| Popis: |
Abstract The simulated annealing solution technique has been a powerful reservoir characterization tool in geostatistics. This paper proposes an algorithm that uses this method to constrain the permeability distribution of a given reservoir model to the well test data collected at several wells. The technique can be used for single or multiple well tests. In order to keep the execution time of this algorithm within an acceptable range, the perturbation on the pressure transient due to a local permeability heterogeneity is determined in the form of an analytic influence function. The results given by this approximation are compared to the results given by a simulator, and its use in the simulated annealing algorithm is defined according to its reliability. The algorithm is tested on an example, showing that the use of the analytic influence function allows considerable reduction in the computing time without decreasing the robustness of the method. Introduction Recent years have seen the emergence of geostatistics and stochastic modelling techniques as promising approaches for reservoir characterization and the description of heterogeneous reservoirs. One of the main features of these techniques is their ability to integrate several sources of information, such as geological and engineering data. Deutsch has pointed out the important role that the well test data could play in reservoir description, however the actual integration of these data into the geostatistical description has been running against the problem of impractical computing time, because of the need to use of a flow simulator for a large number of runs. The objective of this work was to develop an analytical approximation which could be used as a replacement for the simulator run. The final use of this analytical solution is within a simulated annealing process. Simulated Annealing The simulated annealing technique is a solution method based on an analogy with the physical process of annealing, a process by which a material undergoes extended heating and is slowly cooled. Thermal vibrations permit a reordering of the atoms to a highly structured lattice, i.e. a low energy state. In the context of reservoir characterization, the annealing process can be simulated through the following steps:An initial image of the reservoir is created by assigning random parameter values at each grid block.An objective function (O) is defined as the measure of difference between desired features and those of the realization.The image is perturbed according to a procedure replacing the thermal vibrations in true annealing and a new value of the objective function Onew is generated. This procedure can be for example:Swapping the values of two randomly chosen nodal locations.Randomly select a node and consider replacing its value with a random selection from the global histogram. P. 733^ |
