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Multi Layer Fractional Flow Model

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The following text is taken directly from the Waterdrive chapter of Dake's "The Practice of Reservoir Engineering", and very appropriately describes the purpose of this section.

 

"The previous section described the basic theory of waterdrive on the scale of a one-dimensional core flooding experiment. The same theory of Buckley-Leverett and the practical application technique of Welge will now be extended to the description of waterflooding in macroscopic, heterogeneous reservoir sections, which is a two-dimensional problem. In this respect, the engineer must be aware that in practice, waterflooding is conducted in "hillsides", not core plugs and the efficiency of the process is governed by three physical factors, namely:

 

mobility ratio (M)
heterogeneity
gravity"

 

Dake goes on to present a recipe for evaluating vertical sweep efficiency in heterogeneous reservoirs, which is listed below, and forms the basis for how the routines contained within this sections are structured.

 

"No matter what the nature of the vertical heterogeneity, the following recipe is applied to assess the sweep efficiency in edge waterdrive reservoirs.

 

Divide the section in to N layers, each characterised by the following parameters: thickness, permeability, porosity, Swc, Sor, krw', kro'.
Decide whether there is vertical pressure communication between the layers or not.
Decide upon the flooding order of the N layers and generate pseudo-relative permeabilities to reduce the description of the macroscopic displacement to one dimension.
Use the pseudos to generate a fractional flow relationship which is used in the Welge equation to calculate the oil recovery, Npd as a function of cumulative water influx, Wid.
Convert the oil volume to a fractional oil recovery, Np/N, and relate this to the surface watercut, fws."

References:

Dake, L., "The Practice of Reservoir Engineering", Elsevier Scientific Publishing Company, 1994.

 


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