtures (including N2steam system, CO2-steam system, and synthetic flue gas-steam system) into authentic core at 750 psia and 80oC.14 The results showed that before the gas breakthrough, flue gas-steam injection had the highest recovery efficiency. But after the breakthrough, CO2-steam injection achieved the highest recovery efficiency. Dong et al. measured CO2 and the flue gas solubility in heavy oil at the temperature up to 120oC and 12 MPa.3 Their results showed that, the flue gas solubility in heavy oil decreased with an increasing temperature at a given pressure. In the same work, they also conducted 2D and 3D steam-flooding experiments examining the oil-recovery performance of different injection fluids. Their results showed that the displacement efficiency of different injection fluids followed the order of: CO2-steam injection> multi-thermal fluids injection>steam injection>N2-steam injection.3 A simulation model was established to simulate these four injection processes, and a good match between the experimental results and simulated results could be obtained. However, the number of phases and compositions of each phases have 5 ACS Paragon Plus Environment

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significant variations in the multi-thermal-fluids-assisted SAGD process due to the injection of multi-thermal fluids (mainly comprised of steam, N2 and CO2) and the varied temperature/pressure conditions. To accurately capture the behavior of multi-thermal fluids during injection, it is necessary to have a profound understanding of the phase behavior of multithermal fluids at varied temperature/pressure conditions. It becomes even more important when this technology is applied in deep extra heavy oil reservoirs. In the reservoir, the presence of extra heavy oil can make the phase behavior become much more complex, justifying the need for conducting phase behavior measurements on the multi-thermal fluids and extra heavy oil mixtures. This research conducts a series of laboratory experiments to measure the phase behavior of multi-thermal fluids and extra heavy oil mixtures at high pressure and elevated temperature conditions. Modeling efforts using Peng-Robinson Equation of State (PR EOS) together with two binary interaction parameter (BIP) correlations are also made to represent the measured phase behavior data. Optimized exponent in each BIP correlation is developed to match the measured solubility of N2 or CO2 in extra heavy oil at each given temperature.15 A good accuracy can be found when using the optimized BIP exponents to reproduce the measured saturation pressures and swelling factors of the N2/CO2/heavy-oil mixtures.

2. Experimental Section Experiments are conducted to measure the basic properties of extra heavy oil sample such as density, viscosity, and molecular weight. We also measure the solubility (equivalent to saturation pressure measurements) of non-condensate gas (N2 and CO2) in extra heavy oil sample at different temperatures and pressures. 6 ACS Paragon Plus Environment


2.1 Materials The extra heavy oil samples are collected from one block in Xinjiang oil field in China. The reservoir temperature and pressure are 80oC and 200 bar, respectively. The viscosity of the crude oil is 2379 mPa·s at reservoir temperature (Haake Mars, Thermo Fisher Corporation, Germany). When the temperature increases from 54oC to 180oC, the viscosity of extra heavy oil decreases from 21090 mPa·s to 20.1 mPa·s (Fig. 1). The molecular weight and specific gravity are 574.5 g/mol and 1.0352 g/cm3, respectively. The molecular weight of the extra heavy oil is measured by the vapor pressure osmometry method. The instrument model is JI833-100-00 (UIC, Inc.). Distilled water is used in the experiments. The CO2 and N2 used in the experiments have purities of 99.999 mol% and 99.998 mol%, respectively.

Fig. 1. Measured viscosity of the extra heavy oil at different temperatures 2.2 Experimental Setup

The major experimental setup used in this work is a high pressure PVT cell (1500FV-240, ST Corporation, France). Its core component is a visual PVT cell, while its peripheral components 7 ACS Paragon Plus Environment

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include high pressure metering pump, digital gas meter, ultrahigh-temperature electronic pressure gauge et al. This system can be used to measure some essential PVT properties, such as saturation pressure and swelling factor. The operating temperature range of the PVT cell is from 20oC to 300oC. The PVT cell can sustain pressure as high as 100 MPa. The total pump volume is 300 ml. The accuracies of the pressure, temperature and volume measurement are 0.001 MPa, 0.1oC and 0.01 ml, respectively. A gas chromatograph (GC) apparatus (7890B, Agilent, US) is used to measure the crude oil composition. The standard GB/T 30430-2013, a Chinese official standard, is applied for the GC analysis. Fig. 2 presents the schematic diagram of the experimental setup for conducting PVT measurements. Table 1 shows the carbon number distribution of extra heavy oil sample measured with the GC apparatus. Table 1 Compositional analysis results of the extra heavy oil. Carbon No. C1 C2 C3 iC4 nC4 iC5 nC5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17

wt% 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.73 0.49 0.87 1.00 1.21 1.10 1.26 1.37

mol% 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 2.5534 1.5624 2.5328 2.6784 2.9850 2.5028 2.6603 2.7094

