The Dykstra-Parsons method is the general approach to calculating vertical sweep efficiency in reservoirs with no vertical pressure communication between layers, since it is appropriate for all values of the mobility ratio. It therefore caters for velocity dispersion of the flood front between the individual layers.
The Dykstra-Parsons procedure is as follows :
1. | Inspect the core and log data and divide the section into a total of N separate layers |
2. | Order the N layers in the sequence in which they will successively flood-out with water, by applying the following velocity equation. |
3. | As each layer floods, calculate the frontal positions in all the remaining unflooded layers by solution of the following quadratic equation : |
where A is defined as :
4. | Calculate the fractional flow, which for a section of fixed width and individual layer thickness, hi, may be evaluated using the following equation : |
which is the condition pertaining after the nth layer out of a total of N has flooded. According to Dake, since the kh-product is predominant over the other parameters, the second expression is usually a perfectly acceptable approximation.
5. | The corresponding thickness averaged water saturation can be calculated using the following equation : |
Welge's equation, expressed in hydrocarbon pore volumes, is provided below :
where.
The expression to calculate surface watercut from the reservoir fractional flow value is provided below;
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