A Novel Formula for Estimating Oil Compressibility Below Bubble Point Pressure Using Group Method of Data Handling: A Comparative Approach

Abstract

Oil compressibility (co) plays a vital role in vast aspects ranging from upstream to downstream. For reservoir with pressure below bubble point, the effect of co to the fluid flow is insignificant as it is overshadowed by the presence of large gas compressibility (cg). This study aims to increase the range of applicability and accuracy of the formula used for estimating the co by eliminating the limitations of other existing correlations. A new formula for the estimation of oil compressibility below bubble point pressure is devised using Group Method Data Handling (GMDH). The approach is a combination of neural networks and some high-level statistical methods which rely on generating simple relations among the input parameters and the dependent parameter. The relations then result in eliminating some parameters with low impact on the output. A series of consecutive layers with the link is generated, and polynomial terms are created. A total number of 322 data points were collected from different sources from literature. Systematic trend analysis has been conducted to verify that the proposed GMDH model honours the exact physical behaviour. The new proposed model found to follow the correct trend, which implies its soundness. Besides, a comparative study was carried out using the best available correlations to confirm the significance of the results of the oil compressibility prediction using GMDH. Different statistical analyses have been conducted to verify the robustness of the newly developed model. The statistical analyses showed a positive outcome whereby the proposed model obtained the lowest average absolute percentage relative error of 5.17% and the highest correlation coefficient of 96.8%. The best model tested among the other models has five input parameters and an average absolute percentage relative error of 10.955% and a correlation coefficient of 95.6%. The new approach managed to reduce the curse of dimensionality as four input parameters have found to have a strong dependency on co (solution gas-oil ratio, oil density, reservoir temperature, and reservoir pressure). The new proposed model overcome the limitations described by the locality of some correlations as they depend on data from specific locations.

An Accurate Reservoir’s Bubble Point Pressure Correlation

“…On the next layer, the values found from the previous layer are regressed along with the input parameter, and the process continues until no better result is reached. 40 Figure 2 shows the self-organizing GMDH algorithm. 51 …”

“… 38 The GMDH was successfully employed to detect lithofacies present in the South Yellow Sea. 39 Ayoub et al 40 applied GMDH to obtain oil compressibility below P b . However, different statistical error analyses were deployed to show the GMDH model’s robustness.…”

“…However, different statistical error analyses were deployed to show the GMDH model’s robustness. 40 Mathew Nkurlu et al 41 used GMDH to obtain permeability utilizing well log data in their calculations. They presented that the GMDH model outperformed the neural network.…”

Prediction of Permeability Using Group Method of Data Handling (GMDH) Neural Network from Well Log Data

“…The algorithms for the GMDH were first developed by Professor Alexey Grigorevich Ivakhnenko in 1968 with the goal of identifying the affiliation between the involvement layer and output layer in nonlinear systems [25][26][27]. According to Ayoub et al [28], GMDH may also be represented as a polynomial neural networks as well as an algorithm modeling method to define nonlinear input-output variable relationships. Ma et al [29] explained that GMDH algorithm operates by linking sets of neurons connected to quadratic polynomials, resulting in new sets of neurons in the subsequent layer.…”

“…Shen et al [31], developed a GMDH model that can detect the various lithofacies using pre-processing techniques composed of dimensionality reduction (DR) and wavelet analysis (WA). Ayoub et al [28] in their publication, utilized GMDH to model the oil compressibility below the bubble point pressure. Teng et al [32] proposed a GMDH model to predict China's transport energy demand, the proposed model showed very satisfactory predictions.…”