scholarly journals A Fractal Model for Predicting the Relative Permeability of Rough-Walled Fractures

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Zuyang Ye ◽  
Wang Luo ◽  
Shibing Huang ◽  
Yuting Chen ◽  
Aiping Cheng
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Relative Permeability ◽  
Fractal Model ◽  
Numerical Results ◽  
Flow Paths ◽  
Capillary Model ◽  
Lognormal Distributions ◽  
Fractal Characteristics ◽  
Aperture Distribution

The relative permeability and saturation relationships through fractures are fundamental for modeling multiphase flow in underground geological fractured formations. In contrast to the traditional straight capillary model from porous media, the realistic flow paths in rough-walled fractures are tortuous. In this study, a fractal relationship between relative permeability and saturation of rough-walled fractures is proposed associated with the fractal characteristics of tortuous parallel capillary plates, which can be generalized to several existing models. Based on the consideration that the aperture distribution of rough-walled fracture can be represented by Gaussian and lognormal distributions, aperture-based expressions between relative permeability and saturation are explicitly derived. The developed relationships are validated by the experimental observations on Gaussian distributed fractures and numerical results on lognormal distributed fractures, respectively.

A NEW RELATIVE PERMEABILITY MODEL OF UNSATURATED POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽  
2020 ◽  
Vol 28 (01) ◽  
pp. 2050002
Author(s):  
KE CHEN ◽  
HE CHEN ◽  
PENG XU
Keyword(s):  
Experimental Data ◽  
Porous Media ◽  
Fractal Dimension ◽  
Multiphase Flow ◽  
Relative Permeability ◽  
Volume Fraction ◽  
Fractal Model ◽  
Accurate Estimation ◽  
Unsaturated Porous Media ◽  
Flow Through

The multiphase flow through unsaturated porous media and accurate estimation of relative permeability are significant for oil and gas reservoir, grounder water resource and chemical engineering, etc. A new fractal model is developed for the multiphase flow through unsaturated porous media, where multiscale pore structure is characterized by fractal scaling law and the trapped water in the pores is taken into account. And the analytical expression for relative permeability is derived accordingly. The relationships between the relative permeability and capillary head as well as saturation are determined. The proposed model is validated by comparison with 14 sets of experimental data, which indicates that the fractal model agrees well with experimental data. It has been found that the proposed fractal model shows evident advantages compared with BC-B model and VG-M model, especially for the porous media with fine content and texture. Further calculations show that water permeability decreases as the fractal dimension increases under fixed saturation because the cumulative volume fraction of small pores increases with the increment of the fractal dimension. The present fractal model for the relative permeability may be helpful to understand the multiphase flow through unsaturated porous media.

Multiphase-Flow and Reactive-Transport Validation Studies at the Pore Scale by Use of Lattice Boltzmann Computer Simulations

SPE Journal ◽  
2017 ◽  
Vol 22 (03) ◽  
pp. 940-949 ◽  
Author(s):  
Edo S. Boek ◽  
Ioannis Zacharoudiou ◽  
Farrel Gray ◽  
Saurabh M. Shah ◽  
John P. Crawshaw ◽  
...  
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Computer Simulations ◽  
Relative Permeability ◽  
Lattice Boltzmann ◽  
Reactive Transport ◽  
Pore Space ◽  
Processing Unit ◽  
Space Images

Summary We describe the recent development of lattice Boltzmann (LB) and particle-tracing computer simulations to study flow and reactive transport in porous media. First, we measure both flow and solute transport directly on pore-space images obtained from micro-computed-tomography (CT) scanning. We consider rocks with increasing degree of heterogeneity: a bead pack, Bentheimer sandstone, and Portland carbonate. We predict probability distributions for molecular displacements and find excellent agreement with pulsed-field-gradient (PFG) -nuclear-magnetic-resonance (NMR) experiments. Second, we validate our LB model for multiphase flow by calculating capillary filling and capillary pressure in model porous media. Then, we extend our models to realistic 3D pore-space images and observe the calculated capillary pressure curve in Bentheimer sandstone to be in agreement with the experiment. A process-based algorithm is introduced to determine the distribution of wetting and nonwetting phases in the pore space, as a starting point for relative permeability calculations. The Bentheimer relative permeability curves for both drainage and imbibition are found to be in good agreement with experimental data. Third, we show the speedup of a graphics-processing-unit (GPU) algorithm for large-scale LB calculations, offering greatly enhanced computing performance in comparison with central-processing-unit (CPU) calculations. Finally, we propose a hybrid method to calculate reactive transport on pore-space images by use of the GPU code. We calculate the dissolution of a porous medium and observe agreement with the experiment. The LB method is a powerful tool for calculating flow and reactive transport directly on pore-space images of rock.

