Pore-scale compositional modeling of gas-condensate flow: Effects of interfacial tension and flow velocity on relative permeability

2021 ◽  
Vol 202 ◽  
pp. 108454
Author(s):  
P.K.P. Reis ◽  
M.S. Carvalho
1999 ◽  
Vol 2 (04) ◽  
pp. 393-402 ◽  
Author(s):  
H.L. Chen ◽  
S.D. Wilson ◽  
T.G. Monger-McClure

Summary Coreflood experiments on gas condensate flow behavior were conducted for two North Sea gas condensate reservoirs. The objectives were to investigate the effects of rock and fluid characteristics on critical condensate saturation (CCS), gas and condensate relative permeabilities, hydrocarbon recovery and trapping by water injection, and incremental recovery by subsequent blowdown. Both CCS and relative permeability were sensitive to flow rate and interfacial tension. The results on gas relative permeability rate sensitivity suggest that gas productivity curtailed by condensate dropout can be somewhat restored by increasing production rate. High interfacial tension ultimately caused condensate relative permeability to decrease with increasing condensate saturation. Condensate immobile under gas injection could be recovered by water injection, but more immediate and efficient condensate recovery was observed when the condensate saturation prior to water injection exceeded the CCS. Subsequent blowdown recovered additional gas, but incremental condensate recovery was insignificant. Introduction Reservoirs bearing gas condensates are becoming more commonplace as developments are encountering greater depths, higher pressures, and higher temperatures. In the North Sea, gas condensate reservoirs comprise a significant portion of the total hydrocarbon reserves. Accuracy in engineering computations for gas condensate systems (e.g., estimating reserves, sizing surface facilities, and predicting productivity trends) depends upon a basic understanding of phase and flow behavior interrelationships. For example, gas productivity may be curtailed as condensate accumulates by pressure depletion below the dew point pressure (Pd). Conceptual modeling on gas condensate systems suggests that relative permeability (kr) curves govern the magnitude of gas productivity loss.1,2 Unfortunately, available gas and condensate relative permeability (krg and krc) results for gas condensates are primarily limited to synthetic systems. Such results show that higher CCS and less krg reduction were observed for a conventional gas/oil system compared to a gas condensate system.3,4 If condensate accumulates as a continuous film due to low interfacial tension (IFT), then high IFT gas/oil and water/oil kr data may not be applicable to gas condensates.5 Water invasion of gas condensate reservoirs may enhance hydrocarbon recovery or trap potential reserves. Laboratory results suggest water invasion of low IFT gas condensates may not be represented using high IFT water/oil and water/gas displacements.6 Subsequent blowdown may remobilize hydrocarbons trapped by water invasion. The presence of condensate may hinder gas remobilization, thus conventional gas/water blowdown experiments may not be appropriate in evaluating the feasibility of depressurization for gas condensates.7,8 Other laboratory evaluations of gas condensate flow behavior indicate measured results depend upon experimental procedures, fluid properties, and rock properties.3,9–20 Factors to consider include the history of condensate formation (i.e., imbibition or drainage), how condensate was introduced (i.e., in-situ dropout versus external injection or inflowing gas), flow rate, differential pressure, system pressure, IFT, connate water saturation, core permeability, and core orientation. Experiments performed to evaluate the consequences of water invasion suggest optimum conditions depend upon IFT, initial gas saturation, and core permeability.7,21,22 Reported blowdown experiments imply gas recovery depends upon the degree of gas expansion.7,8 The kr results obtained in this study represent gas condensate flow between the far-field and the near-wellbore region. The results are useful input for numerical simulation, especially to test rate- or IFT-sensitive relative permeability functions. Results on hydrocarbon recovery and trapping from water injection and blowdown are beneficial in evaluating improved recovery options for gas condensates. Experimental Procedures Coreflooding experiments were performed under reservoir conditions using rock and fluid samples from two distinct North Sea gas condensate reservoirs. A detailed description of the experimental methods is provided in the Appendix. Briefly, the experiments were conducted in a horizontal coreflood apparatus equipped with in-line PVT and viscosity measuring devices. The entire system experienced in-situ condensate drop out by constant volume depletion (CVD) from above Pd to either the pressure corresponding to CCS, or to the pressure of maximum condensate saturation Scmax Steady-state krg was measured by injecting equilibrated gas (before CCS). Steady-state krg and krc were measured by injecting gas condensate repressurized to above Pd (after CCS). The gas/oil fractional flow rate was defined by the pressure level in the core which was controlled by the core outlet back-pressure regulator. During krg measurements, the injection rate was varied to access rate effects. After the krg or krg and krc measurements to Scmax were completed, water injection was performed to quantify hydrocarbon trapping and recovery. Blowdown followed to evaluate additional hydrocarbon recovery. Recombined Reservoir Fluid Properties. Two North Sea gas condensate reservoir fluids were recombined using separator oil and synthetic gas. Tables 1 and 2 list compositions and PVT properties for the reconstituted fluids. The Pd was 7,070 psig at 250°F for Reservoir A, and 6,074 psig at 259°F for Reservoir B (Table 2). The maximum liquid dropout under constant composition expansion (CCE) was 31.7% for Reservoir A, and 42.5% for Reservoir B (Fig. 1). Reservoir B is a richer gas condensate and exhibits more near-critical phase behavior than Reservoir A.


