Implicit Pressure Explicit Saturation Method Research Articles

Numerical investigation of gas and sand production from hydrate-bearing sediments by incorporating sand migration based on IMPES method

Accurately predicting gas and sand production from oceanic gas hydrate reservoirs considering multi-field coupling effects is crucial. To address this, we first systematically summarized the multi-field coupling effect of gas hydrate-bearing sediments (GHBS) during sand production and gas production. After that, we developed a thermo-hydro-mechanical coupled model that incorporates both sand detachment and sand migration (THMS) to describe the complex behaviors of fluid and solid flow. We then solved this model using the implicit pressure-explicit saturation (IMPES) method and incremental scheme for a cylindrical core and presented a detailed algorithm derivation process for reproducibility. The newly developed model was validated through comparison with available experimental data. Subsequently, several parameter effects, including outlet pressure, initial hydrate saturation, load stress, and sand detachable ratio, on the behaviors of fluid and solid flow were studied. The computation results indicate that high sand production can be induced by low outlet pressure, high initial hydrate saturation, high load stress, and high sand detachable ratio. Meanwhile, high cumulative gas production can be caused by low outlet pressure, low initial hydrate saturation, high load stress, and high sand detachable ratio.

An adaptive time stepping algorithm for IMPES with high order polynomial extrapolation

Two-phase flows in oil reservoirs can be modeled by a coupled system of elliptic and hyperbolic partial differential equations. The transport velocity of the multiphase fluid system is related to the pressure through Darcy’s law and it is coupled to a conservation law for the saturation variable of one of the phases. A time step of the classical IMPES (IMplicit Pressure Explicit Saturation) method consists of first solving the elliptic problem for pressure and Darcy velocity, and then updating the saturation with an explicit numerical scheme for conservation laws. This method is very computationally costly, since the time-consuming elliptic solver must be invoked at time intervals defined by the stability limit of the hyperbolic solver. A popular variant is not to update the velocity at all hyperbolic time steps, but to skip a fixed number C of them, with C determined by the user. In this work we propose a more accurate and systematic procedure for time stepping in IMPES codes. The velocity is updated at all transport time steps, though the elliptic solver is only invoked every C steps. In the time steps at which the elliptic problem is not solved, the velocity is extrapolated from previously computed values with polynomials of high degree. Further, we introduce an error estimator that allows for the number C to be adaptively determined without user intervention. The algorithm was tested in several relevant benchmark problems. This allowed for the optimization of its parameters and comparisons with previous variants. The results show that the proposed algorithm is very stable, reliable and time-cost effective. It is also easily implemented in pre-existent IMPES codes.

Application of Implicit Pressure-Explicit Saturation Method to Predict Filtrated Mud Saturation Impact on the Hydrocarbon Reservoirs Formation Damage

Hydrocarbon reservoirs’ formation damage is one of the essential issues in petroleum industries that is caused by drilling and production operations and completion procedures. Ineffective implementation of drilling fluid during the drilling operations led to large volumes of filtrated mud penetrating into the reservoir formation. Therefore, pore throats and spaces would be filled, and hydrocarbon mobilization reduced due to the porosity and permeability reduction. In this paper, a developed model was proposed to predict the filtrated mud saturation impact on the formation damage. First, the physics of the fluids were examined, and the governing equations were defined by the combination of general mass transfer equations. The drilling mud penetration in the core on the one direction and the removal of oil from the core, in the other direction, requires the simultaneous dissolution of water and oil flow. As both fluids enter and exit from the same core, it is necessary to derive the equations of drilling mud and oil flow in a one-dimensional process. Finally, due to the complexity of mass balance and fluid flow equations in porous media, the implicit pressure-explicit saturation method was used to solve the equations simultaneously. Four crucial parameters of oil viscosity, water saturation, permeability, and porosity were sensitivity-analyzed in this model to predict the filtrated mud saturation. According to the results of the sensitivity analysis for the crucial parameters, at a lower porosity (porosity = 0.2), permeability (permeability = 2 mD), and water saturation (saturation = 0.1), the filtrated mud saturation had decreased. This resulted in the lower capillary forces, which were induced to penetrate the drilling fluid to the formation. Therefore, formation damage reduced at lower porosity, permeability and water saturation. Furthermore, at higher oil viscosities, due to the increased mobilization of oil through the porous media, filtrated mud saturation penetration through the core length would be increased slightly. Consequently, at the oil viscosity of 3 cP, the decrease rate of filtrated mud saturation is slower than other oil viscosities which indicated increased invasion of filtrated mud into the formation.

