Production Rate Improvement by Suppressing the Effect of Water Coning with the Aid of Vertical Fractures

Abstract

This paper was prepared for the SPE-European Spring Meeting 1974 of the Society of Petroleum Engineers of AIME, held in Amsterdam, the Netherlands, May 29–30, 1974. 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 OF PETROLEUM TECHNOLOGY or the SOCIETY OF publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Netherland Section of the Society of Petroleum Engineers, P. O. Box 228, The Hague, the Netherlands. 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 From theoretical considerations if follows that the production improvement factor (PIF) for dry oil or gas production due to natural and/or hydraulically induced vertical fractures in bottom water reservoir showing water coning is identical with the PIF obtainable with the same fracture configuration in a reservoir without bottom water. This is generally derived for a single, symmetrical fracture of arbitrary shape. It has been found that the highest PIF is obtained for a fracture with a PIF is obtained for a fracture with a technically-optimised tapered cross section. Results of calculated examples are discussed. Introduction In oil reservoirs with bottom water the height of a steady-state water cone depends on the potential gradient of the fluid moving along the interface: the greater the gradient (production rate), the higher is the cone. A decrease of the potential gradient, and thus a suppression of the cone, can be achieved by means of a fracture that effectively reduces the resistance to flow. Alternatively, if the cone is allowed to reach the same height, a higher production rate would be achieved. Hydraulically-induced vertical fractures would thus permit higher critical rates (maximum water-free oil production-rates), and make it possible to reduce the number of wells to be drilled for a required off-take. The shape of vertical fractures can be better controlled nowadays. This prompted us to investigate the problem of steady-state fluid flow in the presence of vertical fractures in reservoirs with presence of vertical fractures in reservoirs with bottom water, in order to derive the production improvement factors (PIF) for fractures of various prescribed practicable shapes. The PIF is prescribed practicable shapes. The PIF is defined as the ratio between the critical production rates with and without a fracture. The following considerations are generally valid for the movement of a fluid in the presence of a second non-flowing fluid of different density. hence, the results are equally applicable to the case of oil production over bottom water, respectively from under a gas cap, as to the case of gas production over bottom water. production over bottom water.

Nonlinear least squares estimation

“…out [1]: this value gives information about the termination of the process; out[l]=O: normal termination; out[l]=l: the process has been broken off, because the number of calls of funct exceeded the number given in in [5];…”

“…out [5]: the total number of iterations performed; note that in each iteration one evaluation of the jacobian matrix had to be made; out [6]: the improvement of the euclidean norm of the residual vector in the last iteration step; J * out [7]: the condition number of x J , i.e. the ratio of its largest to smallest eigenvalues; data and results: if this procedure is used for curve fitting then the relative accuracy in the calculation of the residual vector depends strongly on the errors in the experimental data and this should be reflected in the parameters in [3] and in [4];…”

“…T function has a zero at (5,4) , but all procedures converged to a point that proved to be a local minimum of the euclidean norm of the residual function. The starting guess is (15,-2)T. P 3 : A badly scaled problem (see POWELL [17]).…”

“…We tested the problem for (n,m) = (5,5), (5,10), (5,15), (10,10), (10,15) and (10,20). The number of observations is 33.…”