Carbon No. C18 C19 C20 C21 C22 C23 C24 C25 C26 C27 C28 C29 C30 C31 C32 C33 C34 C35 C36+ 8

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wt% 1.13 0.93 0.87 0.85 0.83 0.84 0.87 0.97 1.08 1.37 1.64 1.82 1.52 1.15 0.90 0.77 0.86 1.20 72.37

mol% 2.1101 1.6574 1.4828 1.3691 1.2755 1.2381 1.2320 1.3178 1.4101 1.7169 1.9812 2.1220 1.7126 1.2535 0.9501 0.7880 0.8540 1.1573 54.1870


Fig. 2. Schematic diagram of the experimental setup for conducting PVT measurements for the N2/CO2/extra heavy oil mixtures 2.3 Experimental Procedure Two types of experiments are conducted: solubility measurements for pure N2, pure CO2 and (85 mol% CO2, 15 mol% N2) mixture in extra heavy oil (Exp Groups #1, #2, and #3) and saturation pressure measurements for one N2/CO2/H2O-extra heavy oil mixture (Exp Group #4). Table 2 lists the conditions used in the PVT experiments on multi-thermal fluids and extra heavy oil mixtures. Firstly, the solubility of pure N2, pure CO2 and CO2-N2 mixture in extra heavy oil is measured at different temperature/pressure conditions. The degassing experiments are conducted to measure the solubility. The procedure for conducting the degassing experiments is briefly explained here. At a given temperature, the extra heavy oil is first loaded into the PVT cell. The non-condensable gas is then injected to the PVT cell. After gas injection, the PVT cell volume is then adjusted so


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as to reach the predetermined pressure. A single liquid phase should be observed during the noncondensable gas injection if the heavy oil can still dissolve more gas. When a vapor phase appears at a given temperature and a fixed pressure, the liquid phase cannot dissolve more gas, and then gas supply should be cut off. The dissolution process has been done in a stepwise manner, and at each step the mixture is being stirred and maintained at the preset temperature and pressure for more than 12 hours. When the dissolution capacity is reached, we flash the single-phase fluid to standard conditions, and record the volume of non-condensable gas released as well as the volume of the remaining heavy oil. Table 2 Conditions used in the PVT experiments on multi-thermal fluids and extra mixtures. Composition, mol% Exp Experimental Group Extra Heavy Temperature, oC Type CO2 N2 H2O No. oil To be To be 1 measure 0.0 0.0 80, 150, 280 measured d To be To be Solubility 2 0.0 measure 0.0 80, 150, 280 measured Measurements d To be To be To be 3 measure measure 0.0 80, 150, 280 measured d d CCE 4 0.3 1.6 48.1 50.0 80, 150, 280 Experiments

heavy oil

Pressure, bar 50, 100, 150, 200 50, 100, 150, 200 50, 100, 150, 200 To be measured

Secondly, the constant composition expansion (CCE) experiment is conducted to measure the saturation pressure and swelling factor of the N2/CO2/H2O-extra heavy oil mixture (Exp Group #4). The PVT cell should be cleaned and vacuumed before the experiments. After cleaning and vacuuming, a certain amount of multi-thermal fluids and extra heavy oil sample is first transferred into the PVT cell at a given temperature. At each temperature, the CCE experiment is



initiated starting from a single liquid phase. The initial pressure is kept higher than 200 bar in order to maintain the mixture as one single liquid phase. The mixture is being stirred and maintained at the preset temperature for more than 12 hours. Then the pressure is gradually decreased in a continuous manner (i.e., a slow withdrawal rate of 3 cm3/hr is applied). The mixture should be stirred rigorously during the measurements. When volume reading is needed, the stirrer is temporarily shut off to enable the volume reading on the sample. The saturation pressure (i.e., the two-phase/three-phase boundary) and saturation volume can be determined by pinpointing the inflection point of the pressure-volume relationship curves. After the test at 80oC is finished, the CCE experiments are repeated at higher temperatures of 150oC and 280oC. 3. Modeling Methodology In this section, we describe how to characterize the extra heavy oil as well as how to model the phase behavior of N2/CO2/heavy-oil mixtures. The C7+ fraction is firstly split into single carbon numbers (SCNs) and then lumped into several pseudo-components. The thermodynamic properties of each SCN should be calculated by using correlations, while the thermodynamic properties of each pseudo-component should be estimated with a particular mixing rule. The detailed equations used can be referred to Appendix B. After C7+ characterization is completed, two correlations used to calculate the BIPs between the non-condensable gas (N2 or CO2) and pseudo-components are implemented in PR EOS. The exponents in the two BIP correlations are tuned to match the measured solubility of either N2 or CO2 in extra heavy oil at different temperatures. Finally, the optimized indices in the BIP correlations are validated with the measured saturation pressures and swelling factors of ternary N2/CO2/heavy-oil mixtures. 3.1 Heavy Oil Characterization 3.1.1 Splitting of C7+ Fraction and Determination of Critical Properties of Each SCN 11 ACS Paragon Plus Environment

