Porosity and Permeability Estimation by Gradient Based History Matching using Time-Lapse Seismic Data

Abstract

Abstract A method based on the Gauss-Newton optimization technique for continuous model updating with respect to 4D seismic data is presented. The study uses a commercial finite difference black oil reservoir simulator and a standard rock physics model to predict seismic amplitudes as a function of porosity and permeabilities. The main objective of the study is to test the feasibility of using 4D seismic data as input to reservoir parameter estimation problems. The algorithm written for this study, which was initially developed for the estimation of saturation and pressure changes from time-lapse seismic data, consists of three parts: the reservoir simulator, the rock physics petro-elastic model, and the optimization algorithm. The time-lapse seismic data are used for observation purposes. In our example, a simulation model generated the seismic data, then the model was modified after this the algorithm was used to fit the data generated in the previous step. History matching of reservoir behavior is difficult because of the problem is not unique. More than one solution exists that matches the available data. Therefore, empirical knowledge about rock types from laboratory measurements are used to constraint the inversion process. The Gauss-Newton inversion reduces the misfit between observed and calculated time-lapse seismic amplitudes. With this method, it is possible to estimate porosity and permeability distributions from time-lapse data. Since these parameters are estimated for every single grid cell in the reservoir model, the number of model parameters is high, and therefore the problem will be underdetermined. Therefore, a good fit with the observation data is not necessary for a good estimation of the unknown reservoir properties. The methods for reducing the number of unknown parameters and the associated uncertainties is discussed. Introduction Parameter estimation using new geophysical knowledge like time-lapse seismic data is a new and probably underdeveloped method so far. The main challenges are to develop a method for estimation of key reservoir parameters with the lowest possible estimation error. Parameter estimation is an iterative trial-and-error process that estimates uncertain parameters by perturbing these parameters in order to make the model fit observed data. History matching is difficult since it requires a lot of experience and knowledge of the field. In addition, the process is inherently non-unique. History matching is not new, and various optimization techniques have been suggested1–5. This process is non-unique and this is the main reason for using time-lapse information in addition to other information to limit the solution space. Time-lapse seismic data are time dependent dynamic measurements6–10, aiming at determining the reservoir changes that have occurred in the intervening time. Most of the reservoir parameters, which are used in reservoir simulators, come from laboratory measurements that are not representative for the entire reservoir and therefore there is a need for correlation. The main advantage of using time-lapse seismic data is that they do not need any correlation, which means they are representative for the entire reservoir. However, the results are associated with errors and uncertainties, which are related to the repeatability of data acquisition, data processing sequences, lack of understanding of rock physics and error in up-scaling and cross-scaling seismic and simulation data. Time-lapse seismic technology was first introduced in the early 1980s and many works have been published since that time in this area 11–17. Porosity and permeability are two of the most important parameters in each reservoir simulation model and they have the largest impact on reserves, production forecasts and economics of the reservoir. These two parameters are most difficult to estimate. The main reasons for these difficulties in the estimation of permeability and porosity are 18: