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Efficient Algorithm for the Prediction of Pressure−Volume− Temperature Properties of Crude Oils Using the Perturbed-Chain Statistical Associating Fluid Theory Equation of State Mohammed I. L. Abutaqiya, Sai R. Panuganti, and Francisco M. Vargas* Department of Chemical and Biomolecular Engineering, Rice University, Houston, Texas 77005, United States S Supporting Information *

ABSTRACT: A new simplified approach is presented for characterizing crude oils using the perturbed-chain version of the statistical associating fluid theory equation of state (PC-SAFT EoS). The new approach models the liquid phase in crude oil as one pseudocomponent called the “single liquid fraction” (SLF). The SLF approach requires a single fitting parameter called aromaticity (γSLF) which is fitted to the experimental bubble point and density at saturation. Simulation results for 10 light crudes from the Middle East are presented in this work and compared to 2078 data points for the predictions of constant composition expansion (CCE), differential liberation (DL), separator test, and swell test experiments. It is found that the model predictions of density are the most accurate, with an average absolute percent deviation (AAPD) of 0.5% in the CCE, 0.7% in the DL, 0.8% in the separator test, and 2.1% in the swell test. The swell test study included modeling of blends of live oil with different gases such as lean and rich hydrocarbon gases, CO2, N2, and H2S, with injection up to 71.43 mol %. The new model can predict the bubble pressure of these blends with an AAPD of 3.4%.

1. INTRODUCTION The development of models for the prediction of crude oil properties has been the topic of extensive research since the 1940s.1,2 Understanding the behavior of crude oils at reservoir conditions is essential in developing efficient production scenarios and establishing successful field development plans. The early attempts for modeling crude oil properties were based on empirical correlations of an extensive set of data which correlate bulk oil properties to each other, without taking into account the actual composition of the crude oil.1−11 Although this approach found some use in the oil industry motivated by its simplicity, it can be unreliable and lead to significant errors in modeling crudes that are different from the samples used for the regression procedure. More recently, advanced regression techniques have been implemented to obtain a more accurate correlation for the crude oil properties through the use of artificial neural networks (ANNs).12−17 Neural networks are highly adaptive informationprocessing systems that can be trained to match a set of inputs to a set of outputs. Despite being more accurate than empirical equations, ANNs generally depend on the data set used for the training process, which can lead to significant deviations in the predictions if not implemented with care. Alternatively, the oil industry currently heavily relies on equations of state (EoS) for modeling the phase behavior of crude oils, taking into account their compositional analysis. This approach, however, requires proper characterization of the crude © XXXX American Chemical Society

oil to reduce the number of components into a reasonable number of pseudocomponents and define their simulation parameters. The majority of this type of PVT calculations carried out for oil and gas applications are based on cubic EoS.18−20 These methods are widespread in the oil industry mainly due to their simple implementation. However, when performing predictions outside the range of fitting, these models usually perform poorly, requiring further tuning of simulation parameters to match experimental data. A proper crude oil characterization procedure coupled with a powerful EoS model should be capable of accurately capturing the phase behavior of crude oil without the need for additional tuning. More advanced EoS such as the statistical associating fluid theory21,22 (SAFT) and the perturbed-chain version of the statistical associating fluid theory23 (PC-SAFT) are becoming increasingly popular and have proven to perform better than cubic EoS in modeling the phase behavior of complex systems at high pressures and temperatures.24−26 Ting et al.27 and Gonzalez et al.28 developed a crude oil characterization procedure based on the content of saturates, aromatics, resins, and asphaltenes (SARA) to model asphaltene precipitation. Punnapala and Vargas29 improved the characterization procedure by reducing Received: Revised: Accepted: Published: A

January 25, 2017 May 3, 2017 May 3, 2017 May 3, 2017 DOI: 10.1021/acs.iecr.7b00368 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

