Porosity, permeability and other parameters must be specified at every node within a petroleum reservoir simulator. The parameters are developed from sparse and noisy data so that they are not known exactly. After preliminary assignment of porosity and permeability data, simulators are run in the forward mode, but they can seldom match the observed production history adequately. Consequently, using solution techniques such as the Marquardt method.
Time-lapse seismic surveys produce images at different times in a rehistory. The seismic response of a reservoir may change due to changes in pressure, fluid saturation and temperature. Given appropriate rock physics models, the output of the reservoir simulator can be used to predict the change in seismic response. The difference between the predicted change in seismic response and the observed change in seismic response forms another set of residuals. These residuals are squared, weighted and added to the objective function.
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