High Resolution Reservoir Models Integrating Multiple-Well Production Data
Authors: Wen Xian-Huan , Deutsch Clayton V. , Cullick A.S. 
Published: December 2007

Abstract
This paper presents a methodology to generate maps of high resolution permeability from multiple well single-phase flow rate and pressure data. The dynamic, i.e. temporal, production data contains important information about the interwell permeability distribution that should be integrated with static data, such as well and seismic data, to generate reservoir models to provide reliable input to reservoir simulation and reservoir management. A two-step procedure is proposed for such data integration:establish the spatial constraints on large-scale permeability trends due to the production data using an inverse technique, andconstruct the detailed geostatistical reservoir models subject to those spatial constraints using geostatistical techniques.
The single-phase pressure and production data could be provided by permanent pressure gauges, simultaneous multiple well tests, or flow rates under primary depletion. Production data and reservoir petrophysical properties, specifically permeability. are nonlinearly related through flow equations. Establishing the spatial constraints on permeability due to production data calls for the solution of a difficult inverse problem. This paper adapts the Sequential Self-Calibration (SSC) inverse technique to single-phase multiple- well transient pressure and rate data. The SSC method is an iterative geostatistically-based inverse method coupled with an optimization procedure that generates a series of coarse grid 2-D permeability realizations, whose numerical flow simulations correctly reproduce the production data. Inverse results using two synthetic data sets show this SSC implementation to be flexible, computationally efficient, and robust.
Fine-scale models generated by down-scaling the SSC generated coarse-scale models (using simulated annealing) are shown to preserve the match to the production data at the coarse-scale. Finally, reservoir performance prediction results show how the integration of production data can dramatically improve the accuracy of production forecasting with significantly less uncertainty.

Introduction
Optimal reservoir management requires reliable performance forecasts with as little uncertainty as possible. Incomplete data and inability to model the physics of fluid flow at a suitably small scale lead to uncertainty. Uncertainties in the detailed description of reservoir lithofacies porosity, and permeability are large contributors to uncertainty in reservoir performance forecasting. Reducing this uncertainty can only be achieved by integrating additional data in reservoir modeling.
A large variety of geostatistical techniques have been developed that construct reservoir models conditioned to diverse types of static data including hard well data and soft seismic data. Commonly, a number of techniques are applied sequentially to model the large reservoir geometry, the lithofacies, and then petrophysical properties such as porosity and permeability. However, conventional geostatistical techniques including Gaussian, indicator, annealing-based, or object-based methods are not suited to directly integrate dynamic production data.
Production data and reservoir petrophysical properties are related to each other through flow equations which are highly nonlinear. As a consequence, accounting for dynamic engineering data in geostatistical reservoir modeling is a difficult inverse problem. Nevertheless, historical production data are often the most important information because they provide a direct measure of the actual reservoir response to the recovery process that form the basis for reservoir management decisions. Integrating dynamic production data is an important outstanding problem in reservoir characterization. Ideally, we want to directly match all types of production data in the reservoir model at the required resolution simultaneously with other types of geological and geophysical data. A number of inverse techniques have been developed for this purpose.
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