less polarizable components of crude oils. In this way, the number of required simulation parameters is reduced to a minimum without sacrificing the accuracy of the results. 2.2. SARA-Based Crude Oil Characterization. 2.2.1. Lumping of Crude Oil Components. The characterization of crude oil using the PC-SAFT EoS studied in this work has been in continuous development over the past several years.25,27−29 The original purpose for developing the PC-SAFT characterization procedure was to study asphaltene precipitation in crude oil systems. In general, these developments followed the same lumping procedure for crude oil components but differed in the parameter estimation technique. The gas and liquid phases are characterized separately and then combined to form the live oil on the basis of the gas-to-oil ratio reported from the zero flash experiment. The gas phase is characterized as seven components: six pure components, which are nitrogen (N2), carbon dioxide (CO2), hydrogen sulfide (H2S), methane (C1), ethane (C2), and propane (C3), and one pseudocomponent, which is a “heavy gas”. The heavy gas consists of C4 and heavier fractions in the flashed gas. Experimental flashed gas compositional data are required as an input for gasphase characterization. In the currently published characterization procedure,25,27−29 the liquid phase is represented by three pseudocomponents: saturates, aromatics + resins (A+R), and asphaltenes. Experimental flashed liquid compositional data are required as an input for the liquid-phase characterization. Also, SARA analysis is required as an input to know the relative amounts of saturates, A+R, and asphaltene in the crude oil that form the plus fraction. Therefore, this approach is referred to as the SARA-based approach in this paper. Figure 1 presents a schematic of the SARA-based approach. 2.2.2. PC-SAFT Parameter Estimation of Crude Oil Components. For pure components, the PC-SAFT parameters are available in the literature.23 For pseudocomponents the PC-SAFT parameters are obtained from correlations. An advantage of using the PC-SAFT EoS is that the simulation parameters represent some molecular characteristics of the modeled components. Gonzalez et al.50 correlated the PC-SAFT parameters of different homologous series of hydrocarbons such as alkanes and polynuclear aromatics (PNAs) on the basis of only their molecular weight. Figure 2 shows the relation between the PC-SAFT parameters and molecular weight for n-alkanes and PNAs. The heavy gas and saturates pseudofractions are assumed to consist of n-alkanes. Therefore, the PC-SAFT parameters can be obtained from the correlations of Gonzalez et al. on the basis of their molecular weight. According to the latest development of the characterization procedure proposed by Punnapala and Vargas,29 the PC-SAFT parameters for the A+R pseudofraction are obtained by introducing an aromaticity factor (γA+R) which ranges from 0 to 1 representing n-alkanes and PNAs, respectively. Therefore, the correlation for each PC-SAFT parameter for the A+R pseudocomponent is calculated as a linear combination of the alkanes’ correlation and the PNAs’ correlation from Gonzalez et al.50 weighed by the aromaticity parameter as shown in eqs 1−3. The aromaticity of the A+R pseudofraction is then fit to match the bubble pressure and density of the reservoir fluid at saturation.

the number of tuning parameters for the asphaltene pseudofraction from three to two parameters. Although one of the main objectives of the SARA-based characterization procedure is to accurately model asphaltene precipitation, it was shown that the model can also predict the density, gas-to-oil ratio, oil formation volume factor, and composition of differentially liberated gas.29,30 Since experimental values of the SARA analysis are required as an input for this modeling method, the simulation results can be greatly affected by the uncertainty in the reported SARA. Furthermore, SARA analysis is not usually performed in crude oils that do not present asphaltene problems in the field. The purpose of this work is to investigate the capability of characterizing the liquid phase as a single pseudofraction where SARA is not required as an input. A comprehensive set of PVT properties will be investigated, including properties from routine PVT experiments and swell test experiments.

2. BACKGROUND ON THE SARA-BASED CHARACTERIZATION USING THE PC-SAFT EOS 2.1. Introduction to the PC-SAFT EoS. The statistical associating fluid theory equation of state (SAFT EoS) was developed by Chapman et al.21,22 by extending Wertheim’s firstorder perturbation theory.31−35 SAFT EoS models molecules as flexible chains of spherical segments. It is a molecule-based noncubic EoS which has proven to accurately predict the phase behavior for molecules with large size differences and complex fluids.27,36 Several variations of SAFT have been developed and applied over the years.23,37−40 Of particular importance to the current study is the modification by Gross and Sadowski,23 who applied the perturbation theory of Barker and Henderson to a hard-chain reference fluid, which is referred to as the perturbedchain SAFT (PC-SAFT). Similar to SAFT, it has been shown that the PC-SAFT EoS can accurately capture the phase behavior of complex systems such as polymer solutions41−45 and asphaltenes in crude oil systems with variations in temperature and composition.25,29,46,47 The PC-SAFT EoS is favored in this work due to its availability in commercial simulators such as Multiflash of KBC, VLXE|BLEND of VLXE Aps, and PVTsim of Calsep. The simulation parameters required for modeling using the PC-SAFT EoS are dependent on the type of system under study. For the modeling of nonassociating systems where dispersion forces dominate, each nonassociating component requires definition of three PC-SAFT parameters: the number of segments per molecule (m), the segment diameter (σ), and the segment−segment interaction energy (ε/k). For the modeling of associating components where polar−polar interactions are significant, two additional PC-SAFT parameters are required per component: the association energy (εAB) and association volume (κAB). In this work, it is assumed that dispersion forces dominate the phase behavior of crude oil, and therefore, only three PC-SAFT parameters are required to be defined per component. This assumption follows from the work of Buckley and co-workers, who established that asphaltene phase behavior is dominated by polarizability and not polarity.48,49 Furthermore, it was shown in several research papers that the PC-SAFT EoS without the association term can accurately capture the precipitation of asphaltene in crude oil systems due to changes in temperature and composition.25,29,46,47,50 Because the phase behavior of asphaltenes, the heaviest and most polarizable fraction of crude oil, is not dominated by polar interactions, it is expected that this should also be the case for the lighter and

m = (1 − γA + R )(0.0257(MW) + 0.8444) + γA + R (0.0101(MW) + 1.7296) B

(1)

DOI: 10.1021/acs.iecr.7b00368 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 1. Schematic of the SARA-based characterization method. Adapted with permission from ref 51. Copyright 2015 Society of Petroleum Engineers (SPE).

