Numerical Study on the Benefits of Cold-Water Injection During Steam Flooding
Authors: Zeito G.A. 
Published: December 2007

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 combined effect of steam injection and follow-up cold water on oil recovery in a 5-spot pattern was investigated numerically. The flow of fluids was approximated by 2-dimensional, 2-phase incompressible flow and its difference analog was solved by standard iterative ADI technique. The difference analog of the 3-dimensional flow of heat was solved by the non-iterative method of Brian which was found in this study to be conditionally stable.
Results showed that the variable velocity field which is characteristic of flow in a pattern influences hot flood recoveries pattern influences hot flood recoveries greatly. Because of the high velocities existing along the shortest streamline, cusping of temperatures nearer the producing well takes place. This aggravates the flow and hinders place. This aggravates the flow and hinders rapid drainage of the banked oil. For a moderately heavy oil it was shown that with increasing injection of steam higher peak temperature and early breakthrough of the heat-bank occur thus aggravating the flow further less so in larger patterns.
Although more oil is swept from the upstream region of the pattern with increase in steam injection, a smaller fraction of the banked oil can be recovered at economical water-oil ratios. In terns of energy cost alone, the smaller size stream slugs appeared to yield relatively higher incremental oil per unit of injected heat. per unit of injected heat

Introduction
The energy cost in heating a formation by continuous injection of steam can be prohibitive. Unless the formation is thick and prohibitive. Unless the formation is thick and fuel costs are low steam flooding applications could be viewed as discouraging from an economic standpoint. The possibility of improving the economics by advancing heat through follow-up injection of cold water has been raised frequently but not entirely evaluated judging from the literature. Only recently Spillette and Nielsen, in applying their numerical method to match the oil recovery of a specific heavy oil reservoir undergoing hot waterflooding, discovered through side calculations that a hot water bank could recover nearly as much oil as that by continuous hot water injection. How this generalization holds in pattern flooding and how the recovery compares in sands of different thicknesses, steam slugs of different sizes and flood patterns of different sizes are questions which will be answered in this study by numerical means.