Applications Of Dynamic Gridding To Thermal Simulations
- J.R. Christensen (Total E&P UK plc) | G. Darche (Total) | B. Dechelette (Total) | H. Ma (Computer Modelling Group, Ltd.) | P.H. Sammon (Computer Modelling Group, Ltd.)
- Document ID
- Society of Petroleum Engineers
- SPE International Thermal Operations and Heavy Oil Symposium and Western Regional Meeting, 16-18 March, Bakersfield, California
- Publication Date
- Document Type
- Conference Paper
- 2004. Society of Petroleum Engineers
- 5.1.5 Geologic Modeling, 5.4.6 Thermal Methods, 5.2.1 Phase Behavior and PVT Measurements, 5.4.2 Gas Injection Methods, 5.5.3 Scaling Methods, 4.1.2 Separation and Treating, 5.3.9 Steam Assisted Gravity Drainage, 4.3.4 Scale, 5.5 Reservoir Simulation, 5.4 Enhanced Recovery, 4.6 Natural Gas, 5.5.8 History Matching
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This paper describes a new technique to decrease the computational times of thermal simulations. Effectively, thermal processes are based on the displacement of a thermal front (combustion front, steam chamber interface), around which most fluid flows will take place. Thus, we propose a dynamic gridding approach, to keep a fine scale representation around the thermal front, and a coarser grid away from the front, thus leading to cheaper computations.
We will first describe the principles of this dynamic gridding. Simulations will start with an original fine grid, but will reamalgamate its cells, while keeping some regions (for example around wells) always finely gridded. The gridding will then identify the moving front through large gradients of specific properties (temperatures, fluid saturations and compositions). In the front vicinity, it will de-amalgamate the originally amalgamated cells, and later on re-amalgamate them once the front has passed. Amalgamated cells are assigned up-scaled properties, this upscaling being based upon classical averaging techniques.
We will illustrate this dynamic gridding technique with simulation examples, as it has been successfully implemented in a thermal simulator, STARS, a product of Computer Modelling Group Ltd (CMG). Using examples on combustion and SAGD simulations, we will show that it can divide the CPU time of thermal simulations by a factor of 2 to 3, without loss of accuracy.
Reservoir flow must be represented accurately when modelling processes such as combustion and SAGD (steam-assisted gravity drainage) in a reservoir simulator. These thermal processes involve convective, diffusive and dispersive flows of fluids and energy, which lead to the formation of fluid banks and fronts moving in the reservoir. Some of these fronts represent interfaces between mobilized oil, which is hot and has had its viscosity reduced, and the more viscous oils which are as yet untouched by heat. Other fronts occur between phases, such as where a leading edge of hot combustion gas moves into an uncontacted oil. These interfaces are thin when compared to the typical cell sizes used to model EOR processes in a simulator, so there will always be problems in properly representing important fluid physics near interfaces. For instance, the choice made for upscaling could depend on the fronts being generated by a process and where they are positioned in the upscaled reservoir cell, while the use of fine scale computational cells throughout the reservoir would be prohibitively expensive.
A technique has been presented(1) to address these problems. It suggests using dynamic grid refinement and amalgamation to choose an appropriate cell size near important regions, while using larger cells elsewhere. The ongoing simulation is reviewed periodically and the cells are re-sized depending on the current fluid distribution. The technique is applicable to simulators using sparse matrix solvers and only involves regenerating pointers and properties at selected times during the simulation. Dynamic grid refinement and amalgamation can result in obtaining a several fold decrease in run time while leaving the results unchanged.
User-specified thresholds are used to control when to do grid amalgamation or de-amalgamation. The methods described in this paper will be based on differences in property values between amalgamated cells and their neighbours, or differences among values in a finely divided region. The properties chosen will be designed to find fronts, and include saturations and various compositions. Temperature related thresholds will also be used to give an "early warning" for the leading edge of a front. Pressure related differences are not considered, as different pressure levels do not cause difficulties unless they result in front movement, which would be trapped by the thresholds just described The thresholds should be relatively small so that a buffer region of finer cells is maintained around regions of high activity. This choice sacrifices some speed, but maintains accuracy.
Note that the simulator requires some kind of efficient adaptive (or fully) implicit formulation to make good use of these techniques, as smaller cells could have high throughputs that require implicitness without resort to small time steps.
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