Dynamic Structure Learning of Factor Graphs and Parameter Estimation of a Constrained Nonlinear Predictive Model for Oilfield Optimization

Injector-producer relationships (IPRs) are the key knowledge for oilfield optimization, i.e., maximizing oil production at the minimum operational cost. The difficulty associated with the field optimization is that the underlying reservoir structure is unknown and changes continuously over time. Inferring IPRs is a large-scale constrained nonlinear parameter estimation problem. The state-of-the-art hybrid constrained nonlinear optimization (HCNO) method provides excellent accuracy for solving this problem but with prohibitive computational costs for large oilfields. In this paper, we propose a dynamic structure learning and parameter estimation approach based on inference in a probabilistic graphical model named PETROGRAPH Learning (PGL). The learning is initiated by constructing an initial factor graph based on a locality principle and is guided by belief discrepancies, estimation error, and residual correlation analysis. At each iteration, the sum-product algorithm is applied to estimate the parameters, and the factor graph structure is refined as the input for the next round. The iterative learning continues until convergence. Experimental results and analysis show that PGL is scalable to the large scale of real oilfields with much less running time than that of HCNO while providing virtually exact solutions.