In petroleum engineering, simulation models are used in reservoir performance prediction and in the decision-making process. These models are complex systems, typically characterized by a vast number of input parameters. Typically, the physical state of the reservoir is highly uncertain and, thus, the appropriate parameters of the input choices are also highly uncertain. 4D seismic data can reduce significantly the uncertainty of the reservoir because it has a high area resolution, as opposed to the observed well rates and pressure. However, two main challenges are faced to calibrate the simulation model using 4D seismic data. The process can be time consuming because most models go through a series of iterations before being considered sufficiently accurate to give an adequate representation of the physical system. The consideration of 4D seismic data as an observed parameter in the form of maps would lead to an unfeasibly large number of variables to be matched. To overcome such issues, the construction of an emulator that represents the simulation model and the use of the canonical correlation technique to incorporate 4D seismic data can be used. The present study constructed a stochastic representation of the computer model called an emulator to quantify the reduction in the parameter input space. 4D seismic data was incorporated in the procedure through the canonical correlation technique. The water saturation map derived from seismic data was converted into seven canonical functions. Such functions represent the observable characteristics to be matched in the uncertainty reduction process. A high number of evaluations was necessary to identify the range of input parameters whose outputs matched the historical data (4D seismic data). The large number of evaluations justifies the use of an emulator and the reduction of uncertainties with areal characteristics shows that 4D seismic data was successfully incorporated. The emulator methodology represents a powerful tool in the analysis of complex physical problems such as history matching. The incorporation of 4D seismic data as an observable output to be matched leads to a difficult problem to be solved. However, the canonical correlation permitted a successful incorporation of such data into the problem.
Jin, Long (Shell) | Gao, Guohua (Shell) | Vink, Jeroen C. (Shell Intl. E&P Co.) | Chen, Chaohui (Shell International EP) | Weber, Daniel (Shell Intl. E&P Co.) | Alpak, Faruk Omer (Shell Intl. E&P Co.) | van den Hoek, Paul (Shell) | Pirmez, Carlos (Shell Intl. E&P Co.)
Quantitative integration of 4D seismic data with production data into reservoir models is a challenging task. One important issue is how to properly quantify the uncertainty, or the posterior probability distribution (PPD). The Very Fast Simulated Annealing (VFSA) is a stochastic searching method, whereas the Simultaneous Perturbation and Multivariate Interpolation (SPMI) is a model-based local searching method. The stochastic features of the VFSA provide the feasibility of identifying possible multiple peaks of a PPD, but it converges very slowly. On the other hand, the model-based SPMI method has the advantages of effectively utilizing the smooth features of an objective function, and thus can converge to local optimum very quickly. More importantly, the Hessian of the objective function, or the covariance matrix of the PPD, can be estimated by the SPMI method with satisfactory accuracy. However, it is very difficult to identify multiple optima by applying the SPMI method alone. In this paper, we propose an efficient joint inversion workflow by appropriately integrating the two derivative
free optimization (DFO) methods. The complementary features of the two methods can further improve both applicability and efficiency of this joint inversion workflow. We tested the workflow with a 3D synthetic model and a real field case. Our results show that the integrated method is efficient and can deliver good results for jointly assimilating 4D seismic and production data.