Modeling of multiphase flow in low permeability porous media:Effect of wettability and pore structure properties

Multiphase flow in low permeability porous media is involved in numerous energy and environmental applications.However,a complete description of this process is challenging due to the limited modeling scale and the effects of complex pore structures and wettability.To address this issue,based on the digital rock of low permeability sandstone,a direct numerical simulation is performed considering the interphase drag and boundary slip to clarify the microscopic water-oil displacement process.In addition,a dual-porosity pore network model(PNM)is constructed to obtain the water-oil relative permeability of the sample.The displacement efficiency as a recovery process is assessed under different wetting and pore structure properties.Results show that microscopic displacement mechanisms explain the corresponding macroscopic relative permeability.The injected water breaks through the outlet earlier with a large mass flow,while thick oil films exist in rough hydrophobic surfaces and poorly connected pores.The variation of water-oil relative permeability is significant,and residual oil saturation is high in the oil-wet system.The flooding is extensive,and the residual oil is trapped in complex pore networks for hydrophilic pore surfaces;thus,water relative permeability is lower in the water-wet system.While the displacement efficiency is the worst in mixed-wetting systems for poor water connectivity.Microporosity negatively correlates with invading oil volume fraction due to strong capillary resistance,and a large microporosity corresponds to low residual oil saturation.This work provides insights into the water-oil flow from different modeling perspectives and helps to optimize the development plan for enhanced recovery.

Numerical Approach of a Coupled Pressure-Saturation Model Describing Oil-Water Flow in Porous Media

Two-phase flow in porous media is a very active field of research,due to its important applications in groundwater pollution,CO_(2)sequestration,or oil and gas production from petroleum reservoirs,just to name a few of them.Fractional flow equations,which make use of Darcy's law,for describing the movement of two immiscible fluids in a porous medium,are among the most relevant mathematical models in reservoir simulation.This work aims to solve a fractional flow model formed by an elliptic equation,representing the spatial distribution of the pressure,and a hyperbolic equation describing the space-time evolution of water saturation.The numerical solution of the elliptic part is obtained using a finite-element(FE)scheme,while the hyperbolic equation is solved by means of two dif-ferent numerical approaches,both in the finite-volume(FV)framework.One is based on a monotonic upstream-centered scheme for conservation laws(MUSCL)-Hancock scheme,whereas the other makes use of a weighted essentially non-oscillatory(ENO)reconstruc-tion.In both cases,a first-order centered(FORCE)-αnumerical scheme is applied for inter-cell flux reconstruction,which constitutes a new contribution in the field of fractional flow models describing oil-water movement.A relevant feature of this work is the study of the effect of the parameterαon the numerical solution of the models considered.We also show that,in the FORCE-αmethod,when the parameterαincreases,the errors diminish and the order of accuracy is more properly attained,as verified using a manufactured solution technique.

A Fractal Orifice-Throat Model for Seepage Characteristics of Multiscale Porous Media

The seepage characteristics of multiscale porous media is of considerable significance in many scientific and engineering fields.The Darcy permeability is one of the key macroscopic physical properties to characterize the seepage capacity of porous media.Therefore,based on the statistically fractal scaling law of porous media,fractal geometry is applied to model the multiscale pore structures.And a two-dimensional fractal orifice-throat model with multiscale and tortuous characteristics is proposed for the seepage flow through porous media.The analytical expression for Darcy permeability of porous media is derived,which is validated by comparing with available experimental data.The results show that the Darcy permeability is significantly influenced by porosity,orifice-throat fractal dimension,minimum to maximum diameter ratio,orifice-throat ratio and tortuosity fractal dimension.The present results are helpful for understanding the seepage mechanism of multiscale porous media,and may provide theoretical basis for unconventional oil and gas exploration and development,porous phase transition energy storage composites,CO2 geological sequestration,environmental protection and nuclear waste treatment,etc.

