Conditioning of permeability fields to production data: modelling and simulation algorithm

Conditioning of permeability fields to observed production history, k nown as history matching (Oliver et al., 1997; Deutsch, 1993) in petr oleum related literature, is an important component in evaluation of petroleum reservoirs. We adopt a Bayesian formulation of the problem and assume a multiGaussian prior distribution for permeability valu es in a grid. Two types of data are available, observations of perme ability values in wells and production history. The latter consists o f observed pressure and production rate of oil through time. The ob served history is linked to permeability values by a set of partial differential equations, which we define as expected values in the li kelihood. Sampling from the posterior becomes non-standard as a subs tantial amount of computer resources is required to (numerically) so lve the differential equations. This severely limit the number of it erations of MCMC algorithms that is feasible to perform. In this talk we discuss how to define MCMC algorithms which is able to make large jumps in parameter space without inducing too small acceptance pro babilities. Specifically, we consider how a generalised version of Me tropolis-Hastings combined with use of local optimisation in the gen eration of proposals, allow direct jumps between different modes (Tje lmeland and Hegstad, 1999).