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To characterize the extra heavy oil sample with EOS parameters, the C7+ fraction needs to be split first. Pedersen et al. gives a relationship between a given carbon number and the logarithm of its corresponding mole fraction for the carbon numbers starting at C11;16 this relationship is expressed below,

ln zi

A BNi

(1)

where zi is mole fraction, Ni is carbon number, while A and B are coefficients. The molecular weight of SCN can be calculated based on the carbon number as follows, M i  14 N i  

(2)

where Mi is the molecular weight of each SCN, while  is a constant depending on the hydrocarbon type. The Watson factor Kw can be used to determine the component classes: 1) Kw of aromatic hydrocarbons is between 8.5 to 11.0; 2) Kw of naphthenic hydrocarbons is between 11.0 and 12.5; and 3) Kw of n-alkanes is between 12.5 and 13.5.17 In this study, we assume that the Watson factor is a constant for the extra heavy oil under study. The specific gravity of each SCN can be calculated based on Kw using the formula presented in Appendix B. After determining the molecular weight and specific gravity for each SCN, the boiling point of each SCN can be calculated by the correlation given by Soreide.18 Then, the LeeKesler correlations are used to determine the critical temperature, critical pressure, and acentric factor of each SCN, while the correlations proposed by Hall-Yarborough et al. are used to determine the critical volume of each SCN.19-21 Refer to Appendix B for more details about the equations used to calculate the aforementioned properties of each SCN. 3.1.2 Lumping Scheme



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Due to the large number of SCNs split in the last step, the SCNs should be lumped before performing phase equilibrium calculations in order to reduce the computational cost. In this study, the number of lumped pseudo-components is estimated by the following equation proposed by Whitson, 22 N H  1  3.3log  imax  7 

(3)

where NH is the number of lumped pseudo-components, and imax is the maximum carbon number of the reservoir fluid. The determination of the composition of each group should satisfy the two principles: 1) the term

  z ln M  should be consistent for different pseudo-components; and i

i

2) the lumped pseudo-components should have a consistent thermodynamic behavior with the original one.23-24 After lumping, Hong’s mixing rule listed in Appendix B is applied to estimate the critical properties of the pseudo-components.25 3.2 BIP Models 3.2.1 BIP Correlations BIP plays an important role in ensuring the accuracy of PR EOS in describing the thermodynamic behavior of mixtures. The PR EOS model is listed in Appendix A. Generally, the BIP between pseudo-components and the IP between N2 and CO2 are both regarded as zero.17 To estimate the BIP values between non-condensable gas (N2 or CO2) and pseudo-components, two commonly used correlations are used: the critical volume method and the critical temperature method.26-27 The critical volume method calculates the BIP with the following expression,26 

 2vci1/6 vcj1/6  kij  1   1/3 1/3  v v  cj   ci


(4)

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where kij is the BIP between the ith component and the jth component, vci and vcj are the critical volume of the ith component and the jth component, respectively, and  is the exponent constant for this critical volume method. The critical temperature method calculates the BIP with the following expression,27 

 2Tci1/2Tcj1/2  kij  1    T  T   ci cj 

(5)

where Tci and Tcj are the critical temperature of the ith component and the jth component, respectively, and  is the exponent constant in this correlation. BIP can be temperature dependent. We optimize the exponents in these BIP correlations at different temperatures. Fig. 3 shows the flowchart used to optimize the BIP correlation used for modeling the phase behavior of CO2-extra heavy oil mixtures.



