Experimental and Numerical Modeling Study of Gravity Drainage

Jun 16, 2014 - This paper presents an experimental investigation of gas-assisted gravity drainage (GAGD) performance while taking into account the eff...
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Experimental and Numerical Modeling Study of Gravity Drainage Considering Asphaltene Deposition Rohaldin Miri,† Sohrab Zendehboudi,*,‡ Shahin Kord,# Francisco Vargas,§ Ali Lohi,∥ Ali Elkamel,⊥ and Ioannis Chatzis⊥ †

EOR Division, Department of Reservoir Engineering, National Iranian South Oil Company (NISOC), Ahwaz, Iran Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States # Institute of Reservoir Engineering, Department of Mineral Resources and Petroleum Engineering, Montan University of Leoben, Max Tendler Strasse 4, Leoben 8700, Austria § Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77251-1892, United States ∥ Department of Chemical Engineering, Ryerson University, Toronto, Ontario M5B 2K3, Canada ⊥ Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada ‡

ABSTRACT: This paper presents an experimental investigation of gas-assisted gravity drainage (GAGD) performance while taking into account the effects of asphaltene deposition. The experiments were conducted at high pressures and high temperature (15−37 MPa and 102 °C) using carbonate cores and real reservoir fluids in the absence of water saturation. An 85% methaneenriched hydrocarbon gas mixture was employed as an injection fluid in the laboratory runs. The final recovery factor for a fairly tall core was 52% of the original oil at immiscible conditions during hydrocarbon gas injection when the operating pressure and the amount of injected gas were 28.3 MPa and 1.2 pore volume, respectively. In all of the experiments, the total amount of asphaltene deposition was less than 2 wt % of the original oil and no considerable reduction in permeability was found. A numerical two-phase (gas−oil) simulator coupled with a deposition model was also developed to evaluate the importance of different parameters contributing to the final recovery. There was a good agreement between the modeling and experimental results, showing an average error percentage lower than 5%. This study can aid the prediction of the performance of gas injection processes experiencing asphaltene deposition and also aid in proper design of gravity drainage-assisted enhanced oil recovery methods.

1. INTRODUCTION

controlled rate, as the production process is strongly ratedependent. It has been reported that gravity drainage increases oil recovery factor by more than 60% in a number of reservoirs. The production performance can be as high as 90% microscopic recovery efficiency for tertiary gravity drainage conditions.1,3,5−8 Numerous authors have conducted theoretical and experimental studies on the gravity drainage processes in homogeneous and heterogeneous porous media.3−15 In petroleum engineering, special attention is given to gravity drainage, particularly for gas injection in the form of secondary and tertiary oil recovery methods. A literature survey clearly shows that there is a misunderstanding of process when gas injection comes along with stable gravity drainage. Gravity drainage usually takes place in the two poorly defined forms of the free fall and forced gravity drainage (FFGD and FGD). Steam-assisted gravity drainage (SAGD) is a thermal EOR technology that can be implemented through each of these gravity drainage processes associated with heat transfer.16−18 In addition, FFGD and FGD can be employed in

Gas injection in oil reservoirs aims for three key objectives to be attained, namely, pressure maintenance, miscible displacement of oil, and oil swelling due to mass transfer between the oil and gas phases. The primary candidate gas for injection is normally a dry hydrocarbon gas which can be enriched with other hydrocarbon gases. Viscous fingering and high mobility ratio lead to low sweep efficiency and make the application of gas injection in the form of an enhanced oil recovery (EOR) method unattractive, as reported in the literature.1,2 Many studies revealed that gas injection in most of the petroleum reservoirs can result in significant amount of oil production, particularly when the stable gas oil gravity drainage (GOGD) is active even for conditions of immiscible inert gas injection.3−8 This advantage can be achieved only when the injection or production rates are not so high that they could cause early gas breakthrough in the production well and in conditions where the oil spreads over water in the presence of gas in gas-invaded pore space for the recovery of waterflood residual oil. Therefore, to obtain economically high oil recovery efficiency from a suitable reservoir (e.g., high permeability and a thick pay zone) using gas injection, the most important technical practices are to maintain the reservoir pressure at the crest of a horizontal well, inject gas at low rates, and produce the oil at a © XXXX American Chemical Society

