Full-Field Compositional Modeling on Vector Processors
- L.C. Young (Reservoir Simulation Research Corp.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- February 1991
- Document Type
- Journal Paper
- 107 - 114
- 1991. Society of Petroleum Engineers
- 5.2.2 Fluid Modeling, Equations of State, 4.6 Natural Gas, 5.4.2 Gas Injection Methods, 5.5 Reservoir Simulation, 5.8.8 Gas-condensate reservoirs, 5.4.3 Gas Cycling, 5.4.9 Miscible Methods, 4.1.2 Separation and Treating, 4.1.5 Processing Equipment, 5.2.1 Phase Behavior and PVT Measurements
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Large full-field simulations have not previously been feasible withequation-of state (EOS) compositional models. This paper describes an approachfor efficient EOS calculations. The approach is based on a model formulationthat minimizes the number of calculations together with vector processing tomaximize the calculation rate. Tests of a simulator based on the approach showthat large problems can now be solved. For example, a problem composed of ninecomponents, 20,000 gridpoints, and 1,000 timesteps can be solved in as littleas 15 minutes of CPU time.
Compositional reservoir simulators are used to study hydrocarbon reservoirswith complex fluid phase behavior. Examples of problems requiring compositionalmodels are primary production or injection processes (such as nitrogeninjection) into gas condensate and volatile-oil reservoirs and enhancesrecovery from oil reservoirs by CO2 or enriched-gas increasing need forcompositional reservoir simulation.
Compositional simulators represent the hydrocarbon fluids by a number ofcomponents, typically 8 to 10. Equilibrium between the hydrocarbon gas andliquid phases is calculated with an EOS such as the Peng-Robinson orRedlich-kwong. The phase equilibrium calculations are performed at every pointin a finite-difference grid and are coupled to the discritized materialbalances that govern fluid flow. Because of the large number of gridpoints andthe complexity of the EOS, the calculations are computationally intensive.
In the past, applications that use EOS compositional models have beenrestricted owing to large computation times. Engineers have often been facedwith a choice either to use a black-oil model and neglect importantcompositional effects or to use a compositional model with grids too coarse toresolve important flow effects. For example, the largest reported compositionalstudy consisted of about 8,000 gridpoints and 9 hydrocarbon-phase componentsand required over 8 hours of computing time on an IBM 3033 computer. Theseextensive computing requirements have restricted the application of EOS modelsfor large problems.
This paper describes a simulator designed for the practical solution oflarge EOS minimizes the number of calculations, along with vector processors tomaximize the calculation rate. Tests of the simulator show that large problemsare now practical.
Before this project began, the following goals and objectives wereoutlined.
1. To develop a simulator that will run large problems on a vector computerat least 20 times faster than the scalar time reported in Ref. 3.
2. To develop a formulation that also executes efficiently on conventionalscalar machines.
3. To use a general formulation that can accommodate other fluid propertycorrelations-E.G., black-oil fluids.
4. To achieve high portability by using ANSI standard FORTRAN 77 as much aspossible.
For a typical compositional simulation, more than 50% of the computationtime is spent in the EOS calculations. Obviously, high performance cannot beachieved unless these calculations are executed efficiently. With mostsimulators, these calculations either do not vectorize or vectorize with shortvector lengths.e.g. equal to the number of components or the number ofcontiguous gridpoints with a given " fluid type". The term "fluidtype" classifies points by the calculations required. For example, thesequence of calculations performed for a single hydrocarbon phase is differentfrom that performed for two hydrocarbon phases.
Efficient calculations on vector machines need vector lengths equal to thetotal number of points with a given fluid type. The need for long vectorsdictates that the points be ordered by fluid type rather than by gridpointnumber. The method described in this paper maintains two orderings of thegridpoints, one bases on the computational grid and one based on fluid type. Tominimize the work associated with reordering the data, the major fluid propertyarrays always remain ordered by fluid type. These arrays are rearranged onlywhen the fluid at some point changes from one fluid type to another.
This paper is divided into several parts. First, the generalizedcompositional procedure used in the simulator is described and compared tothose proposed previously. Second, some factors considered in theimplementation of the simulator are discussed. Then, some computationalexperiments are described that illustrate important aspects of the EOScalculations. This section is followed by a description of how fluid-propertyarrays are reordered to achieve efficient calculations on both vector andscalar machines. The next session describes other details of the simulator andhow its performance was tested. The results of the performance tests are thenpresented and discussed have been met or surpassed. Finally the results aresummarized and some consequences of this work are discussed.
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