Method for quickly forming a stochastic method representating the distribution of a physical variable in a heterogeneous environment by appropriate selection of a geostatistic realizations

摘要

A method having an application to production problems in reservoir engineering for quickly forming a stochastic model representative of the distribution of a physical quantity in a porous heterogeneous medium, which is calibrated in relation to dynamic data, by suitable selection of geostatistical realizations to be combined linearly. An iterative gradual deformation process is used, wherein an initial geostatistical realization (y) of the medium and a number (N−1)(N1) of other realizations (z_i)i=1, . . . ,(N−1), which are independent of initial realization (y), are linearly combined at each iteration, by applying constraints to the linear combination coefficients of realizations (y) and (z_i)i=1, . . . ,(N−1), and an objective function (J) measuring the difference between a set of simulated data deduced from said combination by means of a simulator and said dynamic data is minimized. To quickly minimize the objective function, the Lagrange multiplier (λ), λ ε R^N−1 associated with the constraint relating to the specified values of the coefficients of realizations (z_i)i=1, . . . ,(N−1) is calculated. The absolute value λ_i of the i^th component of multiplier λ indicates the sensitivity of the objective function in relation to the i^th geostatistical realization (z_i).