Abstract

A new analytical method of gas and water coning evaluation for horizontal (H) and vertical (V) wells is presented. In dual coning there are five kinds of breakthrough (BT). Both gas and water apex have a parallel evolution and this fact is very important for behaviour of recovery factor (RF). Then analytical correlations for RF are presented followed by examples of calculation. RF depends mainly on well position (and its perforation), oil rate, anisotropy and capillarity.

Introduction

The most remarkable papers on coning phenomenon are Muskat and Wickoff, Sobocinski and Cornelius, Bournazel and Jeanson and Weiping and Wattenbarger. The main sources for analytical solutions are classical books by Carslaw and Jaeger and Muskat and recently books by Chaumet and Streltsova.

Pietraru and Cosentino published in 1993 a new fully analytical approach. This method has been generalized and extented for dual coning. Muskat and Wickoff (figs. 4 and 5) was the source for the new concept of "radius coning". The references, were used for analytical solution of diffusion equations, with various boundary conditions.

This paper presents briefly the new method, after references, then presents criteria for different kinds of breakthrough and new correlations for recovery factor (actual and maximum) in dual coning.

Dual coning
Correlations for dual coning parameters

Fig. 1 presents a geometrical scheme for dual coning. Main hypothesis is that gas oil contact (GOC) and oil water contact (OWC) are influenced by one well only (no interference). Dupuit's hypothesis is accepted (when the vertical flow composants are neglected). The pressure drop controls both gas and water apex and if gas-cap and aquifere are very strong the pressure drop in gas and water are neglected. Then the heights of apexes are given by the following expressions:

(1)

(2)

where po is the pressure drop in oil between the initial pressure and the pressure at the apex. In this condition both height of gas and water apexes are directly proportional to the po and inversely proportional to density difference. Constant C1 depends of unit system (see Table 1).

Coning Radius. Pietraru proposes the new concept of "coning radius" and its empirical expression:

(3)

The radius coning is a very important parameter. It defines the value of abscissa controlling the critical coning height.

Correlation of oil rate versus time of BT

Fig. 2 presents the main correlation of dimensionless rate as function of three dimensionless parameters (see Appendix A)

(4)

General solution. A new solution is given with the hypothesis that the oil rate is the sum of three terms: first term is the rate of an horizontal drain (with length 4, see appendix A) and both second and third terms are equal to half rate of V well.

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