Miscible Displacement Research Articles

Multi-Point Flux MFE Decoupled Method for Compressible Miscible Displacement Problem

In this paper, a multi-point flux mixed-finite-element decoupled method was considered for the compressible miscible displacement problem. For this compressible problem, a fully discrete backward Euler scheme was proposed, in which the velocity and pressure equations were decoupled by a multi-point flux MFE method using BDM1 elements combined with a trapezoidal quadrature rule. The concentration equation was handled by a standard FE method. The error analysis for velocity, pressure, and concentration were rigorously derived. Numerical experiments to verify the convergence rates and simulate the miscible displacement problem of a water–oil system were presented.

Impact of gas composition and reservoir heterogeneity on miscible sour gas flooding — A simulation study

Proper handling of the produced sour gas is a big challenge for operating companies due to the serious environmental and technical problems caused by H2S and CO2. The reinjection of the produced sour gas into oil reservoirs is an environmentally friendly as well as an economically attractive method due to the low investment cost and incremental oil recovery. However, the sour gas injection for enhanced oil recovery (EOR) is a relatively new approach with numerous uncovered perspectives, especially in a heterogeneous reservoir. The objective of this study is to investigate the effect of gas composition and reservoir heterogeneity on the miscible displacement of reservoir oil using sour gas.The reservoir oil consisting of 15 mol% H2S and 4 mol% CO2 from an oilfield in the North Caspian region was used. First, the phase behavior alteration of reservoir oil due to the injection of various gases, namely H2S, CO2, CH4, acid, and sour gas was analyzed. Then, the effect of gas type on minimum miscibility pressure (MMP) was investigated based on a semi-analytical tie-line method. Moreover, 2D and 3D numerical simulations were conducted to understand the oil recovery performance of various gas injection options and the effect of permeability heterogeneity on sour gas flooding efficiency. The findings showed that higher H2S content in the injected gas narrows the two-phase envelope and decreases the bubble point pressure. Moreover, it was observed that MMP decreases with increasing H2S concentration, which provides a favorable condition for achieving miscibility. Additionally, an increase in H2S concentration in sour gas improves its oil recovery efficiency by extending gas breakthrough time and elongating the plateau period of oil rate. These results are useful for designing, optimizing, and implementing sour gas injection for EOR in oil reservoirs that have access to sour gas sources.

Emergence of transient reverse fingers during radial displacement of a shear-thickening fluid

A highly sheared dense aqueous suspension of granular cornstarch particles displays rich nonlinear rheology. We had previously demonstrated the growth and onset of interfacial instabilities when shear-thinning cornstarch suspensions were displaced by a Newtonian fluid, and had suggested methods to maximise displacement efficiency [Palak, R. Sathayanath, S. K. Kalpathy and R. Bandyopadhyay, Colloids Surf. A Physicochem. Eng. Asp., 629 (2021) 127405]. In the present work, we explore the miscible displacement of a dense aqueous cornstarch suspension in its discontinuous shear-thickening regime in a quasi-two-dimensional radial Hele-Shaw cell. We systematically study the growth kinetics of the inner interface between water and the cornstarch suspension, and also of the outer interface between the suspension and air. In addition to the growth of interfacial instabilities at the inner interface, we observe a transient withdrawal of the suspension and the formation of fingering instabilities at the outer interface. We demonstrate that these `reverse fingering' instabilities are extremely sensitive to the injection flow rate of water, the gap of the Hele-Shaw cell and the concentration of the displaced cornstarch suspension, {and emerge irrespective of immiscibility between the fluid pair. We believe that as the cornstarch suspension dilates due to the high shear rate imposed by the displacing fluid, the outer suspension-air interface responds with a restoring force, resulting in the penetration of air into the suspension and the formation of reverse fingers. We note that the growth of reverse fingers significantly reduces the displacement efficiency of the suspension. Finally, we demonstrate a correlation in the growth of inner and outer interfacial patterns by computing the velocity with which stresses propagate in the confined dense suspension. Our findings are useful in understanding the flow of granular materials through constrained geometries and can be extended to study stress propagation in shear-thickening materials due to a sudden imposition of high shear rate, such as in impact behaviour.