The impact of heterogeneity and pore network characteristics on single and multi-phase fluid propagation in complex porous media:An X-ray computed tomography study

This study investigates the impact of pore network characteristics on fluid flow through complex and heterogeneous porous media,providing insights into the factors affecting fluid propagation in such systems.Specifically,high-resolution or micro X-ray computed tomography(CT)imaging techniques were utilized to examine outcrop stromatolite samples of the Lagoa Salgada,considered flow analogous to the Brazilian Pre-salt carbonate reservoirs.The petrophysical results comprised two distinct stromatolite depositional facies,the columnar and the fine-grained facies.By generating pore network model(PNM),the study quantified the relationship between key features of the porous system,including pore and throat radius,throat length,coordination number,shape factor,and pore volume.The study found that the less dense pore network of the columnar sample is typically characterized by larger pores and wider and longer throats but with a weaker connection of throats to pores.Both facies exhibited less variability in the radius of the pores and throats in comparison to throat length.Additionally,a series of core flooding experiments coupled with medical CT scanning was designed and conducted in the plug samples to assess flow propagation and saturation fields.The study revealed that the heterogeneity and presence of disconnected or dead-end pores significantly impacted the flow patterns and saturation.Two-phase flow patterns and oil saturation distribution reveal a preferential and heterogeneous displacement that mainly swept displaced fluid in some regions of plugs and bypassed it in others.The relation between saturation profiles,porosity profiles,and the number of fluid flow patterns for the samples was evident.Only for the columnar plug sample was the enhancement in recovery factor after shifting to lower salinity water injection(SB)observed.

Anisotropic dynamic permeability model for porous media

Based on the tortuous capillary network model,the relationship between anisotropic permeability and rock normal strain,namely the anisotropic dynamic permeability model(ADPM),was derived and established.The model was verified using pore-scale flow simulation.The uniaxial strain process was calculated and the main factors affecting permeability changes in different directions in the deformation process were analyzed.In the process of uniaxial strain during the exploitation of layered oil and gas reservoirs,the effect of effective surface porosity on the permeability in all directions is consistent.With the decrease of effective surface porosity,the sensitivity of permeability to strain increases.The sensitivity of the permeability perpendicular to the direction of compression to the strain decreases with the increase of the tortuosity,while the sensitivity of the permeability in the direction of compression to the strain increases with the increase of the tortuosity.For layered reservoirs with the same initial tortuosity in all directions,the tortuosity plays a decisive role in the relative relationship between the variations of permeability in all directions during pressure drop.When the tortuosity is less than 1.6,the decrease rate of horizontal permeability is higher than that of vertical permeability,while the opposite is true when the tortuosity is greater than 1.6.This phenomenon cannot be represented by traditional dynamic permeability model.After the verification by experimental data of pore-scale simulation,the new model has high fitting accuracy and can effectively characterize the effects of deformation in different directions on the permeability in all directions.

Enduring effect of permeability texture for enhancing accuracy and reducing uncertainty of reservoir fluid flow through porous media

Modeling reservoir permeability is one of the crucial tasks in reservoir simulation studies.Traditionally,it is done by kriging-based methods.More rigorous modeling of the permeability results in more reliable outputs of the reservoir models.Recently,a new category of geostatistical methods has been used for this purpose,namely multiple point statistics(MPS).By this new category of permeability modeling methods,one is able to predict the heterogeneity of the reservoir permeability as a continuous variable.These methods consider the direction of property variation in addition to the distances of known locations of the property.In this study,the reservoir performance of a modified version of the SPE 10 solution project as a pioneer case is used for investigating the efficiency of these methods and paralleling them with the kriging-based one.In this way,the permeability texture concept is introduced by applying some MPS methods.This study is accomplished in the conditions of real reservoir dimensions and velocities for the whole reservoir life.A continuous training image is used as the input of calculation for the permeability modeling.The results show that the detailed permeability of the reservoir as a continuous variable makes the reservoir simulation show the same fluid front movement and flooding behavior of the reservoir similar to the reference case with the same permeability heterogeneity.Some MPS methods enable the reservoir simulation to reproduce the fluid flow complexities such as bypassing and oil trapping during water flooding similar to the reference case.Accordingly,total oil production is predicted with higher accuracy and lower uncertainty.All studied cases are identical except for the permeability texture.Even histograms and variograms of permeabilities for the studied reservoir are quite similar,but the performance of the reservoir shows that kriging-based method results have slightly less accuracy than some MPS methods.Meanwhile,it results in lower uncertainty in outputs for this water flooding case performance.

