Characterization of gas-oil flow in Cyclic Solvent Injection (CSI) for heavy oil recovery

Characterization of gas-oil flow in Cyclic Solvent Injection (CSI) for heavy oil recovery

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Journal of Petroleum Science and Engineering (xxxx) xxxx–xxxx

Contents lists available at ScienceDirect

Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol

Characterization of gas-oil flow in Cyclic Solvent Injection (CSI) for heavy oil recovery ⁎

Sam Yeol Hong, Fanhua Zeng , Zhongwei Du Faculty of Engineering and Applied Science, University of Regina, SK, Canada S4S 0A2

A R T I C L E I N F O

A BS T RAC T

Keywords: Cyclic Solvent Injection Foamy oil Solvent chamber Pressure depletion rate Numerical simulations Relative permeability curves

Cyclic Solvent Injection (CSI) has emerged as an effective follow-up process to the primary cold production, namely, Cold Heavy Oil Production with Sand (CHOPS). In this recovery process, the solvent is designed to maintain a strong nature of gas at in-situ conditions. As a result, the porous medium is spatially divided into two zones with differing fluid properties, which are gas zone, also called solvent chamber, and heavy oil zone. The CSI process is governed by the gas-oil flow as the solvent chamber is predominated by free gas-oil flow and the heavy oil zone by dispersed gas-oil flow (i.e. foamy oil flow). The gas-oil flow in CSI considerably differs from that in heavy oil solution gas drive, and therefore, needs to be investigated separately. The differences mainly arise from the origin of free gas. In CSI, the free gas originates at the solvent chamber, whereas in heavy oil solution gas drive, it evolves from solution gas. The free gas, in accordance with where it originates, yields occurrence time and quantity that have different dependency on the pseudobubblepoint pressure of oil. Consequently, the gas-oil flow in CSI results in the characteristics far more susceptible to the quantity of free gas and the nonequilibrium nature of foamy oil than heavy oil solution gas drive. This study is aimed at characterizing the gas-oil flow in CSI under the effects of pressure depletion rate as well as the solvent chamber. To fulfill this objective, the gas-liquid relative permeability curves were inferred with the use of numerical simulations and modified fractional flow models. The numerical simulations were carried out to history-match seven lab-scale CSI tests performed at different pressure depletion rates. The modified fractional flow models were applied to describe the foamy oil flow. The distinct characteristics of the gas-oil flow were examined based on sensitivity analysis and comparison to the previous findings on heavy oil solution gas drive. The results suggest that, at low pressure depletion rates, the gas-oil flow in CSI yield the characteristics that have also been observed in heavy oil solution gas drive. At sufficiently high pressure depletion rates, however, the free gas that exists even when the dispersed gas bubbles are immobile results in the different behavior of critical gas saturation and gas phase mobility. The solvent chamber misleads the gas-liquid relative permeability curves if the critical gas saturation is too high to properly describe the simultaneous flow of free gas and foamy oil. The solvent injectivity is also affected by the pressure depletion rate due to the foamy oil that has remained as unproduced in the solvent chamber during a previous production period.

1. Introduction Cyclic Solvent Injection (CSI) has emerged as an effective follow-up process to the primary cold production, namely, Cold Heavy Oil Production with Sand (CHOPS). The CSI process is deemed the most suitable for the post-CHOPS reservoirs characterized as thin and unconsolidated formations with a strong wormhole network (Dong et al., 2006). Under CHOPS, the unconsolidated formations induce sand productions and in turn high permeability channels in communication



with each other. These channels develop the wormhole network extending outward the wellbore. CHOPS has been operated in the field over the last decades. The recovery factor, however, has been reported to be only 5–10% of the original oil in place (Chang and Ivory, 2013). That is, the economic life of CHOPS is facing an imminent end of its economic life leaving 90–95% of the reserves untapped afterward. A full understanding of CSI process is immediately required to exploit the vast amount of the heavy oil deposits left underground. Such potential of CSI has led to the field tests on heavy oil reservoirs in Saskatchewan, piloted

Corresponding author. E-mail addresses: [email protected] (S.Y. Hong), [email protected] (F. Zeng), [email protected] (Z. Du).

http://dx.doi.org/10.1016/j.petrol.2017.01.029 Received 20 September 2016; Received in revised form 6 December 2016; Accepted 13 January 2017 0920-4105/ © 2017 Elsevier B.V. All rights reserved.

Please cite this article as: Yeol Hong, S., Journal of Petroleum Science and Engineering (2017), http://dx.doi.org/10.1016/j.petrol.2017.01.029

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differing fluids properties, which are gas zone, also called solvent chamber, and heavy oil zone. The solvent chamber mainly contains the solvent in the form of free gas and under the huff-n-puff operation locates at inner region towards the well. The heavy oil zone represents the bulk oil bordering the outer face of the gas zone. The recovery process of CSI is governed by the gas-oil flow as the solvent chamber is predominated by free gas-oil flow and the heavy oil zone by dispersed gas-oil flow (i.e. foamy oil flow). The gas-oil flow appears as the combined flow of free gas and foamy oil which have originated at the solvent chamber and the heavy oil zone, respectively. The flow paths are formed across the solvent chamber in accordance with the potential gradients traversing the gas zone in both injection and production stages. In the injection stages, the free gas injected travels across the solvent chamber along with the foamy oil that has remained as unproduced during a previous production period. In the production stages, the free gas is discharged from the solvent chamber along with the foamy oil that has generated from the solvent-enriched heavy oil. The gas-oil flow in CSI results in the characteristics that depend on the properties of the solvent chamber in addition to the pressure depletion rate which, as previously discussed, alters the nonequilibrium nature of foamy oil. In fluids flow aspects, the solvent chamber serves as free gas storage in the porous medium and the porous paths that the moving fluids encounter. Its volume and geometry (i.e. dimensions and location compared to the wellbore) therefore govern the quantity of the free gas and the configuration of the flow paths, respectively. The quantity of the free gas determines the relative quantity of the fluid to another. The configuration of the flow paths establishes the extent and degree of the flow resistance. The gas-oil flow in heavy oil systems has been widely studied based on heavy oil solution gas drive (Kumar and Pooladi-Darvish, 2002; Ostos and Maini, 2004; Maini et al., 2010). However, the combined flow of free gas and foamy oil in CSI considerably differs from that in heavy oil solution gas drive and therefore needs to be investigated separately. The differences mainly arise from the origin of free gas. The free gas, in accordance with where it originates, yields occurrence time and quantity that have different dependency on the pseudobubblepoint pressure of oil. Specifically, in CSI, the free gas originates at the solvent chamber containing the gas mainly supplied from an external source. The combined flow of free gas and foamy oil therefore occurs from the beginning at the in-situ pressure higher than the pseudobubblepoint pressure of oil. As a result, the free gas always amounts in addition to the continuous gas phase that develops from the dispersed gas bubbles. While the free gas is present, the foamy oil undergoes when the dispersed gas bubbles nucleate, grow, and sustain strong nonequilibrium nature against thermodynamic phase behavior. In heavy oil solution gas drive, on the other hand, the free gas evolves from solution gas. The combined flow of free gas and foamy oil therefore takes place relatively late at the in-situ pressure lower than the pseudobubblepoint pressure of oil. As a result, the free gas amounts virtually equivalent to the continuous gas phase that develops from the dispersed gas bubbles. While the free gas is present, the foamy oil only undergoes when the dispersed gas bubbles have diminishing nonequilibrium nature in favor of thermodynamic phase behavior. Consequently, the gas-oil flow in CSI considerably differs from that in heavy oil solution gas drive in the significant aspects of occurrence time, quantity of the free gas, and behavior of the foamy oil. It always results in the combined flow of free gas and foamy oil far more susceptible to the quantity of the free gas and the nonequilibrium nature of the dispersed gas bubbles than heavy oil solution gas drive. This study is aimed at investigating the characteristics of the gas-oil flow in CSI. In particular, the gas-liquid relative permeability curves need to be thoroughly understood under the effect of the pressure depletion rate as well as the solvent chamber. Until now, there has been no study specifically examining the two-phase fractional flow curves in