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Fig. 3. Flowchart used to optimize the BIP correlation used for modeling the phase behavior of CO2-extra heavy oil mixtures. The absolute average relative deviation (AARD) in Fig. 3 is calculated as per,

AARD 

1 n X ical  X iexp  X exp n i 1 i

(6)

cal exp where X i is the calculated CO2 (or N2) solubility in extra heavy oil, X i is the measured CO2

(or N2) solubility in extra heavy oil, and n is the number of data points. 15 ACS Paragon Plus Environment

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3.2.2 Swelling Factor Calculation Viscosity reduction and swelling of extra heavy oil are the two important mechanisms contributing to the recovery of heavy oil. Swelling factor can be used to quantify how much swelling occurs to extra heavy oil. The swelling factor of a gas-dissolved heavy oil sample can be calculated by,28

SF =

V2 V1 1  S 

(7)

where SF is swelling factor, V1 is molar volume under saturation temperature and atmospheric pressure (101.3 kPa), V2 is molar volume under saturation temperature/pressure conditions, and S stands for the mole fraction of gas in the heavy oil. 4. Results and Discussion 4.1 Heavy Oil Characterization Fig. 4 shows the mole fraction of each SCN. In this figure, the mole fractions of C10-C35 are measured by GC, while the mole fractions of C36-C100 are estimated by Equation (1). In this study, the heaviest component of extra heavy oil is C101+. The Kw value of extra heavy oil is 11.65, which indicates that the hydrocarbons contained in the extra heavy oil are predominantly naphthenic.



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Fig. 4. Carbon number distributions of extra heavy oil used in this study. 4.2 Lumping In the study by Li’s et al., 6 to 8 pseudo-components are found to be more accurate in describe the phase behavior of solvent(s)/heavy-oil mixtures.29 Following the work by Li et al., in this study, the heavy oil is divided into 8 pseudo-components based on Equation (3).29 We determine the composition of each pseudo-component by satisfying the two aforementioned principles introduced in Section 3.1.2. Table 3 shows the properties of lumped pseudo-components which have been calculated by the equations listed in Appendix B. Table 3 Properties of lumped pseudo-components. Group No.

Carbon No.

z, mol%

Ml-i

Group 1

C10-C13

13.31

164.0

Group 2

C14-C16

13.43

209.8

Pc, psi 332.2 6 281.3 0

Tc, K

ω

γ

Vc ft3/mo l

674.07

0.508

0.8238

10.2618

732.93

0.621

0.8607

13.1724


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Group 3

C17-C20

14.49

256.9

Group 4

C21-C26

13.60

326.3

Group 5

C27-C35

12.50

426.7

Group 6

C36-C50

11.71

592.4

Group 7

C51-C82

10.92

887.7

Group 8

C83-C101+

10.04

1443.5

247.2 7 215.9 2 191.2 2 174.3 9 172.0 4 193.3 1

782.65

0.721

0.8925

15.7792

841.42

0.836

0.9318

19.2124

905.77

0.951

0.9779

24.4443

980.36

1.038

1.0374

32.3774

1063.10

1.062

1.1163

44.7466

1143.31

0.986

1.2168

113.3248

4.3 Solubility Matching Fig. 5 shows the experimental results on the solubility of non-condensable gas in extra heavy oil. As shown in Fig. 5a, the CO2 solubility in extra heavy oil decreases as temperature increases at a given pressure. In contrast, Fig. 5b shows that the N2 solubility in extra heavy oil increases as temperature increases at a given pressure; such trend is becoming more obvious at a higher pressure. By comparing Fig. 5a and Fig. 5b, one can find a larger amount of CO2 can be dissolved in extra heavy oil than N2 under the same condition. At a given temperature, both the two figures show that the gas solubility in the extra heavy oil increases as pressure increases.



(a)

(b)


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Fig. 5. The solubility of non-condensable gas in extra heavy oil: (a) CO2 solubility in extra heavy oil at 80oC, 150oC, and 280oC; (b) N2 solubility in extra heavy oil at 80oC, 150oC, and 280oC. Table 4 shows the optimized exponents in the two BIP correlations at different temperatures. These exponents are optimized with the procedures listed in Section 3.2.2. It is noted that the optimized exponents between CO2 and extra heavy oil are positive, while the optimized exponents between N2 and extra heavy oil are negative. Moreover, the exponents between the non-condensable gas and extra heavy oil tend to decrease with an increasing temperature. Table 4 Optimized exponents in the two BIP correlations at different temperatures. Exponent





in Equation (10) in Equation (11)

Temperature (oC) CO2- Extra Heavy oil N2- Extra Heavy oil CO2- Extra Heavy oil

80 0.562 -1.471 0.435

150 0.398 -2.157 0.235

280 0.141 -2.695 0.095

N2- Extra Heavy oil

-0.487

-0.852

-1.252

Fig. 6 depicts the comparison between the measured and calculated CO2 solubility in extra heavy oil at different conditions for Feed #1. As shown in Fig. 6, both BIP correlations with the optimized exponents can provide good match to the measured CO2 solubility in extra heavy oil.