Thermodynamically consistent modeling of two-phase incompressible flows in heterogeneous and fractured media

Numerical modeling of two-phase flows in heterogeneous and fractured media is of great interest in petroleum reservoir engineering. The classical model for two-phase flows in porous media is not completely thermodynamically consistent since the energy reconstructed from the capillary pressure does not involve the ideal fluid energy of both phases and attraction effect between two phases. On the other hand, the saturation may be discontinuous in heterogeneous and fractured media, and thus the saturation gradient may be not well defined. Consequently, the classical phase-field models can not be applied due to the use of diffuse interfaces. In this paper, we propose a new thermodynamically consistent energy-based model for two-phase flows in heterogeneous and fractured media, which is free of the gradient energy. Meanwhile, the model inherits the key features of the traditional models of two-phase flows in porous media, including relative permeability, volumetric phase velocity and capillarity effect. To characterize the capillarity effect, a logarithmic energy potential is proposed as the free energy function, which is more realistic than the commonly used double well potential. The model combines with the discrete fracture model to describe two-phase flows in fractured media. The popularly used implicit pressure explicit saturation method is used to simulate the model. Finally, the experimental verification of the model and numerical simulation results are provided.

On the efficiency of the IMPES method for two phase flow problems in porous media

In this work, we show a method to efficiently solve the multiphase flow through a porous media in the near wellbore region. The numerical discretisation is based on the IMplicit Pressure Explicit Saturation (IMPES) approach.While most of the works in the literature rely on Fully Implicit Methods (FIM) to simulate the reservoir, this is not suited for the near wellbore region, where smaller computational and physical times are required, therefore parametric models with history matching are used in this zone. However, parametric models present several uncertainties that can affect the estimation of the pressure drop. An accurate and fast simulation of that region is therefore required.Here, we propose a new and robust implementation of the IMPES scheme, aiming to reduce the large computational cost of the (implicit) pressure system of equations and increase the robustness and reliability of the scheme. The method takes advantage of the short physical time steps between iterations, observed in the near wellbore region, to produce a new pressure field at the cost of a numerical explicit scheme. Two and three dimensional numerical experiments are carried out to show the validity of the proposed discretisation. We show that the cost of the method is reduced in a factor of 7–19 when compared to the classical IMPES.

Benchmark of different CFL conditions for IMPES

The IMplicit Pressure Explicit Saturation (IMPES) method is a prevalent way to simulate multiphase flows in porous media. The numerical stability of this sequential method implies limitations on the time step, which may depend on the flow regime studied. In this note, three stability criteria related to the IMPES method, that differ in their construction on the observed variables, are compared on homogeneous and heterogeneous configurations for different two-phase flow regimes (viscous/capillary/gravitational). This highlights that there is no single optimal criterion always ensuring stability and efficiency. For capillary dominated flows, the Todd's condition is the most efficient one, while the standard Coat condition should be preferred for viscous flows. When gravity effects are present, Coat's condition must be restricted, but remains more efficient than the Todd's condition.