by Nexen at Plover Lake (Saskatchewan Petroleum Research Incentive, 2006), and Husky at Mervin (Saskatchewan Petroleum Research Incentive, 2011). CSI is a huff-n-puff process operated cyclically by a single well with the use of solvent as the injectant. A CSI cycle consists of three sequential stages: injection, soaking, and production, in the order of precedence. In general, the solvent is composed of light hydrocarbons (e.g. methane, propane, etc.) and carbon dioxide in a pure or mixed form. It is designed in a manner that the gaseous compound at atmosphere is put slightly below its dew point at the end of the injection stages. In this phase equilibria, the solvent is equipped with a tendency to liquefy, and yet the nature of gas is preserved to the utmost. It attains a high solubility while its inventory in the oil phase is minimized apart from the dissolved quantity. As a result, the solvent dilutes heavy oil without being excessively liquefied. At the same time, the dissolved quantity is effectively retrieved with the aid of high gas phase mobility. The mechanisms of CSI involve those of solvent-based processes as well as heavy oil solution gas drive. The mechanisms of heavy oil solution gas drive take place due to the in-situ pressure depletion in the absence of an external driving source during the production stages. The solvent dissolved in heavy oil therefore not only adds light components in the oil phase but also restores solution gas oil ratio (GOR). The resulting recovery mechanisms are summarized into oil viscosity reduction including in-situ upgrading of heavy oil, surface tension reduction, oil swelling, and foamy oil flow (Das et al., 1998; Luo et al., 2007; Maini et al., 2010). The foamy oil flow appears as the dispersed gas-oil flow in which the gas in the form of microbubbles migrates in company with the oil rather than flowing independently as a continuous phase. Its generation was delineated by Maini et al. (2010) based on the evolution process of gas bubbles, divided into: bubble nucleation, bubble growth, bubble trapping-mobilization, and bubble coalescence/breakup. The gas bubbles that have undergone such evolution process eventually develop free gas flow in a continuous gas phase at a local pressure below the pseudobubblepoint pressure of oil (Kraus et al., 1993). The nonequilibrium nature of foamy oil varies as a function of pressure depletion rate. Bora et al. (2000) visualized the foamy oil flow in a pore scale with the use of transparent glass micromodel at different pressure depletion rates (380–3100 kPa/h). At slow depletion rates, the gas-oil flow behaved analogously to the conventional solution gas theories - the gas bubbles grew without migrating until a continuous gas phase was formed. At fast depletion rates, however, the gas bubbles evolved into dispersed gas-oil flow before a continuous gas phase was formed. Maini et al. (2010) explained this phenomenon as a result of high viscous forces comparable to capillary forces. In other words, the fast depletion rates induce large pressure gradients and thereby increase the capillary number, defined as the ratio of viscous force to capillary force (Eq. (1)), high enough to mobilize the isolated gas bubbles.

Nca =

k ∂p σog ∂x

(1)

where Nca: capillary number; k: absolute permeability; σog: surface tension between oil and gas; ∂p/∂x : pressure gradient. Maini et al. (2010) utilized a sandpack model to investigate the heavy oil solution gas drive under the effect of the pressure depletion rate (7–170 kPa/min). It was observed that the recovery factor increased with the depletion rate. Such effect of the pressure depletion rate prompted the application of cyclic pressure depletion in continuous solvent injection processes (Jia et al., 2013; Jiang et al., 2014). It was suggested that the foamy oil flow was generated, promoting the heavy oil recovery. In CSI, the injection of the solvent that maintains a gas state at insitu conditions spatially divides the porous medium into two zones of 2

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CSI process. The specific objective of this study is:

30.48 cm 10.16 cm



to investigate the gas-liquid relative permeability curves in CSI process and understand the effects of the pressure depletion rate and the solvent chamber on these fractional flow curves.

15.24 cm 7.62 cm

7.62 cm

(a)

15.24 cm

0.32 cm

2. Methods and materials 2.1. Experiments 0.32 cm

This study utilizes the experimental data obtained from the previous CSI tests (Du et al., 2013, 2015, 2016). Nine CSI tests with the same sandpack dimensions were adopted. Propane was utilized as the solvent in these tests. Each of the tests physically simulated a labscale CSI process until the end of its productivity life. The use of propane as the solvent particularly advantages the research studies, including this study, in need of a strong argument that its findings are unique for CSI. It has been recently found that propane yields the unique characteristics of the foamy oil when accounting for a fraction of the solution gas (Zhou et al., 2016). The simulation of the entire productivity life further justifies that the experimental result is unique for that specific recovery process and thus the history-matching result. The experimental design of the nine CSI tests is illustrated as follows. More detailed information can be found elsewhere (Du et al., 2013, 2015, 2016). The nine CSI tests are differentiated in two main design considerations: mimic wormhole location and pressure depletion rate, as tabulated in Table 1. The pressure depletion rates are classified from the lowest to the highest in comparison between the numerators in the given fraction forms without being reduced by the denominators. The CSI tests were performed individually in a cylindrical sandpack model in a horizontal layout with a mimic wormhole located at center, top, or bottom, also positioned horizontally. Fig. 1 displays the dimensions of the sandpack models as well as the mimic wormholes set at different locations. The cylindrical sandpack in a horizontal alignment was fabricated by dry-packing potters glass beads with an average pore size of 90– 150 µm. A spring wrapped by filter gauzes was assembled together. The inner cavity of the spring was devoid of solids during both pre- and post-sandpacking operations. The resulting open channel was defined as the mimic wormhole. The length*diameter of the sandpack and the mimic wormhole were 30.48*15.24 cm and 10.16*0.32 cm, respectively. The mimic wormhole therefore covered one third of the sandpack in length and approximately 2% in diameter. The length of the mimic wormhole allowed simulating a large enough area under a minimal influence of the open channel. Tremblay (2005) estimated the diameter of an open channel to range from 5 to 24 cm in 6 m thick formation. As a result, the diameter of the mimic wormhole was within the range in ratio estimated in a field scale (0.8–4.0%). Tremblay (2005) described a single wormhole as a combination of a

