This investigation presents a powerful predictive model to determine crude oil formation volume factor (FVF) using state-of-the-art computational intelligence (CI) techniques. FVF is a vital pressure-volume-temperature (PVT) parameter used to characterize hydrocarbon systems and is pivotal to reserve evaluation studies and reservoir engineering calculations. Ideally, FVF is measured at the laboratory scale; however, prognostic tools to evaluate this parameter can aid in optimizing time and cost estimates. The database utilized in this study is obtained from open literature and covers statistics of crude oils of Pakistan, Iran, UAE, and Malaysia. Resultantly, this allows to move step forward towards the creation of a generalized model.
Multiple CI algorithms are considered, including Artificial Neural Networks (ANN) and Artificial Neural Fuzzy Inference Systems (ANFIS). Models for CI are developed utilizing an optimization strategy for various parameters/hyper-parameters of the respective algorithms. Unique permutations and combinations for the number of perceptron and their resident layers is investigated to reach a solution that provides the most optimum output. These intelligent models are produced as a function of the parameters intrinsically affecting FVF; reservoir temperature, solution GOR, gas specific gravity, and crude oil API gravity. Comparative analysis of various CI models is performed using visualization/statistical analysis and the best model pointed out. Finally, the mathematical equation extraction to determine FVF is accomplished with the respective weights and bias for the model presented.
Graphical analysis using scatter plots with a coefficient of determination (R2) illustrates that ANN equation produces the most accurate predictions for oil FVF with R2 in excess of 0.96. Moreover, during this study an error metric is developed comprising of multiple analysis parameters; Average Absolute Error (AAE), Root Mean Squared Error (RMSE), correlation coefficient (R). All models investigated are tested on an unseen dataset to prevent the development of a biased model. Performance of the established CI models are gauged based on this error metric, which demonstrates that ANN outperforms the other models with error within 2% of the measured PVT values. A computationally derived intelligent model proves to provide the strongest predictive capabilities as it maps complex non-linear interactions between various input parameters leading to FVF.