**Salaheldin Elkatatny**

College of Petroleum Engineering & Geosciences, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia; elkatatny@kfupm.edu.sa; Tel.: +966-594663692

Received: 14 August 2019; Accepted: 11 September 2019; Published: 12 September 2019

**Abstract:** The rheological properties of drilling fluids are the key parameter for optimizing drilling operation and reducing total drilling cost by avoiding common problems such as hole cleaning, pipe sticking, loss of circulation, and well control. The conventional method of measuring the rheological properties are time-consuming and require a high effort for equipment cleaning, so they are only measured twice a day. There is a need to develop an automated system to measure the rheological properties in real-time based on the frequent measurements of mud density, Marsh funnel time, and solid percent. The main objective of this paper is to apply a modified self-adaptive differential evolution technique to determine the optimum combination of an artificial neural network's variables to precisely predict the rheological properties of water-based drill-in fluid using the frequent measuring of mud density, Marsh funnel time, and solid percent. The second objective is whitening the black box of an artificial neural network by developing five new empirical correlations to determine the rheological properties without the need for the artificial neural network models. Actual field measurements (900 data points) were used to train, test, and validate the artificial neural network models and the developed empirical correlations. The optimization process illustrated that the best training function was Bayesian regularization backpropagation (trainbr), and the best transferring function was Elliot symmetric sigmoid (elliotsig). The optimum number of neurons was 30 for the plastic viscosity and the flow consistency index, while it was 29 for apparent viscosity, yield point, and the flow behavior index. The developed artificial neural network models and empirical correlations predicted the rheological properties with high accuracy. The correlation coefficient (R) was more than 90%, and the average absolute percentage error was less than 8.6%. The new technique for rheological properties estimation is an example of the new development which will help the new generation to discover and extract oil and gas with less cost and with safer operations.

**Keywords:** empirical correlations; rheological properties; real-time; water-based drill-in fluid; artificial neural network