AN ANALYTICAL MODEL FOR TWO-PHASE RELATIVE PERMEABILITY WITH JAMIN EFFECT IN POROUS MEDIA

Fractals ◽  
2018 ◽  
Vol 26 (03) ◽  
pp. 1850037 ◽  
Author(s):  
MINGCHAO LIANG ◽  
YINHAO GAO ◽  
SHANSHAN YANG ◽  
BOQI XIAO ◽  
ZHANKUI WANG ◽  
...  
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Pressure Difference ◽  
Applied Pressure ◽  
Fractal Model ◽  
Low Permeability ◽  
Two Phase ◽  
Low Permeability Reservoir ◽  
Model Predictions ◽  
Flow Through

Jamin effect, which is a capillary pressure obstructing the drop/bubble flow through the narrow throat, has an important effect on the multiphase flow in the low permeability reservoir porous media. In this work, a novel model for the relative permeability with Jamin effect is developed to study the two-phase flow through porous media based on the fractal theory. The proposed relative permeability is expressed as a function of the applied pressure difference, shape parameters of the drop/bubble, the physical parameters of the wetting and nonwetting fluids, and microstructural parameters of porous media. Good agreement between model predictions and available experimental data is obtained, and the advantage of the present fractal model can be highlighted by comparisons with the empirical model predictions. Additionally, the influences of Jamin effect on the two-phase relative permeability are discussed comprehensively and in detail. The model reveals that the length ratios ([Formula: see text] and [Formula: see text]) have significant effects on the relative permeabilities. It is also found that the nonwetting phase relative permeability strongly depends on the interfacial tension, applied pressure difference, viscosity ratio and porosity of porous media at the lower wetting phase saturation. Furthermore, the fractal model will shed light on the two-phase transport mechanism of the low permeability reservoir porous media.

scholarly journals Stress-Dependent Pore Deformation Effects on Multiphase Flow Properties of Porous Media

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Amir H. Haghi* ◽  
Richard Chalaturnyk ◽  
Stephen Talman
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Effective Stress ◽  
Core Flooding ◽  
Flow Properties ◽  
Micro Scale ◽  
Stress Dependent

Abstract Relative permeability and capillary pressure are the governing parameters that characterize multiphase fluid flow in porous media for diverse natural and industrial applications, including surface water infiltration into the ground, CO2 sequestration, and hydrocarbon enhanced recovery. Although the drastic effects of deformation of porous media on single-phase fluid flow have been well established, the stress dependency of flow in multiphase systems is not yet fully explored. Here, stress-dependent relative permeability and capillary pressure are studied in a water-wet carbonate specimen both analytically using fractal and poroelasticity theory and experimentally on the micro-scale and macro-scales by means of X-ray computed micro-tomography and isothermal isotropic triaxial core flooding cell, respectively. Our core flooding program using water/N2 phases shows a systematic decrease in the irreducible water saturation and gas relative permeability in response to an increase in effective stress. Intuitively, a leftward shift of the intersection point of water/gas relative permeability curves is interpreted as an increased affinity of the rock to the gas phase. Using a micro-scale proxy model, we identify a leftward shift in pore size distribution and closure of micro-channels to be responsible for the abovementioned observations. These findings prove the crucial impact of effective stress-induced pore deformation on multiphase flow properties of rock, which are missing from the current characterizations of multiphase flow mechanisms in porous media.

scholarly journals A Numerical Study on Gas Flow through Anisotropic Sierpinski Carpet with Slippage Effect

