Use of Geostatistical Modeling and Automatic History Matching to Estimate Production Forecast Uncertainty - A Case Study

Abstract

Abstract Determining production forecast uncertainty from simulation models is one of the major challenges facing reservoir engineers. Often a single deterministic model or geostatistical realization with a single permeability transform and set of relative permeability curves is taken from a history match and then used to prepare forecasts. Geostatistical realizations inconsistent with the chosen set of permeability transforms or SCAL data are discarded. This leads to troubling questions as to the uniqueness of the history-matched model, the uncertainties associated with the forecasts and the magnitude of risk for reservoir development. In this paper these concerns are addressed with an approach that uses automated history matching based on the gradient method to obtain a history match for more than one geostatistical representation. This approach takes into consideration both geological uncertainties and uncertainties in pressure and saturation matching parameters. In addition, the approach is fast and can be partially automated to complete history matches and forecasts of stochastic models as they are updated with the drilling of additional wells. It can also be used to reject realizations that require absolute or relative permeabilities outside their range of uncertainty or lead to large differences between observed and simulated data. For the example reservoir - a fluvial-deltaic system in the eastern part of Venezuela, nine geostatistical realizations composed of 2.6 million cells each were generated, based on the range of structural interpretations and static parameters that could be expected. These realizations were then upscaled to 90,000 cell models and history matched in parallel. The automated history matching procedure involved the determination of the gradient sensitivity for key absolute and relative permeability parameters and subsequently the regression on the most sensitive and independent of these to obtain a minimum of the objective function. The realizations that resulted in best matches of field pressure and water production were brought forward to produce forecasts that resulted in an estimate of uncertainty for various field development options. Introduction A review of reservoir engineering and geology over the last decade has seen two parallel developments. On the reservoir side there has been an increase in the use of automated or assisted history matching techniques in order to reduce the time spent in model calibration. The impetus behind this is the need for more efficient use of human resources, and for faster identification of development potential. On the geological side, there has been increasing use of geostatistical or stochastic modeling techniques to address uncertainty in geological modeling. The common objective is to reduce development risk by reducing subjectivity and generating more diverse reservoir descriptions. Coupled with these developments is the increasing integration of the work of geologists and engineers and increasing recognition of a mismatch in objectives. The assisted history matching techniques have, until recently, been applied to deterministic models, and have involved the manipulation of variables (practically or theoretically) outside of the control of geologists. The algorithms used to achieve a history match for these models, as described by Tan and Kalogerakis1 and others are generally known as the gradient method, which arrive at a rapid minimization of the differences between observed and simulated data (otherwise known as the objective function). The disadvantage of these methods is that because of the models' deterministic nature, they do not take into account the full range of geological possibilities available. For this and other reasons they often result in local instead of global minimums of the objective function. Further, if this method is applied to modify a geostatistical realization, it often violates the assumptions on which the realization is based. From a practical standpoint, simulation engineers generally ignore this rule, which often provokes much discussion at peer reviews!