Real-Time Prediction of Plastic Viscosity and Apparent Viscosity for Oil-Based Drilling Fluids Using a Committee Machine with Intelligent Systems

Abstract

The prediction of drilling mud rheological properties is a crucial topic with significant importance in analyzing frictional pressure loss and modeling the hole cleaning. Based on Marsh viscosity, mud density, and solid percent, this paper implements a committee machine intelligent system (CMIS) to predict apparent viscosity (AV) and plastic viscosity (PV) of oil-based mud. The established CMIS combines radial basis function neural network (RBFNN) and multilayer perceptron (MLP) via a quadratic model. Levenberg–Marquardt algorithm was applied to optimize the MLP, while differential evolution, genetic algorithm, artificial bee colony, and particle swarm optimization were used to optimize the RBFNN. A databank of 440 and 486 data points for AV and PV, respectively, gathered from various Algerian fields was considered to build the proposed models. Statistical and graphical assessment criteria were employed for investigating the performance of the proposed CMIS. The obtained results reveal that the developed CMIS models exhibit high performance in predicting AV and PV, with an overall average absolute relative deviation (AARD %) of 2.5485 and 4.1009 for AV and PV, respectively, and a coefficient of determination (R²) of 0.9806 and 0.9753 for AV and PV, respectively. A comparison of the CMIS-AV with Pitt's and Almahdawi's models demonstrates its higher prediction capability than these previously published correlations.

Appendices

Appendix A. Statistical Formulas

The statistical criteria employed to evaluate the proposed models are expressed as follows:

$$RMSE = \sqrt {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left( {Y_{{{\text{exp}}}} - Y_{{{\text{pred}}}} } \right)^{2} }$$

(A.1)

$$R^{2} = 1 - \frac{{\mathop \sum \nolimits_{i = 1}^{n} (Y_{{{\text{exp}}}} - Y_{{{\text{pred}}}} )^{2} }}{{\mathop \sum \nolimits_{i = 1}^{n} (Y_{{{\text{exp}}}} - Y_{{{\text{pred}}}} )^{2} }}$$

(A.2)

$$AARD = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left| {\frac{{Y_{{{\text{exp}}}} - Y_{{{\text{pred}}}} }}{{Y_{{{\text{exp}}}} }}} \right| \times 100$$

(A.3)

where $Y_{{{\text{exp}}}}$ and $Y_{{{\text{pred}}}}$ represent the experimental and predicted values of viscosity, respectively.

Appendix B. Supplementary Data

A supplementary file was uploaded to the system. This file contains the obtained weight factors $C_{1} ,C_{2} \ldots C_{10}$ of the AV-CMIS and PV-CMIS, the centers $C_{ij}$, the weights $w_{i}$, and the bias of the AV-RBFNN-ABC, AV-RBFNN-DE, AV-RBFNN-PSO, PV-RBFNN-ABC, PV-RBFNN-DE, and PV-RBFNN-PSO;