Reservoir Simulation With History-Dependent Saturation Functions

1976 ◽  
Vol 16 (01) ◽  
pp. 37-48 ◽  
Author(s):  
J.E. Killough
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Reservoir Simulation ◽  
Correct Prediction ◽  
Hysteresis Model ◽  
Relative Permeabilities ◽  
Capillary Hysteresis ◽  
Scanning Curves ◽  
Capillary Pressures ◽  
Smooth Transitions

Abstract A history-dependent model for saturation functions, combined with a three-dimensional, three-phase, semi-implicit reservoir simulator, has been developed. In water-coning simulations with variable rates, for waterflooding in the presence of free gas saturations, and for gas-cap shrinkage, use of hysteresis in saturation functions shows results significantly different from those obtained by conventional methods. To some extent, the model is based upon remembering the saturation history of the reservoir. In doing this, smooth transitions of both relative permeabilities and capillary-pressures from permeabilities and capillary-pressures from drainage-to-imbibition or imbibition-to-drainage states are allowed. In addition, the effect of trapped gas or oil saturations on relative permeabilities and capillary pressures is accounted for. Tests of the model indicate that simulation with hysteresis is a stable-procedure requiring little more computation time and storage than normal simulations. In addition, results of these tests agree qualitatively with experimental and field results. Introduction Present-day reservoir simulators have allowed investigation of complex recovery schemes and production schedules. Although simulators can production schedules. Although simulators can handle such problems numerically, most treat saturation functions in a simplified manner. For example, only one set of saturation functions may be used for initialization and/or simulation in a particular part of the reservoir. It is assumed that particular part of the reservoir. It is assumed that saturation changes occur in a given direction - drainage or imbibition-for most of the simulation. Cutler and Rees pointed out that hysteresis in capillary pressures may affect well coning behavior. Other authors have shown that hysteresis in relative permeabilities is important in the correct prediction of reservoir behavior. Unless treated prediction of reservoir behavior. Unless treated more realistically, the history dependence of saturation functions could cause significant errors in reservoir simulation. This paper describes a reservoir simulation technique in which saturation-function hysteresis is accounted for. A model for hysteresis is incorporated, permitting smooth transitions in either direction between drainage and imbibition relative permeability and capillary pressure curves as observed in experimental data. Including this hysteresis model allows the simulator to predict more realistically many reservoir situations. THE HYSTERESIS MODEL The hysteresis model allows both capillary pressures and relative permeabilities to range pressures and relative permeabilities to range between imbibition and drainage curves via intermediate "scanning" curves. Experimental data are required only for the bounding imbibition and drainage functions since the model provides an interpolative scheme for arriving at the intermediate values. However, regression parameters are incorporated allow a closer fit with experimental scanning states, should these data exist. The model also allows the use of analytical curves for the bounding relative-permeability functions, for which data may not exist. The hysteresis model has been designed so that saturation functions derived from the hysteresis algorithm approach physical reality. To this extent, the existing experimental data have been used as the basis for the model. The following sections describe these data and the associated procedures for calculating hysteretic relative permeabilities and capillary pressures. Further details and equations are given in the Appendix. CAPILLARY HYSTERESIS Capillary hysteresis is characterized by bounding imbibition and drainage curves and intermediate scanning curves, as shown in Fig. 1. SPEJ P. 37

Artificial-Intelligence Technology Predicts Relative Permeability of Giant Carbonate Reservoirs

2009 ◽  
Vol 12 (01) ◽  
pp. 96-103 ◽  
Author(s):  
Saud M. Al-Fattah ◽  
Hamad A. Al-Naim
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Reservoir Simulation ◽  
Nonlinear Problems ◽  
Carbonate Reservoir ◽  
Carbonate Reservoirs ◽  
Porous Rocks ◽  
Data Set ◽  
Ann Models ◽  
Permeability Data

