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Abstract

Constraining reservoir models such as permeability distribution to dynamic well data has been traditionally accomplished using inverse theory. The resulting ill-conditioned system of equations needs to be solved for the required model parameters. Gradient-based optimization schemes require efficient computation of sensitivity coefficients (Chu, Reynolds and Oliver, 1992). Markov chain Monte Carlo (Omre and Tjelmeland, 1996), frequently used in earth sciences, is another iterative approach in which a prior distribution of permeability is perturbed into a posterior distribution using a probabilistic perturbation acceptance criteria. However, that technique like the pervious methods is expensive in term of CPU usage.<br><br>This paper investigates an approach to alleviate the computational expense associated with the iterative conditioning of reservoir models to dynamic information. A multiple point proxy is proposed that accounts for the configuration and orientation of geological patterns in the reservoir and their relationship to flow. The non-linear relationship between the multiple point connectivity and the flow response is established by calibration. Once calibrated, the proxy expression acts as a surrogate to the full physics based flow simulators and can be used within an iterative framework such as Markov chain Monte Carlo algorithm to build reservoir models conditioned to well test responses. The mathematical formulation and calibration of such a proxy function for matching well pressure characteristics is presented in this paper. <br><br>Building reservoir models based on just static data using multiple point statistics instead of just two point statistics has received a lot of attention recently. The SNESIM algorithm (Strebelle, 2002) is such a multiple point (mp) simulation algorithm. This paper presents a multipoint simulation algorithm that is distinctly different from all other mp-based simulation algorithms available in the literature. The presented approach is extended to integrate dynamic data using an efficient probability perturbation based approach. The proposed method is computationally fast for retrieving mp statistics (scanning) and simulation using a unique pattern growth-based methodology. Dynamic data integration is achieved by gradually perturbing the multiple point probability distribution using a deformation parameter. The perturbed multiple point probability distribution is then merged with the prior multiple point distribution inferred from a training image. The permanence ratio of hypothesis is used to perform the merge. The resultant reservoir model is thus consistent with both the available production data as well as the prior geology.<br>

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/content/papers/10.3997/2214-4609.201402543
2006-09-04
2020-10-26
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