Matching All Observed Data

In this case the observed data consisted of the water-oil ratios, gas-oil ratios, flowing bottom hole pressure measurements and the reservoir pressures at two locations of the well (layers 7 and 8). In the first run, the horizontal permeabilities of layers 6 to 9 were estimated by using the value of 200 md as the initial guess. 

It was also attempted to estimate permeability values for eight zones but it was not successful. It was concluded that in order to extent the reservoir that can be identified from measurements one needs observation data over a longer history. Finally, in another run, it was shown that the porosities of layers 5 to 10 could be readily estimated within 10 iterations. However, it was not possible to estimate the porosity values for eight layers due to the same reason as the permeabilities. 

Having performed all the above computer runs, a simple linear correlation was found relating the required cpu time as model equivalent runs (MER) with the number of unknown parameters regressed. The correlation was 

This indicates that after an initial overhead of 0.319 model runs to set up the algorithm, an additional 0.07 of a model-run was required for the computation of the sensitivity coefficients for each additional parameter. This is about 14 times less compared to the one additional model-run required by the standard implementation of the Gauss-Newton method. Obviously these numbers serve only as a guideline however, the computational savings realized through the efficient integration of the sensitivity ODEs are expected to be very significant whenever an implicit or semi-implicit reservoir simulator is involved. 

3 A Three-Dimensional, Three-Phase Automatic History-IVlatching Model Reliability of Parameter Estimates 

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