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# Curve of pressure with the nonstationary inflow of two-phase fluid to the well, which works with the constant productive rate

UDK: 622.276.038:532.11
Key words: two-phase filtration, the effective parameters, the curve of pressure
Authors: A.M. Svalov (Oil and Gas Research Institute of RAS, RF, Moscow)

In the classical theory of filtration it is known the exact analytical solution for the problem of nonstationary inflow of single-phase fluid to a well working with a constant flow rate in a homogeneous infinite reservoir, widely used for the well test analysis of hydrodynamic research data. A similar exact analytical solution for the problem, describing the transient inflow of two-phase fluid in the well, does not exist, although the solution of this problem is of special practical value, because in most cases the filtration flow in reservoirs, at least, two-phase, i.e., formation fluid is represented by two phases - oil and water, water and gas etc. In mathematical modeling processes of the two-phase fluid flow to the well frequently use analytical dependences corresponding to the exact solution as a single phase formulation of the problem, in some way averaging the parameters of two-phase medium.

This paper presents a mathematical model describing the change in reservoir pressure at the two-phase flow in the reservoir, caused work well with a constant flow rate. The problem is posed in Buckley -Leveret approximation, i.e. neglecting the capillary forces that causes scaling of solutions and therefore, simplification of the system of equations describing this solution.

Based on the analysis of the results of numerical solution of similar problem we propose an effective method of averaging the parameters of two-phase medium, which ensures high accuracy (1-3 %) when using conventional exact analytical solutions for the flow of a single-phase fluid flow in the description of the two-phase fluid. The proposed method can be practically used for the interpretation of well test data.

References

1. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey v prirodnykh

plastakh (The movement of fluids in natural reservoirs), Moscow: Nedra Publ.,

1984, 211 p.

2. Shchelkachev V.N., Osnovy i prilozheniya teorii neustanovivsheysya fil’tratsii

(Fundamentals and applications of the theory of unsteady filtration),

Moscow: Neft’ i gaz Publ., 1995.

In the classical theory of filtration it is known the exact analytical solution for the problem of nonstationary inflow of single-phase fluid to a well working with a constant flow rate in a homogeneous infinite reservoir, widely used for the well test analysis of hydrodynamic research data. A similar exact analytical solution for the problem, describing the transient inflow of two-phase fluid in the well, does not exist, although the solution of this problem is of special practical value, because in most cases the filtration flow in reservoirs, at least, two-phase, i.e., formation fluid is represented by two phases - oil and water, water and gas etc. In mathematical modeling processes of the two-phase fluid flow to the well frequently use analytical dependences corresponding to the exact solution as a single phase formulation of the problem, in some way averaging the parameters of two-phase medium.

This paper presents a mathematical model describing the change in reservoir pressure at the two-phase flow in the reservoir, caused work well with a constant flow rate. The problem is posed in Buckley -Leveret approximation, i.e. neglecting the capillary forces that causes scaling of solutions and therefore, simplification of the system of equations describing this solution.

Based on the analysis of the results of numerical solution of similar problem we propose an effective method of averaging the parameters of two-phase medium, which ensures high accuracy (1-3 %) when using conventional exact analytical solutions for the flow of a single-phase fluid flow in the description of the two-phase fluid. The proposed method can be practically used for the interpretation of well test data.

References

1. Barenblatt G.I., Entov V.M., Ryzhik V.M., Dvizhenie zhidkostey v prirodnykh

plastakh (The movement of fluids in natural reservoirs), Moscow: Nedra Publ.,

1984, 211 p.

2. Shchelkachev V.N., Osnovy i prilozheniya teorii neustanovivsheysya fil’tratsii

(Fundamentals and applications of the theory of unsteady filtration),

Moscow: Neft’ i gaz Publ., 1995.

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