Integrated Computer-Aided Engineering 14 (2007) 213–223 213 IOS Press A neural stochastic multiscale optimization framework for sensor-based parameter estimation Rafael E. Banchs ∗ , Hector Klie, Adolfo Rodriguez, Sunil G. Thomas and Mary F. Wheeler CSM, ICES, The University of Texas at Austin, Texas, USA E-mail: {klie, adolfo, sgthomas, mfw}@ices.utexas.edu Abstract. This work presents a novel neural stochastic optimization framework for reservoir parameter estimation that combines two independent sources of spatial and temporal data: oil production data and dynamic sensor data of flow pressures and concentrations. A parameter estimation procedure is realized by minimizing a multi-objective mismatch function between observed and predicted data. In order to be able to efficiently perform large-scale parameter estimations, the parameter space is decomposed in different resolution levels by means of the singular value decomposition (SVD) and a wavelet upscaling process. The estimation is carried out incrementally from low to higher resolution levels by means of a neural stochastic multilevel optimization approach. At a given resolution level, the parameter space is globally explored and sampled by the simultaneous perturbation stochastic approximation (SPSA) algorithm. The sampling yielded by SPSA serves as training points for an artificial neural network that allows for evaluating the sensitivity of different multi-objective function components with respect to the model parameters. The proposed approach may be suitable for different engineering and scientific applications wherever the parameter space results from discretizing a set of partial differential equations on a given spatial domain. 1. Introduction Subsurface behavioral surveillance and real-time sensing data acquisition is becoming available in an increasing number in environmental and energy reser- voir applications (see e.g. [11,19]). The deployment of sensors is offering unlimited possibilities to monitor and obtain a dynamic understanding of the different processes taking place at different spatial and temporal scales. These advances, in conjunction with time-lapse seismic studies and reservoir production data, are re- vealing enormous potentials to reduce the uncertainty in both reservoir characterization and production sce- narios. Meanwhile, new stochastic optimization and statistical learning methods are arising as promising tools to find nontrivial correlations between data mea- ∗ Corresponding author: Department of Signal Theory and Com- munications, Polytechnic University of Catalonia, Barcelona, Spain. E-mail: rbanchs@gps.tsc.upc.edu. surements and responses and to develop optimal reser- voir exploitation plans (see e.g. [4,8,13,14,17,18]). Nevertheless, parameter estimation in reservoir en- gineering is a very challenging task as there is always the increasing interest in capturing higher resolution levels and more complex physical processes. Figure 1 illustrates the key factors characterizing the uncertainty and high-computational cost associated with these ap- plications. Data are scarce, insufficient and subject to different sources of noise to be able to cope with the es- timation of a large number of parameters. Multiphase flow in porous media is a highly nonlinear process since the fluids may undergo through different regimes at different locations and time intervals due to the het- erogeneous and anisotropic nature of the media and to perturbations induced by well operations. Reservoirs are generally large (3-D and extending to several miles) thus implying the generation of hundreds of thousands to millions of grid-blocks on which the flow equations need to be numerically solved for long time simulation periods (e.g., 10–30 years). Consequently, a high de- ISSN 1069-2509/07/$17.00  2007 – IOS Press and the author(s). All rights reserved