Received: December 29, 2013 Revised: May 10, 2014 Accepted: June 16, 2014

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permeability functions. (4) The last class, models based on empirical correlations, can be well matched with gravity drainage production history.1,2,11−15,27 Schechter and Guo (1996) reported that many of these models are unsatisfactory in predicting the production response (or history) of a reservoir within a wide range of process conditions.28 In this paper, the performance of the GOGD process in oil production from the Asmari carbonate reservoir rocks in Iran with special reference to the effects of asphaltene deposition is investigated. Various reservoir fluid samples and carbonate core samples from Asmari reservoir were used for core flood experiments to study the amount of oil production and permeability impairment due to damage caused by asphaltene deposition. Another interesting aspect is that the height of the porous system was about 1.6 m, which eliminates the effect of end points. The core permeability was evaluated by injecting methane-enriched hydrocarbon gas mixture through the core and measuring the asphaltene content of the produced oil sample. An attempt was also made to characterize the behavior of asphaltene deposition under these conditions, in which experiments could be continued for over 42 h. It is important to note that both Eclipse and CMG have an asphaltene feature or option in the compositional models. However, a numerical twophase (gas−oil) simulator was developed in the current study and then coupled with the asphaltene deposition model proposed by Wang et al. (1999).29 The developed reservoir simulator is used to assess the importance of different parameters contributing to the final oil recovery. Such model integration provides more flexibility in alteration of input variables and also attains results with greater accuracy while researchers and engineers decide to investigate asphaltene deposition over gas injection processes. Employing this modeling strategy assists in the further understanding of the physics and mechanisms of asphaltene deposition phenomena occurring in oil reservoirs. Highlighting the research contribution, this study enables the development of best-case scenarios for producing oil from porous systems (e.g., sandstones and carbonates) using forced gravity drainage as a method of oil recovery.

both conventional and unconventional (e.g., fractured) oil reservoirs.18,19 Zendehboudi (2010) focused on important aspects of FFGD, FGD, and controlled gravity drainage (CGD) processes through experimental and modeling studies. Visualization tests of gravity drainage in fractured systems using glass bead packed models with fractures were carried out, mainly focusing on oil recovery efficiency, residual oil saturation, gas− liquid (G-L) interface movement through matrix and fractures, and oil production mechanism for different cases. In addition, the experimental results were simulated using COMSOL. Then, the outputs of simulation runs were compared with the experimental data obtained in this study.11−15 In conventional reservoirs, when the gas cap is large enough to maintain the pressure or when gas is injected with a low flow rate and oil is produced at a constant pressure, the process is controlled by the gravity forces. This production technique is referred to as free fall gravity drainage or gravity dominated processes.3,11−15,20 FFGD usually leaves very small residual oil saturation in thick formations with high permeability if the rate of oil production is carefully controlled such that there is no gas breakthrough at the production well. For example, it is practically accepted to keep the production rate below the critical rate.11−15,20 On the other hand, the use of a high production rate, which implies high external pressure difference applied between the top and bottom of the reservoir, is likely to distort the stable displacement front and reduce or eliminate the importance of the gravity force in comparison with viscous forces, where the process is forced gas injection. A similar phenomenon occurs in dual permeability reservoirs where gas or water invade the higher permeability zones (fracture) ahead of the oil present in the pore matrix of lower permeability. The pressure gradient of the two fluids causes the force required for transportation of the fluid to the low permeability zone, leading to oil displacement.11−15,20 Naturally fractured reservoirs (NFRs) often are in the category of tight carbonate rocks which are limited by discontinuities in the form of barriers and/ or fractures. Thus, higher saturations of residual oil are observed in this type of NFR with hydrocarbons. This is the main reason the oil recovery is about 30% or lower in fractured reservoirs when the production mechanism is natural depletion and the matrix permeability is less than 1 millidarcy (mD).11−15,20,21 In spite of having a large sweep efficiency and recovery factor in GAGD, uncertainties related to GAGD always limit the use of this production technology because of economic considerations. One of the main concerns in gas injection processes is the probability of asphaltene deposition, which needs to be tackled carefully. Asphaltenes are usually defined as the fraction of crude oil insoluble in excess normal alkanes, such as npentane or n-heptane, but soluble in aromatic compounds (benzene or toluene) at room temperature.22−24 Asphaltene deposition results in undesirable phenomena such as rock wettability alteration and permeability impairment, which influence the flow of immiscible fluids.25,26 Production response of the reservoirs in GAGD traditionally was modeled by the following models: (1) The first class of models is based on the moving demarcator (distance between gas−oil interface and reservoir top) concept combined with the Buckley and Leveret equation. In these models, the transition zone is assumed to be small. (2) The next class of models uses a combination of film flow theory and Darcy law to predict the demarcator depth. (3) The third class of models essentially includes logarithmic capillary pressure and linear relative