Summary Determination of relative permeability data is required for almost all calculations of fluid flow in petroleum reservoirs. Water/oil relative permeability data play important roles in characterizing the simultaneous two-phase flow in porous rocks and predicting the performance of immiscible displacement processes in oil reservoirs. They are used, among other applications, for determining fluid distributions and residual saturations, predicting future reservoir performance, and estimating ultimate recovery. Undoubtedly, these data are considered probably the most valuable information required in reservoir simulation studies. Estimates of relative permeability are generally obtained from laboratory experiments with reservoir core samples. In the absence of the laboratory measurement of relative permeability data, developing empirical correlations for obtaining accurate estimates of relative permeability data showed limited success, and proved difficult, especially for carbonate reservoir rocks. Artificial-neural-network (ANN) technology has proved successful and useful in solving complex structured and nonlinear problems. This paper presents a new modeling technology to predict accurately water/oil relative permeability using ANN. The ANN models of relative permeability were developed using experimental data from waterflood-core-tests samples collected from carbonate reservoirs of giant Saudi Arabian oil fields. Three groups of data sets were used for training, verification, and testing the ANN models. Analysis of results of the testing data set show excellent agreement with the experimental data of relative permeability. In addition, error analyses show that the ANN models developed in this study outperform all published correlations. The benefits of this work include meeting the increased demand for conducting special core analysis (SCAL), optimizing the number of laboratory measurements, integrating into reservoir simulation and reservoir management studies, and providing significant cost savings on extensive lab work and substantial required time.

Experimental Study and History-Match of Near-Miscible WAG Coreflood Experiments on Mixed-Wet Carbonate Rocks

2021 ◽  
Author(s):  
Mohamed Mehdi El Faidouzi
Keyword(s):  
Relative Permeability ◽  
Carbonate Rocks ◽  
Hysteresis Model ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Recovery Method ◽  
Phase Displacement ◽  
Three Phase ◽  
Displacement Experiments ◽  
Phase Water

Abstract Water-alternating-gas (WAG) injection, both miscible and immiscible, is a widely used enhanced oil recovery method with over 80 field cases. Despite its prevalence, the numerical modeling of the physical processes involved remains poorly understood, and existing models often lack predictability. Part of the complexity stems from the component exchange between gas and oil and the hysteretic relative permeability effects. Thus, improving the reliability of numerical models requires the calibration of the equation of state (EOS) against phase behavior data from swelling/extraction and slim-tube tests, and the calibration of the three-phase relative permeability model against WAG coreflood experiments. This paper presents the results and interpretation of a complete set of two-phase and thee-phase displacement experiments on mixed-wet carbonate rocks. The three-phase WAG experiments were conducted on the same composite core at near-miscible reservoir condition; experiments differ in the injection order and length of their injection cycles. First, the two-phase water/oil and gas/oil displacement experiments and first cycles of WAG were used to estimate the two-phase relative permeabilities. Then, a synchronized history-matching procedure over the full set of WAG experiments and cycles was carried out to tune Larsen ans Skauge WAG hysteresis model—namely the Land gas traping parameter, the gas reduction exponent, the residual oil reduction factor and three-phase water relative permeability. The second part of this paper deals with the multiphase upscaling of microscopic displacement properties from plug to coarse grid reservoir scale. The two-phase relative permeability curves and three-phase WAG parameters were upscaled using a sector model to preserve the displacement process and reservoir performance. The result of the coreflood calibration indicate that the two-phase displacement and first cycles of WAG yield a consistent set of two-phase relative permeabilities. Including the full set of WAG experiments allowed a robust calibration of the hysteresis model.

