Inversion of seismic attributes for petrophysical parameters and rock facies

Abstract

Prediction of rock and fluid properties such as porosity, clay content, and water saturation is essential for exploration and development of hydrocarbon reservoirs. Rock and fluid property maps obtained from such predictions can be used for optimal selection of well locations for reservoir development and production enhancement. Seismic data are usually the only source of information available throughout a field that can be used to predict the 3D distribution of properties with appropriate spatial resolution. The main challenge in inferring properties from seismic data is the ambiguous nature of geophysical information. Therefore, any estimate of rock and fluid property maps derived from seismic data must also represent its associated uncertainty. In this study we develop a computationally efficient mathematical technique based on neural networks to integrate measured data and a priori information in order to reduce the uncertainty in rock and fluid properties in a reservoir. The post inversion (a posteriori) information about rock and fluid properties are represented by the joint probability density function (PDF) of porosity, clay content, and water saturation. In this technique the a posteriori PDF is modeled by a weighted sum of Gaussian PDF’s. A so-called mixture density network (MDN) estimates the weights, mean vector, and covariance matrix of the Gaussians given any measured data set. We solve several inverse problems with the MDN and compare results with Monte Carlo (MC) sampling solution and show that the MDN inversion technique provides good estimate of the MC sampling solution. However, the computational cost of training and using the neural network is much lower than solution found by MC sampling (more than a factor of 104 in some cases). We also discuss the design, implementation, and training procedure of the MDN, and its limitations in estimating the solution of an inverse problem. In this thesis we focus on data from a deep offshore field in Africa. Our goal is to apply the MDN inversion technique to obtain maps of petrophysical properties (i.e., porosity, clay content, water saturation), and petrophysical facies from 3D seismic data. Petrophysical facies (i.e., non-reservoir, oil- and brine-saturated reservoir facies) are defined probabilistically based on geological information and values of the petrophysical parameters. First, we investigate the relationship (i.e., petrophysical forward function) between compressional- and shear-wave velocity and petrophysical parameters. The petrophysical forward function depends on different properties of rocks and varies from one rock type to another. Therefore, after acquisition of well logs or seismic data from a geological setting the petrophysical forward function must be calibrated with data and observations. The uncertainty of the petrophysical forward function comes from uncertainty in measurements and uncertainty about the type of facies. We present a method to construct the petrophysical forward function with its associated uncertainty from the both sources above. The results show that introducing uncertainty in facies improves the accuracy of the petrophysical forward function predictions. Then, we apply the MDN inversion method to solve four different petrophysical inverse problems. In particular, we invert P- and S-wave impedance logs for the joint PDF of porosity, clay content, and water saturation using a calibrated petrophysical forward function. Results show that posterior PDF of the model parameters provides reasonable estimates of measured well logs. Errors in the posterior PDF are mainly due to errors in the petrophysical forward function. Finally, we apply the MDN inversion method to predict 3D petrophysical properties from attributes of seismic data. In this application, the inversion objective is to estimate the joint PDF of porosity, clay content, and water saturation at each point in the reservoir, from the compressional- and shear-wave-impedance obtained from the inversion of AVO seismic data. Uncertainty in the a posteriori PDF of the model parameters are due to different sources such as variations in effective pressure, bulk modulus and density of hydrocarbon, uncertainty of the petrophysical forward function, and random noise in recorded data. Results show that the standard deviations of all model parameters are reduced after inversion, which shows that the inversion process provides information about all parameters. We also applied the result of the petrophysical inversion to estimate the 3D probability maps of non-reservoir facies, brine- and oil-saturated reservoir facies. The accuracy of the predicted oil-saturated facies at the well location is good, but due to errors in the petrophysical inversion the predicted non-reservoir and brine-saturated facies are ambiguous. Although the accuracy of results may vary due to different sources of error in different applications, the fast, probabilistic method of solving non-linear inverse problems developed in this study can be applied to invert well logs and large seismic data sets for petrophysical parameters in different applications.