Mimic Wormhole Location

Pressure Depletion Rate

Pressure Depletion Rate Classification

1 2 3 4 5 6 7 8 9

Center Center Center Center Center Center Center Bottom Top

1 kPa/min 3 kPa/min 5 kPa/min 12.5 kPa/min 50 kPa/4 min 100 kPa/4 min 500 kPa/5 min 500 kPa/5 min 500 kPa/5 min

Lowest Very Low Low Middle High Very High Highest Highest Highest

(b)

15.24 cm

(c)

15.24 cm 1.7 cm

0.32 cm Fig. 1. Diagram of sandpack models with a mimic wormhole at (a) center; (b) top; and (c) bottom.

sand-free open channel and sand-filled channels surrounding the open channel. The wormhole was estimated to have a roughly 50% porosity and a diameter up to 1.5 m. The sand-filled channels, however, were excluded in the experiments of this study due to the difficulties in reproducing the sand production. To include the sand-filled channels, the experiments need to simulate the sand production in a manner that can be reproduced. Otherwise, the experiments cannot be performed under the identical physical conditions, blurring the effect of the parameter to be investigated, such as the pressure depletion rate. The sandpack model was first completely saturated with water. The dead heavy oil was then gently introduced into the sandpack model until the connate water saturation was achieved. The rock properties and connate water saturation were obtained during this period. The properties of the dead heavy oil at different temperatures are presented in Table 2. The rock properties and connate water saturations are tabulated in Table 3. The high porosity and permeability in conjunction with the mimic wormhole were intended to imitate the post-CHOPS reservoirs typified as the unconsolidated formations with a wormhole network. A connection port was coupled with the outer tip of the mimic wormhole. A pressure transducer was installed at the port to transmit the inlet or outlet pressure. Another one was located at the center of the opposite surface from the port for the model pressure. The transducers were wired to a computerized system. A programmable back pressure regulator (BPR) was set at the flow line downstream of the port. The port linked to the mimic wormhole is termed as the inlet or outlet port, hereafter. The pressure at the adjoining upstream of the BPR is referred to as the drawdown pressure. Each CSI test was performed in the sandpack model filled with the dead heavy oil and connate water. From the start to the end of the test, the temperature was reasonably unchanging at 22 °C (ambient

Table 1 Distinguishing experimental set-up and type of data generated. Test #

1.7 cm

Table 2 Dead oil properties at 101.325 kPaa.

3

Temperature (°C)

Density (kg/m3)

Viscosity (cp)

15 25 75

967.9 961.8 929.5

4330 1830 72.3

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knowledge, there has been no attempt to analytically solve the twophase relative permeability curves in CSI process. The numerical simulations of CSI process unavoidably necessitate the incorporation of a foamy oil flow model. Among the existing models, the modified-fractional flow model was selected for being more suitable than the others in evaluating relative permeability curves. The existing models are built upon the empirical adjustments to the conventional theories in the absence of a reliable theoretical solution. These models are summarized into two broad categories based on the time dependency of the resulting phase behavior, which are equilibrium and kinetic (Maini, 2001). The equilibrium models assume the complete and instantaneous equilibrium between phases. The nonequilibrium behavior of the foamy oil flow is incorporated through the adjustments to the fluid or rock-fluid properties. Under this category, the pseudobubblepoint and modified-fractional flow models have been widely accepted for reservoir simulation studies. The modified properties in these models are, in the order listed above: thermodynamic bubblepoint pressure of oil and relative permeability to gas, respectively. The oil bubblepoint pressure is decreased to a hypothetical pseudobubblepoint to account for the supersaturation of oil. The gas relative permeabilities are reduced to reflect the low mobility of the discontinuous gas phase. The kinetic models incorporate the chemical equations to account for the time-dependent changes in gas dispersion. The oil phase is redefined with a plural number of non-volatile components including the dispersed gas bubbles. A typical example is the dead oil, dissolved gas, and dispersed gas bubbles. The stoichiometry and reaction-rate constants are adjusted to control the transformation frequencies between these components. Among the existing foamy oil flow models, the modified-fractional flow model favors over the others in regard to the evaluation of the gasliquid relative permeability curves in CSI process. The numerical simulations of CSI process inevitably require tuning of two-phase relative permeability curves. These curves cannot be obtained from laboratory experiments since the analytical flow equations are currently deficient in describing the solvent mass transfer in CSI process. Therefore, all of the existing foamy oil flow models necessarily involve the fractional flow parameters as variables to be tuned. In the modifiedfractional flow model, however, these parameters exist as the only variables, whereas in the rest models, the additional variables (e.g. thermodynamic bubblepoint pressure of oil) are collectively involved in the tuning process. The additional variables result in a higher dimension of the numerical matrix. The higher dimensional numerical matrix substantially hinders the uniqueness of the tuned parameters including the relative permeability curves. Consequently, the modified-fractional flow model yields more reliable gas-liquid relative permeability curves than the other models by containing the fractional flow parameters as the only variables to be tuned. The applicability of the modifiedfractional flow model has been attested by the early study of Kumar and Pooladi-Darvish (2002). In the modified-fractional flow model, two sets of two-phase relative permeability curves were incorporated separately for the injection and production stages. Ostos and Maini (2004) suggested that, in heavy oil systems, the relative permeability curves obtained from external gas drive and solution gas drive can be different. Similarly, Maini (1998) claimed that these fractional flow curves should be inferred under the driving conditions that fit the target recovery process. Although these studies did not intend to raise the discussion of CSI process, an implication is that the differing sets of two-phase relative permeability curves - one set for injection stages and another for production stages - are necessary to properly simulate the CSI process. In the previous studies, Ivory et al. (2009) and Chang and Ivory (2013) incorporated two sets of relative permeability curves separately for the injection and production stages for the numerical simulations of CSI process. Two sets of gas-liquid relative permeability curves were incorpo-

Table 3 Porosity, permeability, and connate water saturation of sandpack models. Test #

Porosity (%)

Permeability (D)

Connate Water Saturation (%)

