Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
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The prospect of injecting particles or sensors of sufficiently small size into reservoirs for improved reservoir characterization has become an active topic of research, yet little is known about the possible improvements in model resolution or reduction in uncertainty that could be achieved through in-situ sensor observations. In this paper, we investigate the information content provided by potential repeated measurements of particle pressure and/or location for particles that are transported passively with an injected fluid in heterogeneous reservoirs. Observations of locations of drifting particles at relatively frequent intervals provide substantial reduction in uncertainty in reservoir properties, except in regions through which the particles are unable to travel. Low permeability regions within flow zones, however, do affect the flow paths and are mapped relatively well through assimilation of the data. Pressure observations appear to be much less useful than observations of location, except in the neighborhood of wells where pressure gradients are quite high. The reservoir properties near the well, however, can be estimated relatively well using pressure data at wells. The results of this study show quantitatively that potential Lagrangian sensor measurements can provide additional information compared to standard production data for reservoir characterization. Despite the small size of the sensors, the model resolution is limited due to the spatial averaging in the sensitivity of the Lagrangian data to reservoir model parameters. High frequency of sensor measurements can improve the model resolution, but the improvement is marginal unless the accuracy of the measurements is quite high.