Direct Prediction of Reservoir Performance With Bayesian Updating Under a Multivariate Gaussian Model

Abstract Conventional geostatistics aims at creating models of heterogeneity and uncertainty in static rock properties such as facies, porosity, and permeability. This approach is appropriate for calculating in place resources and providing nput to flow simulation. 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 practical and useful 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 provides a likelihood distribution. The spatial distribution of each variable by itself is mapped independently of the secondary variable information; this provides a prior distribution. The likelihoods and priors are merged to provide an updated posterior distribution. This technique has been successfully applied in a number of cases. We describe the methodology and show a synthetic example for illustration. Introduction Our goal is to directly predict reservoir performance potential summarized by some production variables. The production variables we are predicting are measures of hydrocarbon flow rate and projected cumulative production. Implicitly we assume that the wells are far enough apart so that they are not interacting together in any significant way. Reservoir characterization uses every data source and interpretive tool possible to improve understanding of the reservoir performance potential at locations where we have no wells. In general, we can group the available data into:Geological variables that take two forms:maps of interpreted variables where the regional depositional setting is taken into consideration and some expert judgement is accounted for in the map making, anddirect well measurements of variables such as porosity, pay thickness and so on. Another grouping of geological variables is into structural and geological variables where the structural variables relate to the container size and shape and the geological variables relate to the 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

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