(a)

(b)


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(c) Fig. 6. Measured and calculated CO2 solubility in extra heavy oil at (a) 80oC, (b) 150oC, and (c) 280oC. Fig. 7 describes the comparison between the measured and calculated N2 solubility in extra heavy oil at different conditions for Feed #2. A good agreement can be seen between the predicted N2 solubility in extra heavy oil and the measured one. Nevertheless, the discrepancy between the calculated N2 solubility in extra heavy oil and the measured one become enlarged as temperature and pressure increases.



(a)

(b) 23 ACS Paragon Plus Environment

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(c) Fig. 7. Measured and calculated N2 solubility in extra heavy oil (a) 80oC, (b) 150oC, and (c) 280oC. Fig. 8 shows the AARDs of the solubility prediction for Feed #1 and Feed #2 by using the two BIP correlations. As shown in Fig. 8, the largest AARD is smaller than 8%, indicating that the two BIP correlations can both have a good prediction of the solubility of non-condensable gas in extra heavy oil. The AARDs at 280oC are larger than those obtained at 80oC and 150oC for both Feed #1 and Feed #2. It can be noted that AARDs obtained by the critical volume correlation are smaller than those obtained by the critical temperature correlation at the same condition. It indicates that the critical volume correlation provides more accurate BIPs to describe the solubility of non-condensable gas in extra heavy oil, although this might be only specifically true for the fluid mixtures studied in this work. In the following predictions, the BIPs calculated by the critical volume correlation are applied.



(a)

(b)


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Fig. 8. AARD of the solubility prediction for (a) CO2-extra heavy oil mixtures and (b) N2-extra heavy oil mixtures using the two BIP correlations Fig. 9 presents the BIPs between CO2 and pseudo-components obtained by the critical volume correlation at different temperatures, while Fig. 10 shows the BIPs between N2 and pseudocomponents obtained by the critical volume correlation at different temperatures. As shown in these two figures, the BIPs between non-condensable gas and pseudo-components decrease as temperature increases at a given pressure. At a given temperature, the BIPs between CO2 and pseudo-components increase with an increasing molecular weight of pseudo-component, while the BIPs between N2 and pseudo-components decrease with an increasing molecular weight of pseudo-component.

Fig. 9. BIPs between CO2 and pseudo-components at 80oC, 150oC and 280oC predicted by using the critical volume BIP correlation



Fig. 10. BIP between N2 and pseudo-components at 80oC, 150oC and 280oC predicted by using the critical volume BIP correlation Fig. 11 describes the comparison between measured and predicted mole fraction of gas mixture (85 mol% N2 +15 mol% CO2) in extra heavy oil at different conditions for Feed #3. The BIPs between non-condensable gas and pseudo-components used in the predictions are shown in Figs. 9 and 10. As shown in Figure 11, at 50 bar and 100 bar, the mole fraction of N2-CO2 mixture in extra heavy oil at 280oC is smaller than those at 80oC and 150oC. However, the mole fraction of N2-CO2 mixture in extra heavy oil follows the order of 280oC>80oC>150oC at both 150 bar and 200 bar. A good agreement can be found between the measured and predicted solubility of N2CO2 mixture in extra heavy oil, indicating that the tuned BIPs are able to provide a satisfactory description of the mole fraction of N2-CO2 mixture in extra heavy oil. However, a larger discrepancy between the measured and predicted mole fraction of N2-CO2 mixture in extra heavy oil appears at 280oC. The possible reason leading to such larger error can be that the extra heavy 27 ACS Paragon Plus Environment

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oil might experience thermal cracking under such higher temperature, which could generate additional hydrocarbon components in the mixture. This will result in a change in extra heavy oil properties, leading to inaccurate description of the extra heavy oil by the original characterization scheme described above as well as shifting in the phase equilibrium.34

