Abstract

Oil and gas reservoir modelling involves two broad classes of data: static (core, well logs and seismic interpretation, for example) and dynamic (pressure and fluid production observed at wells). Integration of dynamic data together with the static data enhances the quality of the reservoir models generated and provides the reservoir engineers with a better basis for reservoir simulation and management. The uncertainty of simulated production scenarios is then reduced, allowing more realistic economic evaluation. In general, however, integrating these two sources of data is still a challenge in petroleum reservoir modelling.

In this work, an approach, based on the Bayesian formalism, for combining static and dynamic data is discussed. The geological relevant parameters are determined by minimizing an objective function that measures the misfit between observed and calculated dynamic data, using static data as prior information. The use of efficient techniques for calculating derivatives of observed data with respect to parameters and for the optimization algorithm are essential to build a computationally feasible procedure.

Introduction

The main focus of the reservoir characterization and simulation area is the construction of a reservoir model. This model is represented numerically in a 3D collection of data and then serves as the input for a numerical reservoir flow simulator. This numerical tool will solve the flow equations representative of the flow of oil, gas and water inside the reservoir. Its output is the expected performance production curve given a particular production/injection well pattern. The optimization of huge investments allocated to reservoir exploitation strategies fundamentally depends on the precision of this reservoir performance production forecasts. Consequently the knowledge of this reservoir model is one of the key aspects of the overall reservoir management process.

The construction of the reservoir model is not a trivial problem. It is an inverse problem. Inverse problems are, mathematically speaking, ill posed problems for which several solutions can be equally achieved. To reduce solution non-uniqueness, the strategy is to integrate as much data as possible when solving the inverse problem. For the reservoir description problem, two broad classes of data have to be considered: the static data (such as core, log, and seismic data) and the dynamic data (such as transient pressures, saturations and flow rates). While most of the static data can be easily integrated during the construction of the model, the integration of dynamic data is not so easy. In practice, despite certain developments, improvements, the honoring of all data including the dynamic pressure or historical production data in generating reservoir properties has been a missing component of this reservoir modelling process and there is still a lot to achieve in this field of research.

In this paper, we propose a methodology that uses an optimization algorithm to account for the dynamic data. A so-called objective function quantifies the difference between observed and simulated values and reservoir model construction amount to minimizing this function. The next sections will describe in more details the methodology, the optimization algorithm used, and a sample application case with results to be discussed.

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