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Article
Publication date: 19 July 2019

Jingfa Li, Tao Zhang, Shuyu Sun and Bo Yu

This paper aims to present an efficient IMPES algorithm based on a global model order reduction method, proper orthogonal decomposition (POD), to achieve the fast solution and…

Abstract

Purpose

This paper aims to present an efficient IMPES algorithm based on a global model order reduction method, proper orthogonal decomposition (POD), to achieve the fast solution and prediction of two-phase flows in porous media.

Design/methodology/approach

The key point of the proposed algorithm is to establish an accurate POD reduced-order model (ROM) for two-phase porous flows. To this end, two projection methods including projecting the original governing equations (Method I) and projecting the discrete form of original governing equations (Method II) are respectively applied to construct the POD-ROM, and their distinctions are compared and analyzed in detail. It is found the POD-ROM established by Method I is inapplicable to multiphase porous flows due to its failed introduction of fluid saturation and permeability that locate on the edge of grid cell, which would lead to unphysical results.

Findings

By using Method II, an efficient IMPES algorithm that can substantially speed up the simulation of two-phase porous flows is developed based on the POD-ROM. The computational efficiency and numerical accuracy of the proposed algorithm are validated through three numerical examples, and simulation results illustrate that the proposed algorithm displays satisfactory computational speed-up (one to two orders of magnitude) without sacrificing numerical accuracy obviously when comparing to the standard IMPES algorithm that without any acceleration technique. In addition, the determination of POD modes number, the relative errors of wetting phase pressure and saturation, and the influence of POD modes number on the overall performances of the proposed algorithm, are investigated.

Originality/value

1. Two projection methods are applied to establish the POD-ROM for two-phase porous flows and their distinctions are analyzed. The reason why POD-ROM is difficult to be applied to multiphase porous flows is clarified firstly in this study. 2. A highly efficient IMPES algorithm based on the POD-ROM is proposed to accelerate the simulation of two-phase porous flows. 3. Satisfactory computational speed-up (one to two orders of magnitude) and prediction accuracy of the proposed algorithm are observed under different conditions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 January 2016

Mehdi Jamei and H Ghafouri

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…

Abstract

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 28 October 2014

Mehdi Mosharaf Dehkordi, Mehrdad T. Manzari, H. Ghafouri and R. Fatehi

– The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model.

Abstract

Purpose

The purpose of this paper is to present a detailed algorithm for simulating three-dimensional hydrocarbon reservoirs using the blackoil model.

Design/methodology/approach

The numerical algorithm uses a cell-centred structured grid finite volume method. The blackoil formulation is written in a way that an Implicit Pressure Explicit Saturation approach can be used. The flow field is obtained by solving a general gas pressure equation derived by manipulating the governing equations. All possible variations of the pressure equation coefficients are given for different reservoir conditions. Key computational details including treatment of non-linear terms, expansion of accumulation terms, transitions from under-saturated to saturated states and vice versa, high gas injection rates, evolution of gas in the oil production wells and adaptive time-stepping procedures are elaborated.

Findings

It was shown that using a proper linearization method, less computational difficulties occur especially when free gas is released with high rates. The computational performance of the proposed algorithm is assessed by solving the first SPE comparative study problem with both constant and variable bubble point conditions.

Research limitations/implications

While discretization is performed and implemented for unstructured grids, the numerical results are presented only for structured grids, as expected, the accuracy of numerical results are best for structured grids. Also, the reservoir is assumed to be non-fractured.

Practical implications

The proposed algorithm can be efficiently used for simulating a wide range of practical problems wherever blackoil model is applicable.

Originality/value

A complete and detailed description of ingredients of an efficient finite volume-based algorithm for simulating blackoil flows in hydrocarbon reservoirs is presented.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 24 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 17 October 2018

Mehdi Mosharaf-Dehkordi and Hamid Reza Ghafouri

The purpose of this paper is to present detailed algorithms for simulation of individual and group control of production wells in hydrocarbon reservoirs which are implemented in a…

Abstract

Purpose

The purpose of this paper is to present detailed algorithms for simulation of individual and group control of production wells in hydrocarbon reservoirs which are implemented in a finite volume-based reservoir simulator.