Figure 2. Variation of the PC-SAFT parameters as a function of the MW for n-alkanes and PNAs. Adapted with permission from ref 50. Copyright 2008 Rice University.

⎛ ln(MW) ⎞ ⎟ σ (Å) = (1 − γA + R )⎜4.047 − 4.8013 ⎝ MW ⎠ ⎛ 93.98 ⎞⎟ + γA + R ⎜4.6169 − ⎝ MW ⎠

(2)

⎛ ⎛ 9.523 ⎟⎞⎞ ⎟ ε/k (K) = (1 − γA + R )⎜exp⎜5.5769 − ⎝ ⎝ MW ⎠⎠ ⎛ 234100 ⎞ ⎟ + γA + R ⎜508 − ⎝ MW1.5 ⎠

(3)

For cases where asphaltene precipitation studies are required, the PC-SAFT parameters for the asphaltene pseudofraction are obtained by fitting the molecular weight and aromaticity of asphaltene (γasphaltene) to match the available data for the onset of asphaltene precipitation.29 2.3. PVT Experiments Conducted on Oil Samples. The volumetric changes of a live oil taking place in the reservoir, during passage through the well and pipelines to the processing plant, can be studied by performing PVT experiments. Those experiments are the constant composition expansion (CCE), C


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Industrial & Engineering Chemistry Research Table 1. Summary of PVT Experiments and the Properties Modeled

* Reported experimental values for isothermal compressibility are obtained by curve-fitting a given function to relative volume values and then obtaining the analytical derivative from the fitted function.

characterization method as described in section 2.2.2. For pure components, the PC-SAFT parameters are obtained from the literature.23 The heavy gas pseudofraction is assumed to consist of n-alkanes, and its PC-SAFT parameters are obtained from the correlations of Gonzalez et al.50 For the SLF, an aromaticity parameter (γSLF) is used in eqs 1−3 instead of γA+R. The aromaticity of SLF is then fit to match the experimental bubble pressure and density of the reservoir fluid at saturation. The purpose of this work is to investigate the capability of PC-SAFT to model routine PVT experiments and swell tests using the SLF method and compare the results to those of the SARA-based method. A detailed step-by-step example of the full characterization of one of the crude oils using the SLF method can be found in the Supporting Information.

differential liberation (DL), separator test, and swell test. Pedersen et al.52 provide excellent background on those experiments. Table 1 demonstrates an overview of the experiments and the PVT properties that are generally reported for crude oils. The CCE, DL, and separator test experiments are usually referred to as “routine PVT experiments”. Swell tests are more specialized experiments where the phase behavior of crude oil is investigated with different injection gases, which is of particular interest for enhanced oil recovery (EOR) projects.

3. NEW CHARACTERIZATION PROCEDURE USING THE SINGLE LIQUID FRACTION Similar to the SARA-based method, the general procedure in the proposed single liquid fraction (SLF) method is to characterize the gas and liquid phases separately and then combine them to form the live oil on the basis of the experimental gas-to-oil ratio from ambient flash experiments. The gas phase in the SLF method is characterized similarly to that in the SARA-based method as described in section 2.2.1. However, the liquid phase is modeled as a single pseudocomponent called “SLF” rather than three pseudocomponents, “saturates”, “A+R”, and “asphaltene”. The SLF pseudocomponent has an MW similar to the STO MW reported experimentally. Furthermore, the SLF molar composition in the live oil matches the reported zero flash GOR. Since the liquid phase is lumped into a single pseudocomponent, the experimental flashed liquid composition and SARA analysis are no longer required as an input for the liquid-phase characterization. It is important to note that the asphaltene fraction is lumped into the SLF, since all crude oils studied contain a very small amount of asphaltenes, which would not affect the PVT properties. Figure 3 presents a schematic of the SLF characterization method. The PC-SAFT parameter estimation for the crude oil components is performed similarly to that of the SARA-based

4. SIMULATION RESULTS AND DISCUSSION In this study, 10 crude oils from the Middle East region are investigated for the modeling of constant composition expansion (CCE), differential liberation (DL), separator test, and swell test experiments. The properties of the modeled crudes are found in Table 2. The composition of the flashed gas, which is necessary for the SLF characterization, can be found in the Supporting Information. Table 3 provides a list of the available PVT experimental data for each crude. Table 4 shows the characterized crude oils and the PC-SAFT parameters for all components. The kij values used in this work are reported in Table 5. The kij values between pure components are taken from the work of Panuganti et al.25 The kij values between pure-pseudocomponents and pseudo-pseudocomponents are chosen to match bubble pressure data with gas injection for crude A. No further tuning of kij values is performed for the other crudes. In the results shown in this section, the symbols represent the experimental data points and the lines represent the PC-SAFT D


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Figure 3. Schematic of the characterization of crude oil using the single liquid fraction (SLF) characterization method proposed in this work.

