Capillary Pressures and Gas Relative Permeabilities of Low-Permeability Sandstone

1987 ◽  
Vol 2 (03) ◽  
pp. 345-356 ◽  
Author(s):  
Jill S. Ward ◽  
Norman R. Morrow
Keyword(s):  
Low Permeability ◽  
Relative Permeabilities ◽  
Capillary Pressures

A COMPREHENSIVE MODEL FOR OIL–WATER RELATIVE PERMEABILITIES IN LOW-PERMEABILITY RESERVOIRS BY FRACTAL THEORY

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050055
Author(s):  
HAIBO SU ◽  
SHIMING ZHANG ◽  
YEHENG SUN ◽  
XIAOHONG WANG ◽  
BOMING YU ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Fractal Theory ◽  
Low Permeability ◽  
Comprehensive Model ◽  
Relative Permeabilities ◽  
Oil Water ◽  
Seepage Characteristics ◽  
Low Permeability Reservoirs

Oil–water relative permeability curve is an important parameter for analyzing the characters of oil and water seepages in low-permeability reservoirs. The fluid flow in low-permeability reservoirs exhibits distinct nonlinear seepage characteristics with starting pressure gradient. However, the existing theoretical model of oil–water relative permeability only considered few nonlinear seepage characteristics such as capillary pressure and fluid properties. Studying the influences of reservoir pore structures, capillary pressure, driving pressure and boundary layer effect on the morphology of relative permeability curves is of great significance for understanding the seepage properties of low-permeability reservoirs. Based on the fractal theory for porous media, an analytically comprehensive model for the relative permeabilities of oil and water in a low-permeability reservoir is established in this work. The analytical model for oil–water relative permeabilities obtained in this paper is found to be a function of water saturation, fractal dimension for pores, fractal dimension for tortuosity of capillaries, driving pressure gradient and capillary pressure between oil and water phases as well as boundary layer thickness. The present results show that the relative permeabilities of oil and water decrease with the increase of the fractal dimension for tortuosity, whereas the relative permeabilities of oil and water increase with the increase of pore fractal dimension. The nonlinear properties of low-permeability reservoirs have the prominent significances on the relative permeability of the oil phase. With the increase of the seepage resistance coefficient, the relative permeability of oil phase decreases. The proposed theoretical model has been verified by experimental data on oil–water relative permeability and compared with other conventional oil–water relative permeability models. The present results verify the reliability of the oil–water relative permeability model established in this paper.

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

scholarly journals Pore-by-Pore Modelling, Validation and Prediction of Waterflooding in Oil-Wet Rocks Using Dynamic Synchrotron Data

2021 ◽  
Author(s):  
Sajjad Foroughi ◽  
Branko Bijeljic ◽  
Martin J. Blunt
Keyword(s):  
Contact Angles ◽  
Pore Scale ◽  
Relative Permeabilities ◽  
Network Modelling ◽  
Time Resolved ◽  
High Resolution Image ◽  
Pore Network Modelling ◽  
Synchrotron Imaging ◽  
Capillary Pressures ◽  
Wet Rocks

AbstractWe predict waterflood displacement on a pore-by-pore basis using pore network modelling. The pore structure is captured by a high-resolution image. We then use an energy balance applied to images of the displacement to assign an average contact angle, and then modify the local pore-scale contact angles in the model about this mean to match the observed displacement sequence. Two waterflooding experiments on oil-wet rocks are analysed where the displacement sequence was imaged using time-resolved synchrotron imaging. In both cases the capillary pressure in the model matches the experimentally obtained values derived from the measured interfacial curvature. We then predict relative permeability for the full saturation range. Using the optimised contact angles distributed randomly in space has little effect on the predicted capillary pressures and relative permeabilities, indicating that spatial correlation in wettability is not significant in these oil-wet samples. The calibrated model can be used to predict properties outside the range of conditions considered in the experiment.

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.

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