1 2 3 4 5 6 7 8 9

34.15 35.05 33.42 34.15 33.51 33.51 33.24 33.33 33.09

5.38 5.68 5.29 5.59 5.27 5.29 5.27 5.27 5.62

2.38 8.51 4.05 3.17 7.61 4.1 5.98 5.69 6.25

temperature). The electronic instruments automatically gauged and recorded the pressure specifics into a local computer as frequent as 15 s. In an injection stage, pure propane was introduced into the physical model through the inlet port. The inlet pressure was maintained at 800 kPaa. The porous medium was pressurized to the topmost level (i.e. 800 kPaa). The inlet pressure was intended to be slightly below the vapor pressure of propane. The injection lasted for 45 min. The following soaking stage was continued for 10 min. In a production stage, the physical model was depleted in a stepwise manner. A depletion step consisted of the immediate decrease of the drawdown pressure at the outset as well as the subsequent span over which the pressure was fixed. The given fraction expression of the pressure depletion rate quantifies these components. For example, the numerator specifies the degree of the pressure drop, and the denominator the step duration. These values were preprogrammed into the BPR. The drawdown pressure was declined in agreement with the pressure depletion rate. In the event that the oil flux continued, the pressure was reduced as far as the ambient level. The further recovery proceeded at the same conditions. The cycle was ended at any depletion step when the oil ceased to flow. In contrast to the injection and soaking phases, the period of the production stage was unconstrained. It was rather determined by the productivity of the cycle. The highest (i.e. 500 kPa/5 min) depletion process was exceptionally operated. The drawdown was maintained at the ambient pressure. The BPR was not applied. This strategy was necessary to prompt the release of a large portion of the initial pressure (i.e. ~800 kPaa) at the outlet port. The rapid and large pressure drop resulted in the short duration of the oil flow. To ensure the enough exhaustion of the porous medium, the production period was fixed for 5 min. The oil production was gauged in mass and converted to volume. The exaggerated portion due to the foamy bubbles was excluded by this means. The gas production was measured in volume and read off from the flow meter. The production data were logged once at the end of the cycle. The ensuing cycle was carried out in the identical manner as above. The test was terminated if the oil recovery was trivial for two consecutive cycles. Due to the deficiency in the measuring devices, the gas production was not gathered in Test 7 and 8 as well as the model pressure in Test 7, 8, and 9.

2.2. Numerical simulations In this study, numerical simulations were utilized to infer the gasliquid relative permeability curves. A selection is needed when inferring two-phase relative permeability curves in heavy oil systems between two methodological tools: numerical simulations and analytical twophase flow equations derived from Darcy’s Law. In case CSI is the objective recovery process, the application of numerical simulations is more appropriate and currently a sole approach. The main reason is that the numerical modelssimulations are comprehensive in solvent mass transfer mechanisms, which are intrinsic in CSI process, whereas the analytical flow equations are not. Until now, to the author’s 4

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Producer & Injector

rated as the only uncertain parameters dependent on the pressure depletion rate. Capillary pressure between oil and gas phases, dispersion coefficient of propane in oil phase, and formation compressibility were also included as the uncertain parameters independent of the depletion rate. The nine CSI tests were history-matched with different purposes in regard to the dependency of these parameters on the depletion rate. Test 1–7 were utilized to analyze the trends of the gas-liquid relative permeability curves changing with the pressure depletion rate. These tests in common were carried out under the center mimic wormhole at the different pressure depletion rates (Table 1). Therefore, all experimental conditions apart from the pressure depletion rate were deemed identical. Any differences in the experimental results were considered to solely indicate the effect of the pressure depletion rate. As a result, the history-matching of these tests incorporated the gas-liquid relative permeability curves as the only variables tuned individually. In contrast, Test 7–9 were employed to determine and validate the uncertain parameters independent of the pressure depletion rate and thus kept constant for the history-matching of all CSI tests. These tests were conducted under the different mimic wormhole locations at the identical pressure depletion rate (Table 1). Therefore, all experimental conditions except for the mimic wormhole location were regarded as the same. Any differences in the experimental results were considered to be solely due to the changes in the mimic wormhole location. As a result, the history-matching of these tests incorporated the same variable matrix although performed on the three totally different experimental results. Consequently, Test 7, 8, and 9 were history-matched preliminarily to determine and validate the uncertain parameters independent of the pressure depletion rate, as well as the gas-liquid relative permeability curves for these tests. The rest CSI tests (Test 1–6) were historymatched subsequently by applying the validated uncertain parameters and tuning the gas-liquid relative permeability curves. In this study, the commercial numerical simulator, CMG STARS, was employed. The mimic wormhole was defined as two wells, injector and producer, at the same location. The experimental data of the inlet and outlet pressure at the port were used as the well constraint (i.e. bottomhole pressure) for both injection and production stages. The experimental results obtained (i.e. cumulative oil and gas productions and model pressure) were history-matched. The grid modeling was performed on the basis of the orthogonal corner-point grid system to properly describe the cylindrical sandpack and the mimic wormhole both in horizontal positions as well as the resulting fluids flow directions. In addition to the injector and producer, another well named observer was defined to match the model pressure. Fig. 2 displays the grid system with the mimic wormhole at center as an example. The number of the grids was 12*10*10 (2.54*1.524*1.524 cm) in i*j*k directions. The grid blocks outside the model boundaries were given the null properties. The grid blocks accommodating the injector (or producer) were refined to conform to the location of the mimic wormhole. The dimension of the refined grid blocks containing the well was 2.54*0.19*0.19 cm in the Cartesian directions. The diameter of the well was 0.01 cm. With such grid size and well diameter, the location of the mimic wormhole was respected as much as possible, while a sufficiently large well index was incorporated. The grid block contacting the observer was refined in the same way. The observer was shut-in at all times to serve its only purpose to match the model pressure. The total number of the grid blocks in effect was 1071 and 1068 with and without the model pressure, respectively. The PVT modeling was conducted by using CMG WinProp. The dead heavy oil viscosity at different temperatures (Table 3) and the dead heavy oil-propane mixture viscosity at varying pressure and temperature (Table 4) were matched. The PVT properties were obtained from the bulk-volume laboratory experiments at equilibrium conditions. These experiments were implemented and provided by

Producer & Injector

Observer

Observer Producer & Injector

k i j Fig. 2. Grid system with the well (mimic wormhole) located at center. Table 4 PVT data of dead heavy oil-propane mixture (provided by SRC). Temperature (°C)

Pressure (kPaa)

Propane Mole Fraction

Viscosity (cp)

15.4 15.4 15.4 15.4 75.0 75.0 75.0 75.0

300 400 500 625 500 1000 1500 2000

0.38 0.50 0.59 0.761 0.212 0.392 0.545 0.681

435 129 49.4 7.24 40.3 18.7 8.66 3.75

5,000 4,500 4,000

Viscosity (cp)

3,500 3,000 2,500 2,000 1,500 1,000 500 0

0

10

20

30

40

50

60

70

80

Temperature ( oC) Lab Matched

Fig. 3. Dead oil viscosity matching at 1 atm.