Table 2. Properties of Crude Oils Studied in This Work property

crude A

crude B

crude C

crude D

crude E

crude F

crude G

crude H

crude I

crude J

STO MW (g/mol) STO API gravity GOR (Sm3/m3) density at saturation (kg/m3) reservoir Psat (MPa) reservoir Tsat (°C) saturates concn, wt % aromatics concn, wt % resins concn, wt % asphaltene concn, wt %

212.9 35.7 286 610.5 27.45 121.1 44.9 46.3 6.7 2.1

212.4 31.7 38 764.0 5.76 100.0 59.4 22.57 13.97 1.73

201.9 36.9 148 654.7 16.39 121.1 70.42 22.64 6.24 0.18

204.0 36.9 192 636.2 19.79 126.7 70.20 22.89 4.85 0.12

193.5 40.5 190 624.2 15.79 120.6 49.5 40.2 7.2 3.1

208.0 38.0 164 647.6 17.35 121.1

195.5 40.2 68

189.0 41.1 606 483.0 27.21 135.0 52.53 36.82 1.86 0.00

193.0 38.4 171 632.4 15.88 123.9

191.0 38.0 142

fluid

available PVT experiments routine PVT experiments, bubble pressure vs gas injection (CO2) routine PVT experiments, bubble pressure vs gas injection (rich, N2, H2S, CO2) routine PVT experiments routine PVT experiments routine PVT experiments, bubble pressure vs gas injection (CO2) routine PVT experiments, swell test (lean gas, rich gas, CO2) bubble pressure vs gas injection (rich gas) constant composition expansion for live oil, swell test (N2) routine PVT experiments bubble pressure vs gas injection (rich gas)

crude C crude D crude E crude F crude G crude H crude I crude J

14.57 121.1 75.56 20.08 4.13 0.21

absolute difference (MAD), which are defined for property x by eqs 4 and 5, respectively.

Table 3. Simulated PVT Experiments for Each Crude in This Study crude A crude B

7.61 126.7 80.64 17.44 1.47 0.45

AAPD (%) =

∑ all data points

abs(xmeasured − xcalculated) × 100 xmeasured (4)

MAD (property unit) =

∑ all data points

abs(xmeasured − xcalculated) (5)

The simulation results that are presented in sections 4.1−4.4 are predictions that required no additional parameter fitting. The simulation parameters are only fitted to the bubble pressure and density at saturation, if available, or the density of the stock tank oil. The AAPD and/or MAD reported in the caption of Figures 4−16 correspond to all crudes studied in this work, not only the crudes shown in each figure. 4.1. Simulation of Constant Composition Expansion (CCE) Experiments. Figure 4 shows the measured and predicted liquid oil density for pressure depletion at the reservoir temperature. The data above Psat are from the CCE

predictions. The PC-SAFT flash calculations were performed using two commercial software systems: Multiflash of KBC and VLXE|BLEND of VLXE Aps. The numerical values for the experimental and simulation data for all crude oils in this work can be found in the Supporting Information. The properties used for statistical analysis in this work are the absolute average percent deviation (AAPD) and the mean E


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Industrial & Engineering Chemistry Research Table 4. Characterized Reservoir Fluids A−J

Table 5. Binary Interaction Parameters (kij) Used for the PC-SAFT Modeling with the SLF Method component

N2

CO2

H2S

C1

C2

C3

heavy gas

SLF

N2 CO2 H2S C1 C2 C3 heavy gas SLF

−

0 −

0.090 0.0678 −

0.030 0.057 0.062 −

0.040 0.097 0.058 0 −

0.060 0.107 0.053 0 0 −

0.075 0.090 0.080 0.080 0.050 0.030 −

0.100 0.100 0.050 0 0 0 0.067 −

and those below Psat from differential liberation experiments which are combined in this figure for convenience. The simulation results are in excellent agreement with the experimental data.

Figure 5 shows relative volume predictions using PC-SAFT, while Figure 6 shows the Y-factor predictions, both matching very well with the experimental data. It is observed that, for the fluids studied here, the Y-factor is small. Because these oils are F


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Figure 7. Predicted isothermal compressibility in CCE for selected crudes. AAPD is 12.4% for all crudes.

