This paper was prepared for presentation at the 47th Annual Fall Meeting of the Society of Petroleum Engineers held in San Antonio, Tex., Oct. 8–11, 1972. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by who the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines.
Critical gas production rates of interfering wells over bottom water have been calculated for three different well patterns. The calculations are based on the generalized Girinskii potential, which enables one to account for stratification and real gas flow, assuming Darcy's law to hold. This analysis is applicable when the well may be considered as fully perforated.
PVT data are used to establish empirical analytic relationships with respect to pressure. This makes it possible to calculate the generalized Girinskii potential for practical cases. A computer program has been developed which calculates critical rates for clusters of interfering wells in stratified horizontal formations of constant thickness. The program forms an Appendix to this paper.
Many gas reservoirs contain bottom water. This imposes a restriction on the gas production from individual wells because above a certain critical rate, which may be different for each well, these wells cut water. The critical rate is defined as the steady-state gas production rate under a drawdown just small enough to prevent water production from bottom water. This critical rate is associated with the phenomenon of upconing bottom water. The form of the steady-state cone depends essentially on the perforation at the well and the reservoir parameters such as stratification.
The majority of the investigations concerned with the determination of critical rates are based on steady-state conditions and segregated flow of the fluids. Many of them, as here, deal with the case of fully perforated wells.
Lehner gives in the introduction to this paper a survey of the work published to date on the steady-state coning problem for compressible flow in stratified layers. The truly three-dimensional problem of free-surface flow in a stratified. problem of free-surface flow in a stratified. formation had already been treated by Girinskii. Girinskii, however, in his considerations applied the so-called 'Dupuit assumptions'.
