Modification of the Dykstra-Parsons method to incorporate Buckley-Leverett displacement theory for waterfloods

The Dykstra-Parsons model describes layer 1-D oil displacement by water in multilayered reservoirs. The main assumptions of the model are: piston-like displacement of oil by water, no crossflow between the layers, all layers are individually homogeneous, constant total injection rate, and injector-producer pressure drop for all layers is the same. Main drawbacks of Dykstra-Parsons method are that it does not take into account Buckley-Leverett displacement and the possibility of different oil-water relative permeability for each layer. A new analytical model for layer 1-D oil displacement by water in multilayered reservoir has been developed that incorporates Buckley-Leverett displacement and different oilwater relative permeability and water injection rate for each layer (layer injection rate varying with time). The new model employs an extensive iterative procedure, thus requiring a computer program. To verify the new model, calculations were performed for a two-layered reservoir and the results compared against that of numerical simulation. Cases were run, in which layer thickness, permeability, oil-water relative permeability and total water injection rate were varied. Main results for the cases studied are as follows. First, cumulative oil production up to 20 years based on the new model and simulation are in good agreement. Second, model water breakthrough times in the layer with the highest permeability-thickness product (kh) are in good agreement with simulation results. However, breakthrough times for the layer with the lowest kh may differ quite significantly from simulation results. This is probably due to the assumption in the model that in each layer the pressure gradient is uniform behind the front, ahead of the front, and throughout the layer after water breakthrough. Third, the main attractive feature of the new model is the ability to use different oil-water relative permeability for each layer. However, further research is recommended to improve calculation of layer water injection rate by a more accurate method of determining pressure gradients between injector and producer.