A Geostatistical Approach to History Matching Pressure and Flow Data on Non-Uniform Grids

Abstract

Fine scale heterogeneities can have significant effects on flow performances in subsurface formations. Fine-scale geostatistical realizations generated from well-log and seismic data are required to quantify the impact of such heterogeneities on flow. These realizations in many cases require number of grid cells on the order of 10 6-10 7 , hence making it too demanding CPU wise to directly history match geostatistical models. Non-uniformly gridding these models for emphasizing the heterogeneities does not necessarily present a solution since the practice of geostatistics on non-uniform grids is inefficient. In this paper we provide an entirely new approach to these problems by proposing a solution which is geostatistics based yet having the flexibility to work on non-uniformly gridded models. Hence coupling geostatistics with non-uniformly upscaled models results in an effective history matching technique incorporating all information at their scales. With the proposed approach we mainly target three advantages. Well and seismic data will still be effectively incorporated in the realizations. Flow simulations will be performed on non-uniformly upscaled models hence will be relatively fast. Finally the resulting field which is history matched will include the geology and will be on a non-uniformly gridded model for emphasizing heterogeneities or desired specifications, hence future predictions can be made fast, no posterior upscaling is required.

A parallel, multiscale approach to reservoir modeling

“…The results of the example given by Tureyen and Caers [13] are given in figure 5. Figure 5a gives the flow responses of 20 realizations conditioned only to hard data (no history matching has been performed).…”

“…To make a better understanding of the proposed approach by Tureyen and Caers [13], an example will be briefly reviewed in this section. Figure 4 gives the reference permeability field along with its corresponding water cut curve and sample statistics regarding the generation of the reference field.…”

“…Here S represents the upscaling technique applied on z(r) and represent the upgridding parameters regarding the upscaling technique S. In the method of Tureyen and Caers [13] (figure 3), both S and are determined prior to the history matching and remain fixed while history matching. Once the coarse model is determined, the flow response is obtained by evaluating the full flow simulation (FSM) on the coarse model through the following relationship:…”

“…This sequence of steps is repeated until a history match is achieved. This approach is not new and has been successfully applied by the authors Caers [2], Mezghani and Roggero [9] and Tureyen and Caers [13] and also others.…”

“…The further outline of this paper can now be defined clearly: we will first review the work of Tureyen and Caers [13] and show a counter example of what can go wrong in such a procedure. Next we introduce a fairly general optimization framework for reducing upscaling errors between fine and coarse scale realizations.…”