A novel discontinuous Galerkin model for two-phase flow in porous media using an improved IMPES method

Purpose– The purpose of this paper is to present an efficient improved version of Implicit Pressure-Explicit Saturation (IMPES) method for the solution of incompressible two-phase flow model based on the discontinuous Galerkin (DG) numerical scheme.Design/methodology/approach– The governing equations, based on the wetting-phase pressure-saturation formulation, are discretized using various primal DG schemes. The authors use H(div) velocity reconstruction in Raviart-Thomas space (RT_0 and RT_1), the weighted average formulation, and the scaled penalties to improve the spatial discretization. It uses a new improved IMPES approach, by using the second-order explicit Total Variation Diminishing Runge-Kutta (TVD-RK) as temporal discretization of the saturation equation. The main purpose of this time stepping technique is to speed up computation without losing accuracy, thus to increase the efficiency of the method.Findings– Utilizing pressure internal interpolation technique in the improved IMPES scheme can reduce CPU time. Combining the TVD property with a strong multi-dimensional slope limiter namely, modified Chavent-Jaffre leads to a non-oscillatory scheme even in coarse grids and highly heterogeneous porous media.Research limitations/implications– The presented locally conservative scheme can be applied only in 2D incompressible two-phase flow modeling in non-deformable porous media. In addition, the capillary pressure discontinuity between two adjacent rock types assumed to be negligible.Practical implications– The proposed numerical scheme can be efficiently used to model the incompressible two-phase flow in secondary recovery of petroleum reservoirs and tracing immiscible contamination in aquifers.Originality/value– The paper describes a novel version of the DG two-phase flow which illustrates the effects of improvements in special discretization. Also the new improved IMPES approach used reduces the computation time. The non-oscillatory scheme is an efficient algorithm as it maintains accuracy and saves computation time.

An open-source toolbox for multiphase flow in porous media

Multiphase flow in porous media provides a wide range of applications: from the environmental understanding (aquifer, site-pollution) to industrial process improvements (oil production, waste management). Modeling of such flows involves specific volume-averaged equations and therefore specific computational fluid dynamics (CFD) tools. In this work, we develop a toolbox for modeling multiphase flow in porous media with OpenFOAM®, an open-source platform for CFD. The underlying idea of this approach is to provide an easily adaptable tool that can be used in further studies to test new mathematical models or numerical methods. The package provides the most common effective properties models of the literature (relative permeability, capillary pressure) and specific boundary conditions related to porous media flows. To validate this package, solvers based on the IMplicit Pressure Explicit Saturation (IMPES) method are developed in the toolbox. The numerical validation is performed by comparison with analytical solutions on academic cases. Then, a satisfactory parallel efficiency of the solver is shown on a more complex configuration. Program summaryProgram title: porousMultiphaseFoamCatalogue identifier: AEUR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public LicenseNo. of lines in distributed program, including test data, etc.: 36355No. of bytes in distributed program, including test data, etc.: 1106569Distribution format: tar.gzProgramming language: C++.Computer: Any x86.Operating system: Generic Linux.Classification: 12.External routines: OpenFOAM® (version 2.0 and superior)Nature of problem:This software solves multiphase flow in porous media.Solution method:The numerical approach is based on the finite-volume method (FVM). Mass conservation equations for each fluid phase are reformulated into a pressure–saturation system. The generalized Darcy’s law is used to compute phase velocities in the porous medium. The pressure–saturation is solved using a segregated method based on the IMPES method. Parallel computing can be performed using the standard domain decomposition method of OpenFOAM®.Running time:The Buckley–Leverett examples provided only take a few seconds to run.

A control volume finite element method for adaptive mesh simulation of flow in heap leaching

Accurate determination of fluid flow within heap leaching is crucial for understanding and improving performance of the process. Numerical methods have the potential to assist by modelling the process and studying the transport phenomena within the porous medium. This paper presents an adaptive mesh numerical scheme to solve for unsaturated incompressible flow in porous media with applications to heap leaching. The governing equations are Darcy’s law and the conservation of mass. An implicit pressure explicit saturation method is used to decouple the pressure and saturation equations. Pressure is discretized using a control volume (CV) finite element method, while for saturation a node-centred CV method is employed. The scheme is equipped with dynamic anisotropic mesh adaptivity to update the mesh resolution as the leaching solution infiltrates through the heap. This allows for high-fidelity modelling of multiscale features within the flow. The method is verified against the Buckley–Leverett problem where a quasi-analytical solution is available. It is applied for two-phase flow of air and leaching solution in a simplified two-dimensional heap geometry. We compare the accuracy and CPU efficiency of an adaptive mesh against a static mesh and demonstrate the potential to achieve high spatial accuracy at low computational cost through the use of anisotropic mesh adaptivity.