2. THEORETICAL ASPECTS 2.1. Gravity Drainage Theory. Cardwell and Parsons (1949) introduced the first analytical model for the gravity drainage process on the basis of hydrodynamic equilibrium relationships for experiments conducted in vertical sand columns.30 The model originally assumed that the free gas phase causes production of a single liquid phase during the gravity drainage process; the fraction of liquid recovered is obtained based on the area below the plot of model height versus saturation when the breakthrough capillary height is excluded from the total height.31 Using the Buckley and Leverett displacement theory, Terwilliger et al. (1951) proposed a gravity drainage model similar to that of Cardwell and Parsons (1949).31 They also employed the shock-front method proposed by Welge (1952) to match the gravity drainage tests at steady-state conditions.31,32 Based on their model, the oil recovery by gravity drainage is inversely proportional to production rate. They proposed the following equation to obtain the maximum production rate due to gravity drainage:31,32 KA qgr = e g Δρ sin θ μL (1) B

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where qgr is the gravity drainage rate and Ke represents the effective permeability to liquid phase when the liquid saturation is 100%. A is the cross-sectional area of flow, μL the liquid viscosity, g the gravitational acceleration, and Δρ the density difference between the liquid and gas; θ stands for the dip angle. Equation 1 is generally used to determine the critical injection rate such that lower injection rates are selected to maintain frontal stability throughout the production process. 2.2. Immiscible Gas Injection Patterns. Immiscible gas injection is typically categorized into two groups, crestal and pattern-like, depending on the position of the injection wells. Crestal gas injection, known as gas cap injection, employs vertical injection wells at higher structural locations. This displacement method (or external gas injection) is usually applicable in oil reservoirs with considerable structural relief or large pay zones that have high vertical permeability. Injection wells are placed to offer a good areal distribution and also to gain the highest profit of the gravity drainage process. GAGD happens when the crestal injection is practical.1−5 Thus, crestal gas injection GAGD is the crucial technique in which the immiscible gas displacement is employed. Gas injection involves a plan of injection wells to cause uniform gas distribution in the productive section of the oil reservoir. This technique is generally useful in fairly homogeneous reservoirs with low structural relief and small vertical permeability. Low areal sweep efficiency occurs in thin stringers due to gas override and viscous fingering.1−5 The main reasons for these undesirable phenomena include high flow velocities and unfavorable mobility ratios. Common concerns while using pattern type injection in low-dip petroleum reservoirs are early gas breakthrough, elevated GOR, high compression expenses for gas reinjection, and a recovery factor lower than 10%.1−5,11−15 2.3. Important Factors in GAGD Processes. An immiscible GAGD process should include fluids (e.g., oil and gas) with some specific characteristics. In general, the interfacial tension (IFT) between the oil and gas phases is considered to be an important parameter for determining the type of displacement in terms of being miscible or immiscible. For example, if IFT is low (e.g., 0−2.0 mN/m), the displacement is miscible or near-miscible. However, if IFT is high enough (e.g., >3.0 mN/m) at reservoir conditions (e.g., temperature and pressure), the immiscible displacement is maintained throughout the flow in the porous medium. Thus, IFT can considerably affect the displacement process (and/or pattern). The second parameter is the mobility ratio which appears to be very essential for an efficient GAGD. When the mobility ratio is in the range of 10−100, gas displacements are considered unfavorable processes.1−5,11 The high mobility ratio results in the occurrence of viscous fingering. If the gas displacement happens vertically downward, the gravity force will aid in stabilizing the flood front and lowering the probability of viscous fingering. Another factor that influences the production performance of the immiscible gas displacement is the initial value of oil saturation. The gas saturation will reduce the magnitude of producible oil if gas injection is started right after reservoir pressure is decreased less than the bubble point.1−5 If the saturation of free gas goes beyond the breakthrough saturation, no oil bank formation will be experienced. However, instantaneous gas production begins along with oil production. In addition, oil viscosity and reservoir dip angle are two important parameters that affect the efficiency of GAGD. Oils

