Dynamic Data Integration in Stochastic Reservoir Models

Abstract Developing geostatistical reservoir models that are geologically realistic and correctly reflect production history is important for accurately assessing the uncertainty associated with production forecasts. Conditioning reservoir models to dynamic data is challenging due to the non-linear relationship between the measured flow response data and the model parameters (porosity, permeability etc.). Recently, a novel methodology was presented to integrate geological as well as production information into reservoir models in a probabilistic manner (CIM paper 2002–125). In this paper we investigate the convergence aspects of the algorithm and propose an extension to account for multiple flow domains in a reservoir and locally varying deformation parameters. The improved methodology is validated on a complex reservoir model. Introduction Reservoir modeling is a crucial step in the development and management of petroleum reservoirs. Development decisions made during the life of a reservoir such as depletion strategy, number and location of production/injection wells, reservoir pressure maintenance schemes, etc. require an accurate model of reservoir heterogeneities and topology. In order to be able to predict future reservoir performance accurately, it is necessary to generate a reservoir model that honors all available data, accounting for the scale and precision at which they are available. The challenge is to extract the maximum possible reservoir specific information from all available data. A flow simulation on reservoir models conditioned to static data alone might not always match the field production response. These models then have to be manually adjusted to reproduce the historic data (historymatched), and this is a very tedious and time-consuming process. In the process of adjusting to "history match", the spatial covariance model that reflects the geological structure may be destroyed. Hence even after obtaining a very good match to the historical data, the model may fail to deliver accurate performance predictions. This problem could be alleviated if the historical dynamic data is integrated into the reservoir model generation step such that the final model is conditioned to all the available static data as well as the dynamic data. Since production data contains valuable information pertaining to the connectivity characteristics of the reservoir, performance predictions using the dynamically constrained reservoir model are likely to be more accurate. However, production data are related to the intrinsic characteristicsof the rock generally through a complex, non-linear transfer function and this makes the conditioning of reservoir models to production data more demanding. Data Integration - A Probabilistic Approach Recounting the methodology outlined in Kashib and Srinivasan, 2002. Consider a Markov chain (Caers, J., 1999, Goodman, R., 1999) comprising of iterative steps l,..,L such that the outcome of the indicator RV I (u) at step l is dependent only on the outcome at the previous step l. The chain is parameterized by a dynamic factor rD €[0,1] (Caers, J., 2002) that quantifies the probability of transitioning from indicator category k at step l to the category k' at step l given the historic production data. The parameterization is written as: Equation (1) (Available in full paper) Equation (2) (Available in full paper)

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