Geofluids ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Shuxia Qiu ◽  
Lipei Zhang ◽  
Zhenhua Tian ◽  
Zhouting Jiang ◽  
Mo Yang ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Gas Flow ◽  
Gas Permeability ◽  
Fractal Model ◽  
Numerical Results ◽  
Pore Scale ◽  
Gas Slippage ◽  
Slippage Effect ◽  
Flow Through

A pore-scale model has been developed to study the gas flow through multiscale porous media based on a two-dimensional self-similar Sierpinski carpet. The permeability tensor with slippage effect is proposed, and the effects of complex configurations on gas permeability have been discussed. The present fractal model has been validated by comparison with theoretical models and available experimental data. The numerical results show that the flow field and permeability of the anisotropic Sierpinski model are different from that of the isotropic model, and the anisotropy of porous media can enhance gas permeability. The gas permeability of porous media increases with the increment of porosity, while it decreases with increased pore fractal dimension under fixed porosity. Furthermore, the gas slippage effect strengthens as the pore fractal dimension decreases. However, the relationship between the gas slippage effect and porosity is a nonmonotonic decreasing function because reduced pore size and enhanced flow resistance may be simultaneously involved with decreasing porosity. The proposed pore-scale fractal model can present insights on characterizing complex and multiscale structures of porous media and understanding gas flow mechanisms. The numerical results may provide useful guidelines for the applications of porous materials in oil and gas engineering, hydraulic engineering, chemical engineering, thermal power engineering, food engineering, etc.

Three-Phase Relative Permeabilities from Displacement Experiments with Full Account for Capillary Pressure

1998 ◽  
Vol 1 (02) ◽  
pp. 92-98 ◽  
Author(s):  
H.M. Helset ◽  
J.E. Nordtvedt ◽  
S.M. Skjaeveland ◽  
G.A. Virnovsky
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Capillary Pressure ◽  
Relative Permeability ◽  
Single Phase ◽  
Flow In Porous Media ◽  
Relative Permeabilities ◽  
The Core ◽  
Three Phase ◽  
Displacement Experiments

Abstract Relative permeabilities are important characteristics of multiphase flow in porous media. Displacement experiments for relative permeabilities are frequently interpreted by the JBN method neglecting capillary pressure. The experiments are therefore conducted at high flooding rates, which tend to be much higher than those experienced during reservoir exploitation. Another disadvantage is that the relative permeabilities only can be determined for the usually small saturation interval outside the shock. We present a method to interpret displacement experiments with the capillary pressure included, using in-situ measurements of saturations and phase pressures. The experiments can then be run at low flow rates, and relative permeabilities can be determined for all saturations. The method is demonstrated by using simulated input data. Finally, experimental scenarios for three-phase displacement experiments are analyzed using experimental three-phase relative permeability data. Introduction Relative permeabilities are important characteristics of multiphase flow in porous media. These quantities arise from a generalization of Darcy's law, originally defined for single phase flow. Relative permeabilities are used as input to simulation studies for predicting the performance of potential strategies for hydrocarbon reservoir exploitation. The relative permeabilities are usually determined from flow experiments performed on core samples. The most direct way to measure the relative permeabilities is by the steady-state method. Each experimental run gives only one point on the relative permeability curve (relative permeability vs. saturation). To make a reasonable determination of the whole curve, the experiment has to be repeated at different flow rate fractions. To cover the saturation plane in a three-phase system, a large number of experiments have to be performed. The method is therefore very time consuming. Relative permeabilities can also be calculated from a displacement experiment. Typically, the core is initially saturated with a single-phase fluid. This phase is then displaced by injecting the other phases into the core. For the two-phase case, Welge showed how to calculate the ratio of the relative permeabilities from a displacement experiment. Efros was the first to calculate individual relative permeabilities from displacement experiments. Later, Johnson et al. presented the calculation procedure in a more rigorous manner, and the method is often referred to as the JBN method. The analysis has also been extended to three phases. In this approach, relative permeabilities are calculated at the outlet end of the core; saturations vs. time at the outlet end is determined from the cumulative volumes produced and time derivatives of the cumulative volumes produced, and relative permeabilities vs. time are calculated from measurements of pressure drop over the core and the time derivative of the pressure drop. Although the JBN method is frequently used for relative permeability determination, it has several drawbacks. The method is based on the Buckley-Leverett theory of multiphase flow in porous media. The main assumption is the neglection of capillary pressure. In homogenous cores capillary effects are most important at the outlet end of the core and over the saturation shock front. To suppress capillary effects, the experiments are performed at a high flow rate. Usually, these rates are significantly higher than those experienced in the underground reservoirs during exploitation.