Fig. 11. Comparison of measured and predicted mole fraction of gas mixture (85 mol% N2 +15 mol% CO2) in extra heavy oil at 80oC, 150oC, and 280oC. 4.4 Prediction of Upper Three-Phase Boundary of N2/CO2/H2O/Heavy-Oil Mixtures Next, to further validate the predictive capability of the EOS model developed above, we show its prediction results on the upper three-phase boundary of N2/CO2/H2O/heavy-oil mixtures. Fig. 12 shows the comparison between the measured and predicted swelling factors for Feed #4 at different temperatures, while it also depicts the comparison between the measured and predicted saturation pressures for Feed #4 at different temperatures. The BIPs between non-condensable gas and pseudo-components applied in the prediction of the swelling factor are shown in Fig. 9 and Fig. 10. The BIPs between water and pseudo-components are 0.5, while the BIPs for CO228 ACS Paragon Plus Environment


H2O pair and N2-H2O pair are set as 0.2 and 0.275, separately. Again, a reasonably good agreement can be found between the predicted and measured swelling factors and saturation pressures. However, larger deviations appear again at high temperatures.

Fig. 12. Comparison of measured and predicted upper three-phase boundary (boundary between aqueous-oleic two phases and vapor-oleic-aqueous three phases) for the Feed #4 mixture (1.6 mol% N2 +0.3 mol% CO2+48.1 mol% H2O+50 mol% extra heavy oil) at 80oC, 150oC and 280oC. To check if thermal degradation occurs at 280oC, we measured the composition of the extra heavy oil sample after the experiment. Table 5 compares the compositions of the extra heavy oil sample measured before and after the experiment at 280oC. After the high-temperature experiments, we can see that the components lighter than C10 appear in the oil sample and the mole fraction of C36+ decreases. The emergence of C6-C9 illustrates that thermal degradation indeed happens at 280oC. As such, due to the compositional change in the extra heavy oil sample, the static EOS model described above cannot fully capture the true thermodynamic behavior of the gas/heavy-oil mixtures at 280oC.


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Table 5 Comparison of the compositions of the extra heavy oil sample measured before and after the phase-behavior experiment at 280oC Carbon No.

Before experiment at 280oC

After experiment at 280oC

C1

wt% 0

mol% 0

wt% 0

mol% 0

C2

0

0

0

0

C3

0

0

0

0

iC4

0

0

0

0

nC4

0

0

0

0

iC5

0

0

0

0

nC5

0

0

0

0

C6

0

0

1.01

0.1984

C7

0

0

1.55

0.3478

C8

0

0

0.82

0.2043

C9

0

0

1.54

0.4370

C10

0.73

2.5534

2.20

0.6907

C11

0.49

1.5624

4.56

1.5686

C12

0.87

2.5328

2.53

0.9537

C13

1.00

2.6784

2.67

1.0921

C14

1.21

2.9850

3.89

1.7264

C15

1.10

2.5028

2.50

1.2058

C16

1.26

2.6603

2.56

1.3293

C17

1.37

2.7094

2.61

1.4464

C18

1.13

2.1101

2.11

1.2387

C19

0.93

1.6574

1.61

0.9887

C20

0.87

1.4828

1.48

0.9537

C21

0.85

1.3691

1.36

0.9276

C22

0.83

1.2755

1.27

0.9084

C23

0.84

1.2381

1.24

0.9207

C24

0.87

1.2320

1.23

0.9522

C25

0.97

1.3178

1.32

1.0627

C26

1.08

1.4101

1.41

1.1839

C27

1.37

1.7169

1.72

1.5010

C28 C29

1.64 1.82

1.9812 2.1220

1.98 2.08

1.7977 1.9565



C30

1.52

1.7126

1.71

1.6657

C31

1.15

1.2535

1.25

1.2601

C32

0.90

0.9501

0.95

0.9865

C33

0.77

0.7880

0.79

0.8441

C34

0.86

0.8540

0.85

0.9427

C35

1.20

1.1573

1.16

1.3154

C36+

72.37

54.1870

46.04

67.3932

To gain further insight into the multiphase equilibria that can possibly take place under actual reservoir conditions, we calculate the two-phase and three-phase envelopes for Feed #4 mixture by using PR EOS with the critical-volume BIP correlation. Fig. 13 shows the calculation results. It can be seen from Fig. 13 that three-phase equilibria (vapor+HC liquid+water) or two-phase equilibria (HC liquid+water or vapor+HC liquid) can possibly take place under normal heavy-oil reservoir conditions. Such complex phase equilibria would exert significant impact on the oil recovery performance of the multi-thermal fluids injection process. For example, the N2/CO2/H2O mixture should ideally stay in the single phase before being injected into the reservoir because overheated N2/CO2/H2O mixture carries more heat than that carried by a two-phase mixture. Future wellbore flow simulation and reservoir simulation works need to be conducted to elucidate how such complex phase behavior would affect the flow behavior of the multi-phases across the reservoir as well as the final recovery performance. It is suggested that comprehensive phase behavior measurements and modeling should be conducted and considered in the field implementation of multi-thermal fluid injection.


