This paper describes one solution to the problem of constraining geostatistical models by well-test results which has been obtained within the frame of the HELIOS research project conduced by Elf and IFP in the field of reservoir engineering.
To do so, a numerical simulation program devoted to the simulation of well-tests has been coupled with a nonlinear constrained optimization program to make an inversion loop. The resulting software package provides the reservoir engineer with a tool to compute the set of optimal facies or rock-type properties and the well skin which give the best fit between the simulated and the measured well pressure during the test duration. Any petrophysical facies or rock-type property can be assigned either a constant value everywhere or a Gaussian distribution defined by its mean and its standard deviation.
On one hand the numerical program is able to compute not only the pressure and its derivative but also the gradients of this pressure with respect to the petrophysical facies or rock-type properties and with respect to the well skin. The gradients used by the optimization program to control the search algorithm can also be used as a stand alone diagnosis tool to analyze the simulation results.
Several examples are given which show the efficiency of the various algorithms. These examples also demonstrate the wide range of applicability of the software package to analyze and to interpret well-tests as well as to integrate dynamic data in geostatistical modeling.
As a conclusion, the paper sets forth several new research axes to extend this work toward the inversion of the shape of the geostatistical images themselves.
