Relative Permeabilities And Capillary Pressure In The Burgan And Wara Sands

10.2118/81-ms ◽  
1961 ◽  
Author(s):  
George Hetherington
Keyword(s):  
Capillary Pressure ◽  
Relative Permeabilities

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.

A Water-Gas Relative Permeability Relationship for Tight Gas Sand Reservoirs

1990 ◽  
Vol 112 (4) ◽  
pp. 239-245 ◽  
Author(s):  
S. D. L. Lekia ◽  
R. D. Evans
Keyword(s):  
Capillary Pressure ◽  
Relative Permeability ◽  
Water Saturation ◽  
Gas Permeability ◽  
Tight Gas ◽  
Relative Permeabilities ◽  
The North ◽  
Tight Gas Sands ◽  
Straight Line ◽  
Phase Saturation

This paper presents a new approach for the analyses of laboratory-derived capillary pressure data for tight gas sands. The method uses the fact that a log-log plot of capillary pressure against water saturation is a straight line to derive new expressions for both wetting and nonwetting phase relative permeabilities. The new relative permeability equations are explicit functions of water saturation and the slope of the log-log straight line of capillary pressure plotted against water saturation. Relative permeabilities determined with the new expressions have been successfully used in simulation studies of naturally fractured tight gas sands where those determined with Corey-type expressions which are functions of reduced water saturation have failed. A dependence trend is observed between capillary pressure and gas permeability data from some of the tight gas sands of the North American Continent. The trend suggests that the lower the gas permeability, the higher the capillary pressure values at the same wetting phase saturation—especially for saturations less than 60 percent.

The Modeling of a Three-Dimensional Reservoir with a Two-Dimensional Reservoir Simulator-The Use of Dynamic Pseudo Functions

1973 ◽  
Vol 13 (03) ◽  
pp. 175-185 ◽  
Author(s):  
Hugh H. Jacks ◽  
Owen J.E. Smith ◽  
C.C. Mattax
Keyword(s):  
Capillary Pressure ◽  
Cross Section ◽  
Relative Permeability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Relative Permeabilities ◽  
Large Reservoir ◽  
Model Simulations ◽  
Wide Range ◽  
Section Model

Abstract Dynamic pseudo-relative permeabilities derived from cross-section models can be used to simulate three-dimensional flow accurately in a two-dimensional areal model of a reservoir Techniques are presented for deriving and using dynamic pseudos that are applicable over a wide range of rates and initial fluid saturations. Their validity is demonstrated by showing calculated results from comparable runs in a vertical cross-section model and in a one-dimensional areal model using the dynamic pseudo-relative permeabilities and vertical equilibrium (VE) pseudo-capillary pressures. Further substantiation is provided by showing the close agreement in calculated performance for a three-dimensional model and corresponding two-dimensional areal model representing a typical pattern on the flanks of a large reservoir. The areal pattern on the flanks of a large reservoir. The areal model gave comparable accuracy with a substantial savings in computing and manpower costs. Introduction Meaningful studies can be made for almost all reservoirs now that relatively efficient three-dimensional reservoir simulators are available. In many instances, however, less expensive two-dimensional areal (x-y) models can be used to solve the engineering problem adequately, provided the nonuniform distribution and flow of fluids in the implied third, or vertical, dimension of the areal model is properly described. This is accomplished through the use of special saturation-dependent functions that have been labeled pseudo-relative permeability (k ) and pseudo-capillary pressure permeability (k ) and pseudo-capillary pressure (P ) or, for simplicity "pseudo functions", to distinguish them from the conventional laboratory measured values that are used in their derivation. Two types of reservoir models have been suggested in the past to derive pseudo functions: the vertical equilibrium (VE) model of Coats et al., which is based on gravity-capillary equilibrium in the vertical direction; and the stratified model of Hearn, which assumes that viscous forces dominate vertical fluid distribution. Neither of these models accounts for the effects of large changes in flow rate that take place as a field is developed, approaches and place as a field is developed, approaches and maintains its peak rate, and then falls into decline. This paper presents an alternative method for developing pseudo functions that are applicable over a wide range of flow rates and over the complete range of initial fluid saturations. The functions may be both space and time dependent and, again for clarity and convenience in nomenclature, we have labeled them "dynamic pseudo functions". DESCRIPTION OF PSEUDO-RELATIVE PERMEABILITY FUNCTIONS PERMEABILITY FUNCTIONS Methods for developing pseudo functions have been presented in the literature. The distinction between our method and those used by others lies in the technique for deriving the vertical saturation distribution upon which the pseudo-relative permeabilities are based. In our approach, the permeabilities are based. In our approach, the vertical saturation distribution is developed through detailed simulation of the fluid displacement in a vertical cross-section (x-z) model of the reservoir. The simulation is run under conditions that are representative of those to be expected during the period to be covered in the areal model simulations. period to be covered in the areal model simulations. Results of the cross-section simulation are then processed to give depth-averaged fluid saturations processed to give depth-averaged fluid saturations (S ) and "dynamic" pseudo-relative permeability values (k ) for each column of blocks in the cross-section model at each output time. The above approach can result in a different set of dynamic pseudo functions for each column of blocks due to differences in initial saturation, rate of displacement, reservoir stratification, and location. However, differences between columns are frequently minor or they can be accounted for by correlation of the data. In this and several other reservoir studies, it was possible to reduce the complexity of the pseudo function sets through correlations with initial fluid saturations and fluid velocities. SPEJ P. 175