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Fig. 13. Predicted three-phase and two-phase boundaries for Feed #4 mixture (1.6 mol% N2 +0.3 mol% CO2+48.1 mol% H2O+50 mol% extra heavy oil) by using PR EOS coupled with the critical-volume BIP correlation.

5. Conclusions In this work, extensive experiments have been conducted to quantify the phase behavior of N2/CO2/heavy-oil mixtures at temperatures up to 280oC and pressures up to 200 bar. Experimental results indicate that the CO2 solubility in extra heavy oil decreases as temperature increases at a given pressure, while the N2 solubility in extra heavy oil increases as temperature increases at a given pressure. At pressures of 150 bar and 200 bar, the solubility of N2/CO2 mixture (85 mol% N2 and 15 mol% CO2) in extra heavy oil follows the order of: 280oC> 80oC >150oC, indicating that the best viscosity reduction effect appears at 280oC. At a given temperature, the solubility of all of the aforementioned gases in the extra heavy oil increases as 32 ACS Paragon Plus Environment


pressure increases. PR EOS model with two BIP correlations (i.e., the critical volume method and critical temperature method) has been applied to reproduce the measured phase behavior data; at a given temperature, the exponent in each BIP correlation is tuned to match the measured saturation pressure of N2 (or CO2) and extra heavy oil mixture. Comparison of the AARDs calculated by these two BIP correlations indicates that the BIPs obtained by the critical volume method are more accurate in reproducing the measured saturation pressures. PR EOS coupled with the BIPs calculated by the critical volume BIP correlations is then applied to predict the saturation pressures and swelling factors of Feed #3 (N2/CO2/heavy-oil mixture) and Feed #4 (N2/CO2/H2O/heavy-oil mixture); the calculated results agree reasonably well with the measured data, which verifies the accuracy of the BIPs obtained. However, the discrepancy between the measured and predicted phase behavior for Feeds #3 and #4 is relatively large at 280oC, possibly due to the fact that the extra heavy oil experiences thermal cracking at such high temperature.

Nomenclature a = EOS constant in Equation 4 A = coefficient in Equation 1 AARD = absolute average relative deviation b = EOS constant in Equation 4 B = coefficient in Equation 1 i = carbon number imax = maximum carbon number of the reservoir fluid Kw = Watson factor kij = BIP between the ith component and the jth component 33 ACS Paragon Plus Environment

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Mi = molecular weight of ith component Ni = carbon number NH = number of lumped pseudo-components P = pressure, bar Pc = critical pressure, bar R = universal gas constant S = mole fraction of gas in the heavy oil SF = swelling factor T = temperature, oC TbR = normal boiling temperature at 1 atm, oR Tc = critical temperature, K Tr = reduced temperature Tci = critical temperature of the ith component Tcj = critical temperature of the jth component vc = critical volume, ft3/mol vcl = critical volume of lumped component

vci = critical volume of the ith component vcj = critical volume of the jth component V = molar volume V1 = molar volume under saturation temperature and atmospheric pressure (101.3 kPa) V2 = molar volume under saturation temperature/pressure conditions xi = molar fraction of ith component in the liquid phase Xi cal = calculated CO2 (or N2) solubility in heavy oil



Xi exp = measured CO2 (or N2) solubility in heavy oil yi = molar fraction of ith component in the vapor phase zi = molar fraction of ith component in the feed (i=1……l)  = a constant depending on the hydrocarbon type

 = exponent constant in critical volume BIP correlation

 = exponent constant in critical temperature BIP correlation  = acentric factor  = component-dependent correlation term in Equation 6 i = critical properties (Tc, Pc,  , or M) of ith component l = critical properties (Tc, Pc,  , or M) of lumped components  i = specific gravity of ith component  l = specific gravity of lumped components

Acknowledgments Q. Zhao greatly acknowledges a Discovery Grant from the National Natural Science Foundation of China (NO.51504223) and National Science and Technology Major Project (Grant No. 2017ZX05009001 and 2017ZX05009-005) and a Visiting PhD Scholarship from the China Scholarship Council (CSC) (201606400036) for the financial support. H. Li acknowledges the financial support provided by one Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Open Science Fund provided by the Key Laboratory of Strategy Evaluation for Shale Gas, Ministry of Land and Resources (China University of Geosciences, Beijing).


