Multi-scale Modelling of 1-D Permeability Fields

Abstract

Abstract Permeability plays an important role in subsurface fluid flow studies, being one of the most important quantities for the prediction of fluid flow patterns. The estimation of permeability fields is therefore critical and necessary for the prediction of the behavior of contaminant plumes in aquifers and the production of petroleum from oil fields. In general, there are two types of information that can be used in the estimation of the permeability field: static data and dynamic data. Static data can be regarded as measurements of the permeability field, and are available at different levels of resolution as a result of geological studies, well tests, and laboratory measurements. Dynamic data are obtained through the production from a collection of wells, being the production history in the case of a mature oil field or the result of tracer experiments in the case of aquifers. To incorporate the dynamic data in formal statistical analysis, corresponding likelihood functions for the high-dimensional random field parameters representing the permeability field can be computed with the help of a fluid flow simulator (FFS). The FFS can run at different scales of resolution of the permeability field, lower levels providing faster but less accurate results. In this paper, we incorporate the static information available at the different scales of resolution by using a multi-scale time series model as a prior for 1-D permeability fields. Estimation of the multi-scale permeability field is then performed using an MCMC algorithm with an embedded . FFS running at different scales to incorporate the dynamic data. We use simulated data to study the performance of the proposed approach with respect to the recovery of the original permeability field.