A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem

A two-grid combined mixed finite element and discontinuous Galerkin method for a compressible miscible displacement problem

Simulation of Microscopic Seepage Characteristics of Interphase Mass Transfer in CO2 Miscible Flooding under Multiphysics Field Coupling Conditions.

CO2 miscible flooding in low permeability reservoirs is conducive to significantly improving oil recovery. At present, the microscopic displacement simulation of CO2 miscible flooding is mainly reflected in the simulation of the seepage process, but the pressure control of the seepage process is lacking, and the simulation of the characterization of CO2 concentration diffusion is less studied. In view of the above problems, a numerical model of CO2 miscible flooding is established, and the microscopic seepage characteristics of interphase mass transfer in CO2 miscible flooding are analyzed by multiphysics field coupling simulations at the two-dimensional pore scale. The injection velocity, contact angle, diffusion coefficient, and initial injection concentration are selected to analyze their effects on the microscopic seepage characteristics of CO2 miscible flooding and the concentration distribution in the process of CO2 diffusion. The research shows that after injection into the model, CO2 preferentially diffuses into the large pore space and forms a miscible area with crude oil through interphase mass transfer, and the miscible area expands continuously and is pushed to the outlet by the high CO2 concentration area. The increase in injection velocity will accelerate the seepage process of CO2 miscible displacement, which will increase the sweep area at the same time. The increase in contact angle increases the seepage resistance of CO2 and weakens the interphase mass transfer with crude oil, resulting in a gradual decrease in the final recovery efficiency. When the diffusion coefficient increases, the CO2 concentration in the small pores and the parts that are difficult to reach at the model edge will gradually increase. The larger the initial injection concentration is, the larger the CO2 concentration in the large pore and miscible areas in the sweep region at the same time. This study has guiding significance for the field to further understand the microscopic seepage characteristics of CO2 miscible flooding under the effect of interphase mass transfer.

Effect of sinusoidal injection velocity on miscible viscous fingering of a finite sample: Nonlinear simulation

The effect of a sinusoidal injection on the fingering instability in a miscible displacement in the application of liquid chromatography, pollutant contamination in aquifers, etc., is investigated. The injection velocity, U(t) is characterized by its amplitude of Γ and time-period of T. The solute transport, flow in porous media, and mass conservation in a two-dimensional porous media is modeled by the convection-diffusion equation, Darcy's equation, and the continuity equation, respectively. The numerical simulation is performed in COMSOL Multiphysics utilizing a finite-element based approach. The fingering dynamics for various time-period have been studied for two scenarios namely, injection-extraction (Γ>1) and extraction-injection (Γ<−1). The onset of fingers and vigorous mixing is observed for Γ>1, whereas for Γ<−1, the onset gets delayed. The viscosity contrast between the sample and the surrounding fluid is characterized by the log-mobility ratio R. When R>0 the rare interface becomes unstable, while for R<0 the frontal interface deformed. In the case of R<0, the extraction-injection process attenuates the fingering dynamics, which is beneficial in chromatographic separations or pollutant dispersion in underground aquifers. The injection-extraction process is observed to have a longer mixing length, indicating early interaction between both interfaces. The degree of mixing χ(t) is more pronounced for injection-extraction scenario and least for extraction-injection R<0,Γ=−2. The average convective forces are more dominant for Γ>1,R=2 till the deformed rare interface interact with diffusive frontal interface. The average diffusive forces are significant for Γ<−1,R=−2 which can be helpful in separation of chemicals in chromatography. This study therefore provided new insights into the role of alternate injection-extraction injections in altering the fingering dynamics of the miscible sample.