Saskatchewan Research Council (SRC). The matching results are shown in Fig. 3 and 4. The capillary pressure curves were computed with Li and Horne’s empirical model (2004) with the use of normalized liquid saturation, S*l , (Eq. (2) and (3)) (Li and Horne, 2004). −1 λ

Pcgo = Pcgo, max (1 − Sl*)

Sl* =

(2)

Sl − Soirg − Swcon 1 − So0irg − Swcon − Sgcon

(3)

where Pcgo: capillary pressure between oil and gas phases; Pcgo, max: Pcgo at connate liquid saturation (sum of gas-oil irreducible oil saturation and connate water saturation); λ: capillary pressure curve constant; S*l : normalized liquid saturation; Sl: liquid saturation; Soirg: gas-oil irreducible oil saturation; Swcon: connate water saturation; and 5

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S.Y. Hong et al. 1,000

40

900

35

350

30

300 25 250 20 200 15

150

Viscosity (cp) @ 75 oC

Viscosity (cp) @ 15.4 oC

400

45

10

100 50

5

0

0 2,500

4.0E+06 3.5E+06

800 3.0E+06 700 2.5E+06

600 500

2.0E+06

400

1.5E+06

300 1.0E+06 200 5.0E+05

100 0

0

500

1,000

1,500

2,000

0

10,000

15,000

20,000

25,000

0.0E+00 30,000

Time (min)

Pressure (kPaa) Lab @ 15.4 deg C Lab @ 75 deg C

5,000

Cumulative Gas Production (scm3)

450

Cumulative Oil Production (scm3)

500

Matched @ 15.4 deg C Matched @ 75 deg C

Fig. 4. Dead oil & propane mixture viscosity matching at 15.4 °C and 75 °C.

Experiment Oil

History Match Oil

Experiment Gas

History Match Gas

900 800

Sgcon: connate gas saturation. For all tests, the Pcgo, max was 1 kPa. The low range of capillary pressure (0 ~ 1 kPa) was adopted from Ivory et al. (2009). The capillary pressure constant (λ) was −0.0979. The connate gas saturation and gas-oil irreducible oil saturation were 0 and 0.01, respectively. The connate water saturation varied from test to test (Table 2). The variances in connate water saturation resulted in slightly different curves between the tests. The capillary pressure curve of Test 1 as an example is shown in Fig. 5. The dispersion coefficients of propane in oil phase were 2*10−6 cm2/min in all i, j, and k directions. The formation compressibility was 4*10−5 1/kPa with the porosity reference pressure at 101 kPa. The gas-liquid relative permeability curves were generated with the use of Corey’s correlations (Eq. (4) and (5)). These correlations were successful in history-matching Test 1, 2, 7, 8 and 9. However, for the rest tests (Test 3, 4, 5 and 6), the relative permeability curves in part had to be adjusted manually. The sole application of the correlations could not yield successful history-matching results.

⎛ ⎞ Ng Sg − Sgcrit ⎟⎟ Krg = Krgcl ⎜⎜ ⎝ 1 − Sgcrit − Soirg − Swcon ⎠

(4)

⎛ ⎞ Sl − Sorg − Swcon ⎟⎟ Krog = Krogcg⎜⎜ ⎝ 1 − Sgcon − Sorg − Swcon ⎠

(5)

Model Pressure (kPaa)

700 600 500 400 300 200 100 0 0

1,000

2,000

3,000

4,000

Time (min) Experiment

History Match

Fig. 6. History matching results (a) production profiles (b) model pressure of Test 1 (1 kPa/min, center wormhole).

ability; Krogcg: Krog at connate gas saturation; Sorg: gas-oil residual oil saturation; and Nog: gas-oil oil relative permeability curve exponent For the injection stages, the end points, Krgcl and Krogcg, were fixed at 1. The exponents, Ng and Nog, were adjusted prior to the critical gas saturation and residual oil saturation. The critical gas saturation and residual oil saturation were increased only if necessary. For the production stages, the exponents (Ng and Nog) and end-points (Krgcl and Krogcg) were adjusted first. The critical gas saturation and residual oil saturation were increased only when imperative.

Nog

where Krg: gas relative permeability; Krgcl: Krg at connate liquid saturation; Sg: gas saturation; Sgcrit: critical gas saturation; Ng: gas relative permeability curve exponent; Krog: gas-oil oil relative perme-

3. Results 3.1. History matching results The experimental and history-matching results of the CSI tests are shown in Fig. 6–14 in the order of the test number. The model pressure is presented for the beginning five cycles only because a massive number of the data points make the plots undistinguishable. The figures demonstrate that all CSI tests were successfully historymatched with the use of the modified fractional flow models. The deviations in the gas production profiles of Test 1 and 6 (Figs. 6a and 11a) are due to the faulty experimental measurements in the late cycles after approximately 15,000 and 4000 min, respectively. The history-matching results show that the model pressure did not fall off to the level of the experimental data in the early cycles of Test 2 and 3 (Figs. 7 b and 8 b). Such inaccurate matching was due to the high critical gas saturations as well as the spatial and temporal conditions

Fig. 5. Capillary pressure curve between gas and oil phases (Test 1).

6

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S.Y. Hong et al.

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History Match Gas

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500

1,000

1,500

2,000

Time (min) Experiment

History Match

(b) Fig. 7. History matching results (a) production profiles (b) model pressure of Test 2 (3 kPa/min, center wormhole).

Fig. 8. History matching results (a) production profiles (b) model pressure of Test 3 (5 kPa/min, center wormhole).

under which the transient flow dominated. The high critical gas saturations indicate 7% in Test 2 and 10% in Test 3, as will be presented later. The spatial and temporal conditions represent the farouter region (i.e. where the model pressure was located) and the early cycles, respectively. In numerical simulations, a high critical gas saturation over-describes the foamy oil effect at the far-outer region where the pressure propagates at a slower depletion rate during transient flow periods. The transient flow dominates in the early cycles with the aid of the high oil saturation and viscosity. The over-described foamy oil effect sustains the local pressure and thereby caused the model pressure to insufficiently decline. Nonetheless, the resulting deviations to the experimental data were within a tolerable degree due to the minimal contribution of the far-outer region to the oil and gas productions in the early cycles. The history-matching results of Test 7, 8, and 9 (Fig. 12–14) are fairly reasonable in consideration that the identical set of uncertain parameters were applied, including the gas-liquid relative permeability curves. In fact, these tests were individually evaluated, in which a very good agreement was yielded by slight changes in the gas-liquid curves in the injection stages. The uncertain parameters independent of the pressure depletion rate are therefore validated as well as the gas-liquid relative permeability curves of Test 7.

relative permeability in injection stages is denoted as Krog_inj, the gas relative permeability in injection stages as Krg_inj, the oil relative permeability in production stages as Krog_prd, and the gas relative permeability in production stages as Krg_prd. 4. Discussions 4.1. Gas-liquid relative permeability curves for production stages The tuned fractional flow models show that the gas relative permeability in the production stages increases very slowly and eventually results in an abnormally low end-point as is the typical shape in heavy oil solution gas drive. Such shape is best described with the critical gas saturation, lowness of the curve, and end-point. In this study, a hypothetical property, named the low mobility gas saturation, is defined as the gas saturation below which the gas relative permeability is lower than 0.01. With this definition, the low mobility gas saturation quantifies the lowness of the gas relative permeability curves. Table 5 summarizes the properties of the tuned gas relative permeability curves in the production stages. 4.1.1. Effect of pressure depletion rate As Table 5 illustrates, the critical gas saturation increases with the pressure depletion rate from 3% at 1 kPa/min to 10% at 5 kPa/min. It then drops abruptly to 3% at the next high depletion rate, 12.5 kPa/ min, and remains constant up to 500 kPa/5 min. The increasing trend at the low pressure depletion rates agrees with the findings of Ostos

3.2. Tuned gas-liquid relative permeability curves The tuned gas-liquid relative permeability curves are presented in Fig. 15–21 in the order of the test number. For simplicity, the oil 7

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7.0E+06

1,200

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7.0E+06

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S.Y. Hong et al.

