Fingering and Coning of Water and Gas in Homogeneous Oil Sand

Abstract

Abstract This paper is a theoretical analysis of fingering of water and coning of waterand gas in homogeneous sand. Investigation of this idealized case illustratesthe relative magnitude of the factors involved in actual conditions. The bodyof the report presents equations, example calculations, and charts thatfacilitate solution of such problems. Derivation of the equations introduced inthis paper and a discussion of previously published equations are included inthe appendix. Introduction Production of water from oil wells as a result of the pressure gradientsestablished by flow of fluids through oil-producing sands is a commonoccurrence, which influences the cost of oil production, the degree ofdepletion and the efficiency of expulsion of oil from naturally occurringreservoirs. Control of water production and encroachment are important both inprimary and secondary phases of oil-field exploitation in order to produce oiland gas at lowest cost and in order to achieve the greatest ultimate recoveryof the oil in the reservoir. Although many actual oil reservoirs present amultitude of variables that influence fingering and coning of water and gas, aninspection of the relationship and magnitude of the forces involved in the caseof a homogeneous sand may indicate satisfactory methods of controlling waterproduction. Application of equations relating the variables may indicate thegeometric type of drainage that exists in a particular reservoir or in thevicinity of a particular well. A homogeneous sand body is assumed within the portion of the reservoirinfluenced by the well. Two geometric types of drainage are consideredtheoretically. The first is water fingering into an oil sand that is relativelythin compared with the lateral extent of the sand. This sand may represent theentire oil-producing reservoir or it may represent one interval in an oilreservoir, which is separated from other producing intervals by competentlithologic barriers to flow of fluids. For the condition of completepenetration of a well in such a sand body, it may be assumed that no flowoccurs across bedding planes. A mathematical relation is developed between thelimit of approach of a water finger to the well without being drawn into thewell and the corresponding operating pressure drawdown. The second condition considered is that of water or gas entry into an oil wellas the result of coning through bedding planes. The theory and graphicalsolution developed by Muskat for the limit of approach of a water or gas coneto a well, without its entry into the well, related to the correspondingmaximum pressure drawdown, is reviewed and amplified. Charts are presented, which facilitate graphical solution of the problem. A method is presented forthe extension of this type of graphical solution to the case where gas andwater coning occurs simultaneously. T.P. 1723