Scale up

The flow simulation blocks for the 200,000 block model are approximately 1000 times larger than the geological model. The details in the geological model provide the ground truth petrophysical properties and are transferred to flow simulation as effective block properties. The scaled-up porosity was taken as the arithmetic average of the constituent porosity values (the fourth panel of Figure  shows a cross section through the scaled up porosity model), the scaled-up horizontal permeability was taken as the arithmetic average of the constituent permeability values, and the scaled-up vertical permeability K_v was taken as a power average of the n constituent permeability values K_i, $K_v = \left[ \sum_i^n K_i^\omega \right]^{\frac{1}{\omega}}$,with $\omega = -0.2$. This power average for the vertical permeability takes into account that the flow paths are more tortuous in the vertical direction because of lateral continuity.

 

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Figure 3 The steps in constructing the numerical geological model: (1) layer definition, (2) object-based channel modeling, (3) cell-based porosity and permeability modeling, and (4) scale up to a resolution for flow simulation.

 

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Figure 4 Histograms of porosity and permeability within channel sand.

 

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Figure 5 Scatterplot of porosity and permeability within channel sand.