Numerical simulations of miscible displacement in an inclined channel by lattice Boltzmann method

The interfacial instability between miscible fluids in a channel is determined by many factors, such as viscosity contrast and the inclination angle. Considering the effect of the gravity field, we investigate the displacement phenomenon between two miscible fluids with different viscosities in an inclined channel. The results show that when the concentration Rayleigh number RaC&amp;lt;105, the inclination angle θ ranges from 0° to 90°, and the natural logarithm of the viscosity ratio R &amp;gt; 0; there are three fluid–fluid interfacial instability regions, namely, viscous fingering, “Kelvin–Helmholtz” (K–H) instability, and “Rayleigh–Taylor” (R–T) instability. A scaling analysis is developed to describe the time evolution of the displacement as described by the displacement efficiency at a fixed viscous ratio. Our analysis indicates that in the viscous fingering region, the time evolution of the displacement efficiency gradually increases with t scaling due to fingering formations; in the K–H and R–T regions, the displacement efficiency rapidly increases with t1+RaC/106. When considering the effect of the viscosity ratio in the K–H instability region, the displacement efficiency scales as η∼t1+RaC/106R0.1. In addition, when the inclination angle is negative or R &amp;lt; 0, the instability phenomenon is not obvious, and the displacement efficiency decreases as the inclination angle or R decreases.

Simulation of Nonlinear Viscous Fingering in a Reactive Flow Displacement: A Multifractal Approach

fractal analysis of viscous fingering of a reactive miscible flow displacement in homogeneous porous media is investigated and multifractal spectrum, and fractal dimension are introduced as two essential features to characterize the irregularity of finger patterns. The Reaction of the two reactant fluids generates a miscible chemical product C in the contact zone. Considering the similarity between chemical products and coastline, monofractal and multifractal analyzes are performed. In monofractal analysis, the box-counting method is implemented on binary images and in multifractal analysis, due to the image processing; the fractal characteristics of viscous fingering instability are analyzed by means of fractal quantities such as Holder exponent, multifractal spectrum, f (α)-image and fractal dimension dynamics. Fractal analysis shows that the fractal dimension increases with time. Also, by considering five different nonlinear simulations, the results show that in the case both sides of the chemical product C are unstable, the multifractal spectrum curve has the highest peak, which means the more complex finger patterns lead to more values of fractal dimension. In addition, a comparison between different values of Ar is conducted and the results show similar behavior. However, small value of aspect ratio leads to a broader width of the multifractal spectrum curve. Furthermore, f (α)-images of concentration contour were investigated for different precisions and some undetectable finger patterns were observed in these images. It can be concluded that the use of f (α)-image represents more detailed image than concentration contours.

A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem

A multipoint flux mixed finite element method with mass-conservative characteristic finite element method for incompressible miscible displacement problem

Interfacial Dynamics of Miscible Displacement of Shear-Thinning Fluid in a Vertical Channel

The displacement of a shear-thinning fluid by a denser and less viscous Newtonian fluid in a vertical duct is investigated using experiments and numerical simulations. We study how shear-thinning and increased viscosity contrast between the fluids affect the displacement. Our results show that the degree of shear-thinning significantly influences the development of interfacial patterns and the growth of perturbations. In the weakly shear-thinning regime, the displacement progresses as a stable displacement with no visible instabilities. Increasing the viscosity of the displaced fluids result in a Saffman–Taylor type instability with several finger-shaped channels carved across the width of the duct. In the strongly shear-thinning regime, a unique viscous finger with an uneven interface is formed in the middle of the displaced fluid. This finger eventually breaks through at the outlet, leaving behind considerably stagnant wall layers at the duct side walls. We link the onset of viscous fingering instability to the viscosity contrast between the fluids, and the stabilizing density difference, as expressed through a modified, unperturbed pressure gradient for the two fluids. Numerical simulations are performed with both an initial flat interface, and with a perturbed interface, and we find good qualitative agreement between experimental observations and computations.

A two‐grid discontinuous Galerkin method for an incompressible miscible displacement problem

AbstractAn incompressible miscible displacement problem in porous media is studied. A two‐grid algorithm based on an interior penalty discontinuous Galerkin method is proposed. With this algorithm, solving a nonlinear system on the discontinuous finite element space is reduced to solving a nonlinear problem on a coarse grid and a linear problem on a fine grid. The error estimate for the concentration in H1‐norm and the error estimate for the velocity in L2‐norm are obtained. The numerical experiments are provided to confirm our theoretical analysis.

