ES-MDA applied to estimate skin zone properties from injectivity tests data in multilayer reservoirs

Evaluating the Impact of the Inflation Factors Generation for the Ensemble Smoother With Multiple Data Assimilation

“…From Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), we obtain a value of m such that ∇O(m) = 0. This vector corresponds to the maximum a posteriori estimate of the vector of model parameters and is denoted as m map .…”

“…Opposite to the left-hand side of Equation (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15), the right-hand side of the same equation displays a matrix problem of size N d × N d , which is more feasible when N d N m , as explained before. Therefore, one may compute m map as follows:…”

“…5. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21) and (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22) for different ensembles.…”

“…Rafiee and Reynolds (2017) [10] also claim that it is possible to yield good ES-MDA final results even with a low number of assimilations, but with proper inflation factors selection. This claim was investigated in the work of [13]. Using the method of Rafiee and Reynolds (2017) [10], [13] showed that increasing N a from 4 to 8 did not produce significant improvements in the final results when estimating the reservoir skin properties.…”

“…This claim was investigated in the work of [13]. Using the method of Rafiee and Reynolds (2017) [10], [13] showed that increasing N a from 4 to 8 did not produce significant improvements in the final results when estimating the reservoir skin properties. Emerick (2019) [12] proposed to select the last inflation factor a priori, and the previous ones are generated geometrically in increasing order.…”