A Fully Coupled Three-Phase Model for Capillary Pressure and Relative Permeability for Implicit Compositional Reservoir Simulation

SPE Journal ◽  
2010 ◽  
Vol 15 (04) ◽  
pp. 1003-1019 ◽  
Author(s):  
Odd Steve Hustad ◽  
David John Browning
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Reservoir Simulation ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Capillary Pressures ◽  
And Performance ◽  
Model Features ◽  
2D And 3D

Summary A coupled formulation for three-phase capillary pressure and relative permeability for implicit compositional reservoir simulation is presented. The formulation incorporates primary, secondary, and tertiary saturation functions. Hysteresis and miscibility are applied simultaneously to both capillary pressure and relative permeability. Two alternative three-phase capillary pressure formulations are presented: the first as described by Hustad (2002) and the second that incorporates six representative two-phase capillary pressures in a saturation-weighting scheme. Consistency is ensured for all three two-phase boundary conditions through the application of two-phase data and normalized saturations. Simulation examples of water-alternating-gas (WAG) injection are presented for water-wet and mixed-wet saturation functions. 1D homogeneous and 2D and 3D heterogeneous examples are employed to demonstrate some model features and performance.

Measurement of Three-Phase Relative Permeability with IFT Variation

2005 ◽  
Vol 8 (01) ◽  
pp. 33-43 ◽  
Author(s):  
Yildiray Cinar ◽  
Franklin M. Orr
Keyword(s):  
Experimental Data ◽  
Relative Permeability ◽  
Oil And Gas ◽  
Gas Injection ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Rich Phase ◽  
Injection Process ◽  
Three Phase ◽  
Relative Permeability Curves

Summary In this paper, we present results of an experimental investigation of the effects of variations in interfacial tension (IFT) on three-phase relative permeability. We report results that demonstrate the effect of low IFT between two of three phases on the three-phase relative permeabilities. To create three-phase systems in which IFT can be con-trolled systematically, we used a quaternary liquid system composed of hexadecane(C16), n-butanol (NBA), water (H2O), and isopropanol (IPA). Measured equilibrium phase compositions and IFTs are reported. The reported phase behavior of the quaternary system shows that the H2O-rich phase should represent the "gas" phase, the NBA-rich phase should represent the "oil" phase, and the C16-rich phase should represent the "aqueous" phase. Therefore, we used oil-wet Teflon (PTFE) bead packs to simulate the fluid flow in a water-wet oil reservoir. We determined phase saturations and three-phase relative permeabilities from recovery and pressure-drop data using an extension of the combined Welge/Johnson-Bossler-Naumann (JBN) method to three-phase flow. Measured three-phase relative permeabilities are reported. The experimental results indicate that the wetting-phase relative permeability was not affected by IFT variation, whereas the other two-phase relative permeabilities were clearly affected. As IFT decreases, the oil and gas phases become more mobile at the same phase saturations. For gas/oil IFTs in the range of 0.03 to 2.3 mN/m, we observed an approximately 10-fold increase in the oil and gas relative permeabilities against an approximately 100-fold decrease in the IFT. Introduction Variations in gas and oil relative permeabilities as a function of IFT are of particular importance in the area of compositional processes such as high-pressure gas injection, where oil and gas compositions can vary significantly both spatially and temporally. Because gas-injection processes routinely include three-phase flow (either because the reservoir has been water-flooded previously or because water is injected alternately with gas to improve overall reservoir sweep efficiency), the effect of IFT variations on three-phase relative permeabilities must be delineated if the performance of the gas-injection process is to be predicted accurately. The development of multicontact miscibility in a gas-injection process will create zones of low IFT between gas and oil phases in the presence of water. Although there have been studies of the effect of low IFT on two-phase relative permeability,1–14 there are limited experimental data published so far analyzing the effect of low IFT on three-phase relative permeabilities.15,16 Most authors have focused on the effect of IFT on oil and solvent relative permeabilities.17 Experimental results show that residual oil saturation and relative permeability are strongly affected by IFT, especially when the IFT is lower than approximately 0.1 mN/m (corresponding to a range of capillary number of 10–2 to 10–3). Bardon and Longeron3 observed that oil relative permeability increased linearly as IFT was reduced from approximately 12.5 mN/m to 0.04 mN/m and that for IFT below 0.04, the oil relative permeability curves shifted more rapidly with further reductions in IFT. Later, Asar and Handy6 showed that oil relative permeability curves began to shift as IFT was reduced below 0.18 mN/m for a gas/condensate system near the critical point. Delshad et al.15 presented experimental data for low-IFT three-phase relative permeabilities in Berea sandstone cores. They used a brine/oil/surfactant/alcohol mixture that included a microemulsion and excess oil and brine. The measurements were done at steady-state conditions with a constant capillary number of 10–2 between the microemulsion and other phases. The IFTs of microemulsion/oil and microemulsion/brine were low, whereas the IFT between oil and brine was high. They concluded that low-IFT three-phase relative permeabilities are functions of their own saturations only. Amin and Smith18 recently have published experimental data showing that the IFTs for each binary mixture of brine, oil, and gas phases vary as pressure increases(Fig. 1). Fig. 1 shows that the IFT of a gas/oil pair decreases as the pressure increases, whereas the IFTs of the gas/brine and oil/brine pairs approach each other.

