Measurement of Two Phase Flow in Porous Medium Using High-resolution Magnetic Resonance Imaging

Measurement of two phase flow in porous medium for sequestration was carried out using high-resolution magnetic resonance imaging (MRI) technique. The porous medium was a packed bed of glass beads. Spin echo multi sequence was used to measure the distribution of CO2 and water in the porous medium. The intensity images show that the fluid distribution is non-uniform due to its viscosity and pore structure of porous medium. The velocity distribution of fluids is calculated from the saturation of water and porosity of porous medium. The experimental results show that fluid velocities vary with time and position. The capillary dispersion rate donated the effects of capillary, which was largest at water saturations of 0.45. The displacement process is different between in BZ-02 and BZ-2. The final water residual saturation depends on permeability and porosity.

Volumetric lattice Boltzmann method for pore-scale mass diffusionadvection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams.To improve absorption efficiency in nuclear waste treatment,a thorough understanding of the diffusion-advection process within porous structures is essential for material design.In this study,we present advancements in the volumetric lattice Boltzmann method(VLBM)for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures.These structures are created using the phase field method(PFM)to precisely control pore architectures.In our VLBM approach,we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function.To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields,we implement graphics processing unit(GPU)parallelization.Validation of the developed model involves examining the flow and diffusion fields in porous structures.Remarkably,good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment(MOOSE),and the concentration field from VLBM and the finite difference method(FDM).Furthermore,we investigate the effects of background flow,species diffusivity,and porosity on the diffusion-advection behavior by varying the background flow velocity,diffusion coefficient,and pore volume fraction,respectively.Notably,all three parameters exert an influence on the diffusion-advection process.Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability,respectively.Conversely,increasing the porosity has a less significant effect,causing a slight slowdown of the diffusion-advection process due to the expanded pore volume.This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures,facilitating the development of porous materials for nuclear waste treatment applications.

Soft Template-Induced Porous Polyvinylidene Fluoride Membrane for Vanadium Flow Batteries

Vanadium flow batteries(VFBs)are considered ideal for grid-sc ale,long-duration energy storage applications owing to their decoupled output power and storage capacity,high safety,efficiency,and long cycle life.However,the widespread adoption of VFB s is hindered by the use of expensive Nafion membranes.Herein,we report a soft template-induced method to develop a porous polyvinylidene fluoride(PVDF)membrane for VFB applications.By incorporating water-soluble and flexible polyethylene glycol(PEG 400)as a soft template,we induced the aggregation of hydrophilic sulfonated poly(ether ether ketone),resulting in phase separation from the hydrophobic PVDF polymer during membrane formation.This process led to the creation of a porous PVDF membrane with controllable morphologies determined by the polyethylene glycol content in the cast solution.The optimized porous PVDF membrane enabled a stable VFB performance for 200 cycles at a current density of 80 mA/cm^(2),and the VFB exhibited a Coulombic efficiency of 95.2%and a voltage efficiency of 87.8%.These findings provide valuable insights for the development of highly stable membranes for VFB applications.

TWO PHASE COMPRESSIBLE FLOW IN POROUS MEDIA

We study the mathematical model of two phase compressible flows through porous media. Under the condition that the compressibility of rock, oil, and water is small, we prove that the initial-boundary value problem of the nonlinear system of equations admits a weak solution.

A Comparison Results of Some Analytical Solutions of Model in Double Phase Flow through Porous Media

In this paper, we consider Variational Iteration Method （VIM） and q-Homotopy Analysis Method （q-HAM） to sotve me partial differential equation resulted from Fingero Imbibition phenomena in double phase flow through porous media. We further compare the results obtained here with the solution obtained in [ 12] using Adomian Decomposition Method. Numerical results are obtained, using Mathematica 9, to show the effectiveness of these methods to our choice of problem especially for suitable values ofh and n.

