An Intelligent Functional Network Approach to Develop Mathematical Model to Predict Sonic Waves Travel Time for Carbonate Rocks

Abstract

Abstract Compressional and shear wave travel times are used to determine rock dynamic elastic parameters. Elastic parameters are used in obtaining the in-situ stresses of the rock, calculate safe mud weight, avoid wellbore instability problems and design optimum hydraulic fracture geometry. Often overlooked, weakness in the calculation of elastic parameters studies is a major cause of well-bore problems and unsuccessful well stimulation jobs. In well logging, compressional and shear wave travel time logs are one of the common logs to be recoreded in almost every formation. In cases when the sonic logs are missing, these logs values are estimated using empirical correlations. So far, none of the available models or correlations are universally accepted by log analysts since every model estimates the log values significantly different from the others, which may be suitable for one reservoir and not for other. As a result, inaccurate values can potentially raise major concerns throughout the life of the well. The error in sonic log values affects the elastic parameters, which can result in either underestimation or overestimation of the in-situ stresses. So, the objective of this paper is to develop robust empirical model for compressional and shear wave travel times using different functional network approach. For this purpose, well logs data, such as; gamma ray, bulk density, and neutron porosity were collected from different wells which are drilled in a carbonate formation. Functional network tool is used to develop mathematical model for compressional and shear wave travel times. This AI model were trained on the data of several well and validated on the remaining wells. Different types of functional network tools were studied, namely; forward selection model FNFSM, backward elimination model FNBEM, forward backward model FNFBM and backward forward model FNBFM. Then based on correlation coefficient R and average absolute percentage error AAPE, a comparison was made and the one which performed better was selected for prediction of sonic wave transit times. The novelty of this work is that for the first time, the explicit mathematical model is developed from functional network to estimate compressional and shear wave travel time. The mathematical model developed from the functional network is easier to implement. The new model will eliminate the need to use expensive software to run AI model. The new model for sonic transit time significantly reduces the uncertainties in calculating the sonic transit times in carbonate formation.