Application of Function Approximations to Reservoir Engineering

Abstract

The need for function approximations arises in many branches of engineering, and in particular, petroleum engineering. A function approximation estimates an unknown function, which then finds an underlying relationship within a given set of input-output data. In this study, a Multiple Regression Analysis (MRA), Artificial Neural Network (ANN), and Least Squares Support Vector Machine (LS-SVM) are applied to address some of the most three important ongoing challenges in reservoir engineering. The three ongoing challenges are reservoir fluid properties in the absence of PVT analysis, average reservoir pressure and oil production prediction.

The PVT properties of crude-oil such as the bubble point pressure (P[subscript b]), oil formation volume factor (B[subscript ob]), dissolved GOR (R[subscript sob]) and stock tank vent GOR (R[subscript ST]) play a key role in calculating reserves as well as for identification of reservoir characteristics. The properties are traditionally determined from laboratory analyses of reservoir oil samples. In the absence of experimental analysis, empirical correlations or models can be used to estimate reservoir fluid properties. In this study, MRA, ANN and LS-SVM are applied to develop PVT models with which to estimate the P[subscript b], B[subscript ob], R[subscript sob] and R[subscript ST]. Unlike the present PVT models, the proposed models can be applied in a straightforward manner by using direct field data. Additional correlations or experimental analyses are unnecessary. Insight into average reservoir pressure (P[subscript avg]), and its change over time, plays a critical role in reservoir development. However, in order to determine the P[subscript avg], the well is shut-in for a build up test, resulting in loss of production. In high permeability reservoirs,this may not be a significant issue, but in medium to low permeability reservoirs, the shut-in period during the entire test may last several weeks before a reliable reservoir pressure can be estimated. This loss of production, and cost of monitoring the shut-in pressure, is often unacceptable. It is of great practical value if the P[subscript avg] can be obtained from the historical production and reservoir pressure data without having to shut-in the well. Three different models (BP-ANN, ANN-GA and LS-SVM) are obtained to predict and interpolate P[subscript avg] without closing the producing wells. The results indicate the proposed approach has the ability to accurately interpolate and predict current average reservoir pressure by employing historical production data. The prediction of oil reservoir production performance has been an on-going challenge for engineers. It is an essential component of petroleum reservoir management. Traditionally, numerical simulations and decline curve analysis have been used to predict a reservoir’s future performance based on its current and past performance. Reservoir simulation is very time consuming and offers a non-unique solution with a high degree of uncertainty. On the other hand, decline curve analysis fits the observed production rates of individual wells, groups of wells or an entire reservoir using mathematical functions to predict future production by extrapolating the declining function. In this study, ANN and LS-SVM are presented to predict the performance of oil production within water injection reservoirs. The historical production and injection data are used as inputs. The approach can be categorized as a new and rapid method with reasonable results. Another application of these models is that it can be utilized to find the most economical scenario of water injection to maximize ultimate oil recovery. This method could be a new window for fast simulators. It has reasonable accuracy, requires little data and can forecast quickly.