Parallel Simulations of CO2 Sequestration Using a Non-Isothermal Compositional Model

2008 ◽  
Author(s):  
Mojdeh Delshad ◽  
Sunil G. Thomas ◽  
Mary F. Wheeler
Keyword(s):  
Energy Transfer ◽  
Thermal Energy ◽  
Oil Recovery ◽  
Co2 Sequestration ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Benchmark Problems ◽  
Two Phase ◽  
Pressure System ◽  
Compositional Model

This paper describes an efficient and parallel numerical scheme for multiphase compositional flow. The underlying theory is first presented followed by a brief description of the equation of state (EOS) and the two-phase flash implementation. An iterative “implicit-pressure and explicit-concentrations” (IMPEC) algorithm is then applied to enforce a non-linear volume balance (saturation) constraint. The pressure system is solved using a mixed finite element method, while the concentrations are updated explicitly in a manner that preserves local mass balance of every component. A major application of this scheme is in the modeling of field scale CO2 sequestration, as an enhanced oil recovery (EOR) process or for storage in deep saline aquifers. Thermal energy transfer also plays an important role in such problems since it can effect the phase properties dramatically. Hence, accurate and locally conservative methods are desirable to model the thermal effects. To this end, the paper also presents a time-split scheme for modeling thermal energy transfer which is sequentially coupled to flow. Finally, some numerical results are presented for challenging benchmark problems.

NUMERICAL ANALYSIS OF A TWO PHASE FLOW MODEL

2012 ◽  
Vol 09 (03) ◽  
pp. 1250036 ◽  
Author(s):  
MOHAMED ABDELWAHED ◽  
MOHAMED AMARA
Keyword(s):  
Stokes Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Time Discretization ◽  
Variable Density ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Quality Of Water ◽  
Coupling Characteristics

Due to ever increasing water demand, the preservation of water quality is becoming a very important issue. Eutrophication is amongst the particular problems threatening the quality of water. This paper begins with presenting a mathematical model for aeration process in lake used to combat water eutrophication. Two phases are numerically simulated to study the injected air effect on water by using a corrected one phase model described by Navier–Stokes equations with variable density and viscosity representing the mixture. This model is numerically studied by coupling characteristics scheme for time discretization and mixed finite element method for space approximation. An error estimates in space and time for the velocity are obtained. Numerical results are given firstly in support of the mathematical analysis and secondly to simulate a real application case of the studied problem.

Accurate Cell-Centered Discretizations for Modeling Multiphase Flow in Porous Media on General Hexahedral and Simplicial Grids

SPE Journal ◽  
2012 ◽  
Vol 17 (03) ◽  
pp. 779-793 ◽  
Author(s):  
Mary F. Wheeler ◽  
Guangri Xue ◽  
Ivan Yotov
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Quadrature Rule ◽  
Processing Technique ◽  
Higher Order ◽  
Flow In Porous Media ◽  
Pressure System ◽  
Rock Types ◽  
Variational Framework

Summary We introduce an accurate cell-centered method for modeling Darcy flow on general quadrilateral, hexahedral, and simplicial grids. We refer to these discretizations as the multipoint-flux mixed-finite-element (MFMFE) method. The MFMFE method is locally conservative with continuous fluxes and can be viewed within a variational framework as a mixed finite-element method with special approximating spaces and quadrature rules. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a nonsymmetric quadrature rule on rough grids. The framework allows for handling hexahedral grids with nonplanar faces defined by trilinear mappings from the reference cube. Moreover, the MFMFE method allows for local elimination of the velocity, which leads to a cell-centered pressure system. Theoretical and numerical results demonstrate first-order convergence on rough grids. Second-order superconvergence is observed on smooth grids. We also discuss a new splitting scheme for modeling multiphase flows that can treat higher-order transport discretizations for saturations. We apply the MFMFE method to obtain physically consistent approximations to the velocity and a reference pressure on quadrilateral or hexahedral grids, and a discontinuous Galerkin method for saturations. For higher-order saturations, we propose an efficient post-processing technique that gives accurate velocities in the interior of the gridblocks. Computational results are provided for flow in highly heterogeneous reservoirs, including different capillary pressures arising from different rock types.