A New Way of Compositional Simulation without Phase Labeling

SPE Journal ◽  
2021 ◽  
Vol 26 (02) ◽  
pp. 940-958
Author(s):  
Saeid Khorsandi ◽  
Liwei Li ◽  
Russell T. Johns
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Oil And Gas ◽  
Computational Time ◽  
Relative Permeabilities ◽  
Compositional Simulation ◽  
Three Phase ◽  
Compositional Simulator ◽  
Capillary Pressures ◽  
Compositional Variations

Summary Current relative permeability models rely on labeling a phase as “oil” and “gas” and cannot therefore capture accurately the effect of compositional variations on relative permeabilities and capillary pressures in enhanced oil recovery processes. Discontinuities in flux calculations caused by phase labeling problems not only cause serious convergence and stability problems but also affect the estimated recovery factor owing to incorrect phase mobilities. We developed a fully compositional simulation model using an equation of state (EoS) for relative permeabilities (kr) to eliminate the unphysical discontinuities in flux functions caused by phase labeling issues. The model can capture complex compositional and hysteresis effects for three-phase relative permeability. Each phase is modeled separately based on physical inputs that, in part, are proxies to composition. Phase flux calculations from one gridblock to another are also updated without phase labels. The tuned kr-EoS model and updated compositional simulator are demonstrated for simple ternary cases, multicycle three-phase water-alternating-gas (WAG) injection, and three-hydrocarbon-phase displacement with complex heterogeneity. The approach improves the initial estimates and convergence of flash calculations and stability analyses, as well as the convergence in the pressure solvers. The new compositional simulator allows for high-resolution simulation that gives improved accuracy in recovery estimates at significantly reduced computational time.

Equation of State for Relative Permeability, Including Hysteresis and Wettability Alteration

SPE Journal ◽  
2017 ◽  
Vol 22 (06) ◽  
pp. 1915-1928 ◽  
Author(s):  
Saeid Khorsandi ◽  
Liwei Li ◽  
Russell T. Johns
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Surface Properties ◽  
Relative Permeability ◽  
Contact Angles ◽  
Wettability Alteration ◽  
Rock Surface ◽  
Relative Permeabilities ◽  
Tuning Parameters ◽  
Rock Structure

Summary Commercial compositional simulators commonly apply correlations or empirical relations that are based on fitting experimental data to calculate phase relative permeabilities. These relations cannot adequately capture the effects of hysteresis, fluid compositional variations, and rock-wettability alteration. Furthermore, these relations require phases to be labeled, which is not accurate for complex miscible or near-miscible displacements with multiple hydrocarbon phases. Therefore, these relations can be discontinuous for compositional processes, causing inaccuracies and numerical problems in simulation. This paper develops for the first time an equation-of-state (EOS) to model robustly and continuously the relative permeability as a function of phase saturations and distributions, fluid compositions, rock-surface properties, and rock structure. Phases are not labeled; instead, the phases in each gridblock are ordered on the basis of their compositional similarity. Phase compositions and rock-surface properties are used to calculate wettability and contact angles. The model is tuned to measured two-phase relative permeability curves with very few tuning parameters and then is used to predict relative permeability away from the measured experimental data. The model is applicable to all flow in porous-media processes, but is especially important for low-salinity polymer, surfactant, miscible gas, and water-alternating-gas (WAG) flooding. The results show excellent ability to match measured data, and to predict observed trends in hysteresis and oil-saturation trapping, including those from Land's model and for a wide range in wettability. The results also show that relative permeabilities are continuous at critical points and yield a physically correct numerical solution when incorporated within a compositional simulator (PennSim 2013). The model has very few tuning parameters, and the parameters are directly related to physical properties of rock and fluid, which can be measured. The new model also offers the potential for incorporating results from computed-tomography (CT) scans and pore-network models to determine some input parameters for the new EOS.