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Time (min) History Match Oil

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(a)

Experiment Oil

History Match Oil

Experiment Gas

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800 800

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Model Pressure (kPaa)

Model Pressure (kPaa)

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(b)

Experiment

Fig. 9. History matching results (a) production profiles (b) model pressure of Test 4 (12.5 kPa/min, center wormhole).

History Match

Fig. 10. History matching results (a) production profiles (b) model pressure of Test 5 (50 kPa/min, center wormhole).

and Maini (2004), whereas the trend beyond that is in conflict. Ostos and Maini (2004) presented the changing trend of the gas-liquid relative permeability curves at different pressure depletion rates in a lab-scale heavy oil solution gas drive. In their study, the critical gas saturation increased with the pressure depletion rate up to a maximum attainable value (9%) and remained at that level even if the depletion rate further increased. Therefore, the critical gas saturation, which drops to and plateaus at the lowest value in this study, oppositely remained constant at the highest level. In order to justify the unlike behavior of the critical gas saturation, the low critical gas saturations of Test 4–7 need first to be validated. The additional simulation runs were therefore made on these tests to show the sensitivity of the recovery process to the critical gas saturation. In these runs, the critical gas saturations were increased to 10% as is the maximum value obtained from Test 3 to comply with the findings of Ostos and Maini (2004). Fig. 22–25 present the results of the additional runs in comparison to the history-matching results. The figures demonstrate that the additional runs yielded noticeable deviations in the cumulative oil and gas productions as well as the cumulative producing GOR. Such deviations show that the recovery process is highly sensitive to the critical gas saturation. The additional run of Test 4 resulted in the relatively small deviations (Fig. 22). In Test 4, the increase of the critical gas saturation only required reducing the gas relative permeability by maximum 4*10−4 due to the very slowly increasing gas relative permeability. The recovery factor, however, improved unexpectedly high about 2% at the end cycle and even greater in the earlier cycles. The high critical gas saturation is therefore

disproved, which reversely validates the low critical gas saturations that successfully history-matched the CSI tests. Provided that the low critical gas saturations are imperative, the dominating differences between this study and the study of Ostos and Maini (2004) explain the phenomena responsible for the different behavior of the critical gas saturation. The differences appear in the recovery process, component of solution gas, and range of the pressure depletion rate, as tabulated in Table 6. As discussed earlier, in CSI, the free gas that originates at the solvent chamber is independent of the pseudobubblepoint pressure of oil, while in heavy oil solution gas drive, it is completely dependent on the pseudo-pressure property. In CSI, therefore, the free gas exists even when the dispersed gas bubbles are immobile as opposed to in heavy oil solution gas drive. A rapid pressure drop puts the free gas under turbulence and at the same time promotes the nucleation of the gas bubbles. When the turbulence is strong enough, the free gas happens to come in contact with the gas bubbles. The more the gas bubbles nucleate, the higher the probability is for the free gas to contact the gas bubbles. At a sufficiently high pressure depletion rate, the free gas eventually adjoins and by cohesion draws the gas bubbles into the continuous gas phase. The gas bubbles that are immobile gain mobility during such process. The critical gas saturation drops and remains low even if the depletion rate further increases. Propane is highly soluble than methane, yielding a greater amount of the dissolved gas in oil phase. In propane-based systems, therefore, the dispersed gas bubbles are more heavily populated in the porous

8

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1,200

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0

500

1,000

1,500

Time (min)

Experiment

Experiment Oil

History Match Oil

Experiment Gas

History Match Gas

2,000

2,500

History Match

Fig. 13. History matching results of Test 8 (500 kPa/5 min, bottom wormhole). 2.5E+06

500

Cumulative Oil Production (scm3)

700 600 500 400 300 200

450 2.0E+06

400 350

1.5E+06

300 250

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200 150

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100

Cumulative Gas Production (scm3)

800

Model Pressure (kPaa)

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0 0

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150

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400

Time (min) Experiment

History Match

Experiment Oil

History Match Oil

Experiment Gas

History Match Gas

Fig. 14. History matching results of Test 9 (500 kPa/5 min, top wormhole).

Fig. 11. History matching results (a) production profiles (b) model pressure of Test 6 (100 kPa/min, center wormhole). 900

Cumulative Oil Production

(scm3)

800 700 600 500 400 300 200 100 0 0

500

1,000

1,500

2,000

2,500

Fig. 15. Tuned gas-liquid relative permeability curves of Test 1 (1 kPa/min).

3,000

Time (min) Experiment

History Match

properties (i.e. well geometry, dimensions of porous medium, rock permeability, etc). The low mobility gas saturation also exhibits the effect of the pressure depletion rate on the gas relative permeability curves. It reflects how low the gas relative permeability evolves with increasing gas saturation. Fig. 26 displays the low mobility gas saturation changing with the pressure depletion rate as well as the critical gas saturation. The figure shows that the low mobility gas saturation in general increases with the pressure depletion rate when the depletion rate ranges from 1 to 12.5 kPa/min. It then decreases and nearly plateaus at 100 kPa/min as the depletion rate further increases. The disagreeing

Fig. 12. History matching results of Test 7 (500 kPa/5 min, center wormhole).

medium. As a result, the free gas gains a higher probability to adjoin the gas bubbles and thus to result in the low critical gas saturation. The pressure depletion rates in this study are one or more order of magnitude higher than those in the study of Ostos and Maini (2004). The considerably higher depletion rates may have caused the unlike behavior of the critical gas saturation. However, such argument requires the analysis that is complex and thus impractical. In this analysis, the pressure propagation should be compared between the different systems as a function of complexly related well and/or rock 9

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Fig. 16. Tuned gas-liquid relative permeability curves of Test 2 (3 kPa/min).

Fig. 19. Tuned gas-liquid relative permeability curves of Test 5 (50 kPa/4 min).

Fig. 17. Tuned gas-liquid relative permeability curves of Test 3 (5 kPa/min).

Fig. 20. Tuned gas-liquid relative permeability curves of Test 6 (100 kPa/4 min).

Fig. 18. Tuned gas-liquid relative permeability curves of Test 4 (12.5 kPa/min).