Numerical investigation of simultaneous effects of nanofluid flow and porous baffle on thermal energy transfer and flow features in a circular channel

2021 ◽  
pp. 1-21
Author(s):  
Hossein Namadchian ◽  
Javad Sodagar Abardeh ◽  
Ahmad Arabkoohsar ◽  
K.A.R. Ismail
Keyword(s):  
Porous Medium ◽  
Energy Transfer ◽  
Thermal Energy ◽  
Simple Algorithm ◽  
Darcy Number ◽  
Circular Channel ◽  
Axially Symmetric ◽  
Nanofluid Flow ◽  
Two Phase ◽  
Porous Region

Abstract In the present work, the forced-convection heat transfer features of different nanofluids in a circular channel with porous baffles are numerically investigated. Nanofluid flow in the porous area is simulated by the simultaneous use of Darcy-Brinkman-Forchheimer and two-phase mixture models. The flow is considered to be laminar, two-dimensionall, steady, axially symmetric, and incompressible. The simulations are conducted in Fluent software and by using the finite volume method and SIMPLE algorithm. The influences of various parameters, including Reynolds number, volume fractions of nanoparticles, Darcy number, porous region height, and various nanofluid types on the nanofluid flows and their thermal energy transfer features, are investigated. Results show that porous blocks significantly change the flow characteristics and thermal energy transfer features. For instance, at low Darcy numbers, the permeability of the porous region decreases, and the porous baffles have greater resistance against the nanofluid flow. As a result, the vortex area becomes stronger and taller, and streamlines near obstacles are tighter. However, in high Darcy numbers, due to the high permeability of the porous medium, the flow will be the same as the flow in the channel without barriers, and the porous baffles will not have much influence on the flow. For example, at Darcy number Da = 10-4 the vortex area almost disappears. The growth of conductivity ratio increases the local Nu in the vicinity of the barriers. Properties of the porous medium and nanofluid flow affect the thermal energy transfer rate, and it can be improved by making appropriate changes to these features.

An Efficient Implicit-Pressure/Explicit-Saturation-Method-Based Shifting-Matrix Algorithm To Simulate Two-Phase, Immiscible Flow in Porous Media With Application to CO2 Sequestration in the Subsurface

SPE Journal ◽  
2013 ◽  
Vol 18 (06) ◽  
pp. 1092-1101 ◽  
Author(s):  
Amgad Salama ◽  
Shuyu Sun ◽  
M.F.. F. El-Amin
Keyword(s):  
Porous Media ◽  
Oil Recovery ◽  
Co2 Sequestration ◽  
Numerical Technique ◽  
Immiscible Fluids ◽  
Flow In Porous Media ◽  
Processing Unit ◽  
Two Phase ◽  
Central Processing ◽  
Solution Algorithms

Summary The flow of two or more immiscible fluids in porous media is widespread, particularly in the oil industry. This includes secondary and tertiary oil recovery and carbon dioxide (CO2) sequestration. Accurate predictions of the development of these processes are important in estimating the benefits and consequences of the use of certain technologies. However, this accurate prediction depends—to a large extent—on two things. The first is related to our ability to correctly characterize the reservoir with all its complexities; the second depends on our ability to develop robust techniques that solve the governing equations efficiently and accurately. In this work, we introduce a new robust and efficient numerical technique for solving the conservation laws that govern the movement of two immiscible fluids in the subsurface. As an example, this work is applied to the problem of CO2 sequestration in deep saline aquifers; however, it can also be extended to incorporate more scenarios. The traditional solution algorithms to this problem are modeled after discretizing the governing laws on a generic cell and then proceed to the other cells within loops. Therefore, it is expected that calling and iterating these loops multiple times can take a significant amount of computer time. Furthermore, if this process is performed with programming languages that require repeated interpretation each time a loop is called, such as Matlab, Python, and others, much longer time is expected, particularly for larger systems. In this new algorithm, the solution is performed for all the nodes at once and not within loops. The solution methodology involves manipulating all the variables as column vectors. By use of shifting matrices, these vectors are shifted in such a way that subtracting relevant vectors produces the corresponding difference algorithm. It has been found that this technique significantly reduces the amount of central-processing-unit (CPU) time compared with a traditional technique implemented within the framework of Matlab.

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