NUMERICAL SIMULATION OF A NATURALLY FRACTURED RESERVOIR.

This research is concerned with the development of a numerical model for stratified normally fractured reservoirs. Three dimensional three phase flow black oil simulation model is adopted. The dual porosity-dual permeability model is used. The IMPES (Implicit Pressure Explicit Saturation) method is used to solve the difference equations. The Tertiary trap in K oil field (an Iraqi oil field) was simulated by the numerical model. The trap consists of six layers having different properties. Equally spaced Cartesian grids were used to divide each layer into 1600 cells in the x-y plane with the thickness as the dimension of each grid block in z direction. Applying the two IMPES pressure equations to each grid of the simulated domain resulting in a block seven diagonal coefficient matrix.

A Three-Phase, Two-Dimensional Compositional Thermal Simulator For Steam Injection Processes

Abstract A numerical model for simulating steam injection into a porous medium is described. The model simulates three-phase, three-dimensional, multi-component flow, with interphase mass and heat transfer, and thus accounts for changes in oil composition during steam injection. The example problems consider a system made up of water (or steam) and three hydrocarbon components. The partial differential equations describing the mass balance for each component were solved, together with a heat balance and auxiliary relations. Examples are presented illustrating the use of the model for cyclic steam stimulation and steamflooding. The sensitivity of the predictions to the input parameters is examined. It was found that steam distillation and gravity segregation are important mechanisms in the steam injection processes. Simultaneous solution of heat and mass balances and compositional constraint equations appear to represent the best procedure for efficient simulation. Other solution schemes tested are also discussed. Introduction EARLY EFFORTS in the mathematical modeling of steam injection processes utilized modifications of the Buckley-Leverett equation to allow for temperature variations(1,2), flow-pattern representation by means of stream tubes and subsequent temperature4 dependent Buckley-Leverett type displacement (3,4), and still simpler treatments where oil recovery was based only on the oil saturation reduction in the steam zone. Three-phase, one- and two-dimensional models for steam injection were first presented by Shutler (5,6). He solved the three-phase (oil, water and gas) mass balances simultaneously using Newtonian iteration. The energy balance equation was solved separately by the non-iterative ADIP. Interphase mass transfer between water and gas phases was allowed, but the oil phase was assumed to be nonvolatile, and the hydrocarbon gas was insoluble in the liquid phases. The implicit-pressure, explicit-saturation (IMPES) method was used by Abdalla and Coats'" to simulate steam drive. They developed a two-dimensional, three-phase (oil, water and steam) model. A new stabilized IMPES method was described by Vinsome(8). He simulated steam drive and steam soak by means of a three-phase (oil, water and steam) model. This model did not account for steam distillation. Coats, George, Chu and Marcum(10) presented a three-phase (oil, water and steam), three-dimensional numerical model for the steam injection process. The mass and energy balance equations were solved simultaneously. Water and steam equations were combined to avoid iteration on the mass transfer condensation term. No distillation of the oil was assumed. Weinstein, Wheeler and Woods(11) developed a model that describes three-phase (oil, water and gas) flow in one dimension and accounts for inter-phase mass transfer. The model does not include gravity and capillary pressure effects. "Sequential solution" (Spillette, Hillestad and Stone 12) was basically used as the method of solution. Recently, Coats(13) described a three-dimensional, three-phase (oil, water and gas) model that accounted for steam distillation. Sequential solution(15) was basically used as the method of solution. The present work describes a compositional simulator designed to simulate the steam injection processes in two-dimensional geometry.