Average of numerically calculated pressure values in 9-cell area A_{e9} of reservoir flow simulation model (see also Fig. 1 below):
| (1) | p_{e9, \ i,j} = \frac{1}{8} \left( \quad \sum_{k=i-1 }^{i+1} \ \sum_{l=j-1}^{j+1} p_{k,l} - p_{i,j} \right) |
or in explicit form:
| (2) | p_{e9, \ i,j} = \frac{1}{8} ( 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} ) |
The averaging Fig. 1 is showing the
An area around a given well, located in (i,j) cell and surrounded by 8 cells of corer point grid.
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 |
| Fg. 1. Averaging schematic around 9-grid area. Yellow colour marls the cells which pressure is accounted for in averaging. | ||