Digital image processing of saturation for two-phase flow in planar porous media model

In this paper, the accuracy of estimating stained non-wetting phase saturation using digital image processing is examined, and a novel post-processing approach for calculating threshold is presented. In order to remove the effect of the background noise of images and to enhance the high-frequency component of the original image, image smoothing and image sharpening methods are introduced. Depending on the correct threshold, the image binarization processing is particularly useful for estimating stained non-wetting phase saturation. Calculated saturation data are compared with the measured saturation data during the two-phase flow experiment in an artificial steel planar porous media model. The results show that the calculated saturation data agree with the measured ones. With the help of an artificial steel planar porous media model, digital image processing is an accurate and simple method for obtaining the stained non-wetting phase saturation.

Numerical simulation of two-phase flow in fractured porous media using streamline simulation and IMPES methods and comparing results with a commercial software

Streamline simulation is developed to simulate waterflooding in fractured reservoirs. Conventional reservoir simulation methods for fluid flow simulation in large and complex reservoirs are very costly and time consuming. In streamline method, transport equations are solved on one-dimensional streamlines to reduce the computation time with less memory for simulation. First, pressure equation is solved on an Eulerian grid and streamlines are traced. Defining the "time of flight", saturation equations are mapped and solved on streamlines. Finally, the results are mapped back on Eulerian grid and the process is repeated until the simulation end time. The waterflooding process is considered in a fractured reservoir using the dual porosity model. Afterwards, a computational code is developed to solve the same problem by the IMPES method and the results of streamline simulation are compared to those of the IMPES and a commercial software. Finally, the accuracy and efficiency of streamline simulator for simulation of two-phase flow in fractured reservoirs has been proved.

Linear instability of the electrified free interface between two cylindrical shells of viscoelastic fluids through porous media

In this paper, we have discussed the linear stabil- ity analysis of the electrified surface separating two coaxial Oldroyd-B fluid layers confined between two impermeable rigid cylinders in the presence of both interfacial insoluble surfactant and surface charge through porous media. The case of long waves interfacial stability has been studied. The dispersion relation is solved numerically and hence the ef- fects of various parameters are illustrated graphically. Our results reveal that the influence of the physicochemical pa- rameterβ is to shrink the instability region of the surface and reduce the growth rate of the unstable normal modes. Such important effects of the surfactant on the shape of in- terfacial structures are more sensitive to the variation of the βcorresponding to non-Newtonian fluids-model compared with the Newtonian fluids model. In the case of long wave limit, it is demonstrated that increasing r, has a dual role in- fluence （de-stabilizing effects） depending on the viscosity of the core fluid. It has a destabilizing effect at the large values of the core fluid viscosity coefficient, while this role is ex- changed to a regularly stabilizing influence at small values of such coefficient.

CONJUGATE MODEL FOR HEAT AND MASS TRANSFER OF POROUS WALL IN THE HIGH TEMPERATURE GAS FLOW

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency.

Numerical Calculation of Transient Flow of Polymer Foam in Porous Media

Based on the mathematical model of one dimension transient flow of the polymer foam in porous media, the numerical calculation method of the flow mentioned above by using the finite difference method is given. Through the experiments of one dimension transient flow of HPAM (Hydrolytic Polyacrylamide) foam in the artificial sandstone core, the HPAM foam generation and coalescence coefficient of the mathematical model mentioned above are determined. The profiles of the liquid phase saturation, the pressure drop and the number density of one dimension transient flow of HPAM foam with the dimensionless time in artificial sandstone core are numerically calculated and analyzed by using the numerical calculation method.

A fractal approach to low velocity non-Darcy flow in a low permeability porous medium

In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient （TPG） is also obtained. It is notable that the TPG （J） and permeability （K） of the porous medium analytically exhibit the scaling behavior J ~ K-D＇r/（l＋Or）, where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.

The Construction Method for Solving Radial Flow Problem through the Homogeneous Reservoir

On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.

Research on Well Testing Interpretation of Low Permeability Deformed Dual Medium Reservoir

Considering the influence of quadratic gradient term and medium deformation on the seepage equation, a well testing interpretation model for low permeability and deformation dual medium reservoirs was derived and established. The difference method was used to solve the problem, and pressure and pressure derivative double logarithmic curves were drawn to analyze the seepage law. The research results indicate that the influence of starting pressure gradient and medium deformation on the pressure characteristic curve is mainly manifested in the middle and late stages. The larger the value, the more obvious the upward warping of the pressure and pressure derivative curve;the parameter characterizing the dual medium is the crossflow coefficient. The channeling coefficient determines the time and location of the appearance of the “concave”. The smaller the value, the later the appearance of the “concave”, and the more to the right of the “concave”.

