Estimation of subsurface petrophysical properties using different stochastic algorithms in nonlinear regression analysis of pressure transients

Accurate characterization of the underground energy resources is crucial in rigorous prediction of their future behavior. Well testing is one of the main operations used in the oil and gas industry to characterize the underground hydrocarbon reservoirs. Among the various factors which affect the accuracy of the well testing, robustness of the optimization algorithm in nonlinear regression is of great important. Therefore, in this study, efficiency and computational time of four different population-based algorithms in solving the well testing regression problem are thoroughly investigated. The employed algorithms consist of a biological evolutionary algorithm, GA (Genetic Algorithm), two swarm-based algorithms, PSO (Particle Swarm Optimization) and FA (Fireflies Algorithm), and a social-based algorithm, ICA (Imperialist Competitive Algorithm). These algorithms have been applied on two different reservoir models including a homogenous infinite-acting, and a heterogenous fractured reservoir. Performances of the employed algorithms are then evaluated both statistically and graphically. The comparison study showed that FA fails to macth the data for both homogenous and heterogenous reservoirs. Although PSO, GA, and ICA come up with lower relative errors for the homogenous model, they still cannot accurately predict all the state variables for the fractured model. Based on relative error and residual plots, PSO and ICA outperform the other algorithms due to their localized searching capabilities. In detail, PSO and ICA end up with the R-squared values of 0.93 and 0.99 for the homogenous and heterogonous fractured models, respectively. Evolution of error over time unveiled that the indicated algorithms encounter problems in matching the transitional wellbore storage and infinite acting zones for the homogenous model; for the fractured model, however, most of the errors are distributed around the transitional matrix-fracture zone. The indicated stochastic algorithms were compared with a well-known derivative-based algorithm, namely LM (Levenberg-Marquardt), and sensitivity analysis showed that LM is very sensitive to the location of the initial point. On average, LM led to higher magnitudes of relative error for both homogenous and heterogenous reservoir models. The computational time for ICA was also lower than the other algorithms, indicating that ICA has the lowest relative error and computational time among the investigated algorithms.