Novel Way to Predict the MMP of a CO2–Oil System Using Stacking Models

CO2-enhanced oil recovery (EOR) is an important development method for the third oil recovery stage, which occupies a certain position in carbon capture, utilization, and storage (CCUS). CO2–EOR has two kinds of displacement states in the reservoir, namely, miscible displacement and immiscible displacement, and the recovery of miscibility is far better than that of immiscible flooding. Minimum miscible pressure (MMP) plays a crucial role in whether the CO2–oil system can achieve miscibility, so accurate MMP prediction is required to formulate the reservoir development plan. Traditional methods such as slim tube experiments are expensive and time-consuming. Empirical formulas perform slightly inferiorly in terms of accuracy and range of use. In recent years, machine learning, which uses more, has improved in accuracy, but the performance of this prediction still needs to be further optimized. The work used a stacking approach, one of the ensemble models, to filter and fuse several basic machine learning models to further improve the regression effect of MMP data. First, the correlation analysis and variance inflation factor of the MMP data in the dataset are carried out, and the redundant data are excluded for the correlation and collinearity problems. A total of 147 pretreated MMP data were then regressed using 7 baseline models, whose results were preliminarily screened and combined with empirical formula data to form a new dataset. After that, the final output result is obtained through a stacking model and evaluated. In addition to fitting curves, the results of the Stacking model demonstrate the improvement of the stacking model in MMP prediction from three aspects: mean absolute error (MAE), root-mean-square error (RMSE), and decision coefficient (R2).

The weak Galerkin method for the miscible displacement of incompressible fluids in porous media on polygonal mesh

In this paper, we develop a robust weak Galerkin discretization for the incompressible miscible displacement problem in porous media, which is a nonlinear time-dependent system. The scheme we constructed is positive definite and flexible by arbitrarily shaped polygonal mesh without imposing extra conditions on the stabilization. The other feature of our method is that there is no limitation on the ratio of time-step and spatial mesh size. Error estimates are derived for concentration and pressure in the L2 norm and energy norm, respectively. Extensive numerical experiments, including realistic test cases, have been conducted to verify our theoretical results and the efficiency of the method.

Dynamic Criteria for Physical Modeling of Oil Displacement by Gas Injection

In this work, slim tube displacement tests for minimum miscibility pressure MMP were carried out. Based on the displacement data, the MMP was calculated by statistical regression using linear and quadratic extrapolation with threshold values of 90% and 95% oil recovery as well as the intersection of trend lines for immiscible and miscible displacement regimes. The obtained data show a significant variation in the range of MMP values depending on the calculation method. To clarify the MMP value, an analysis of displacement dynamics was carried out. The ratio of the volume flow rate of reservoir oil to the volume flow rate of the injected gas—flow rates ratio (FFR)—was used as a new parameter. The MMP value calculated from the FRR value extrapolation was determined as 37.09 MPa. According to the results obtained, the proposed methodology based on the displacement dynamics can be useful as a criterion for clarifying the MMP value in slim tube displacement experiments.

A case study of the Severo-Danilovskoye field on experimental and numerical determination of miscibility parameters when justifying gas injection

Miscibility largely determines the performance of gas injection. Miscible displacement allows achieving maximum effect. The minimum miscibility pressure (MMP) is a key parameter, which is determined when justifying a gas injection project. For the conditions of East Siberian reservoirs, the accuracy of correlation equations is 10-50 %, and A. M. Maklavani, H. M. Sebastian, and M. Dong equations demonstrate the most accurate values. The equation of state matched to the results of routine studies evaluates the MMP with an error of up to 30 %. Additional data from special studies (swell test) increased the estimating accuracy by up to 10 %. An express laboratory method for measuring the miscibility parameter (a method of vanishing interfacial tension) showed high accuracy of MMP estimate. The method also allows describing the process of changing the interfacial tension with increasing pressure or changing the gas composition, and complements the process of adjusting the equation of state when setting up a slim tube experiment.

