Direct Prediction of Reservoir Performance With Bayesian Updating
Authors: Deutsch C.V. , Zanon S.D. 
Published: March 2010

Abstract
Conventional geostatistics aims at creating models of heterogeneity and uncertainty in static rock properties such as facies, porosity and permeability. This is appropriate for providing input to flow simulations. There are times, however, when no flow simulation is going to be performed and we would like to directly predict reservoir flow characteristics. Different techniques are required when the aim is to directly create maps of the (uncertainty in) production potential. This paper summarizes a technique for this purpose.
The petroleum industry is reliant on many types of geological and geophysical information to predict reservoir performance. This data covers different areas, provides data on different scales and is variably correlated to the production characteristics we are trying to predict. Statistical techniques can be used to summarize the relationships between the variables, however, they do not account for spatial correlation. Geostatistical techniques incorporate spatial structure but these techniques are cumbersome in the presence of many secondary variables. We propose that all secondary data be merged statistically by a multivariate Gaussian approach into a single variable that contains all of the secondary variable information. This would provide a likelihood distribution. The spatial distribution of each variable by itself is mapped independently of the secondary variable information, which provides a prior distribution. The likelihoods and priors are merged to provide an updated posterior distribution. We describe the methodology and show an example application.

Introduction
Our goal is to directly predict reservoir performance potential summarized by production variables. The production variables we are predicting are measures of hydrocarbon flow rate and projected cumulative production. We assume that the wells are far enoughapart to avoid any significant interactions.
Reservoir characterization aims to use all data to improve the understanding of reservoir performance potential at locations where we have no wells(1). In general, we can group the available data into the following categories:Geological variables that take two forms:maps of interpreted variables based on expert judgment and regional depositional setting; anddirect well measurements of variables such as porosity, pay thickness and so on.Alternatively, these variables can be grouped in structural variables dealing with container size and shape, and geological variables dealing with internal reservoir quality.Geophysical variables that have high areal resolution, low vertical resolution and variable correlation to actual rock properties and production variables. These variables can be direct attributes such as amplitudes, or processed variables such as interpreted fracture densities or P/S impedances.Production variables that we are trying to predict, such as initial production rate and projected cumulative production. These variables would typically be interpreted from the production at existing wells; that is, some kind of decline analysis.
The production variables have some spatial correlation that we can exploit, however, we must also exploit the information contained in the geological and geophysical variables that are related to the production variables we are trying to predict. These secondary data sources are also redundant with each other and we need to establish the true information content in all data sources.