Figure 4. Measured and predicted liquid density at constant temperature as a function of pressure. AAPD above Psat is 0.5% and AAPD below Psat is 0.7% for all crudes.

obtained by using the analytical derivative of the fitted function. Therefore, the reported values are heavily dependent on the type of fitted function and the quality of the experimental values for the relative volume. Also, fitting to the relative volume does not guarantee a good match to the isothermal compressibility since it is a derivative property. 4.2. Simulation of Differential Liberation (DL) Experiments. Experimental values and PC-SAFT predictions for differential liberation experiments are plotted in Figures 8−11 for the solution GOR (Rs), oil formation volume factor (Bo), gas formation volume factor (Bg), gas Z-factor, and gas gravity of the liberated gas. The predictions of the solution GOR in Figure 8 are demonstrated in two plots to locate the main source of deviation. Figure 8a shows a comparison between predictions and experimental data, while Figure 8b shows a residual plot for the Rs predictions as a function of pressure along with the ±10%

Figure 5. Relative volume in the CCE experiment for selected crudes. AAPD is 0.8% for all crudes.

Figure 6. Y-function for the CCE experiment for selected crudes. AAPD is 2.0% for all crudes.

light with a relatively high GOR, they release a good amount of gas with decreasing pressure below the bubble point, and as the gas takes up more volume than the liquid, the volumetric changes with decreasing pressure are large. The isothermal compressibility recorded above the bubble point is shown in Figure 7. It is found that, for all the crudes studied, the isothermal compressibility predictions from PC-SAFT are in good agreement with the experimental data at high pressures, but as the pressure gets closer to the bubble point, the deviation becomes larger. It is worth mentioning, however, that experimental isothermal compressibility data are obtained by fitting a certain function to match the relative volume data as a function of pressure. The experimental isothermal compressibility is then

Figure 8. Modeling results of the solution gas-to-oil ratio (Rs) plotted as (a) measured and predicted values for selected crudes and (b) percent deviations vs pressure for all crudes. The AAPD is 10.3% for all crudes. G


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During a differential liberation test, knowledge of the composition of the evolved gas during different stages is useful in designing process equipment. Figure 11 shows the accuracy of such PC-SAFT predictions for the composition of methane, ethane, propane, N2, CO2, and H2S in the liberated gas. Those hydrocarbon gases (Figure 11a−c) constitute the major portion of the liberated gas, and it can be seen how well the model predicts the compositions as a function of pressure. Furthermore, the model can accurately predict the composition of nonhydrocarbon gases (Figure 11d−f) even for amounts as low as 0.5 mol % for the case of N2. Except for the value for the H2S composition at the last stage at atmospheric pressure, the prediction of the model is in excellent agreement with the experimental data for H2S concentrations as high as 15 mol %, which is very important in choosing material for designing highpressure process equipment. Also, within ±1 mol %, PC-SAFT prediction of the composition of CO2 matches the experimental data very well. In general, it is found that the deviations in predicting the composition are largest in the atmospheric pressure stage, which explains the deviations in gas gravity in that stage as shown earlier (Figure 10c). 4.3. Simulation of Separator Test Experiments. Different separator test results are given in Figure 12 showing the comparison between the simulation results and the corresponding experimental data for the liquid oil density, GOR, Bo, gas gravity, and molar composition of the liberated gas at every flash stage for the different crudes. Because the separator test for different crudes is conducted at various temperatures and pressures, the comparison is better achieved for all the crude oils with a reference diagonal line, which represents a perfect agreement between the simulations and experimental data. The results for the prediction of the liquid density and oil formation factor are in excellent agreement with the experimental data. The prediction of the gas gravity is consistent with the experimental data for the relatively lighter gases, which correspond to

reference deviation lines. It can be concluded from Figure 8b that most of the deviation is located near the low-pressure stages, where experimental error in measuring the amount of liberated gas has accumulated the most. Also, Figure 8b implies that the model mostly underpredicts the solution GOR. This is due to the use of a single liquid fraction in the characterization method, which inhibits the partitioning of the light components from the liquid phase to the gas phase. When only considering the values of the solution GOR at saturation (Rssat), the AAPD of the predictions is 8.1%. The predictions of the oil formation volume factor are in excellent agreement with the experimental data as shown in Figure 9. Also, the predictions of the gas-phase properties

Figure 9. Measured and predicted oil formation factor (Bo) during the differential liberation test up to the bubble pressure for selected crudes. The AAPD is 3.2% for all crudes.

match very well with the experimental data as shown in Figure 10. It is observed, however, that the predictions of the gas gravity are usually off at the atmospheric pressure stage (last stage).

