A New Adaptively Scaled Production Data Integration Approach Using the Discrete Cosine Parameterization Conference Paper uri icon

abstract

  • History matching problems are typically underdetermined and can have problems with uniqueness and stability of the solution and preserving geologic realism which is critical for a reliable forecast of not only future production but also the distribution of bypassed hydrocarbon in the reservoir. We propose a new adaptive multi-stage history matching formulation that parameterizes the reservoir properties in the frequency domain where the geologic model updating is carried out by successively increasing the level of detail up to a spatial scale sufficient to match the observed data. The method begins by constructing a coarse representation of the field using the lowest-frequency components of its discrete cosine parameterization. This substantially reduces the number of unknown parameters to be resolved during history matching. A gradient-based minimization is then performed to match the production data. Next, the updated model is incrementally refined in the frequency domain and the minimization is repeated until the data misfit is reduced below a pre-specified criterion. During minimization, components of the gradient insensitive to production information are removed by truncated singular value decomposition (TSVD), facilitating iterative convergence and providing additional regularization. In this manner a balance is achieved between parameter reduction which is required for stability, and the spatial resolution of heterogeneity required for reproduction of the data. The low-frequency approximation of the field helps to honor geologic continuity and is particularly suited for resolving the large-scale heterogeneity that has a dominant influence on the production response. Applications of the approach are demonstrated using the SPE1O and PUNQ-S3 models and involve waterflood history matching with water-cut and bottom-hole pressure data. Our results show that the principle geologic features of the reference field are adequately resolved only if we begin at very low resolution. As the resolution is iteratively increased, the history match is improved while the TSVD step automatically removes insensitive parameter combinations that can result in convergence to a local minimum. Notably, in all our applications an adequate history match is achieved using less than one percent of the original parameter dimension, which leads to increased solution stability and computational savings in history matching large geologic models. Copyright 2010, Society of Petroleum Engineers.

author list (cited authors)

  • Bhark, E. W., Jafarpour, B., & Datta-Gupta, A.

citation count

  • 6

publication date

  • January 2010