Effect of Spherical Flow in Gas Well Deliverability
Authors: Chaudhary V.K. , Guerrero E.T. , Carter R.D. 
Published: December 2007

Chaudhary, V.K., Junior Member AIME, Mobil Oil Corp., Bakersfield, Calif., Guerrero, E.T., Member AIME, U. of Tulsa, Tulsa, Okla. and Carter, R.D., Member AIME, Pan American Petroleum Corp., Tulsa, Okla. Pan American Petroleum Corp., Tulsa, Okla. Copyright 1968
American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
This paper was prepared for the 43rd Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Tex., Sept. 29-Oct. 2, 1968. 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 whom 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.

Abstract
The Forscheimer equation is integrated for spherically converging gas flow. The resulting expression indicates that the pressure drop due to "turbulent" or "nondarcy" flow con be strongly dependent on how a well is completed.
The equation for spherical flow pressure drop is compared to the corresponding radial flow equation, and the spherical flow equation is used to estimate turbulent flow pressure drop for perforation completions. For perforation completions perforation completions. For perforation completions and spherical flow, the turbulent pressure drop is higher and/or the gas flow rate is lower than for corresponding radial flow.

Introduction
Forscheimer's equation has previously been integrated for radially converging gas flow. The radial equation shows that pressure drop caused by the "turbulence" term is a strong function of the internal or well radius. Thus, the pressure drop due to "turbulence" is indicated to be caused principally by the relatively high velocity principally by the relatively high velocity developed by the gas very near the wellbore. Many wells produced at high rates are completed by setting pipe through the pay interval and then perforating. In these cases, the flow velocity in perforating. In these cases, the flow velocity in the immediate vicinity of each perforation (and the wellbore) can perhaps be better approximated by the spherical rather than the radial flow assumption. Numerical integration of actual three-dimensional problems would provide even better pressure drop information. pressure drop information. In this paper, the problem is idealized by treating simple, spherically converging flow (see figure 1). Comparison of spherical and radial flow is made, and the integrated equation for spherical flow is used to obtain estimates of turbulent pressure drop for perforated wells at varying gas flow rates.