Design/methodology/approach

The algorithm for individual control is described for the multi-lateral multi-connection ones based on the multi-segment model considering cross-flow. Moreover, a general group control algorithm is proposed which can be coupled with any well model that can handle a constraint and returns the flow rates. The performance of oil production process based on the group control criteria is investigated and compared for various cases.

Findings

The proposed algorithm for group control of production wells is a non-optimization iterative scheme converging within a few number of iterations. The numerical results of many computer runs indicate that the nominal power of the production wells, in general, is the best group control criterion for the proposed algorithm. The production well group control with a proper criterion can generally improve the oil recovery process at negligible computational costs when compared with individual control of production wells.

Research/limitations/implications

Although the group control algorithm is implemented for both production and injection wells in the developed simulator, the numerical algorithm is here described only for production wells to provide more details.

Practical/implications

The proposed algorithm can be coupled with any well model providing the fluid flow rates and can be efficiently used for group control of production wells. In addition, the calculated flow rates of the production wells based on the group control algorithm can be used as candidate solutions for the optimizer in the simulation-optimization models. It may reduce the total number of iterations and consequently the computational cost of the simulation-optimization models for the well control problem.

Originality/value

A complete and detailed description of ingredients of an efficient well group control algorithm for the hydrocarbon reservoir is presented. Five group control criteria are extracted from the physical, geometrical and operating conditions of the wells/reservoir. These are the target rate, weighted potential, ultimate rate and introduced nominal power of the production wells. The performance of the group control of production wells with different group control criteria is compared in three different oil production scenarios from a black-oil and highly heterogeneous reservoir.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 4 January 2016

Jion Sean Pau, William Pao and Suet Peng Yong

The purpose of this paper is to introduce the solution to two-phase flow in CO2/brine system with salt precipitation by applying mixed hybrid finite element (MHFE) method to…

Abstract

Purpose

The purpose of this paper is to introduce the solution to two-phase flow in CO2/brine system with salt precipitation by applying mixed hybrid finite element (MHFE) method to pressure equation and finite volume (FV) method to saturation equation. Mixed finite element method solves pressure and velocity in two subspaces while hybrid method is an extension of mixed method, where the Lagrange multiplier is added to the former in order to ensure the continuity from one element to the adjacent elements. The authors propose the modeling of salt precipitation using core flood experimental result and adapt to be applicable for numerical modeling.

Design/methodology/approach

The governing equations are discretized using Mixed Hybrid Finite Element-Finite Volume (MHFE-FV) method. This method has the feature of localized conservation which is attractive for application on heterogeneous porous media. In addition to this, the salt precipitation effect is modeled using the data from core flood experiment (Ott et al., 2011). The random data are linearized to obtain the relationship between salt precipitate and CO2 saturation and implemented to the algorithm for two-phase flow in CO2 and brine system.

Findings

The solution of MHFE-FV scheme has good agreement with the solution using implicit pressure and explicit saturation (IMPES) reported by Negara et al. (2011), with average error of 4.20 percent. Localized conservation is demonstrated in the case of randomized heterogeneous porous media where fingering effects are explicitly observed. Salt precipitation prediction using the proposed method is able to predict the decrement of porosity by 16.71 percent and permeability by 22.19 percent. This results in the decreased amount of CO2 injected by 64.70 percent.

Research limitations/implications

This paper presents the solution of two-phase flow in CO2 brine system during CO2 injection in saline aquifer using MHFE-FV method with the additional salt precipitation model obtained based on core flood experiment result.

Practical implications

A methodology to predict the salt precipitation based on CO2 saturation.

Social implications

Contribution to green house gas reduction.

Originality/value

The authors use MHFE-FV to solve hyperbolic PDE to obtain accurate results of CO2 saturation, and subsequently use this to compute the salt precipitation.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 1988

M.B. Reed

The aim of the model is to represent the main features of soft or brittle rock strata, using a small number of physically‐meaningful material parameters. The yield surface is…

Abstract

The aim of the model is to represent the main features of soft or brittle rock strata, using a small number of physically‐meaningful material parameters. The yield surface is based on either the Mohr—Coulomb or Hoek—Brown criterion, and a simple small‐dilation flow rule allows the implicit algorithm of elasto‐viscoplasticity to be used. Elastic—brittle plastic behaviour is modelled, resulting in stress discontinuities across the interface between intact and failed rock. The effects of lamination and jointing are taken into account. Results are presented for a tunnelling problem with axial symmetry.

