In recent decades, complex-architecture wells have been extensively substituted for vertical wells. Slanted, horizontal, multilateral horizontal wells, fractured horizontal wells hold much promise as regards improvement of tight reservoirs’ performance and increase of final oil recovery. In this connection, a great number of equations describing steady-state and unsteady-state flows in such wells have been offered by different authors, but, most regrettably, flow formulae for these wells can only be obtained in particular cases given of idealization of flow. Besides, a great number of different flow equations for horizontal wells in contrast to the only Dupuit equation for vertical wells cannot but testify to a low level of solution to this problem.
The previous papers discussed an alternative approach to describe fluid flow in complex-architecture horizontal wells. This approach involved a set of closely spaced nodes (vertical wells) and pseudo-skin effect for horizontal wells differentiating between flow to fracture and flow to horizontal wellbore. However, complete solution can only be obtained by representing a wellbore by a set of closely spaces spheres. One of the challenges of the solution to the problem is that in order to take into account the effect of impermeable formation tops and bottoms, summation from minus to plus infinity is necessary. Because of that, the solution is not infrequently simplified; furthermore, the known equations do not consider interference of spheres. These drawbacks have been duly considered, and a calculation algorithm has been worked out, as well as an external program to Saphir to determine steady-state and unsteady-state flows to wellbore(s), no matter how complex its architecture, not involving finite-difference methods. This method not only considers different well types, it also considers the limited entry completions. The calculation algorithm tested for particular cases for horizontal and vertical wells demonstrated high extent of matching with modeled PBU calculated in Saphir. It is noteworthy that it is incomparably faster than numerical solution methods.
The offered method to describe steady- and unsteady-state flows to complex-architecture wellbores using the spherical flowing approach enabled (a) to replace a great number of formulae applicable to particular cases, (b) to describe flow and PUB for wells with no analytic formulae, and (c) to select the most effective well drainage architecture considering reservoir characteristics, operational and technological aspects, etc.
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