Well Test Analysis: Wells Producing by Solution Gas Drive

1976 ◽  
Vol 16 (04) ◽  
pp. 196-208 ◽  
Author(s):  
R. Raghavan
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Relative Permeability ◽  
Oil And Gas ◽  
Function Concept ◽  
Permeability Characteristics ◽  
Fluid Properties ◽  
Diffusivity Equation ◽  
Gas Drive ◽  
Solution Gas

Abstract Drawdown and buildup data in a homogeneous, uniform, closed, cylindrical reservoir containing oil and gas and producing by solution gas drive at a constant surface oil rate were investigated. The well was assumed to be located at the center of the reservoir. Gravity effects were not included. Though the reservoir systems studied were assumed to be homogeneous, the effect of a damaged region in the vicinity of the wellbore was examined. Recently, alternate expressions for describing multiphase flow through porous media have been presented. These expressions incorporate changes presented. These expressions incorporate changes in effective permeability and fluid properties (formation volume factor, viscosity, gas solubility) with pressure by means of a pseudopressure function. The validity of applying the pseudopressure-function concept to drawdown and pseudopressure-function concept to drawdown and buildup testing for multiphase-flow situations was investigated. The pseudopressure function for analyzing drawdown behavior is calculated difrerently from that required to analyze buildup data. Consequently, two pseudopressure functions are required for analysis of well behavior in multiphase-flow systems. Dimensionless groups are used to extend the results to other situations having different permeabilities, spacing, reservoir thickness, well permeabilities, spacing, reservoir thickness, well radii, porosity, etc., provided the PVT relations and relative-permeability characteristics are identical to those used in this study. The pseudopressure-function concept used to analyze pseudopressure-function concept used to analyze drawdown and buildup behavior extends the applicability of the results to a wide range of PVT relations and relative-permeability characteristics. Introduction During the past 30 years, more than 300 publications have considered various problems publications have considered various problems pertaining to well behavior. Except for a few (about pertaining to well behavior. Except for a few (about 10), most papers examining transient pressure behavior assume that the fluids in the reservoir obey the diffusivity equation. This implies the use of a single-phase, slightly compressible fluid. The reason for the popularity of this approach is twofold:(1)the ease with which the diffusivity equation can be solved for a wide variety of problems, and(2)the demonstration by some problems, and(2)the demonstration by some workers that, for some multiphase-flow situations, single-phase flow results may be used provided appropriate modifications are made. The necessary modifications are summarized in Ref. 1. The main objective of this study is to present a method for rigorously incorporating changes in fluid properties and relative-permeability effects in the properties and relative-permeability effects in the analysis of pressure data when two phases of oil and gas are flowing. This should enable the engineer to calculate the absolute formation permeability rather than the effective permeability to each of the flowing phases. This method is based on an idea suggested by Fetkovich, who proposed that if an expression similar to the real gas pseudopressure is defined, then equations describing pseudopressure is defined, then equations describing simultaneous flow of oil and gas through porous media may be simplified considerably. The validity of the equations and methods for calculating the pseudopressure function, however, was not presented pseudopressure function, however, was not presented by Fetkovich. LITERATURE REVIEW AND THEORETICAL CONSIDERATIONS General equations of motion describing multiphase flow in porous media have been known since 1936. These equations, and the assumptions involved in deriving them, are discussed thoroughly in the literature and will not be considered here. Equations for two-phase flow were first solved by Muskat and Meres for a few special cases. Evinger and Muskat studied the effect of multiphase flow on the productivity index of a well and examined the steady radial flow of oil and gas in a porous medium. Under conditions of steady radial porous medium. Under conditions of steady radial flow the oil flow rate is given by (1) SPEJ P. 196

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