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Average of numerically calculated pressure values in 9-cell grid area

LaTeX Math Inline

body	A_{e9}

of reservoir flow simulation model (see also Fig. 1 below):

LaTeX Math Block

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p_{e9}(i,j) = \frac{1}{9} \cdot  \left( \quad \sum_{k=i-1 }^{i+1} \ \sum_{l=j-1}^{j+1} p_{k,l} \right)

or in explicit form:

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p_{e9, \ i,j} = \frac{1}{9} \cdot \bigg( p_{i, \, j} + p_{i, \, j+1} + p_{i, \, j-1}
+ p_{i-1, \, j} + p_{i-1, \, j}
+ p_{i-1 \, j-1} + p_{i+1, \, j+1}
+ p_{i-1 \, j+1} + p_{i+1, \, j-1} \bigg)

p _{i-1, j+1}

p _{i, j+1}

p _{i+1, j+1}

p _{i-1, j}

p _{i, j}

p _{i+1, j}

p _{i-1, j-1}

p _{i, j-1}

p _{i+1, j+1}

Fig. 1. Averaging schematic around 9-grid area.

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