Can we comfortably deduce “interpreted transmissibility” (that is associated with a reservoir physical space) – from field data?
With ‘reservoir permeability’ acting as a log-normally distributed Gaussian spatial random function; and given the difficulty of quantifying the reservoir heterogeneity; and its associated high levels of uncertainty, can we comfortably define a representative reservoir permeability/transmissibility/mobility under convergent flow towards the production well?
When deducing such effective parameters, whether applying spatial average techniques in deducing the equivalent transmissibility – using single realization of a heterogeneous reservoir – would really reflect an up-scaled substitute for the actual heterogeneous transmissibility a reservoir block that would allow the same fluid flux under the same pressure-gradient and its associated boundary conditions?
Similarly, when deducing such effective parameters, whether deducing an average in the probability space using stochastic approach (where, the ensemble average of production rate and ensemble average of the pressure gradient – deduced over multiple realizations) is really justified?
Whether ensemble averages can be replaced by spatial averages using ‘ergodicity’ in an actual heterogeneous reservoir (so that the equivalent and effective transmissibility becomes identical?
In the presence of a definite well-pattern associated an oil field, which are essentially to be treated either as a source or a sink, will it be feasible to deduce an uniform effective transmissibility? Isn’t pseudo-effective or apparent transmissibility?
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