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(28)Teja, A. S.; Sandler, S. I.; A Corresponding states equation for saturated liquid densities. II. Applications to the calculation of swelling factors of CO2-crude oil systems. AIChE J. 1980, 26(3), 341-345. (29)Li, X.; Li, H.; Yang, D. Determination of multiphase boundaries and swelling factors of solvent (s)-CO2-heavy oil systems at high pressures and elevated temperatures. Energy Fuels 2013, 27(3), 1293-1306. (30)Henderson, J. H.; Weber, L. Physical upgrading of heavy crude oils by the application of heat. J. Can. Pet. Tech. 1965, 4(04), 206-212. (31)Soave, G. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci. 1972, 27(6), 1197-1203. (32)Robinson, D. B.; Peng, D. Y.; Ng, H. J. Capabilities of the Peng-Robinson programs. Part

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Three-phase and hydrate calculations. Hydro. Proc. 1979, 58(9), 269-273. (33)Robinson, D. B.; Peng, D. Y. The characterization of the heptanes and heavier fractions for the GPA Peng-Robinson programs. Research report. Tulsa, Oklahoma. Gas processors association 1978. (34)Edmister, W. C.; Lee, B. I. Applied hydrocarbon thermodynamics: Volume

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Appendix A: PR-EOS and van der Waals’ Mixing Rule The following PR EOS is used as the thermodynamic model in this study,15

P

RT a  V  b V (V  b)  b(V  b)

(A1)

where   a R 2Tc2  Tr  ,  a  0.457235 a  Pc   b   a RTc ,   0.077796 b  Pc

(A2)

where P is pressure, T is temperature, V is molar volume, Pc is critical pressure, Tc is critical temperature, R is universal gas constant, and Tr is reduced temperature. The Soave alpha function is given as,31  Tr   1  m 1  Tr0.5  

2

(A3)

If the acentric factor is below 0.49,15

m  0.37464  1.54226  0.26992 2

(A4)

If the acentric factor is above 0.49,32-33

m  0.3796  1.485  0.1644 2 +0.01667 3 For mixtures, the van der Waals’ mixing rule is applied to calculate the parameter a and b as follows,34


(A5)


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a   xi x j aij  i j  b   yi bi i  a  a a 1  k  i j ij  ij

(A6)

where kij is the BIP between each two components. Appendix B: Correlations Used for Estimating SCN Properties (1) Specific Gravity 17, 35

 i  6.0108M i 0.17947 K w1.18241

  n 0.82053    0.16637 C7+   zi M i   i 1    Kw    zC7+ M C7+    

(B1) 0.84573

(B2)

(2) Boiling Point Temperature (Soreide) 18

Tb  1928.3  1.695 105  M i 0.03522 i3.266  exp    4.922 103  M i  4.7658 i   3.462 103  M i i   

(B3)

(3) Critical Temperature and Pressure (Kesler-Lee) 19

Tc  341.7  811 +  0.4244+0.1174  Tb   0.4699  3.2623  105 Tb1


(B4)

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ln pc  8.3634 

0.0566 

 2.2898 0.11857  3    0.24244    10  Tb 2       3.648 0.47227  7  2  1.4685    10  Tb  2       1.6977  10  3   0.42019   10  Tb  2    

(B5)

(4) Acentric Factor (Kesler-Lee) 20 If Tbr  Tb / Tc  0.8 ,



 ln  pc /14.7   A1  A2Tbr 1  A3 ln Tbr  A4Tbr 6 A5  A6Tbr 1  A7 ln Tbr  A8Tbr 6

(B6)

where

 A1  5.92714, A2  6.09648, A3  1.28862, A4  0.169347   A5  15.2518, A6  15.6875, A7  13.4721, and A8  0.43577

(B7)

If Tbr  Tb / Tc  0.8 ,

  7.904  0.1352 K w  0.007465 K w2  8.359Tbr  1.408  0.01063K w  Tbr1

(B8)

(5) Critical Volume (Hall-Yarborough) 21 vc  0.025M 1.15 0.7935

(B9)

(6) Hong’s Mixing Rule 25

l

z  z il

il

i i

i


(B10)


l 

z M il

i

 z M il

i

l i

Page 86 of 87

l i

/  l i 

1 3   vcl    zi z j  vci1/3  vc j1/3   /   zi   8 il jl   il 


(B11) 2

(B12)

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