Numerical Reservoir Simulation



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Preface

 
Reservoir simulation is a developing application technique for reservoir development and management. It can be used to forecast the production behavior of oil and gas fields, optimize reservoir development schemes, and evaluate the distribution of remaining oil through history matching, for example. It is an important tool to help reservoir engineers optimize the design of well development schemes, improve the efficiency of reservoir development, and enhance oil and gas recovery.
Here you will find some of the recent developments in the Reservoir Simulation Group led by Dr. John Chen in the following aspects:
  • differential formulations (mathematical modeling),
  • scanners and grid generators,
  • numerical discretization methods,
  • linear system solvers,
  • solution schemes,
  • visualization and post-processing,
  • applications,
  • experiences.


Differential Formulations (Mathematical Modeling)
The governing equations that describe multiphase flow in reservoirs are nonlinear and coupled. They can be rewritten in different differential formulations so that the coupling and nonlinearity of these equations are weakened, efficient and accurate numerical methods can be devised, and simulation time can be reduced. Various formulations of the governing equations, including phase, global, and weighted formulations have been studied and compared for two-phase, black-oil, and compositional flows.


Scanners and Grid Generators
The software we have developed for numerical reservoir simulation includes scanners which
  • scan and extract various geometrical data such as depth, thickness, porosity, permeability, and the location of wells, fractures, and faults;
  • define longitude-latitude coordinates for property maps;
  • possess erase and restart functions for editing maps;
  • display the graphs of these geometrical data;
  • output the information of these geometrical data to grid generation.
The software is also able to
  • read the geometrical data from the scanners;
  • interpolate scattered data;
  • generate various 2D and 3D unstructured grids such as triangles, rectangles, Voronoi (PEBI) and CVFE blocks, tetrahedra, rectangular parallelepipeds, and prisms;
  • display the graphs of these grids.



Numerical Discretization Methods
Many discretization methods have been applied to the numerical solution of the flow and transport equations in reservoirs. These methods range from finite difference methods, finite element methods, discontinuous finite element methods, control volume finite element methods, mixed finite element methods, to control volume function approximation methods. Their limitation, efficiency, accuracy, flexibility, and applicability to reservoir simulation have been described and compared. In particular, we have developed and applied the control volume function approximation method which
  • can be easily used for local grid refinement;
  • can model horizontal wells in arbitrary direction;
  • reduces grid orientation effects;
  • has no limitation on grid shapes;
  • can easily treat faults and fractures;
  • can easily utilize the corner point technique;
  • keeps flux continuity at interfaces;
  • conserves mass locally.

 
 


Linear System Solvers
Fast and accurate solution of linear systems of algebraic equations that arise from the discretization of the governing equations for multiphase flows has been increasingly important. In a numerical reservoir simulator, about 80% of time is spent on the solution of these systems. Various iterative solvers such as ORTHOMIN (orthogonal minimum residual), GMRES (generalized minimum residual), FGMRES (Flexible GMRES), and BiCGSTAB (biconjugate gradients stabilized) and their preconditioned versions have been considered and compared. Particularly, these solvers and their parallel versions for solving linear systems arising from discretization methods on unstructured grids have been applied. The preconditioners include ILUT (dual threshold incomplete LU factorization), ILUK (incomplete ILU with level of fill), and multilevel and domain decomposition based approaches.


Solution Schemes
Since the fluid flow and transport models in reservoirs involve large, coupled systems of nonlinear, time-dependent partial differential equations, an important problem in numerical reservoir simulation is to develop stable, efficient, robust, accurate, and self-adaptive solution schemes. The iterative IMPES (implicitly in pressure and explicitly in saturation), sequential (pressure, saturation, and concentration equations decoupled and each solved implicitly), and fully implicit (simultaneous, implicit solution of all equations) solution schemes have been studied and compared for two-phase, black-oil, and compositional flows. Recently, we have developed an improved IMPES scheme for solving two-phase flow in three-dimensional reservoirs. This improved scheme utilizes an adaptive control strategy on the choice of time steps for saturation and takes much larger time steps for pressure than for saturation. It is capable of solving two-phase coning problems.


Parallel Computing
We have developed parallel codes for thermal simulation of multicomponent, multiphase fluid flow in petroleum reservoirs. These codes utilize the message passing interface (MPI) library, overlapping domain decomposition, and dynamic memory allocation techniques. Their efficiency has been investigated through simulation of three-dimensional multicomponent, multiphase field models for heavy oil crudes. Numerical results for these simulation models indicate that these parallel codes can significantly improve capacity and efficiency for large-scale thermal simulation.

 
 


Visualization and Post-Processing
A successful application of visualization technology to reservoir simulations can help reservoir engineers study more accurately physical data such as the porosity, permeability, depth, and thickness of reservoirs, construct more accurate geological and flow models, and perform more realistic simulations. It also helps them view and analyze water, oil, and gas distribution and history matching. As simulation technology gets more advanced, there are new requirements from reservoir engineering. These requirements include the real-time display of production behavior of oil/gas fields and of flow streamline maps for understanding the essentials of oil recovery processes, the visualization of remaining oil distribution in reservoir layers, the management of drilling new wells, the shortening of history match processes, and interactive capabilities for new design of development projects of oil/gas fields. We have developed visualization software which has most of these features. In particular, it
  • possesses real-time calculation and real-time display capabilities;
  • has layer selection functions for multiple-layer reservoirs;
  • provides streamlines;
  • has graphical display menus: depth, thickness, permeability, porosity, pressure, saturation, and composition;
  • displays reservoir behavior (production/injection rates and ratios, water, oil, and gas cuts, characterization curves of displacement, and history match);
  • views water, oil, and gas distribution;
  • evaluates ultimate oil recovery.


Applications
The models in our reservoir simulators feature
  • black oil flow,
  • extended black oil flow,
  • compositional flow,
  • dual porosity and single/dual permeability,
  • thermal flow.
Our numerical reservoir simulators can apply to
  • primary depletion,
  • water flooding,
  • dry gas injection and gas cycling,
  • undersaturated and saturated reservoirs,
  • investigation of displacement mechanisms in both fractures and matrix blocks,
  • treatment of volatile oil,
  • gas condensate reservoirs,
  • coning studies,
  • WAG processes,
  • steam injection,
  • interpretation of pressure drawdown and buildup tests for wells,
  • modeling of slanted and multilateral wells,
  • and aquifers.



Experiences
We have had research collaborations with some of oil companies such as Mobil Technology Company and PDVSA-Intevep, Venezuela and had experiences with applications of our numerical reservoir simulators to oil fields such as
  • Daqing oil field,
  • Shengli oil field,
  • Tuha oil region,
  • Gas condensate reservoirs in the Bohai gulf,
  • North-China naturally fractured carbonate reservoirs,
  • Oil reservoirs in South and North America.


For More Information,


  • Please e-mail zchen@mail.smu.edu
  • Or call Dr. John Chen at 214-768-4338
  • Professor of Mathematics
  • Director, Center for Scientific Computation
  • Director, the Graduate Program, SMU

Last revision: November 7, 2002.