Figure 10. Measured and predicted gas-phase properties in differential liberation experiments for selected crudes: (a) gas formation volume factor (AAPD is 2.1%), (b) gas compressibility factor Z (AAPD is 2.2%), (c) gas gravity (AAPD is 5.4%). H


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Figure 11. Composition of differentially liberated gas for (a) methane (MAD is 1.67 mol %), (b) ethane (MAD is 1.02 mol %), (c) propane (MAD is 1.62 mol %), (d) nitrogen (MAD is 0.17 mol %), (e) carbon dioxide (MAD is 0.80 mol %), and (f) hydrogen sulfide (MAD is 0.99 mol %).

is adequate for enhanced oil recovery (EOR) applications only if it is capable of predicting the swell test results, i.e., the bubble pressure and density of blends of oil with CO2 or hydrocarbon gas, without additional tuning of the simulation parameters. Figure 13 shows the bubble pressure predictions as a function of gas injection for blends with hydrocarbon gases. Figure 14 shows the bubble pressure predictions as a function of gas injection for oil blends containing H2S, CO2, and N2. The composition of the injection gases for each crude oil can be found in the Supporting Information. The gas injection amount represents the mole fraction of gas in place after injection. It can be seen how accurate the model is for predicting bubble points of mixtures of live oil with up to 66 mol % gas injection for both hydrocarbon and nonhydrocarbon gases. Also, the effect of temperature on the bubble point is studied, and the results are presented in Figure 15, where the complete crude oil phase envelope is shown. It can be seen how well the model captures the effect of temperature on the bubble point for crude oils and for oil−gas blends. Finally, the density and relative volume of oil blends with different types of injection gases are shown in parts a and b, respectively, of Figure 16. The versatility of the model in predicting properties in the swell test experiment is evident.

separation stages at high pressure and temperature. However, for gas gravity values above 1.4, which usually correspond to separation stages near ambient pressure and temperature (last separator stage), there is a deviation between the experimental and simulation results. This observation was also noted for gas gravity in differential liberation (Figure 10c) and in the composition of differentially liberated gas at ambient pressure (Figure 11). One of the reasons for this deviation at near ambient conditions is the difficulty of handling the liberated gas when the experiments are performed. Nevertheless, at relatively high pressures and temperatures, the model is in good agreement with the experimental data. The modeling results for the separator test GOR shown in Figure 12c represent the GOR from all separator stages for each crude. The AAPD of 9.3% corresponds to the total GOR for each crude, which is the summation of the GORs from all separator stages. This property indicates the maximum amount of gas that can be liberated from the crude oil at standard conditions. 4.4. Simulation of Swell Test Experiments. Hydrocarbon gas or CO2 injection into oil reservoirs is becoming a very popular strategy for enhancing the recovery of oil. An EoS model I


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Figure 12. Separator test results for all crudes at different temperatures and pressures for modeling of the (a) liquid density (AAPD is 0.8%), (b) oil formation factor Bo (AAPD is 1.1%), (c) GOR (AAPD is 9.3% for total GOR), (d) gas gravity (AAPD is 12.0%), and (e) gas composition of C1, C2, CO2, and H2S. The line shown is the diagonal reference line.

Figure 13. Measured and predicted bubble pressure vs amount of gas injection for different crudes with hydrocarbon gas injection (AAPD is 3.2%).

4.5. Analysis of the Simulation Results. Table 6 provides the results of the error analysis for all studied experiments in terms of the AAPD between the PC-SAFT predictions

The model has the ability to accurately capture the effect of gas injection on the bubble point and density without the need for any additional parameter tuning. J


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Figure 14. Measured and predicted bubble pressure vs amount of gas injection for different crudes with non-hydrocarbon gas injection (AAPD is 3.7%).

Figure 15. Simulated phase envelope for different crudes and oil−gas blends. Open markers are experimental data for the bubble pressure, and solid lines are PC-SAFT predictions using the SLF model (AAPD is 2.5%). CP = critical point. K


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Figure 16. Modeling of the crude oil blends with different types of gas injection in the swell test showing measured and predicted results for the (a) density (AAPD for CO2, 2.9%; AAPD for H/C, 1.3%; AAPD for N2, 1.5%) and (b) relative volume (AAPD for CO2, 1.1%; AAPD for H/C, 1.7%; AAPD for N2, 1.0%). The diagonal line represents the perfect prediction.

