Production Engineering and Research - Fingering and Coning of Water and Gas in Homogeneous Oil Sand (T.P. 1723, Petr. Tech., March 1944) (With discussion)

This paper is a theoretical analysis of fingering of water and coning of water and gas in homogeneous sand. Investigation of this idealized case illustrates the relative magnitude of the factors involved in actual conditions. The body of the report presents equations, example calculations, and charts that facilitate solution of such problems. Derivation of the equations introduced in this paper and a discussion of previously published equations are included in the appendix. Introduction Production of water from oil wells as a result of the pressure gradients established by flow of fluids through oil-~roducing sands is a common occurrence, which influences the cost of oil production, the degree of depletion and the efficiency of expulsion of oil from naturally occurring reservoirs. Control of water production and encroachment are important both in primary and secondary phases of of exploitation in order to produce oil and gas at lowest cost and in order to achieve the greatest ultimate recovery of the oil in the reservoir. Although many actual oil reservoirs present a multitude of variables that influence fingering and coning of water and gas, an inspection of the relationship and magnitude of the forces involved in the case of a homogeneous sand may indicate satisfactory methods of controlling water production. Application of equations relating the variables may indicate the geometric type of drainage that exists in a particular reservoir or in the vicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoir influenced by the well. Two geometric types of drainage are considered theoretically. The first is water fingering into an oil sand that is relatively thin compared with the lateral extent of the sand. This sand may represent the entire oil-producing reservoir or it may represent one interval in an oil reservoir, which is separated from other producing intervals by competent lithologic barriers to flow of fluids. For the condition of complete penetration of a well in such a sand body, it may be assumed that no flow occurs across bedding planes. A mathematical relation is developed between the limit of approach of a water finger to the well without being drawn into the well and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil well as the result of coning through bedding planes. The theory and graphical solution developed by Muskat' for the limit of approach of a water or gas cone to a well, without its entry into the well, related to the corresponding maximum pressure drawdown, is reviewed and amplified, Charts are presented, which facilitate graphical solution of the problem. A method is presented for the extension of this type of graphical solution to the case where gas and water coning occurs simultaneously~