with low viscosities attain higher efficiency. When the value of permeability is high enough and production flow rates are not greater than the critical rate, high inclination angles appreciably enhance the oil production.1−5 In GAGD, withdrawal rates should be controlled carefully, considering the segregation of gas from oil. The oil phase can either be forced by the gas in any direction when the gas velocity is high or the oil can move downward under gravity at low gas velocities, depending on magnitudes of the gas velocity and the relative permeability.1−5,11−15 The critical gas velocity is of great importance. The solution gas-drive conditions will succeed at velocities greater than this specific velocity. At lower velocities, the gravity drainage mechanism will be dominant and segregation of the free gas and oil will be initiated as the gas segregates at the higher portions of the reservoir and the lower parts are occupied by the oil.1−5,11−15 Another important factor to immiscible displacement accomplishment is the extent to which vertical segregation happens. Thick reservoirs (e.g., >200 m) are the best candidates for the gravity drainage process such that the gas is injected at the structure crest and the oil is produced from down dip.1,2,33−35 Geological structure has a significant contribution in oil recovery through the GAGD technique. The efficiency of oil production by GAGD is also strongly affected by the nature of the sand layers in sandstone reservoirs. The GAGD process is more capable of producing oil if the highest-permeability sands are located on the bottom part of the formation because the vertical distribution of permeability slows the gravity override of the gas phase.1−5 2.4. Production Mechanisms of GAGD and Asphaltene Deposition. The main physical mechanisms during GAGD are partial or complete pressure maintenance, horizontal and vertical displacement of oil by gas, vaporization of the liquid components from the oil phase, and oil swelling if the oil is undersaturated with gas at initial reservoir conditions. GAGD processes usually include all these mechanisms.1,2 For asphaltene to deposit in porous systems, it first should precipitate from crude oil. It should be noted here that only suspended asphaltene might deposit and block the formations. On the basis of the phase behavior studies, asphaltene precipitation begins to happen at a pressure greater than the bubble point, known as the upper asphaltene precipitation pressure, and attains a maximum value in terms of weight percentage of asphaltene precipitated at the bubble point.22−26,29 Then, asphaltene most likely dissolves back in oil phase as dissolved gas is released and the composition of the liquid is changed when the pressure drops below the bubble point.24−26,29 Hence, understanding the asphaltene precipitation envelope (describing deposited asphaltene versus pressure is well-known in petroleum engineering) is necessary to illustrate precipitation and deposition phenomena of the asphaltene. Screening for asphaltene deposition and precipitation is very essential during oil recovery from hydrocarbon reservoirs. There are some widespread techniques, such as De Boer plots, asphaltene resin ratio method, and colloidal instability index, for detecting precipitation of asphaltene.22−26,29

3. EXPERIMENTAL ASPECTS Peripheral Tests describes the primary experiments required for the main laboratory work. The core flooding tests are explained in Experimental Setup and Test Procedure. C

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3.1. Peripheral Tests. Some peripheral tests were necessary prior to commencement of the gas injection experiments. These tests include determination of rock and fluid properties, SARA analysis, asphaltene deposition envelope, and minimum miscibility pressure and concentration. The following sections present the details of these experiments and the obtained results. 3.1.1. Crude Oil Sampling and PVT Properties. To find proper oil samples as representatives of the reservoir fluid, five crude oil samples were taken from the Asmari reservoir by downhole fluid sampling technique. A variety of measurements (composition, API gravity, oil viscosity (μo), gas viscosity (μg), bubble point, etc.) were performed on the fluid samples, and finally a suitable sample was selected. General specifications of the crude oil samples, and composition of the crude oil samples, and injection gas utilized in the experiments are listed in Tables 1, 2, and 3, respectively. The injection gas was the