parameters for the characterized fluids using the SARA-based method. It can be noted from Table 6 that density predictions using both characterization methods have the lowest AAPD as compared to the predictions of other properties in each experiment. The density predictions for the CCE experiment are the most accurate, which is in agreement with the experimental uncertainty expected from the CCE since the measurements are made on single-phase reservoir fluid. Predictions of the isothermal compressibility have the maximum AAPD in the CCE experiment. It was already shown in Figure 7 how the deviation increases as the pressure approaches the bubble pressure. However, at the reservoir pressure and temperature, the predictions provide reasonable accuracy with an AAPD of 4.6%. The SARA-based method provides slightly better predictions for the isothermal compressibility, which may be the result of using two liquid-phase pseudocomponents. The predictions of the solution GOR (Rs) have the maximum deviation as compared to the predictions of other properties in the differential liberation experiment. The SARA-based method with two liquid pseudofractions provides slightly better predictions for the solution GOR. However, as shown in Figure 8b, the major contribution to the AAPD in the predictions of the solution GOR is from the last pressure stages where experimental error has accumulated the most. The predictions of liquid-phase properties in the separator test (i.e., oil formation factor and density) are more accurate than the predictions of gas-phase properties (i.e., GOR and gas gravity) using both characterization methods. This is in agreement with the experimental uncertainty associated with measuring gas-phase properties. Several factors such as the room temperature, equilibration time, and proper gas collection contribute to the greater experimental uncertainty in the gasphase properties. The simulation results for the swell test using both methods show good agreement with the experimental data, with the SLF method predicting the bubble pressure for different gas injection rates more accurately and the SARA-based method predicting the density more accurately. The predictions for the gas composition in the differential liberation and separator tests are compared against the experimental data using the mean absolute difference (MAD) as defined in eq 5. The SLF method predicts the composition of the gas with an MAD of 1.76 mol % for hydrocarbon gases, 0.17 mol % for N2, 0.79 mol % for CO2, and 1.00 mol % for H2S. The coefficient of determination (R2 value) for the prediction

Table 6. Error Analysis for the Modeling of the 10 Crudes Using the PC-SAFT EoS with the SLF Method and the SARA-Based Method SLF method experiment constant composition expansion

differential liberation

separator test

swell test

property

SARA-based method

number AAPD number AAPD of points (%) of points (%)

density

117

0.5

87

0.4

relative volume isothermal compressibility Y-function density

230 112

0.8 12.4

169 78

1.2 8.6

61 57

2.0 0.7

43 40

6.5 1.0

50 64 43 43 50 7 23 21 21 71 289 803 2078

10.3 3.2 2.1 2.2 5.4 9.4 0.8 1.1 12.0 3.4 2.1 1.4

35 47 30 30 35 5 14 14 14 57 102 325 1130

9.1 3.0 1.3 1.2 7.9 9.9 1.4 1.6 8.7 5.5 1.0 2.8

solution GORa oil formation factor gas formation factor gas Z-factor gas gravity total GORb density oil formation factor gas gravity bubble point density relative volume overall

a

Solution GOR (Rs) is the total amount of gases dissolved in a stock tank barrel of crude oil at a specific temperature and pressure (Sm3/m3). b Total GOR is the summation of the gas liberated from all separator stages expressed per stock tank barrel (Sm3/m3).

and experimental data. Table 6 also includes a comparison between the SLF and SARA-based characterization methods. The simulation parameters for the SARA-based characterization of crudes B and J are taken from the work of Punnapala and Vargas.29 Since SARA analysis is not reported for crudes F and I, modeling using the SARA-based method is not performed. For the remaining crudes, SARA-based characterization is performed following the approach of Punnapala and Vargas and neglecting the asphaltene pseudofraction since modeling of asphaltene precipitation is not required. The composition of the flashed liquid, which is an input requirement for the modeling using the SARA-based method, is presented in the Supporting Information along with the simulation L


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hydrocarbon gases, CO2, N2, and H2S. The predictions of the bubble pressure are within 3.4% deviation for gas injection up to 71.43 mol %. This implies that PC-SAFT can be reliably used to reduce the number of required experiments in the development of EOR strategies. Furthermore, the model can also assist in the design of such experiments and also validate the consistency of the experimental results. The range of injection gases included in this study proves the versatility of the PC-SAFT model in predicting swell test properties for light crude oils with a low asphaltene content. The maximum deviation in modeling of the CCE experiment was found in the predictions for the isothermal compressibility. It was found that the SLF method underpredicts the isothermal compressibility of crude oil as the pressure approaches the bubble pressure. However, at high pressures, as found inside the reservoir, the predictions match the experimental data within 4.6% deviation. The maximum deviation in modeling of the DL experiment was found in the predictions of the gas-to-oil ratio. However, it was shown how the deviation from the experimental data in the differential liberation experiment followed a specific trend with increasing deviation at lower pressure stages. This reflects the accumulation of error that occurs during those experiments. For high-pressure stages, however, during the DL and separator test, the model matches experimental data reasonably well. The results from both the SLF characterization and the SARA-based characterization provide similar overall accuracy in predicting PVT experiments. This implies that, even in the absence of SARA analysis, which is necessary to perform the SARA-based characterization procedure, the new SLF method can be used for the predictions of PVT experiments with excellent results. Although the lumping of the liquid components into a single fraction using the PC-SAFT EoS is sufficient to model the bubble point for a wide range of gas injections, the dew point and retrograde condensation phenomena are not expected to be accurately captured. The reason is that the dew point is strongly influenced by the heaviest component in the liquid phase. Therefore, lumping all liquid components into a single fraction is expected to underestimate the dew pressure and liquid dropout at a given temperature. The PC-SAFT characterization method provides a powerful tool to aid in PVT studies and development of EOR or field development scenarios. The ability to perform accurate PVT predictions using either one or two liquid-phase pseudocomponents is a mere reflection of the high capability of PC-SAFT EoS in capturing the phase behavior of reservoir fluids.