Details

Engineering Computations, vol. 5 no. 1
Type: Research Article
ISSN: 0264-4401

Article
Publication date: 2 October 2017

Mohamed El-Amin, Jisheng Kou and Shuyu Sun

This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles’ transport carried by a two-phase flow in a porous medium. The…

Abstract

Purpose

This paper aims to introduce modeling, numerical simulation and convergence analysis of the problem of nanoparticles’ transport carried by a two-phase flow in a porous medium. The model consists of equations of pressure, saturation, nanoparticles’ concentration, deposited nanoparticles’ concentration on the pore-walls and entrapped nanoparticles concentration in pore-throats.

Design/methodology/approach

A nonlinear iterative IMPES-IMC (IMplicit Pressure Explicit Saturation–IMplicit Concentration) scheme is used to solve the problem under consideration. The governing equations are discretized using the cell-centered finite difference (CCFD) method. The pressure and saturation equations are coupled to calculate the pressure, and then the saturation is updated explicitly. Therefore, the equations of nanoparticles concentration, the deposited nanoparticles concentration on the pore walls and the entrapped nanoparticles concentration in pore throats are computed implicitly. Then, the porosity and the permeability variations are updated.

Findings

Three lemmas and one theorem for the convergence of the iterative method under the natural conditions and some continuity and boundedness assumptions were stated and proved. The theorem is proved by induction states that after a number of iterations, the sequences of the dependent variables such as saturation and concentrations approach solutions on the next time step. Moreover, two numerical examples are introduced with convergence test in terms of Courant–Friedrichs–Lewy (CFL) condition and a relaxation factor. Dependent variables such as pressure, saturation, concentration, deposited concentrations, porosity and permeability are plotted as contours in graphs, whereas the error estimations are presented in a table for different values of the number of time steps, number of iterations and mesh size.

Research limitations/implications

The domain of the computations is relatively small; however, it is straightforward to extend this method to the oil reservoir (large) domain by keeping similar definitions of CFL number and other physical parameters.

Originality/value

The model of the problem under consideration has not been studied before. Also, both solution technique and convergence analysis have not been used before with this model.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 10
Type: Research Article
ISSN: 0961-5539

Keywords

Abstract

Details

Advances in Librarianship
Type: Book
ISBN: 978-0-12024-617-5

Article
Publication date: 1 February 2001

H.W. Zhang, O.M. Heeres, R. de Borst and B.A. Schrefler

Extends the stress update algorithm and the tangent operator recently proposed for generalized plasticity by De Borst and Heeres to the case of partially saturated soils, where on…

1083

Abstract

Extends the stress update algorithm and the tangent operator recently proposed for generalized plasticity by De Borst and Heeres to the case of partially saturated soils, where on top of the hydrostatic and deviatoric components of the (effective) stress tensor suction has to be considered as a third independent variable. The soil model used for the applications is the Bolzon‐Schrefler‐Zienkiewicz model, which is an extension of the Pastor‐Zienkiewicz model to partial saturation. The algorithm is incorporated in a code for partially saturated soil dynamics. Back calculation of a saturation test and simulation of surface subsidence above an exploited gas reservoir demonstrate the advantage of the proposed algorithm in terms of iteration convergence of the solution.

Details

Engineering Computations, vol. 18 no. 1/2
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 1984

The new generation of “intelligent robots” is apparently threatening the jobs of 1.2 million West German assembly line jobs. A new study by the Commerzbank indicates that by the…

Abstract

The new generation of “intelligent robots” is apparently threatening the jobs of 1.2 million West German assembly line jobs. A new study by the Commerzbank indicates that by the 1990's this second generation of automation devices will seriously affect the employment situation.

Details

Kybernetes, vol. 13 no. 2
Type: Research Article
ISSN: 0368-492X

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