Table 3. Composition of the Injected Gas

specification

value 15.30 102.00 0.001 45 30.91 0.49 0.60

Table 2. Composition of the Crude Oil Sample component of oil

wt %

H2S CO2 N2 C1 C2 C3 i-C4 n-C4 i-C5 n-C5 C6 C7 C8 C9 C10 C11 C12+ total

1.39 5.18 0.88 22.57 6.94 5.91 0.98 2.97 0.93 1.03 3.07 4.06 4.14 3.69 3.45 2.11 30.7 100

mol %

N2 C1 CO2 C2 C3 i-C4 n-C4 i-C5 n-C5 C6+ total

0.15 84.92 2.76 7.13 2.76 0.53 0.86 0.35 0.29 0.25 100

Table 4. Fluid Properties of the Crude Oil Sample

Table 1. General Specifications of the Crude Oil Sample saturation pressure (MPa) test temperature (°C) density of total gas evolved (g/cm3) gravity of residual oil (°API) viscosity of oil [at saturation pressure] (cp) viscosity of oil [at reservoir pressure, 28.3 MPa] (cp)

component

P (MPa)

RS (scm3/scm3)

Bo (m3/scm3)

Bg (m3/scm3)

μo (cp)

μg (cp)

3.40 6.80 10.20 13.61 15.26 24.87 32.81 39.38 44.69 48.98 52.45 55.28 57.62 59.56 61.17 62.53 63.67 64.63 65.45 66.14 66.73 67.24 67.66

0.02 0.04 0.06 0.09 0.10 0.17 0.24 0.31 0.38 0.45 0.51 0.58 0.64 0.70 0.77 0.82 0.88 0.94 0.99 1.05 1.10 1.15 1.20

1.15 1.21 1.27 1.33 1.36 1.55 1.74 1.91 2.08 2.25 2.41 2.57 2.72 2.87 3.02 3.17 3.32 3.46 3.60 3.74 3.88 4.01 4.14

6.44 3.07 1.98 1.46 1.30 0.85 0.77 0.78 0.80 0.83 0.84 0.80 0.76 0.73 0.71 0.69 0.68 0.66 0.65 0.64 0.63 0.63 0.62

0.83 0.72 0.65 0.56 0.52 0.36 0.29 0.24 0.21 0.19 0.17 0.16 0.15 0.14 0.13 0.12 0.12 0.11 0.11 0.11 0.10 0.10 0.10

0.01 0.02 0.02 0.02 0.02 0.03 0.05 0.08 0.11 0.02 0.02 0.02 0.02 0.03 0.13 0.12 0.12 0.11 0.11 0.11 0.10 0.10 0.10

conditions is usually considered to be the crude asphaltene content.36−38 This value strongly depends on the type of the solvent which is used for deposition and/or precipitation. Here, the precipitant employed is n-heptane and the standard method of IP-143 is used to measure the asphaltene content of the crude samples. The results attained from these tests are presented in Table 5. The value of 2.12 wt % is estimated for the asphaltene content of the crude oil under study. 3.1.3. Asphaltene Precipitation−Deposition Envelopes. Asphaltene content is a key parameter in determining the processing and refining paths of a crude oil.36−38 However, this parameter is not taken into account as a proper criterion to

original gas evolved from the live oil, and it was methaneenriched by a mixture of hydrocarbons. A set of routine PVT analysis was also conducted to determine the molecular weight, °API, solution gas−oil ratio (RS), oil formation volume factor (Bo), gas formation volume factor (Bg), and composition of the samples (see Table 4). 3.1.2. SARA Analysis and Asphaltene Content Determination. It is a common practice to characterize oil into four categories: saturates (S), aromatics (A), resins (R), and asphaltene (A). This classification is conventionally known as SARA analysis, and the procedure of this test is described by the Institute of Petroleum handbook.36−38 The amount of asphaltene that precipitates from a crude oil under atmospheric

Table 5. SARA Analysis

D

specification

value

saturated (wt %) aromatic (wt %) resin (wt %) asphaltene (wt %)

42.67 41.43 13.78 2.12

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Figure 1. Schematic of experimental setup used for asphaltene deposition.

