A Systematic Study of Gas and Water Coning By Potentiometric Models
Authors: Chierici Gian Luigi , Ciucci Giuseppe M. , Pizzi Giuseppe 
Published: December 2007

Abstract
Starting from Muskat's theory of water and gas coning, maximum permissible oil production rates without water and/or free-gas production have been determined, in a broad range of reservoir and well parameters, using the potentiometric model technique. The main assumptions made are as follows:
the reservoir rock is homogeneous (either isotropic or anisotropic); the volume of the aquifer underlying the oil zone is very small, so that it does not contribute to reservoir energy; and the gas cap expands at a very low rate, so that it can be assumed to be in quasi-static conditions.
The results obtained are presented in the form of diagrams which can be used for solving two types of problems:
given the reservoir and fluids characteristics, as well as the position and length of the perforated interval, determine the maximum oil production rate without water and/or free-gas production; and given the reservoir and fluids characteristics only, determine the position and length of the perforated interval which optimize the maximum permissible oil production rate, without water and/or free-gas production.
Introduction
In oil reservoirs where the oil-bearing formation is underlain by an aquifer which does not participate in the production mechanism, water-coning is a limiting factor to the flow rates of producing wells. Production rates are usually kept to a value that will prevent the water from entering the wells. The entry of water into a well lowers its productivity by increasing the weight of the fluid column; moreover, the separation of water from the effluent, at the surface, may constitute a very difficult problem in cases of heavy viscous oils. A similar situation is encountered in oil reservoirs with a gas cap overlying the oil-saturated zone; here a downward gas cone is induced by the flow of oil towards the producing wells. Production rates must be low enough to prevent the gas from being produced; producing gas from the gas cap would be a waste of energy. Of course, water-coning and gas-coning phenomena can occur at the same time in the same reservoir if the oil-producing formation is both overlain by a gas zone and underlain by a water zone. Due to its relevant practical importance, the mechanism of coning was studied by many people. Defining the conditions for getting the maximum water-free and/or gas-free oil production rate is a difficult problem, often encountered under one of the following aspects:1. Predict the maximum flow rate that can be assignedto a completed well without the simultaneousproduction of water and/or free-gas.2. Define the optimum length and position of the intervalto be perforated in a well, in order to obtain themaximum water and gas-free production rate. A systematic study of these problems was made by means of the electrical analog technique. The results of this study are presented here, under the form of a set of curves providing solutions for the above stated problems. These curves are valid only for homogeneous formations, either isotropic or anisotropic. Should the formation be non-homogeneous (by horizontal or vertical variation of permeability, shale diaphragms, fractures, etc.), a specific potentiometric study would be required for each specific case. Especially when shale diaphragms of some radial extension are present, the critical rates observed are much larger than would be expected from the diagrams.
STATEMENT OF THE PROBLEM
In the present study the aquifer is supposed to be of such limited volume that it does not contribute to the energy of the reservoir. Moreover, the gas cap is supposed to expand at such a low rate that the potential gradient in the gas cap is negligible. Under static conditions water-oil and gas-oil interfaces ( and ) are both horizontal. When the reservoir production starts, below each well these interfaces take a cone-like shape (Fig. 1) having as an axis the axis of the well. This shape results from the equilibrium between potential gradients in the oil zone and gravitational forces due to density differences between oil and water and between oil and gas. Assuming the oil-bearing formation to be homogeneous and the oil to be incompressible, the analysis of the problem (see Appendix) shows that the oil-water and gas-oil interfaces are stable only if the oil production rate of the well is not higher than the following values.
JPT
P. 923ˆ