Effects of Grain Size on Deformation in Porous Media

In this paper, experimental and numerical studies were conducted to differentiate solvent exsolution and liberation processes from different heavy oil–solvent systems in bulk phases and porous media. Experimentally, two series of constant-composition-expansion (CCE) tests in a PVT cell and differential fluid production (DFP) tests in a sandpacked model were performed and compared in the heavy oil–CO2, heavy oil–CH4, and heavy oil–C3H8 systems. The experimental results showed that the solvent exsolution from each heavy oil–solvent system in the porous media occurred at a higher pressure. The measured bubble-nucleation pressures (Pn) of the heavy oil–CO2 system, heavy oil–CH4 system, and heavy oil–C3H8 system in the porous media were 0.24 MPa, 0.90 MPa, and 0.02 MPa higher than those in the bulk phases, respectively. In addition, the nucleation of CH4 bubbles was found to be more instantaneous than that of CO2 or C3H8 bubbles. Numerically, a robust kinetic reaction model in the commercial CMG-STARS module was utilized to simulate the gas exsolution and liberation processes of the CCE and DFP tests. The respective reaction frequency factors for gas exsolution (rffe) and liberation (rffl) were obtained in the numerical simulations. Higher values of rffe were found for the tests in the porous media in comparison with those in the bulk phases, suggesting that the presence of the porous media facilitated the gas exsolution. The magnitudes of rffe for the three different heavy oil–solvent systems followed the order of CO2 > CH4 > C3H8 in the bulk phases and CH4 > CO2 > C3H8 in the porous media. Hence, CO2 was exsolved from the heavy oil most readily in the bulk phases, whereas CH4 was exsolved from the heavy oil most easily in the porous media. Among the three solvents, CH4 was also found most difficult to be liberated from the heavy oil in the DFP test with the lowest rffl of 0.00019 min−1. This study indicates that foamy-oil evolution processes in the heavy oil reservoirs are rather different from those observed from the bulk-phase tests, such as the PVT tests.

Capillary behaviour of multi-phase systems in porous media

Insights on the penetration and migration of chemically cross-linked systems in porous media

Foam flooding is an important pathway for enhanced oil recovery. However, the evaluation of foam properties is usually carried out in free space, which can not accurately reflect the performance of foam in porous oil formation. In the present work, by investigating the foamability and stability of foam systems in sand‐pack models with average pore throat radius from 1.24 μm to 4.28 μm, the effects of porous media on foam properties are studied. Compared with foam systems in free space, foam systems in porous media have longer foam half‐life, longer drainage half‐life, and higher foam comprehensive index. The foam volume of foam systems in porous media could be higher or lower than that in free space, depending on the average pore throat radius of the porous media. Generally, in porous media, with the decreasing of pore throat radius, the foamability of the foam systems gradually decreases while the foam stability gradually increases. Moreover, the bubble size and liquid film thickness also decrease with the decreasing of pore throat radius of the porous media. Above all, the behaviors of foams are significantly affected by porous media. When investigating a foam system to evaluate its performance for foam flooding in oil recovery or other applications in porous media, porous models which could reflect the target conditions should be considered to obtain more trustable results.

The scaling laws as formulated by Rapport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions.Two hypothetical systems - a gas reservoir subject to water drive and the laboratory scaled model of that reservoir - were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these particular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system.This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. Introduction Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models.To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoport and others. Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems.It will be recalled that these scaling laws presuppose three conditions:the relative permeability curves must be identical for the model and prototype;the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; andboundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because:The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media.The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent.Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible.The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible.The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. SPEJ P. 164^

Numerical modeling of in situ gelation of biopolymers in porous media

Accurate determination of gas–fluid miscibility conditions is important to optimize the displacement efficiency during CO2-enhanced oil recovery. This paper presents a new technique to investigate the phase behavior and to estimate the minimum miscibility pressure (MMP) of a CO2/n-decane system using an X-ray computerized tomography (CT) scanner. CT scans of the CO2/n-decane system are taken at various pressures during the experiments. The image intensity values taken from the CT images have a linear relationship with the densities of the measured objects; therefore, we can estimate the miscible point of CO2 and n-decane because the difference between the intensity values for each phase decays to zero as the pressure increases toward the MMP. This paper provides experimental evidence for the validity of the new CT method by comparing the results with previous studies and presents an application of the method to investigate the MMP of the CO2/n-decane system in porous media. Additionally, the influence of porous media on the equilibrium state when the CO2/n-decane system is close to miscibility is discussed.

Analytical solutions of critical oil film thickness of negative spreading coefficient in a capillary corner

The binary complex system was composed of the sulphonate Gemini surfactant and the hydrophobically associating polymer at different ratios. Viscosity and interfacial tension were measured before the core flood experiments. After injecting the binary system at different surfactant/polymer ratios and injection phase, the viscosity, interfacial tension, and concentrations of the polymer and the surfactant in the effluent collected at different positions of the long core were measured. Furthermore, the static and dynamic adsorptions of the system were measured. Finally, the variation law of physicochemical properties of surfactant/polymer binary complex system in porous media was obtained. [Received: November 17, 2015; Accepted: July 17, 2016]

The binary complex system was composed of the sulphonate Gemini surfactant and the hydrophobically associating polymer at different ratios. Viscosity and interfacial tension were measured before the core flood experiments. After injecting the binary system at different surfactant/polymer ratios and injection phase, the viscosity, interfacial tension, and concentrations of the polymer and the surfactant in the effluent collected at different positions of the long core were measured. Furthermore, the static and dynamic adsorptions of the system were measured. Finally, the variation law of physicochemical properties of surfactant/polymer binary complex system in porous media was obtained. [Received: November 17, 2015; Accepted: July 17, 2016]