Simultaneous Estimation of Relative Permeabilities and Capillary Pressure

1992 ◽  
Vol 7 (04) ◽  
pp. 283-289 ◽  
Author(s):  
Catherine Chardaire-Riviere ◽  
Guy Chavent ◽  
Jereoe Jaffre ◽  
Jun Liu ◽  
Bernard J. Bourbiaux
Keyword(s):  
Capillary Pressure ◽  
Simultaneous Estimation ◽  
Relative Permeabilities

scholarly journals Analytical modeling and correction of steady state relative permeability experiments with capillary end effects – An improved intercept method, scaling and general capillary numbers

2021 ◽  
Vol 76 ◽  
pp. 61
Author(s):  
Pål Ø. Andersen
Keyword(s):  
Steady State ◽  
Pressure Drop ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Relative Permeabilities ◽  
Total Rate ◽  
Dimensionless Numbers ◽  
End Effects ◽  
Effective Relative Permeabilities ◽  
Saturation Profile

Steady state relative permeability experiments are performed by co-injection of two fluids through core plug samples. Effective relative permeabilities can be calculated from the stabilized pressure drop using Darcy’s law and linked to the corresponding average saturation of the core. These estimated relative permeability points will be accurate only if capillary end effects and transient effects are negligible. This work presents general analytical solutions for calculation of spatial saturation and pressure gradient profiles, average saturation, pressure drop and relative permeabilities for a core at steady state when capillary end effects are significant. We derive an intuitive and general “intercept” method for correcting steady state relative permeability measurements for capillary end effects: plotting average saturation and inverse effective relative permeability (of each phase) against inverse total rate will give linear trends at high total rates and result in corrected relative permeability points when extrapolated to zero inverse total rate (infinite rate). We derive a formal proof and generalization of the method proposed by Gupta and Maloney (2016) [SPE Reserv. Eval. Eng. 19, 02, 316–330], also extending the information obtained from the analysis, especially allowing to calculate capillary pressure. It is shown how the slopes of the lines are related to the saturation functions allowing to scale all test data for all conditions to the same straight lines. Two dimensionless numbers are obtained that directly express how much the average saturation is changed and the effective relative permeabilities are reduced compared to values unaffected by end effects. The numbers thus quantitatively and intuitively express the influence of end effects. A third dimensionless number is derived providing a universal criterion for when the intercept method is valid, directly stating that the end effect profile has reached the inlet. All the dimensionless numbers contain a part depending only on saturation functions, injected flow fraction and viscosity ratio and a second part containing constant known fluid, rock and system parameters such as core length, porosity, interfacial tension, total rate, etc. The former parameters determine the saturation range and shape of the saturation profile, while the latter number determines how much the profile is compressed towards the outlet. End effects cause the saturation profile and average saturation to shift towards the saturation where capillary pressure is zero and the effective relative permeabilities to be reduced compared to the true relative permeabilities. This shift is greater at low total rate and gives a false impression of rate-dependent relative permeabilities. The method is demonstrated with multiple examples. Methodologies for deriving relative permeability and capillary pressure systematically and consistently, even based on combining data from tests with different fluid and core properties, are presented and demonstrated on two datasets from the literature. The findings of this work are relevant to accurately estimate relative permeabilities in steady state experiments, relative permeability end points and critical saturations during flooding or the impact of injection chemicals on mobilizing residual phase.

A NOVEL FRACTAL MODEL FOR RELATIVE PERMEABILITY OF GAS DIFFUSION LAYER IN PROTON EXCHANGE MEMBRANE FUEL CELL WITH CAPILLARY PRESSURE EFFECT

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950012 ◽  
Author(s):  
BOQI XIAO ◽  
WEI WANG ◽  
XIAN ZHANG ◽  
GONGBO LONG ◽  
HANXIN CHEN ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fuel Cell ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Diffusion Layer ◽  
Proton Exchange Membrane ◽  
Gas Diffusion ◽  
Proton Exchange ◽  
Relative Permeabilities ◽  
Exchange Membrane

The investigation of fluids transport through porous gas diffusion layer (GDL) is very important to improve the performance of proton exchange membrane fuel cell (PEMFC). In this paper, the fractal analytical models of capillary pressure for water phase and water and gas relative permeabilities of fibrous GDL are obtained. The determined capillary pressure and relative permeabilities based on the present models are in good agreement with the available experimental data and existing models reported in the literature. Thus the validity of the proposed models for the capillary pressure and relative permeabilities is verified. It is found that the capillary pressure increases with the increase of fiber volume fraction and tortuosity fractal dimension. On the other hand, it is seen that the capillary pressure decreases with increasing water saturation. It is seen that the water relative permeability decreases with increasing tortuosity fractal dimension. On the contrary, it is found that the gas relative permeability increases with tortuosity fractal dimension. Besides, it is observed that the porosity has little effect on the water and gas relative permeabilities.

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