Displacement efficiency and storage characteristics of CO2 in low permeability reservoirs: An experimental work

Over the past decades, CO2 flooding in low-permeability porous media has continued to grow. Furthermore, propelled by the current movement toward CO2 sequestration, the flooding of CO2 is expected to further increase. Thus, it is of scientific significance to study the mechanism of displacement of CO2 flooding as well as the CO2 storage characteristics. In this study, CO2 miscible/immiscible flooding experiments were conducted on two low permeability samples to study the difference between them. Specifically, the effect of oil displacement and CO2 storage coefficient for different displacement models were measured and compared. In addition, nuclear magnetic resonance (NMR) tests and frozen pelleting experiments were conducted. The NMR tests clarified the lower limit of pore throat where oil can be displaced by CO2 miscible/immiscible flooding. Furthermore, the frozen pelleting experiments analyzed the distribution characteristics of the remaining oil before and after CO2 miscible/immiscible flooding. The investigation showed that the development efficiency of CO2 miscible flooding is higher than CO2 immiscible flooding in low permeability reservoirs. The results also indicated that CO2 miscible flooding increases the recovery of hard-to-produce semi-bound oil phase and CO2 storage coefficient with CO2 miscible displacement is more significant than that with CO2 immiscible flooding. The data from this study is a critical input for reservoir simulation, which sheds light on the CO2 miscible/immiscible flooding in low permeability reservoirs.

Sign-preserving second-order IMPEC time discretization and its application in compressible miscible displacement with Darcy-Forchheimer models

In this paper, we construct sign-preserving second-order IMplicit Pressure Explicit Concentration (IMPEC) time methods for generalized coupled non-Darcy flow and transport problems in petroleum engineering, extending the algorithm given in [10] which is only applicable to Darcy flows. We use interior penalty discontinuous Galerkin (IPDG) methods for spatial discretization, and develop bound-preserving technique to obtain physically relevant numerical approximations. The sign-preserving second-order IMPEC method is an important innovation. The method is based on the framework of the second-order strong-stability-preserving Runge-Kutta (SSP-RK2) method. The basic idea is to treat the pressure equation implicitly and the concentration equation explicitly so as to obtain a first-order time integration. Then we introduce a correction stage to compensate the accuracy, maintaining the physical bounds of the numerical cell averages. Unfortunately, the above algorithm is not applicable to non-Darcy problems. There are two main difficulties. Firstly, since the velocity equation is nonlinear and time-independent, all variables in the equation must be calculated at the same time level. However, the treatment in [10] will yield an extremely complicated algorithm and significantly large computational cost, and some iterations whose convergence may not be available if the solutions are not smooth. In our scheme, we linearize the velocity equation and the numerical solutions are not at the same time level, leading to first-order accurate solutions. Therefore, we adopt a completely different approach from [10] to derive the correction stage, keeping the physical bounds of the numerical solutions. Secondly, though with the new correction stage, it is still not easy to solve velocity equations in some stages. In this paper, we construct a direct solver for the velocity equation to save computational cost. Numerical experiments will be given to demonstrate that the improved sign-preserving second-order IMPEC scheme can reduce the computational cost significantly compared with explicit schemes if the diffusion coefficient D is small in the concentration equation. The proposed method also yields much larger CFL number compared with first-order IMPEC schemes. Moreover, the effectiveness of the bound-preserving technique will also be verified.