Coupled meshfree (SPH) and grid based (FDM) procedures for modeling fluid flow through deformable porous media

The modeling of flow and transport in porous media is of the utmost importance in many chemical engineering applications, including catalytic reactors, batteries, and CO2 storage. The aim of this study is to test the use of fully connected (FCNN) and convolutional neural networks (CNN) for the prediction of crucial properties in porous media systems: the permeability and the filtration rate. The data-driven models are trained on a dataset of computational fluid dynamics (CFD) simulations. To this end, the porous media geometries are created in silico by a discrete element method, and a rigorous setup of the CFD simulations is presented. The models trained have as input both geometrical and operating conditions features so that they could find application in multiscale modeling, optimization problems, and in-line control. The average error on the prediction of the permeability is lower than 2.5%, and that on the prediction of the filtration rate is lower than 5% in all the neural networks models. These results are achieved with at least a dataset of ∼100 CFD simulations.

This study simulates the pressure transient behavior of flow of Newtonian/Newtonian and non-Newtonian /Newtonian fluid composite systems in porous media with a finite-conductivity vertical fracture. The main objective of this study is to determine the location of the flood front, reservoir rock and fluid properties and fracture parameters via history matching of the test data. It is assumed that the injected fluid front propagates in the form of an ellipse whose focal length is equivalent to the fracture length, and single-phase flow conditions exist behind and ahead of the flood front. The viscosity of the non-Newtonian fluid in the flooded region was formulated as a function of the average flow rate. Both the injected and the reservoir fluids are treated as being slightly compressible. It is assumed that flow inside the matrix is two-dimensional, and one-dimensional inside the fracture. Two different fluid flow equations, one for the matrix and the other for the fracture, are used to describe the single-phase flow conditions. The equations are coupled through a fluid loss term from the fracture into the matrix and/or from the matrix into the fracture. Four different fluid loss models in three different flow geometries (elliptical, linear and radial) are considered. These two non-linear equations are linearized numerically, and the resulting two systems of linear equations are solved simultaneously using the alternating direction implicit procedure. Extensive testing and validation of this generalized formulation was conducted by using it to study nine special cases previously reported in the literature. A parametric investigation was conducted using dimensionless groups such as non-Newtonian power-law fluid exponent, fracture conductivity, elliptical interface location and mobility and diffusivity ratio. The results indicate that as the power-law index increases, the dimensionless bottomhole pressure increases for a given injection rate. In cases of mobility ratios greater than unity, smaller elliptical interface locations, which represent initial amounts of injected fluid in the reservoir, give greater dimensionless bottomhole pressures, and in cases of mobility ratios less than unity, smaller elliptical interface locations give smaller dimensionless bottomhole pressures. Greater mobility ratios yield greater dimensionless bottomhole pressures; increasing dimensionless fracture conductivities result in decreased bottomhole dimensionless pressures. It is observed that this decrease is not significant for dimensionless conductivities larger than five hundred.

The detailed analogy between flow systems in porous media and thecorresponding potentiometric model systems is developed under conditions whereit may be desirable to take into account variable pay thickness, variableporosity, and permeability, and also the dependence of the fluid density onpressure. It is shown that in such models it is only necessary that theelectrolyte thickness be made everywhere proportional to the millidarcy-feet ofthe formation. In contrast to the iso-vol type model, previously suggested as abasis for the analogy, the porosity does not enter directly in the constructionof the model. It is introduced only in translating the electrical voltagegradient measurements into the equivalent fluid travel times. A discussion ofthis procedure is given. Introduction It is now some 50 years since it was pointed out that on the basis ofDarcy's law Laplace's equation must govern the steady state flow of homogeneousfluids through porous media. It is 16 years since the obvious implication ofthis fact, namely, that such steady state homogeneous flow systems in porousmedia could be simulated by electrical analogies, was first applied to problemsof practical interest with respect to oil production. In these initial studiesmajor emphasis was placed on the use of electrolytic models, made of blottingpaper, to give a direct and graphic history of the fluid particle motion inregular and infinite well networks. However, it was also noted there that thebasic requirement of the model was that it give a potential distributionsimilar to the pressure distribution in the flow system, and that from theelectrical measurement of the potential distribution the fluid particle motioncould be graphically or numerically determined. This was demonstrated byapplication to the fivespot infinite network, for which a conducting metallicsheet was used to establish the equipotential contours. As anticipated, thefluid particle motion computed from these contours agreed well with that givendirectly by the blotting paper model. For irregular well distributions it was found more convenient to useelectrolytic bath analogs rather than metallic sheets. Several investigations, as applied specifically to cycling well patterns, have been reported with thesemodels, which have become known as "potentiometric models." However, the extremely laborious nature of both the electrical measurements by directprobing and the associated interpretive computations retarded the widespreaduse of these procedures. The electrical measurements can be accelerated byusing a four-probe electrode, which provides a means for simultaneouslydetermining the streamline paths along which the fluid particles must move andthe voltage gradients along these paths which are proportional to the fluidvelocities. With the increasing frequency of discovery of condensate pools, asdrilling depths are becoming greater, the applicability of the potentiometricmodel to production problems, and especially to the study of well patterns forcycling, has been given a fresh impetus. T.P. 2490

A mathematical model of the two-phase three-component filtration of the oil–water–supercritical fluid system in a porous medium is developed. The results of numerical simulations of the three-component two-phase filtration during oil displacement by supercritical CO2 from a watered stratum are reported. In the region of oil displacement from watered stratum, there is a significant discrepancy between the experimental and simulation results because of the transient mode of filtration associated with the concurrent saturation of the oil and water with supercritical CO2 under high pressure. In the region of two-phase filtration of the oil–water system and in the region of pumping of three or more pore volumes of supercritical CO2, the deviation of the simulation results from the experimental data does not exceed 10%.