Asphaltene precipitation−deposition envelope during natural depletion is plotted for the crude oil sample in Figure 2.

judge the intensity of the damage likely to occur due to asphaltene deposition. Asphaltene precipitation−deposition envelope provides supporting information that in addition to the rock properties can be used to systematically describe the deposition process. The schematic diagram of the experimental setup utilized to measure asphaltene deposition is shown in Figure 1. In this setup, a mercury pump was used to inject the fluid into the cell and to control the pressure. The main part of the system was a mercury-free and visual JEFRI equilibrium cell. An air bath was also incorporated to control the cell temperature. The designed cell can properly work in temperatures ranging from −30 to 200 °C, and the maximum pressure is 82.7 MPa. Moreover, the cell was equipped with an electrical shaker for mixture agitation and could hold 500 cc of the liquid. A high-pressure high-temperature (HPHT) separator, capable of working on wide range of pressure, was also used to measure the characteristics of the gas collected after the equilibrium at reservoir conditions was achieved. The crude samples were continuously heated and agitated for 3 days to ensure their homogeneity. A known volume of oil was then injected into the cell under single-phase conditions at reservoir pressure. The equilibrium cell was thoroughly maintained at the reservoir temperature by fixing the air bath temperature at a constant value. The sample was allowed to reach equilibrium overnight. To accelerate the equilibrium process, an electric stirrer was used to agitate the sample. A HPHT filtration test was conducted to quantify the amount of asphaltene that might be precipitated at a given pressure. At each point, a high-pressure filtration process was carried out employing two steel sheets, one with thickness of 5 μ and the other with thickness of 0.5 μ. During the filtration process it was important that the oil sample remains as a single phase as it passes through the filter manifold. High-pressure helium gas was utilized to maintain a back-pressure on the downstream end of the filter. This helped the filtration process to be operated at a condition which was very close to isobaric. The filtered oil was flashed in a separator, and the asphaltene content of the residual dead oil was measured using the standard IP-143 procedure. The difference between the asphaltene contents of the original and filtered oil at each pressure determines the amount of the precipitated asphaltene.

Figure 2. Asphaltene precipitation envelope of crude oil sample.

3.1.4. Core Preparation and Routine and Special Core Analysis. In total, 19 core plugs were prepared and cleaned by using Xylene according to ASTM Standard D 2172 methodology, through the Soxhlet extraction technique. Permeabilities of these samples were measured by a mini-permeameter. Several measurements were performed to determine the permeabilities in the horizontal and vertical directions. The geometric average of all permeability measurements was 195 mD. Porosity of the core samples was obtained by the saturation method such that the cores are filled in with toluene and then the amount of injected fluid that is required to attain 100% saturation is measured. Using this method, the porosity of the composite core was determined to be 19.09%. Further experiments were carried out to measure the static capillary pressure and relative permeability through centrifuge and unsteady-state techniques, respectively. The results obtained from these experiments are depicted in Figures 3 and 4, respectively. 3.2. Experimental Setup and Test Procedure. The experimental study employing the Asmari crude oil displacement using enriched hydrocarbon gas was performed when the E

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At the start of the test, the cores were saturated with toluene and toluene was displaced by injection of dead oil with average flow rate of 10 mL/h (Figure 5). This process took 8 days, and in total about 5.7 pore volume (PV) dead oil was injected. Then, live oil was injected into the core holder at a pressure higher than the bubble point pressure of oil. The process was stopped when the GOR of produced oil was equal to the GOR of live oil at injection pressure. In the next step, injection of enriched gas with 85 mol % of methane was performed at an average injection flow rate of 10.5 mL/h under reservoir conditions. Gas breakthrough happened when 44.8% PV gas was injected into the core. The composition of the produced gas was the same as that of the injection gas after injection of 1.2 PV. The production process was stopped at this stage. As depicted in Figure 5, the pressure and temperature of the inlet and outlet remained unchanged (28.3 MPa, 102 °C) throughout the experiment using a precise back-pressure regulator and a digital temperature sensor, respectively. When the gas injection was ended, the remaining oil in the core holder was produced by reducing the outlet pressure stepwise to standard conditions (simulating natural depletion). At this stage, 2.33% of the oil in place was produced. The amount of asphaltene dissolved in the produced oil was measured by the IP-143 method at some random time steps before and after the gas breakthrough. After the amount of asphaltene deposited in the core was measured, the remaining dead oil was displaced by using 3 PV n-heptane at an average injection rate of 10 mL/h. The injected n-heptane was used to wash out the paraffinic components of the remaining dead oil as well. Then 3 PV of toluene were used to dissolve the asphaltene and then extract it through filtration and evaporation processes.