Pressure/Saturation System for Immiscible Two-Phase Flow: Uniqueness Revisited

We give a sufficient condition for uniqueness for the pressure/saturation system. We establish this condition through analytic arguments, and then construct 'mobilities' (or mobility-like functions) that satisfy the new condition (when the parameter is 2). For the constructed 'mobilities', we do graphical experiments that show, empirically, that this condition could be satisfied for other values of . These empirical experiments indicate that the usual smoothness condition on the fractional flow function (and on the total mobility), for uniqueness and convergence, might not be necessary. This condition is also sufficient for the convergence of a family of perturbed problems to the original pressure/saturation problem.

Velocity Projection with Upwind Scheme Based on the Discontinuous Galerkin Methods for the Two Phase Flow Problem

The upwind scheme is very important in the numerical approximation of some problems such as the convection dominated problem, the two-phase flow problem, and so on. For the fractional flow formulation of the two-phase flow problem, the Penalty Discontinuous Galerkin (PDG) methods combined with the upwind scheme are usually used to solve the phase pressure equation. In this case, unless the upwind scheme is taken into consideration in the velocity reconstruction, the local mass balance cannot hold exactly. In this paper, we present a scheme of velocity reconstruction in some H(div) spaces with considering the upwind scheme totally. Furthermore, the different ways to calculate the nonlinear coefficients may have distinct and significant effects, which have been investigated by some authors. We propose a new algorithm to obtain a more effective and stable approximation of the coefficients under the consideration of the upwind scheme.

Rate transient analysis methods for water-producing gas wells in tight reservoirs with mobile water

Tight gas reservoirs with mobile water exhibit multi-phase flow and high stress sensitivity.Accurately analyzing the reservoir and well parameters using conventional single-phase rate transient analysis methods proves challenging.This study introduces novel rate transient analysis methods incorporating evaluation processes based on the conventional flowing material balance method and the Blasingame type-curve method to examine fractured gas wells producing water.By positing a gas-water two-phase equivalent homogenous phase that considers characteristics of mobile water,gas,and high stress sensitivity,the conventional single-phase rate transient analysis methods can be applied by integrating the phase's characteristics and defining the phase's normalized parameters and material balance pseudotime.The rate transient analysis methods based on the equivalent homogenous phase can be used to quantitatively assess the parameters of wells and gas reservoirs,such as original gas-in-place,fracture half-length,reservoir permeability,and well drainage radius.This facilitates the analysis of production dynamics of fractured wells and well-controlled areas,subsequently aiding in locating residual gas and guiding the configuration of well patterns.The specific evaluation processes are detailed.Additionally,a numerical simulation mechanism model was constructed to verify the reliability of the developed methods.The methods introduced have been successfully implemented in field water-producing gas wells within tight gas reservoirs containing mobile water.

Numerical Study of the Injection of Carbon Dioxide in a Homogeneous Porous Media

This work proposes a locally conservative and less restrictive algorithm to solve the problem dealt with in [1], i.e. a two-phase flow in a homogeneous porous medium (water and CO2), with mass absorption between the fluid phases and reaction between the CO2 phase and the rock. The latter is modeled by two non-linear hyperbolic equations that represent the transport of the flowing phases for a given velocity field (equations of saturation and concentration). From the numerical point of view, we use the operator splitting technique to properly treat the time scale of each physical phenomenon and a high-order non-oscillatory central-scheme finite volume method for nonlinear hyperbolic equations proposed by [2] that was extended for a system of equations with source terms to treat the equations that govern the saturation and concentration of phases. In addition, with respect to source terms, the mass flux between fluid phases was handled using the flash methodology, whereas kinetic theory was applied for reproducing the changes in porosity and permeability that are caused by the reaction of CO2 with the rock. The same physical trends observed in [1] were obtained in our numerical results which indicate a good predictive capability. Furthermore, this method avoids the difficulties that arise when adopting small time steps enforced by CFL stability restrictions. Finally, the results obtained show that the applicability of the KT method is beyond just a single nonlinear conservation law with the absence of source terms.