Modeling the competitive sorption and transport of Ni(II) and Zn(II) in soils: Comparing two multicomponent approaches

The mobility of contaminants in soil is controlled by sorption reactions which can be affected by the presence of other solutes that compete for sorption sites. The ability to model such effects is necessary for evaluating the environmental risk of a given contaminant. In this study, the competitive sorption and transport of nickel (Ni) and zinc (Zn) in Olivier and Windsor soils was investigated using batch equilibration and miscible displacement experiments. During batch experiments, the sorption of Ni and Zn was mutually reduced in multicomponent systems, indicating that the metal cations compete for sorption sites. When applied concurrently, the retardation of both ions decreased and peak effluent concentrations increased relative to single ion experiments, demonstrating that competition increased the mobility of both ions during miscible displacement experiments. A novel Freundlich-type multicomponent isotherm (CDI) and its kinetic analog (CDIT) were developed and compared to the commonly used SRS isotherm and SRS-based kinetic approach (SRST) in describing the experimental data. The CDI provided a superior description of the competitive batch data, especially at low surface coverage, and may therefore be more applicable to multicomponent sorption than the SRS. The Olivier and Windsor transport data were best described by the CDIT and SRST, respectively, however, both models generally described the data well. Since both approaches gave comparable descriptions of the transport data while the CDI outperformed the SRS in describing the batch data, the CDI/CDIT may be more generally applicable to multicomponent systems and warrants further study.

MD-CFD simulation on the miscible displacement process of hydrocarbon gas flooding under deep reservoir conditions

In this study, the microscopic miscible mechanism and the macroscopic flow characteristics of hydrocarbon gas and crude oil are investigated by combining molecular dynamic (MD) simulation and computational fluid dynamics (CFD) simulation. Under the deep reservoir conditions, the MD results manifest that compared with water flooding, hydrocarbon gas flooding could be more miscible with oil molecules, due to their stronger interactions. Based on the calculated density, viscosity and diffusion coefficient by the MD method, the CFD model is constructed to study the miscible displacement process of hydrocarbon gas flooding at 413 K and 50 MPa. The CFD results illustrate that the ability of oil displacement of different injection mediums follows the order of methane > ethane > propane > water. Because of the oil-gas miscibility, hydrocarbon gas could weaken the negative effect of the porosity and the wettability, leading to the decrease of the residual oil (RO) content. Moreover, the multi-component injection method is proposed for multi-scale porous media including nano-pore and micron-pore with small pore size. Notably, the variable velocity injection method is firstly designed for enhanced oil recovery. Compared with the constant low-velocity method, the RO content and the injection time of this method are effectively reduced by 12.4% and 66.7%, respectively.

Pore-scale phenomena in carbon geological storage (Saline aquifers—Mineralization—Depleted oil reservoirs)

The injection of CO2 into geological formations triggers inherently coupled thermo-hydro-chemo-mechanical processes. The reservoir pressure and temperature determine the CO2 density, the CO2-water interfacial tension, and the solubility of CO2 in water (hindered by salts and competing gases). The CO2-water interface experiences marked pinning onto mineral surfaces, and contact angles can range from the asymptotic advancing to receding values, in contrast to the single contact angle predicted by Young’s equation. CO2 dissolves in water to form carbonic acid and the acidified water dissolves minerals; mineral dissolution enhances porosity and permeability, triggers settlement, may couple with advection to form “wormholes”, produces stress changes and may cause block sliding and shear bands. Convective currents can emerge beneath the CO2 plume and sustain CO2 and mineral dissolution processes. On the other hand, mineralization is a self-homogenizing process in advective regimes. The crystallization pressure can exceed the tensile capacity of the host rock and create new surfaces or form grain-displacive lenses. Within the rock matrix, coupled reactive-diffusion-precipitation results in periodic precipitation bands. Adequate seal rocks for CO2 geological storage must be able to sustain the excess capillary pressure in the buoyant CO2 plume without experiencing open-mode discontinuities or weakening physico-chemical interactions. CO2 injection into depleted oil reservoirs benefits from time-proven seals; in addition, CO2 can mobilize residual oil to simultaneously recover additional oil through oil swelling, ganglia destabilization, the reduction in oil viscosity and even miscible displacement. Rapid CO2 depressurization near the injection well causes cooling under most anticipated reservoir conditions; cooling can trigger hydrate and ice formation, and reduce permeability. In some cases, effective stress changes associated with the injection pressure and cooling thermoelasticity can reactivate fractures. All forms of carbon geological storage will require large reservoir volumes to hold a meaningful fraction of the CO2 that will be emitted during the energy transition.