Fig. 21. Tuned gas-liquid relative permeability curves of Test 7 (500 kPa/5 min).

trend at 5 kPa/min should be neglected because the corresponding gasliquid relative permeability curves were misled into the distinctive shapes (Fig. 17) due to the effect of the solvent chamber. The solvent chamber significantly affects the gas-liquid relative permeability curves involving a high critical gas saturation as will be discussed later. The critical gas and low mobility gas saturations together characterize the gas relative permeability curves differently at the low, middle, and high depletion rates. At the low pressure depletion rates (i.e. 1–5 kPa/min), both critical and low mobility gas saturations increase with the depletion rate. This phenomenon also appears in the study of Ostos and Maini (2004) and is a recognized effect of the depletion rate on the foamy oil flow under heavy oil solution gas drive. From the perspective of a fluid mobility, it is natural to have a proportional relationship between the critical and

low mobility gas saturations. A higher critical gas saturation represents an extended immobility of the gas phase and thus causes the gas relative permeability to evolve lower. At the middle pressure depletion rate (i.e. 12.5 kPa/min), the critical gas saturation drops to the lowest value (3%) while the low mobility gas saturation increases to the highest level. This phenomenon is opposed to the aforementioned proportional relationship between the critical and low mobility gas saturations. An implication is that the depletion rate is sufficiently high to draw immobile gas bubbles but not as high to improve gas phase mobility. As previously discussed, the critical gas saturation drops because the free gas adjoins and draws the immobile gas bubbles into the continuous gas phase. The low mobility gas saturation, however, increases to the highest level as the gas bubbles that have become mobile initially gain a substantially low mobility. 10

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Pressure Depletion Rate Classification

Pressure Depletion Rate

1 2 3 4

1 kPa/min 3 kPa/min 5 kPa/min 12.5 kPa/ min 50 kPa/ 4 min 100 kPa/ 4 min 500 kPa/ 5 min

5 6 7

Critical Gas Saturation (%)

Low Mobility Gas Saturation (%)

Cumulative Oil Production (scm3)

Test #

End Point

Lowest Very Low Low Middle

3 7 10 3

22 51 32 61

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21

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Cumulative Gas Production (scm3)

Table 5 Summary of tuned gas relative permeability curves in production stages.

Additional Run Oil Additional Run Gas

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Cumulative Producing GOR (scm3/scm3)

6,000

Fig. 23. Additional run with increased Sgcrit (a) cumulative oil and gas productions (b) cumulative producing GOR (Test 5).

5,000

continues only up to a certain level due to the foamy oil flow that does not diminish and still maintains its effect. The end point of the gas relative permeability curve varies more or less proportional to the low mobility gas saturation. It sets at the level following the trend of how high or low the relative permeability evolves. The residual oil saturation ranges from 10% to 50%. The end point of the oil relative permeability curve lies in between 0.25 and 1. The high residual oil saturations were also found in the study of Ostos and Maini (2004). The low end points as well were observed in the study of Ivory et al. (2009). Similar to the gas curve, the end point shows a somewhat proportional relationship to the low mobility gas saturation. It appears low when the gas relative permeability evolves low and relatively high in the opposite case. In summary, the effects of the pressure depletion rate on the gas-oil flow in CSI are as below.

4,000

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Fig. 22. Additional run with increased Sgcrit (a) cumulative oil and gas productions (b) cumulative producing GOR (Test 4).



At the high pressure depletion rates (i.e. 50 kPa/4 min–500 kPa/ 5 min), the critical gas saturation remains constant at the lowest value, while the low mobility gas saturation decreases with the depletion rate and eventually plateaus. This phenomenon suggests that, as the critical gas saturation drops, the gas phase mobility increases with the pressure depletion rate but only up to a certain level. A possible reason is that the dispersed gas bubbles, being drawn by free gas, gain mobility coupled with the velocity of the free gas. In other words, under more rapid pressure drop, the gas bubbles are drawn by faster free gas flow and thereby gain higher mobility. The mobility increase, however,



11

As the pressure depletion rate increases in a low range (e.g. 1 ~ 5 kPa/min), the critical gas saturation increases to a maximum attainable value, which causes the gas relative permeability to evolve lower. This phenomenon is a recognized effect of the pressure depletion rate on the foamy oil flow under heavy oil solution gas drive. As the pressure depletion rate increases further (e.g. 12.5 kPa/min ~ 500 kPa/5 min), the critical gas saturation drops to and remains constant at the lowest attainable value. The gas relative permeability initially appears substantially low but eventually increases. The

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5.0E+06 4.0E+06

600

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History Match Oil History Match Gas

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Additional Run

Additional Run

(b)

Fig. 25. Additional run with increased Sgcrit (a) cumulative oil and gas productions (b) cumulative producing GOR (Test 7).

Fig. 24. Additional run with increased Sgcrit (a) cumulative oil and gas productions (b) cumulative producing GOR (Test 6).



1,500

Time (min)

Time (min) History Match

1,000

8,000

Table 6 Dominating differences between this study and Ostos and Maini (2004).

critical gas saturation drops as the free gas adjoins and draws immobile gas bubbles into the continuous gas phase. The gas relative permeability eventually increases possibly for the reason that the gas bubbles drawn by faster free gas flow gain higher mobility. The end points of the gas-liquid relative permeability curves vary more or less proportional to the low mobility gas saturation. They appear low when the gas relative permeability evolves low and relatively high in the opposite case.

Differences

This study

Ostos and Maini (2004)

Recovery Process

CSI

Solution Gas Pressure Depletion Rate

Propane 1 kPa/min–500 kPa/ 5 min

Heavy Oil Solution Gas Drive Methane 0.2827–2.2545 kPa/min

70

25.0

Critical Gas Saturation (%)

60 20.0 50 15.0

40 30

10.0

20 5.0 10 0

0.0 1 kPa /min

3 kPa /min

5 kPa /min

12.5 kPa /min

50 kPa /4 min

100 kPa /4 min

500 kPa /5 min

Pressure Depletion Rate Critical Gas Saturation

Low Mobility Gas Saturation

Fig. 26. Critical gas saturation and low mobility gas saturation.

12

Low Mobility Gas Saturation (%)

4.1.2. Effect of solvent chamber The solvent chamber has significant effects on the gas-liquid relative permeability curves involving a high critical gas saturation. The relative permeability curves happen to misrepresent the true characteristics of the gas-oil flow. The gas-oil flow occurs under the simultaneous effects of the solvent chamber discharging the free gas and the foamy oil developing the high critical gas saturation. In numerical simulations, the discharge of the free gas becomes insufficient as the high critical gas saturation holds an unnecessary amount of gas in the porous medium. As a result, a conflict arises in describing the simultaneous flow of free gas and foamy oil. The relative permeability curves of Test 3 were misled into the shapes that counterbalance the conflict rather than truly characterizing the gas-oil flow (Fig. 17). Test 3 yielded the highest critical gas saturation (10%) among the CSI tests in this study, as previously discussed. Fig. 27 presents the tuned gas-liquid relative permeability curves in the production stages of Test 3. These curves are divided into the

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Saturation Range 1

0.9

Saturation Range 2

Relative Permeability

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0

0.2

0.4

0.6

0.8

1

Liquid Saturation (S l) Production/Oil (Krog_prd)

Production/Gas (Krg_prd)

Fig. 27. Tuned gas-liquid relative permeability curves in the production stages of Test 3.

