Several published methods for calculating the productivity of horizontalwells are based upon the assumption of uniform flux distribution along thelength of the well.
This assumption, although it simplifies computations, is highly unrealistic.Horizontal wells, like partially-penetrating vertical wells, have a much higherflux at the end than in the center. Furthermore, the distribution of the fluxalong the well depends upon the geometry of the drainage boundary.
Pressure gradient is the driving force for fluid flow within reservoirs andthus pressure distribution along the well is a more natural assumption thanthat of flux. In most cases of oil flow in a reservoir, the constant wellpressure assumption (or infinite conductivity) is a realistic approximation tothe field situation. In comparison to the pressure gradients in the porousmatrix the pressure gradient inside the wellbore is generally negligible.
There are claims in the literature, that both approaches: uniformed flux andconstant pressure produce equivalent results but the study described in thispaper shows that this is not generally true.
In the paper, both models have been examined. The two- dimensionalmathematical model, in conjunction with vertical flow convergence factor, isalso employed to describe fluid flow in relatively thick reservoirs.
The results of calculations shown in the paper extend to the practicalsituations, where the width of the drainage pattern is small compared to itslength. In Canada, spacings of 100 - 200 meters between long horizontal wellsare commonly used for heavy oil recovery. In these circumstances, the capacityof a horizontal well is significantly underestimated when the uniform fluxassumption is made. This is because the extended flow path which results fromthe uniform flux assumption increases the resistance and thus reduces thepredicted productivity. Also the uniform flux assumption leads to unrealisticpressure distribution along the well.
Graphical comparisons of the predicted pressure distributions from the twoapproaches are given in the paper and the agreements and differences with othermodels discussed.