using the SLF method is 0.990, which proves the good agreement with the experimental data. The SARA-based method predicts the composition of the gas with an MAD of 2.3 mol % for hydrocarbon gases, 0.03 mol % for N2, 0.81 mol % for CO2, and 0.87 mol % for H2S. The coefficient of determination (R2 value) for the prediction using the SARA-based method is 0.994, which also proves the good agreement with the experimental data. 4.6. Model Applicability and Limitations. The SLF model in this work has shown promising capability in predicting the PVT properties of crude oils, especially the density and bubble pressure for oil and gas blends. Most liquid-phase properties, except the isothermal compressibility near the bubble pressure, have been predicted with excellent agreement with the experimental data. Although the lumping of the liquid components into a single fraction using the PC-SAFT EoS is sufficient to model the bubble point for a wide range of gas injections, the dew point and retrograde condensation phenomena are not expected to be accurately captured. The reason is that the dew point is strongly influenced by the heaviest component in the liquid phase. Therefore, lumping all liquid components into a single fraction is expected to underestimate the dew pressure and liquid dropout at a given temperature. The crude oils studied in this work have a relatively low asphaltene content (up to 3.1 wt %). Nevertheless, it is expected that even for crudes with higher asphaltene content the model would be able to predict the PVT properties of the mixture, such as the bubble pressure and density. The presence of higher amounts of asphaltenes would have an effect on the value of the fitted aromaticity factor. Understandably, the model is not capable of predicting asphaltene precipitation because that requires a separate consideration for the asphaltene amount and properties. On the other hand, the high molecular weight of asphaltenes as compared to other components implies a much lower mole fraction of asphaltenes in the live oil, which is not expected to affect the bubble pressure and saturation density significantly. The reason is that those properties are mainly controlled by the lighter components in the live oil, which are present at a much higher mole fraction than asphaltenes. The effect of a high asphaltene content would be more pronounced on the density of the dead oil at ambient pressure and temperature. However, this is not expected to affect the modeling results of the high-temperature and high-pressure PVT properties.

5. CONCLUSION In this paper, we have shown a new characterization procedure for the PC-SAFT EoS, which provides a comprehensive tool for modeling a wide range of PVT properties of crude oil systems. The proposed characterization approach models the liquid phase as a single liquid fraction, and a corresponding aromaticity parameter is fitted to the experimental bubble point and density at saturation and/or density of the stock tank oil. The input requirements for the new model are the STO molecular weight, flashed gas composition, zero flash GOR, bubble pressure, and density at saturation and/or density of the stock tank oil. The overall results for modeling the constant composition expansion (CCE), differential liberation (DL), separator test, and swell test provide excellent agreement with the experimental data within experimental uncertainty. The predictions for the density in all experiments are the most accurate, with an AAPD of 0.5% in the CCE experiment, 0.7% in the DL experiment, 0.8% in the separator test, and 2.1% in the swell test. The model shows especially accurate predictions for the bubble point pressure of crude oil with a wide range of injection gases such as lean and rich

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b00368. Detailed step-by-step characterization example for one of the crudes, composition of the modeled crude oils and the injected gases, values for experimental PVT data as well as simulation data using the SLF method, and simulation parameters for the crude oils characterized using the SARA-based method (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: (713) 348-2384. M


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Industrial & Engineering Chemistry Research ORCID

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Mohammed I. L. Abutaqiya: 0000-0002-7161-0733 Sai R. Panuganti: 0000-0001-8107-8691 Francisco M. Vargas: 0000-0001-5686-5140 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was undertaken with the generous support of the Abu Dhabi National Oil Co. (ADNOC) Oil Subcommittee. We are grateful to Dalia S. Abdallah and Sameer Punnapala from the Abu Dhabi Co. for Onshore Petroleum Operations Ltd. (ADCO) and Walter G. Chapman, Caleb Sisco, and Mohammad Tavakkoli from Rice University for fruitful discussions.

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NOMENCLATURE A+R aromatics plus resins AAPD average absolute percent deviation Bg gas formation volume factor Bo oil formation volume factor CCE constant composition expansion DL differential liberation EOR enhanced oil recovery EoS equation of state GOR gas-to-oil ratio lean gas hydrocarbon gas with methane content >85 mol % m number of segments per molecule MAD mean absolute deviation MW molecular weight PC-SAFT perturbed-chain statistical associating fluid theory PNAs polynuclear aromatics PVT pressure−volume−temperature rel relative rich gas hydrocarbon gas with methane content

Efficient Algorithm for the Prediction of Pressure ... - ACS Publications

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