saturation range 1 and 2 to distinguish the differently evolving shapes. The history-matching of Test 3 (Fig. 8) was only reasonable when the gas-liquid relative permeability curves in the production stages involved the high critical gas saturation as well as the shapes as shown in the saturation range 1 and 2. In the saturation rage 1, the gas fractional flow was increased in the extreme. The gas relative permeability was increased steeply along the convex curve to the end point 1, while the oil relative permeability was reduced nearly to 0. In the saturation range 2, on the other hand, the oil fractional flow was increased in the extreme. The gas relative permeability was reduced close to 0, while the oil relative permeability was increased steeply along the convex curve to the end point 1. The high critical gas saturation was essential to match the oil recovery in the early cycles, which was unexpectedly large relative to the gas production. The suppressed gas phase mobility, however, could not match the rising gas production after the early cycles. In the saturation range 1, therefore, the gas fractional flow was increased to match the rising gas production but at the expense of the oil productivity. In the saturation range 2, the oil fractional flow was increased to regain the oil productivity. In order to verify that such distinctive shapes were inevitable, an additional simulation run was made in an utmost attempt to simulate the simultaneous flow of free gas and foamy oil properly. In this run, the convex curves were replaced by the counterparts of Test 4 (Fig. 18) involving the lowest critical gas saturation (3%) and the highest low mobility gas saturation. The critical gas saturation was therefore reduced to 3% and the gas relative permeability to the lowest level. The lowest critical gas saturation eased discharging the free gas to a maximum degree. The critical gas saturation reduction, however, mitigated the foamy oil effect which the gas relative permeability at the lowest level compensated. Fig. 28 presents the result of the additional run in comparison to the history-matching result. As the figure demonstrates, the additional run yielded considerable deviations from the history-matching result despite the utmost attempt to simulate the simultaneous flow of free gas and foamy oil properly. The decrease in oil and gas productions and increase in cumulative producing GOR are opposed to the results of the increased critical gas saturation shown in Fig. 22–25. Such deviations confirm that the recovery process is highly sensitive to the critical gas saturation. The distinctive shapes were therefore inevitable, which further justifies the effect of the solvent chamber on the gas-liquid relative permeability curves involving a high critical gas saturation. In summary, the effects of the solvent chamber on the gas-liquid relative permeability curves are as below.



Fig. 28. Additional run of Test 3 by replacing the krog_prd and krg_prd curves with the ones of Test 4 (a) cumulative oil and gas productions (b) cumulative producing GOR.

solvent chamber insufficiently discharges the free gas as the high critical gas saturation holds an unnecessary amount of gas in the porous medium. As a result, a conflict arises in describing the simultaneous flow of free gas and foamy oil. The gas-liquid relative permeability curves are misled into the shapes that counterbalance the conflict rather than truly characterizing the gas-oil flow.

4.2. Gas-liquid relative permeability curves in injection stages The gas-liquid relative permeability curves in the injection stages vary with the pressure depletion rate as shown by the different shapes of the tuned curves of Test 1 to 7 (Fig. 15–21). The curves of Test 7, validated preliminarily through the history-matching of Test 7, 8 and 9, were utilized in a first attempt to simulate the rest tests (Test 1 to 6). The history-matching, however, was only reasonable when these curves were modified as presented in Fig. 15–20. The tuned curves in the injection stages of Test 5 and 6 (Fig. 19 and 20) resulted in the resembling shapes. These curves are therefore unique as the resembling shapes successfully history-matched the two totally different experimental results (Fig. 10 and 11). The underlying assumption is that the pressure depletion rates classified next to each other (i.e. high and very high) yielded a foamy oil effect. As a result, the modifications of the curves in the injection stages are justified, which further validates the curves of Test 1 to 4. The solvent injectivity is directly related to the gas-liquid relative permeability curves in the injection stages. Therefore, three main relationships have been identified in regard of the gas-oil flow in both

The solvent chamber causes the gas-liquid relative permeability curves involving a high critical gas saturation to misrepresent the true characteristics of the gas-oil flow. In numerical simulations, the 13

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curves involving a high critical gas saturation to misrepresent the true characteristics of the gas-oil flow. In numerical simulations, the solvent chamber happens to discharge the free gas insufficiently due to the conflict in describing the simultaneous flow of free gas and foamy oil. As a result, the relative permeability curves are misled into the shapes that counterbalance the conflict rather than truly characterizing the gas-oil flow. 6. The gas-liquid relative permeability curves in the injection stages are affected by the foamy oil generated in previous production stages and in turn the pressure depletion rate. The solvent injectivity interrelated to the gas and liquid relative permeabilities is also affected.

injection and production stages as below. (a) The solvent injectivity is interrelated to the gas-liquid relative permeability curves in injection stages. (b) The gas-liquid relative permeability curves in injection stages vary with pressure depletion rate. (c) The pressure depletion rate determines the nonequilibrium nature of the foamy oil generated in production stages. Consequently, the gas-liquid relative permeability curves in the injection stages are affected by the foamy oil generated in previous production stages and in turn the pressure depletion rate. The solvent injectivity interrelated to the gas and liquid relative permeabilities is also affected. These relationships are established since the foamy oil remains in the injection stages as much as the quantity unproduced during a previous production period. Ivory et al. (2009) and Chang and Ivory (2013) also suggested the need of incorporating the kinetic foamy oil flow models in the injection stages. Therefore, the numerical simulation studies of CSI have consistently required accounting for the foamy oil effect in the injection stages. To the author’s knowledge, however, there has been no study investigating the solvent or gas injectivity as a function of the foamy oil existing in the injection period.

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5. Conclusions The conclusions of this study are drawn as follows. 1. The numerical simulations of CSI process necessitate incorporating two sets of gas-liquid relative permeability curves separately for the injection and production stages. 2. The modified-fractional flow model is applicable in describing the foamy oil effect in both injection and production stages of CSI process. 3. At low pressure depletion rates (e.g. 1–5 kPa/min), the gas relative permeability curve in the production stages behaves as in heavy oil solution gas drive. As the pressure depletion rate increases: (a) The critical gas saturation increases up to a maximum attainable value (10%). (b) The gas relative permeability evolves lower and sets at a lower end point. 4. In contrast, at sufficiently high pressure depletion rates (12.5 kPa/ min–500 kPa/5 min), the gas relative permeability curve in the production stages yields the behavior that does not occur in heavy oil solution gas drive. As the depletion rate increases: (a) The critical gas saturation drops and remains constant at the lowest attainable value (3%). (b) The gas relative permeability curve initially appears substantially low but eventually increases. (c) The end point sets at the level following the trend that the gas relative permeability evolves. The unlike behavior stems from the innate design of CSI process that the solvent maintains a strong nature of gas at in-situ conditions. Such design results in the free gas that occurs and amounts independent of the pseudobubblepoint pressure of oil. At a sufficiently high pressure depletion rate, the free gas adjoins and draws immobile gas bubbles into the continuous gas phase. The critical gas saturation drops and remains constant at the low value. The gas phase mobility increases with the depletion rate possibly because the gas bubbles drawn by faster free gas flow gain higher mobility. 5. The solvent chamber causes the gas-liquid relative permeability 14