Effect of Temperature on Oil/Water Relative Permeabilities of Unconsolidated and Consolidated Sands

1985 ◽  
Vol 25 (06) ◽  
pp. 945-953 ◽  
Author(s):  
Mark A. Miller ◽  
H.J. Ramey
Keyword(s):  
Relative Permeability ◽  
Room Temperature ◽  
Water Saturation ◽  
High Water ◽  
Distilled Water ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Dynamic Displacement ◽  
Irreducible Water Saturation ◽  
Increasing Temperature

Abstract Over the past 20 years, a number of studies have reported temperature effects on two-phase relative permeabilities in porous media. Some of the reported results, however, have been contradictory. Also, observed effects have not been explained in terms of fundamental properties known to govern two-phase flow. The purpose of this study was to attempt to isolate the fundamental properties affecting two-phase relative permeabilities at elevated temperatures. Laboratory dynamic-displacement relative permeability measurements were made on unconsolidated and consolidated sand cores with water and a refined white mineral oil. Experiments were run on 2-in. [5.1-cm] -diameter, 20-in. [52.-cm] -long cores from room temperature to 300F [149C]. Unlike previous researchers, we observed essentially no changes with temperature in either residual saturations or relative permeability relationships. We concluded that previous results may have been affected by viscous previous results may have been affected by viscous instabilities, capillary end effects, and/or difficulties in maintaining material balances. Introduction Interest in measuring relative permeabilities at elevated temperatures began in the 1960's with petroleum industry interest in thermal oil recovery. Early thermal oil recovery field operations (well heaters, steam injection, in-situ combustion) indicated oil flow rate increases far in excess of what was predicted by viscosity reductions resulting from heating. This suggested that temperature affects relative permeabilities. One of the early studies of temperature effects on relative permeabilities was presented by Edmondson, who performed dynamic displacement measurements with crude performed dynamic displacement measurements with crude and white oils and distilled water in Berea sandstone cores. Edmondson reported that residual oil saturations (ROS's) (at the end of 10 PV's of water injected) decreased with increasing temperature. Relative permeability ratios decreased with temperature at high water saturations but increased with temperature at low water saturations. A series of elevated-temperature, dynamic-displacement relative permeability measurements on clean quartz and "natural" unconsolidated sands were reported by Poston et al. Like Edmondson, Poston et al. reported a decrease in the "practical" ROS (at less than 1 % oil cut) as temperature increased. Poston et al. also reported an increase in irreducible water saturation. Although irreducible water saturations decreased with decreasing temperature, they did not revert to the original room temperature values. It was assumed that the cores became increasingly water-wet with an increase in both temperature and time; measured changes of the IFT and the contact angle with temperature increase, however, were not sufficient to explain observed effects. Davidson measured dynamic-displacement relative permeability ratios on a coarse sand and gravel core with permeability ratios on a coarse sand and gravel core with white oil displaced by distilled water, nitrogen, and superheated steam at temperatures up to 540F [282C]. Starting from irreducible water saturation, relative permeability ratio curves were similar to Edmondson's. permeability ratio curves were similar to Edmondson's. Starting from 100% oil saturation, however, the curves changed significantly only at low water saturations. A troublesome aspect of Davidson's work was that he used a hydrocarbon solvent to clean the core between experiments. No mention was made of any consideration of wettability changes, which could explain large increases in irreducible water saturations observed in some runs. Sinnokrot et al. followed Poston et al.'s suggestion of increasing water-wetness and performed water/oil capillary pressure measurements on consolidated sandstone and limestone cores from room temperature up to 325F [163C]. Sinnokrot et al confirmed that, for sandstones, irreducible water saturation appeared to increase with temperature. Capillary pressures increased with temperature, and the hysteresis between drainage and imbibition curves reduced to essentially zero at 300F [149C]. With limestone cores, however, irreducible water saturations remained constant with increase in temperature, as did capillary pressure curves. Weinbrandt et al. performed dynamic displacement experiments on small (0.24 to 0.49 cu in. [4 to 8 cm3] PV) consolidated Boise sandstone cores to 175F [75C] PV) consolidated Boise sandstone cores to 175F [75C] with distilled water and white oil. Oil relative permeabilities shifted toward high water saturations with permeabilities shifted toward high water saturations with increasing temperature, while water relative permeabilities exhibited little change. Weinbrandt et al. confirmed the findings of previous studies that irreducible water saturation increases and ROS decreases with increasing temperature. SPEJ P. 945

