Determination of Drilling Mud Density Change with Pressure and Temperature Made Simple and Accurate by ANN

Abstract

Abstract An artificial neural networks (ANN) model has been developed to provide accurate predictions of mud density as a function of mud type, pressure and temperature. Available experimental measurements of water-base and oil-base drilling fluids at pressures ranging from 0 to 1400 psi and temperatures up to 400 °F were used to develop and test the ANN model. With the knowledge of the drilling mud type (water-base, or oil-base) and its density at standard conditions (0 psi and 70 °F) the developed model provides predictions of the density at any temperature and pressure (within the ranges studied) with an average absolute percent error of 0.367, a root mean squared error of 0.0056 and a correlation coefficient of 0.9998. Introduction The density of a drilling fluid is normally determined at standard conditions of 0 psi and 70 °F. As the drilling operation progresses, the drilling fluid will be subjected to increasing pressure and temperature. While the higher pressure increases the drilling fluid density, the increased temperature results in density reduction. Proper planning and execution of drilling operations, particularly for HPHT wells, requires complete and accurate knowledge of the behavior of the drilling fluid density as the pressure and temperature change during the drilling operation. Such information can accurately be obtained only through actual measurements of the drilling fluid density at desired pressures and temperatures. This, however, requires special equipment along with difficult and time-consuming procedures. Prediction of the drilling mud density at various pressures and temperatures is, therefore, very useful for mud and drilling engineers in planning drilling operations. McMordie et al1 studied the effect of temperature and pressure on the density of water-base and oil-base drilling fluids. They presented experimental measurements of densities in the temperature range of 70 °F to 400 °F and pressure range of 0 - 14000 psi and concluded that the change in mud density with pressure and temperature is independent of the initial mud density (at 70 °F and 0 psi). They also concluded that for equal densities at surface conditions, oil-base drilling fluids become denser than water-base drilling fluids at high temperatures and pressures. Okoye et al2 used the data of McMordie et al and developed various correlations of water-base mud density as a function of temperature for various values of surface mud density. These correlations, however, ignored the effect of pressure on mud density and are limited to water-base drilling fluids of specific surface density and to the range of temperatures and pressures covered by the experimental measurements. Away from empirical correlations and their inherent limitations, artificial neural networks (ANN) models have been proven in recent years to be very effective means of solving difficult problems in the oil industry. This paper presents an ANN model that provides, with great accuracy, predictions of water-base and oil-base drilling fluids density. Identifying the type of drilling fluid (water-base, or oil-base) and the density at surface conditions, the developed model predicts the density at any temperature and pressure. Artificial Neural Networks An artificial neural network is a computer model that attempts to mimic simple biological learning processes and simulate specific functions of human nervous system. It is an adaptive, parallel information processing system, which is able to develop associations, transformations or mappings between objects or data. It is also the most popular intelligent technique for pattern recognition to date. The basic elements of a neural network are the neurons and their connection strengths (weights). Given a topology of the network structure expressing how the neurons (the processing elements) are connected, a learning algorithm takes an initial model with some "prior" connection weights (usually random numbers) and produces a final model by numerical iterations. Hence "learning" implies the derivation of the "posterior" connection weights when a performance criterion is matched (e.g. the mean square error is below a certain tolerance value). Learning can be performed by a set of known input-output data patterns (or training patterns)3.