SENSITIVITY COEFFICIENTS OF SINGLE-PHASE FLOW IN LOW-PERMEABILITY HETEROGENEOUS RESERVOIRS

Theoretical equations for computing sensitivity coefficients of wellbore pressures to estimate the reservoir parameters in low-permeability reservoirs conditioning to non-Darcy flow data at low velocity were obtained. It is shown by a lot of numerical calculations that the wellbore pressures are much more sensitive to permeability very near the well than to permeability a few gridblocks away from the well. When an initial pressure gradient existent sensitivity coefficients in the region are closer to the active well than to the observation well. Sensitivity coefficients of observation well at the line between the active well and the observation well are influenced greatly by the initial pressure gradient.

Experimental study and theoretical analysis of fluid resistance in porous media of glass spheres

Porous media have a wide range of applications in production and life, as well as in science and technology. The study of flow resistance in porous media has a great effect on industrial and agricultural production. The flow resistance of fluid flow through a 20-mm glass sphere bed is studied experimentally. It is found that there is a significant deviation between the Ergun equation and the experimental data. A staggered pore-throat model is established to investigate the flow resistance in randomly packed porous media. A hypothesis is made that the particles are staggered in a regular triangle arrangement. An analytical formulation of the flow resistance in random porous media is derived. There are no empirical constants in the formulation and every parameter has a specific physical meaning. The formulation predictions are in good agreement with the experimental data. The deviation is within the range of 25%. This shows that the staggered pore-throat model is reasonable and is expected to be verified by more experiments and extended to other porous media.

Effects of physical parameter range on dimensionless variable sensitivity in water flooding reservoirs

The similarity criterion for water flooding reservoir flows is concerned with in the present paper. When finding out all the dimensionless variables governing this kind of flow, their physical meanings are subsequently elucidated. Then, a numerical approach of sensitivity analysis is adopted to quantify their corresponding dominance degree among the similarity parameters. In this way, we may finally identify major scaling law in different parameter range and demonstrate the respective effects of viscosity, permeability and injection rate.

Experimental investigations on the fluid flow mechanism in porous media of enhanced oil recovery by alkli/surfactant/polymer flooding

The fluid flow mechanism in porous media of enhanced oil recovery by Alkli/ Surfactant/Polymer (ASP) flooding is investigated by measuring production performance, pressure distribution and saturation distribution through installing differential pressure transducers and saturation measuring probes in a physical model of vertical heterogeneous reservoir. The fluid flow variation in porous media is the main reason of enhanced oil recovery of ASP flooding. The pressure field and saturation field are nonlinearly coupled together and the interaction between them results in the fluid flow variation in the reservoir. In a vertical heterogeneous reservoir, the ASP agents initially flow in the high permeability layers because the resistance in the high permeability layer is increased under the physical and chemical action of adsorption, retention and emulsion. ASP flooding displaces out not only the residual oil in the high permeability layer, but also the remaining oil in the low and the middle permeability layers by increasing swept volume and displacing efficiency.

HORIZONTAL WELL PRESSURE ANALYSIS IN BOX-BOUNDED RESERVOIRS

In this paper, solutions to the 3D transient flow mathematical model for horizontal wells in box-rounded reservoirs are presented. The solutions are derived in Laplace transform domain by employing integral transform and point-source superposition. Both efficient computation of pressure responses and practical technology of oil field application mentioned here may be used to interpret the data from unsteady-state horizontal well testing.

低渗砂岩油藏多孔介质特性

以中国石化中原油田W区块低渗砂岩油藏为例,针对目前该区块开发效果逐渐变差,气驱开采发生气窜等问题,以室内实验为基础,结合油层物理、分形理论、渗流机理,利用计算机分形分析软件Frac Lab和Frac Lac分析该区块多孔介质的岩石表面粗糙度、孔隙分布均匀程度和均质性,基于Gaussian分布、Fourier分析工具、幂律定律和最小二乘回归分析等数学基础理论计算出该区块多孔介质的分维数。结果表明:W区块低渗砂岩油藏多孔介质具有分形特征,分维数约为2.58,壁面较粗糙,孔隙内结构复杂,微小孔隙较多,不规则非均质性严重,流动阻力大,且Frac Lab和Frac Lac软件得到的分维数具有较好的一致性。研究结果为低渗砂岩油藏提高采收率、油气渗流规律和多孔介质输运性质的研究提供基础研究支撑,具有重要的现实意义。