Oil low to a lateral well in the presence of bottom water

Abstract

Exact solutions are obtained for a number of two-dimensional problems of steady-state fluid flow to a lateral hole in a reservoir with a quiescent bottom fluid of higher density or with a fluid of lower density at the reservoir top.Introduction. In oil production practice, one often encounters situations in which the flow domain can be divided with sufficient accuracy into several parts separated from each other by boundaries which are not known beforehand. The fluid moving in each of the indicated subdomains differs in properties from the fluids in the neighboring subdomains [1,2]. One of the best-known problems related to flows of this type is the problem of the so-called bottom water coning [2][3][4]. Approaches to constructing solutions for such problems, which are mostly of approximate nature, have been developed most fully for straight holes. From a practical point of view, the main goal of these approaches is to determine conditions under which bottom water breakthrough into a producing well is impossible.In recent decades, considerable attention has been paid to similar problems for the case of lateral holes, which have a number of advantages over straight holes. In particular, being located along beddings, they have a considerably larger are of contact with the oil pool, which provides much higher production rates. However, for the same reason, in the case of bottom water through into a lateral hole, the rate of water encroachment is much higher than that in the case of a straight hole. In view of the aforesaid, of particular importance are studies aimed at finding the class of flows that are critical for water-free oil production.Strictly speaking, such regimes can be analyzed only on the basis of exact solutions of the corresponding problems. However, because the latter are difficult to solve, such solutions are few in number not only for unsteady but also for steady-state problems. A simple analytical solution for the critical flow regime in an homogeneous, infinitely thin inclined layer of infinite length was first obtained in [5] where a linear periodic chain of wells was modeled by point drains. Among the advantages of the cited study is the simplicity of the solution constructed. The present paper also deals with constructing exact solutions for the case of horizontal wells but, unlike in [5], the formulation adopted here is more realistic. Formulation of the Problem and Parametric Representation of the Solution.A general flow diagram is presented in Fig. 1. The motion is considered steady-state and two-dimensional in the vertical plane xOy, and the axis Ox is horizontal. It is assumed that the reservoir of thickness T is homogeneous and has finite length and the bottom y = 0 of the reservoir and its top y = T are impermeable. At a distance H from the top there is a producing lateral well, whose axis is perpendicular to the plane xOy. The well operates at a constant capacity 2Q per its unit length. In the flow plane, it is modeled by a point A.We consider flow of a fluid of density ρ 1 and viscosi...

How much floating light nonaqueous phase liquid can a phreatic surface sustain? Riesenkampf's scheme revisited

“…The vertical coordinate is not eliminated from the analysis as in the Dupuit‐Forchheimer approximations of Bear and Ryzhik [1998] because in the vicinity of the sink, flow is essentially radial rather than horizontal. A similar “hydrodynamic” model for immobile DNAPL volumes upconed to horizontal wells has been recently used by Kapranov and Emikh [2008]. The main advantage of our model is in a one‐formula analytical solution to the flow problem, the integral , from which the whole free surface and criticality conditions directly follow.…”