Initial-boundary value problem of three phase flow in porous media

We study the mathematical model of three phase compressible flows through porous media. Under the condition that the rock, water and oil are incompressible, and the compressibility of gas is small, we present a finite element scheme to the initial-boundary value problem of the nonlinear system of equations, then by the convergence of the scheme we prove that the problem admits a weak solution.

Numerical Analysis of Two-Grid Block-Centered Finite Difference Method for Two-Phase Flow in Porous Medium

In this paper,a two-grid block-centered finite difference method for the incompressible miscible displacement in porous medium is introduced and analyzed,which is to solve a nonlinear equation on coarse mesh space of size H and a linear equation on fine grid of size h.We establish the full discrete two-grid block-centered finite difference scheme on a uniform grid.The error estimates for the pressure,Darcy velocity,concentration variables are derived,which show that the discrete L2 error is O(Dt+h2+H4).Finally,two numerical examples are provided to demonstrate the effectiveness and accuracy of our algorithm.

AN ALGEBRAIC MULTIGRID METHOD FOR COUPLED THERMO-HYDRO-MECHANICAL PROBLEMS

An algebraic multigrid method is developed to solve fully coupled multiphase problem involving heat and mass transfer in deforming porous media. The mathematical model consists of balance equations of mass, linear momentum and energy and of the appropriate constitutive equations. The chosen macroscopic field variables are temperature, capillary pressure, gas pressure and displacement. The gas phase is considered to be an ideal gas composed of dry air and vapour, which are regarded as two miscible species. The model makes further use of a modified effective stress concept together with the capillary pressure relationship. Phase change is taken into account as well as heat transfer though conduction and convection and latent heat transfer (evaporation-condensation). Numerical examples are given to demonstrate the computing efficiency of this method.

An aquifer model with a parameter characterizing the inhomogeneity of media

A fissured aquifer model used in petroleum engineering has been studied by the author. It is found that thefissure-induced inhomogeneity which appeared in reservoir media can be expressed by a delay timeτ whichcharacterizes the process of transition from unsteady to steady seepage flow. Comparison between the fissured aquifer model mentioned above and corresponding homogeneous media is given in this paper. The expression of the characteristic delay timeτis independently derived by using the fissured porous media modeland by solving the characteristic time of an one-dimensioned diffusion equation in turn. The result shows thatthe τ value is in direct proportion to L2. L is the average size of aquifer rock blocks cut by fissures network.The larger the L value, the longer the fissures is and the less the density of fissure is. For identifying the inhomogeneity manifestation of aquifer, a criterion related with the characteristic time of external force action isproposed. In addition, a suggestion on the in-situ measurement of the new aquifer parameter, the 1 value, isgiven.

Adjoint based state estimation of compressible flow in porous media

In this paper,we study the state estimation of compressible single phase flow in compressible porous media.The initial pressure distribution is estimated according to discrete adjoint approach based on the collected well pressure data.The first-order Tykhonov regularization method is used to obtain reasonable estimation.By analyzing the optimality condition of estimation problem,the discrete adjoint state equation and discrete adjoint gradient are derived based on the numerical scheme of the continuous equations.A quasi-Newton numerical optimization method related to adjoint gradient is proposed to solve the estimation problem.The estimation results with different regularization coefficients are compared and analyzed by numerical experiments.The deviation between the estimated pressure obtained without regularization and the real pressure is large.Estimation result with smaller deviation and higher smoothness can be obtained through appropriate regularization coefficient.When the observation error is large,the observed values generated by the estimated pressure fit well with the real pressure.

Modern methods of underground hydromechanics with applications to reservoir engineering

In the report the basic principles of new approach to the study of transport processes in porous medium are represented. The ＂percolation＂ approach has arisen as an attempt to overcome the traditional phenomenological approach in the underground hydromechanics, based on the assumption of continuity of saturated porous media, which does not allow to explain and to model a number of effects arising from the fluids flow in porous media. The results obtained are very interesting not only from the scientific point of view but as the scientific basis for a number of enhanced oil recovery technologies.