Comparison of optimization algorithms for parameter estimation of multi-phase flow models with application to geological carbon sequestration

Abstract Optimization of multi-phase transport models is important both for calibrating model parameters to observed data and for analyzing management options. We focus on examples of geological carbon sequestration (GCS) process-based multi-phase models. Realistic GCS models can be very computationally expensive not only due to the spatial distribution of the model but also because of the complex nonlinear multi-phase and multi-component transport equations to be solved. As a result we need to have optimization methods that get accurate answers with relatively few simulations. In this analysis we compare a variety of different types of optimization algorithms to understand the best type of algorithms to use for different types of problems. This includes an analysis of which characteristics of the problem are important in choice of algorithm. The goal of this paper is to evaluate which optimization algorithms are the most efficient in a given situation, taking into account shape of the optimization problem (e.g. uni- or multi-modal) and the number of simulations that can be done. The algorithms compared are the widely used derivative-based PEST optimization algorithm, the derivative-based iTOUGH2, the Kriging response surface algorithm EGO, the heuristics-based DDS (Dynamically Dimensioned Search), and the Radial Basis Function surrogate response surface based global optimization algorithms ‘GORBIT’ and ‘Stochastic RBF’. We calibrate a simple homogeneous model ‘3hom’ and two more realistic models ‘20layer’ and ‘6het’. The latter takes 2 h per simulation. Using rigorous statistical tests, we show that while the derivative-based algorithms of PEST are efficient on the simple 3hom model, it does poorly in comparison to surrogate optimization methods Stochastic RBF and GORBIT on the more realistic models. We then identify the shapes of the optimization surface of the three models using enumerative simulations and discover that 3hom is smooth and unimodal and the more realistic models are rough and multi-modal. When the number of simulations is limited, surrogate response surfaces algorithms perform best on multi-modal, bumpy objective functions, which we expect to have for most realistic multi-phase flow models such as those for GCS.