Cocurrent Spontaneous Imbibition In Porous Media With the Dynamics of Viscous Coupling and Capillary Backpressure

SPE Journal ◽  
2018 ◽  
Vol 24 (01) ◽  
pp. 158-177 ◽  
Author(s):  
Pål Østebø Andersen ◽  
Yangyang Qiao ◽  
Dag Chun Standnes ◽  
Steinar Evje
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Flow Regimes ◽  
Spontaneous Imbibition ◽  
The Other ◽  
Countercurrent Flow ◽  
Relative Permeabilities ◽  
Viscous Coupling ◽  
Generalized Model ◽  
Matrix Block

Summary This paper presents a numerical study of water displacing oil using combined cocurrent/countercurrent spontaneous imbibition (SI) of water displacing oil from a water-wet matrix block exposed to water on one side and oil on the other. Countercurrent flows can induce a stronger viscous coupling than during cocurrent flows, leading to deceleration of the phases. Even as water displaces oil cocurrently, the saturation gradient in the block induces countercurrent capillary diffusion. The extent of countercurrent flow may dominate the domain of the matrix block near the water-exposed surfaces while cocurrent imbibition may dominate the domain near the oil-exposed surfaces, implying that one unique effective relative permeability curve for each phase does not adequately represent the system. Because relative permeabilities are routinely measured cocurrently, it is an open question whether the imbibition rates in the reservoir (depending on a variety of flow regimes and parameters) will in fact be correctly predicted. We present a generalized model of two-phase flow dependent on momentum equations from mixture theory that can account dynamically for viscous coupling between the phases and the porous media because of fluid/rock interaction (friction) and fluid/fluid interaction (drag). These momentum equations effectively replace and generalize Darcy's law. The model is parameterized using experimental data from the literature. We consider a water-wet matrix block in one dimension that is exposed to oil on one side and water on the other side. This setup favors cocurrent SI. We also account for the fact that oil produced countercurrently into water must overcome the so-called capillary backpressure, which represents a resistance for oil to be produced as droplets. This parameter can thus influence the extent of countercurrent production and hence viscous coupling. This complex mixture of flow regimes implies that it is not straightforward to model the system by a single set of relative permeabilities, but rather relies on a generalized momentum-equation model that couples the two phases. In particular, directly applying cocurrently measured relative permeability curves gives significantly different predictions than the generalized model. It is seen that at high water/oil-mobility ratios, viscous coupling can lower the imbibition rate and shift the production from less countercurrent to more cocurrent compared with conventional modeling. Although the viscous-coupling effects are triggered by countercurrent flow, reducing or eliminating countercurrent production by means of the capillary backpressure does not eliminate the effects of viscous coupling that take place inside the core, which effectively lower the mobility of the system. It was further seen that viscous coupling can increase the remaining oil saturation in standard cocurrent-imbibition setups.

Sign in / Sign up

Export Citation Format

Share Document