Figure 3. Drainage capillary pressure curve of core sample for oil−gas system.

4. MATHEMATICAL MODELING APPROACH As exploring the effects of different parameters on performance of gas injection process was not possible in the experimental work, an attempt was made to develop a mathematical model for considering the effect of asphaltene deposition. The goal was to build a model capable of simulating the fluid flow behavior of porous media involved in the GAGD coupled with asphaltene deposition. A three-phase−four- component black oil simulator was proposed in Cartesian (x, y, z) coordinates and then simplified to a 1-D case to describe the GOGD process. This simulator is a combination of both GOGD and asphaltene deposition models. In other words, this is not a conventional black oil simulator. In fact, it is a three-phase twodimensional black oil simulator combined with the Wang model. 4.1. Black Oil Model. The black oil model is designed for three phases: oil, water, and gas. In this model, it is assumed that gas exists in both free and dissolved forms in the reservoir. However, the asphaltene phase exists as a dissolved state in the oil phase (Table 6). For the sake of simplicity, the material balance equation is converted to the volumetric forms using phase density, as presented in Table 6. The following equations describe the material balance for water (w), oil (o), gas (g), and asphaltene components, respectively:

Figure 4. Relative permeability characteristics of core sample for drainage.

HPHT core holder was operated at wide ranges of pressure and temperature. Figure 5 shows a schematic of the core holder and other accessory equipment employed in this experimental investigation. The apparatus consisted of a glass-walled case with metal top and bottom plates supported by a steel frame. This design enables the stack of blocks to be tilted through 360° around a central horizontal axis. Accessory equipment include a vacuum pump, a vacuum gauge, and a balance interfaced to a computer for recording fluid production and also data acquisition. The laboratory room housing the apparatus was provided with a temperature control unit to maintain the temperature within a tolerance of ±0.17 °C. Experiments were run at 28.3 MPa and 102 °C, which are similar to in situ reservoir conditions in the Asmari reservoir, though the water phase was absent in the tests. The same crude oils as those used in the asphaltene deposition and minimum miscibility pressure−minimum miscibility composition (MMPMMC) experiments were also employed in the core flood tests. An original sample of the Asmari rock with total length of 151.9 cm, diameter of 3.85 cm, porosity of 19.09%, and permeability of 195 mD was placed into the core holder. After the annulus was sealed by a flexible rubber sleeve, the experiment was started by injecting fluid at the upper face of the holder while all the rock samples were positioned vertically. F

⎛u ⎞ q ∂ ⎛ ϕS ⎞ −∇·⎜ w ⎟ − wsc = ⎜ w ⎟ Bw ∂t ⎝ Bw ⎠ ⎝ Bw ⎠

(2)

⎛u ⎞ q ∂ ⎛ ϕS ⎞ −∇·⎜ o ⎟ − osc = ⎜ o ⎟ ∂t ⎝ Bo ⎠ Bo ⎝ Bo ⎠

(3)

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Figure 5. Schematic of experimental setup for gas injection.

Table 6. Available Phases and Corresponding Density of Each Phase23−25,32−34 component or phase

oil

oil (o)

×

gas (g)

×

gas

water

ρg = ×

water (w) dissolved asphaltene

×

suspended asphaltene

×

kk rg kk ro kk ∇·Φo , u w = − rw ∇·Φw , ug = − ∇·Φg μo μw μg (5)

density

ρo = ×

uo = −

ρw =

In eq 6, k and kri (i = g, o, w) are the absolute and relative permeability, respectively. Φ represents the flow potential, which is defined as1,2

ρosc + R sρgsc + RAρAsc + CAρAsc Bo

R Sρgsc

Φ = P + ρgZ

Bo

To make a relationship between the pressure and degree of saturation, the following auxiliary equations are presented in order to obtain the final form of PDE equations for mass conservation:1,2

