Scatter Search for Optimizing the Formation-Rate Analysis (FRA) Model

Abstract

Abstract The Formation Rate Analysis (FRA) method applies the multivariate linear regression method to invert pressure test data to estimate formation parameters. This method is simple and works well if the measured pressure transient noise is small. However, if the noise is large, errors in the estimated formation parameters are unacceptably large. To solve this problem, we present a multi-scale scatter search optimization method. The basic idea of this optimization method is to iteratively generate sampling points using Hammersley random sequences in regions of various sizes in the parameter space. A reference data set is generated from the candidate optimal solutions and then used to filter the generated sampling points. The uncertainty of the calibrated formation parameters is quantified based on the searched valid optimal solutions. We test this algorithm with formation test data from low permeability, high permeability, and tight formations. Its accuracy, efficiency, and reliability are validated. We also compare it with the original FRA method. The test results show that: compared with the linear regression method, this algorithm more accurately estimates the formation parameters, particularly for the tight formation; compared with the direct Monte Carlo method, this new algorithm more efficiently provides calibrated formation parameters and quantifies more accurately the associated uncertainties; for high permeability formations, the estimated uncertainty of the calibrated formation pressure is very small; for tight formations, flow-line fluid compressibility can be effectively calibrated. However, the short length of the measured pressure transient results in a large uncertainty in the estimated formation pressure and mobility. Also, the mean value of the formation pressure is underestimated if the pressure transient is far from being stabilized.