2000 ◽  
Vol 3 (02) ◽  
pp. 171-178 ◽  
Author(s):  
G.A. Pope ◽  
W. Wu ◽  
G. Narayanaswamy ◽  
M. Delshad ◽  
M.M. Sharma ◽  
...  

Summary Many gas-condensate wells show a significant decrease in productivity once the pressure falls below the dew point pressure. A widely accepted cause of this decrease in productivity index is the decrease in the gas relative permeability due to a buildup of condensate in the near wellbore region. Predictions of well inflow performance require accurate models for the gas relative permeability. Since these relative permeabilities depend on fluid composition and pressure as well as on condensate and water saturations, a model is essential for both interpretation of laboratory data and for predictive field simulations as illustrated in this article. Introduction Afidick et al.1 and Barnum et al.2 have reported field data which show that under some conditions a significant loss of well productivity can occur in gas wells due to near wellbore condensate accumulation. As pointed out by Boom et al.,3 even for lean fluids with low condensate dropout, high condensate saturations may build up as many pore volumes of gas pass through the near wellbore region. As the condensate saturation increases, the gas relative permeability decreases and thus the productivity of the well decreases. The gas relative permeability is a function of the interfacial tension (IFT) between the gas and condensate among other variables. For this reason, several laboratory studies3–14 have been reported on the measurement of relative permeabilities of gas-condensate fluids as a function of interfacial tension. These studies show a significant increase in the relative permeability of the gas as the interfacial tension between the gas and condensate decreases. The relative permeabilities of the gas and condensate have often been modeled directly as an empirical function of the interfacial tension.15 However, it has been known since at least 194716 that the relative permeabilities in general actually depend on the ratio of forces on the trapped phase, which can be expressed as either a capillary number or Bond number. This has been recognized in recent years to be true for gas-condensate relative permeabilities.8,10 The key to a gas-condensate relative permeability model is the dependence of the critical condensate saturation on the capillary number or its generalization called the trapping number. A simple two-parameter capillary trapping model is presented that shows good agreement with experimental data. This model is a generalization of the approach first presented by Delshad et al.17 We then present a general scheme for computing the gas and condensate relative permeabilities as a function of the trapping number, with only data at low trapping numbers (high IFT) as input, and have found good agreement with the experimental data in the literature. This model, with typical parameters for gas condensates, was used in a compositional simulation study of a single well to better understand the productivity index (PI) behavior of the well and to evaluate the significance of condensate buildup. Model Description The fundamental problem with condensate buildup in the reservoir is that capillary forces can retain the condensate in the pores unless the forces displacing the condensate exceed the capillary forces. To the degree that the pressure forces in the displacing gas phase and the buoyancy force on the condensate exceed the capillary force on the condensate, the condensate saturation will be reduced and the gas relative permeability increased. Brownell and Katz16 and others recognized early on that the residual oil saturation should be a function of the ratio of viscous to interfacial forces and defined a capillary number to capture this ratio. Since then many variations of the definition have been published,17–20 with some of the most common ones written in terms of the velocity of the displacing fluid, which can be done by using Darcy's law to replace the pressure gradient with velocity. However, it is the force on the trapped fluid that is most fundamental and so we prefer the following definition: N c l = | k → → ⋅ ∇ → ϕ l | σ l l ′ , ( 1 ) where definitions and dimensions of each term are provided in the nomenclature. Although the distinction is not usually made, one should designate the displacing phase l ? and the displaced phase l in any such definition. In some cases, buoyancy forces can contribute significantly to the total force on the trapped phase. To quantify this effect, the Bond number was introduced and it also takes different forms in the literature.20 One such definition is as follows: N B l = k g ( ρ l ′ − ρ l ) σ l l ′ . ( 2 ) For special cases such as vertical flow, the force vectors are collinear and one can just add the scalar values of the viscous and buoyancy forces and correlate the residual oil saturation with this sum, or in some cases one force is negligible compared to the other force and just the capillary number or Bond number can be used by itself. This is the case with most laboratory studies including the recent ones by Boom et al.3,8 and by Henderson et al.10 However, in general the forces on the trapped phase are not collinear in reservoir flow and the vector sum must be used. A generalization of the capillary and Bond numbers was derived by Jin 21 and called the trapping number. The trapping number for phase l displaced by phase l? is defined as follows: N T l = | k → → ⋅ ( ∇ → ϕ l ′ + g ( ρ l ′ − ρ l ) ∇ → D ) | σ l l ′ . ( 3 ) This definition does not explicitly account for the very important effects of spreading and wetting on the trapping of a residual phase. However, it has been shown to correlate very well with the residual saturations of the nonwetting, wetting, and intermediate-wetting phases in a wide variety of rock types.