ρwsc Bw

ρAo = WAoρo =

RAρAsc Bo

ρASo = WASoρo = CAρA =

(6)

∑

CAρAsc BA

⎛R u ⎛ R ϕS ϕSg ⎞ ug ⎞ qgsc R Sqosc ⎟ −∇·⎜⎜ S o + ⎟⎟ − − = ⎜⎜ S o + Bg ⎠ Bg Bo Bg ⎟⎠ ⎝ Bo ⎝ Bo

Sl = 1

l = o,w,g

(7)

Pcow = Po − Pw

(8)

Pcog = Pg − Po

(9)

where Pcow and Pcog are the oil−water capillary pressure and oil−gas capillary pressure, respectively. In Table 6, RA represents the volume ratio of soluble asphaltene in the oil phase and CA is the suspended asphaltene saturation. ρA is the density of asphaltene, ρAo the density of dissolved asphaltene, ρASo the density of suspended asphaltene, and BA the asphaltene formation volume factor. Also, WAo and WASo are the weight fractions of dissolved and suspended asphaltene, respectively.

(4)

where S, q, and B stand for saturation, production (injection) rate, and formation volume factor of each fluid phase, respectively. ui (i = g, o, w) is the Darcy velocity of phase i, and subscript “sc” stands for “standard conditions”; Z is the depth (positive downward), and ϕ is the porosity. The Darcy velocity (u) expressions for the oil (o), gas (g), and water (w) phases are defined as follows:1,2 G

dx.doi.org/10.1021/ie404424p | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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has four matching parameters: α is the constant of surface deposition rate; β is the entrainment of deposits constant; γ stands for the constant of pore throat plugging rate; and σ represents the snowball rate constant. 4.3. Plugging Model. The plugging model refers to the effect of asphaltene deposition on porosity and permeability reduction.29,42 Wang et al. (1999) used the following equation to determine local porosity (ϕ) and permeability (k):29

4.2. Asphaltene Deposition Model. Determining formation damage and consequently the amount of reduction in recovery factor caused by asphaltene deposition is of great interest when dealing with any oil recovery process. In general, two common theories are available for modeling asphaltene uptake in porous media.39 The first group is based on the adsorption theory, which incorporates surface excess behavior along with the Langmuir isotherm equation to calculate the rate of asphaltene deposition. The second category is called the mechanical entrapment theory (e.g., Gruesbeck et al., 1982), in which rock morphology effects on the deposition occurrence are taken into the account.36 In this model, two continuous pluggable and nonpluggable pathways for porous medium are supposed. A careful review of the literature indicates that there is an agreement on prevalent contribution of adsorption to total amount of asphaltene deposition compared with the mechanical entrapment.29,40 Asphaltene deposition models should have the capability of computing the concentration of asphaltene ready for deposition and the amount of the deposition retained by the porous medium due to the rock morphology effects.36−40 The amount of asphaltene available for deposition is a dynamic property and appropriately described by the material balance equation. It is important to note that the amount of asphaltene concentration in static conditions, which is usually calculated by using asphaltene precipitation (thermodynamic) models, is necessary to obtain the dynamic concentration through the material balance equation of asphaltene. To take into account the dynamic asphaltene concentration, a material balance equation for asphaltene component is given as the following:29,36,39,40

R ϕS E ⎞ ∂ ⎛ CAϕSo + A o + A⎟ ⎜ ∂t ⎝ Bo Bo BA ⎠

⎛ ϕ ⎞3 k = fp k 0⎜⎜ ⎟⎟ ⎝ ϕ0 ⎠

(14)

Z = 0, qg = ct e

t>0

(15)

Z = 0, EA = ct e

t>0

(16)

To obtain the pressure distribution, eq 5 is combined with eqs 2−4. Therefore, the partial differential pressure equations of second order in position are obtained. This is the main reason that two boundary conditions are required to determine pressure and consequently velocity. Reservoir pressure is normally above the upper asphaltene deposition pressure under experimental conditions at the beginning of the production. It can be concluded that the volume fraction of the suspended asphaltene in the entire reservoir is zero at t = 0 as expressed below. ⎧ CA = 0 ⎪ ⎪ EA = 0 t = 0, ⎨ ,0