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With the increasing acceptance of stochastic workflows in mainstream reservoir engineering studies, many frameworks have been developed to assist in the history match of reservoir models. This paper describes the application of experimental design and response surface methods, not only in conditioning complex reservoir models to the historical production data but also in refining the reservoir models to improve the overall history match results. The reservoirs are in the Niger Delta and consist of faulted layers from both the Benin and Agbada formations. The reservoir models envelop all major reservoir uncertainties ranging from static parameters such as structure and porosity to dynamic parameters such as aquifer strength, relative permeability, and even production records. The experimental design combined all the subsurface uncertainties in different realizations and ensembles to construct response surface models capturing the multiple responses of the simulated historical performance. These response surface models serve three main purposes: identification of the "heavy hitters," improving the reservoir model, and facilitating the stochastic history match. The history-matched ensemble successfully explained the reservoir and drainage point production performance; identified uncertainties that have the most significant impact on the historical performance and development; established the most likely original water contact for one of the reservoir compartments; explained the connectivity between the different fault blocks; and formed the basis for risk mitigation analysis of further development in the reservoir. Introduction The usefulness of a model in supporting future development activities in a reservoir depends largely on how well the model is able to explain past reservoir production performance. This process, known as history match, involves conditioning a reservoir model to the historical production data. However, history match is not only a difficult problem; it is a non-unique and generally time-consuming inverse problem to solve. This non-uniqueness results in several combinations of model parameters that can adequately explain past reservoir performance. Though these models may satisfactorily explain past performance, they often produce divergent outcomes when used for predicting the future performance of the reservoir. This range of outcomes relates directly to the uncertainty associated with any development option and forms a critical input in business decisions. It is, therefore, desirable to have a method that both capture the widest possible combination of model parameters that explains historical production data and is quick to update. Considering the time intensive nature of history match and its other limitations, the traditional deterministic approach that relies on a trial-and-error method may be inappropriate in meeting these objectives. On the other hand, the process of stochastic history matching is different from conventional history matching and is more suited to handling uncertainties consistently. It involves creating a response surface model by fitting the outcomes of an experimental design to an equation containing the most influential parameters.

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Waterflooding is among the oldest and perhaps most economical of oil-recovery processes to extend field life and increase ultimate oil recovery from naturally depleting reservoirs. Today, organizations have to strive for lean and efficient technologies and processes to maximize profits when looking deeper into their reservoir portfolios in order to identify additional waterflooding opportunities. Time and information constraints can limit the depth and rigor of such a screening evaluation. Time is reflected by the effort of screening a vast number of reservoirs for the applicability of implementing a waterflood, whereas information is reflected by the availability and quality of data (consistency of measured and modeled data with the inherent rules of a petroleum system) from which to extract significant knowledge necessary to make good development decisions.A new approach to screening a large number of reservoirs uses a wide variety of input information and satisfies a number of constraints such as physical, financial, geopolitical, and human constraints. In a fully stochastic workflow that includes stochastic back population of incomplete data sets, stochastic proxy models over time series, and stochastic ranking methods using Bayesian belief networks (BBNs), more than 1,500 reservoirs were screened for additional recovery potential with waterflooding operations. The objective of the screening process was to reduce the number of reservoirs by one order of magnitude to approximately 100 potential candidates that are suitable for a more detailed evaluation. Numerical models were used to create response surfaces as surrogate reservoir models that capture the sensitivity and uncertainty of the influencing input parameters on the output. Reservoir uncertainties were combined with expert knowledge and environmental variables and were used as proxy model states in the formulation of objective functions. The input parameters were initiated and processed in a stochastic manner throughout the presented work. The output is represented by a ranking of potential waterflood candidates.The benefit of this approach is in the inclusion of a wide range of influencing parameters while at the same time speeding up the screening process without jeopardizing the quality of the results.

Waterflooding is among the oldest and perhaps most economical of Enhanced Oil Recovery (EOR) processes to extend field life and increase ultimate oil recovery from naturally depleting reservoirs. High oil prices provide incentive for companies to look deeper into their reservoir portfolios for additional waterflooding opportunities. Time and information constraints can limit the depth and rigor of such a screening evaluation. Time is reflected by the effort of screening a vast number of reservoirs for the applicability of implementing a waterflood, whereas information is reflected by the availability of data (consistency of measured and modeled data) with which to extract significant knowledge necessary to make good development decisions.A new approach to screening a large number of reservoirs uses a wide variety of input information and satisfies a number of constraints such as physical, financial, geopolitical, and human constraints. In a fully stochastic workflow that includes stochastic back-population of incomplete datasets, stochastic proxy models over time series, and stochastic ranking methods such as Bayesian belief networks, more than 1,500 reservoirs were screened to reduce their number by one order of magnitude to about 100 potential candidates that are suitable for a more detailed phase of evaluation. Numerical models were used to create response surfaces that capture the sensitivity and uncertainty of the influencing input parameters on the output. Reservoir uncertainties were combined with expert knowledge and environmental variables and were used as proxy model states in the formulation of objective functions. The input parameters were assigned in a stochastic manner. The output is represented by a ranking of potential waterflood candidates.The benefit of this approach is in the inclusion of a wide range of influencing parameters while at the same time speeding up the screening process without jeopardizing the quality of the results.