1983 ◽  
Vol 23 (05) ◽  
pp. 727-742 ◽  
Author(s):  
Larry C. Young ◽  
Robert E. Stephenson

A procedure for solving compositional model equations is described. The procedure is based on the Newton Raphson iteration method. The equations and unknowns in the algorithm are ordered in such a way that different fluid property correlations can be accommodated leadily. Three different correlations have been implemented with the method. These include simplified correlations as well as a Redlich-Kwong equation of state (EOS). The example problems considered area conventional waterflood problem,displacement of oil by CO, andthe displacement of a gas condensate by nitrogen. These examples illustrate the utility of the different fluid-property correlations. The computing times reported are at least as low as for other methods that are specialized for a narrower class of problems. Introduction Black-oil models are used to study conventional recovery techniques in reservoirs for which fluid properties can be expressed as a function of pressure and bubble-point pressure. Compositional models are used when either the pressure. Compositional models are used when either the in-place or injected fluid causes fluid properties to be dependent on composition also. Examples of problems generally requiring compositional models are primary production or injection processes (such as primary production or injection processes (such as nitrogen injection) into gas condensate and volatile oil reservoirs and (2) enhanced recovery from oil reservoirs by CO or enriched gas injection. With deeper drilling, the frequency of gas condensate and volatile oil reservoir discoveries is increasing. The drive to increase domestic oil production has increased the importance of enhanced recovery by gas injection. These two factors suggest an increased need for compositional reservoir modeling. Conventional reservoir modeling is also likely to remain important for some time. In the past, two separate simulators have been developed and maintained for studying these two classes of problems. This result was dictated by the fact that compositional models have generally required substantially greater computing time than black-oil models. This paper describes a compositional modeling approach paper describes a compositional modeling approach useful for simulating both black-oil and compositional problems. The approach is based on the use of explicit problems. The approach is based on the use of explicit flow coefficients. For compositional modeling, two basic methods of solution have been proposed. We call these methods "Newton-Raphson" and "non-Newton-Raphson" methods. These methods differ in the manner in which a pressure equation is formed. In the Newton-Raphson method the iterative technique specifies how the pressure equation is formed. In the non-Newton-Raphson method, the composition dependence of certain ten-ns is neglected to form the pressure equation. With the non-Newton-Raphson pressure equation. With the non-Newton-Raphson methods, three to eight iterations have been reported per time step. Our experience with the Newton-Raphson method indicates that one to three iterations per tune step normally is sufficient. In the present study a Newton-Raphson iteration sequence is used. The calculations are organized in a manner which is both efficient and for which different fluid property descriptions can be accommodated readily. Early compositional simulators were based on K-values that were expressed as a function of pressure and convergence pressure. A number of potential difficulties are inherent in this approach. More recently, cubic equations of state such as the Redlich-Kwong, or Peng-Robinson appear to be more popular for the correlation Peng-Robinson appear to be more popular for the correlation of fluid properties. SPEJ p. 727


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