Nonlinear optimization for reservoir characterization

At IFP, optimization problems are encountered in many different applications, such as seismic tomography, characterization of reservoirs, engine model calibration, etc. Many of them are expressed as inverse problems with a nonlinear forward problem that is generally time consuming. The size of those problems is varying: from 10 up to 10000. Moreover, the underlying optimization problems are often subject to inequality constraints. To solve these problems, we are currently developing a general software package, called SQPAL, which should be flexible enough to fit the large variety of requirements of the applications under study. SQPAL is a Sequential Quadratic Programming algorithm developed to solve general nonlinear programming problems dealing with nonlinear equality and inequality constraints. The originality of our approach is to solve the osculating quadratic problem with linearized constraints by an augmented Lagrangian method, which has the potentiality to cope with many inequality constraints. The performances of SQPAL first on small and then on middle size NLP problems from the CUTEr benchmark are illustrated. The presented industrial application is a reservoir characterization problem, which aims at forecasting the production of an oil or gas field from available production data. Production data are measures of pressure, oil/water/gas rates at the wells and may be completed with 4D seismic data. Parameters to be determined in this inverse problem are for example, the petrophysical properties in some reservoir zones (permeability, porosity, . . . ) or the well productivity indexes. The associated forward problem is a fluid flow simulator for a given reservoir geological model, which may require a large computational time. The potential of the SQPAL solver for this industrial application is illustrated on a 2D realistic static problem including 2D seismic data.