Drawdown test for a stimulated well produced at a constant bottomhole pressure

I. M. Kutasov, L. V. Eppelbaum

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Determination of formation permeability and well skin factor is important for forecasting flow rates of oil and gas wells. A new technique for analysing test data for stimulated oil wells produced at a constant bottomhole pressure (BHP) has been developed. The method presented in this paper allows one to calculate the skin factor and estimate the formation permeability. It is assumed that the instantaneous flow rate and time data are available from a well produced against a constant bottomhole pressure. Only records of the flowing time and flow rate data are required to compute the values of the skin factor and formation permeability. A semi-theoretical equation is used to approximate the dimensionless flow rate. Our objective is to validate the new suggested method (prior to conducting a field test) by using a simulated example, where a numerical solution is used as an "exact" solution. "Bottomhole pressure" means the pressure determined at the face of the producing horizon by means of a pressure-recording instrument. In the case of gas wells or wells having no liquid in the well bore, it means the pressure as calculated by adding the pressure at the surface of the ground to the calculated weight of the column of gas from the surface to the bottom of the hole. Determination of bottomhole pressure (BHP) is an important problem in the oil and gas industry (Akhter and Kreitler, 1990; Schechter, 1992; Yang et al., 2003). At present the majority of well tests are conducted at constant flow rates, where simple solutions of the diffusivity equation can be applied. However, many investigators (Ehlig-Economides and Ramey, 1981; Sengul, 1983; Uraiet and Raghavan, 1980 a.o.) hold to the idea that in practice it is easier to conduct well tests at a constant bottomhole pressure (BHP). It is very difficult to maintain a constant flow rate during long flowing times (especially when testing low permeability formations). The advantages of the constant BHP test are: (1) the fluid production can be easily controlled (at constant flow rate tests the BHP is changing with time); and (2) wellbore storage effects on the test data are short-lived. One of the reasons that constant BHP tests have not been utilized in reservoir engineering is that only numerical solutions of the diffusivity equation for a cylindrical source with a constant BHP have been available. Due to the similarity in Darcy's and Fourier's laws, the same differential diffusivity equation describes the transient flow of incompressible fluid in a porous medium and heat conduction in solids. As a result, a correspondence exists between the following parameters: volumetric flow rate, pressure gradient, mobility (formation permeability and viscosity ratio), hydraulic diffusivity coefficient and heat flow rate, temperature gradient, thermal conductivity and thermal diffusivity. Thus, the same analytical solutions of the diffusivity equation (at corresponding initial and boundary conditions) can be utilized for determination of the above-mentioned parameters. Earlier we suggested a semi-theoretical equation to approximate the dimensionless heat flow rate from an infinite cylindrical source with a constant bore-face temperature (Kutasov, 1987). This equation (in terms of pressure and flow rate) was used to process data of step pressure tests when fluid is produced at two successive bottomhole pressures (Kutasov, 1998). The same equation was used to estimate the efficiency of stimulating operations (Kutasov and Kagan, 2003). In both cases a technique for determining the formation permeability and skin factor from flow tests in stimulated wells was developed. The objective of this paper is to suggest a similar technique for determination of the values of formation permeability and skin factor from drawdown constant BHP tests in stimulated wells. We should also like to mention that for damaged wells, when the dimensionless time based on the apparent well radius is very large, a simple equation can be used to process field data (Sengul, 1983; Earlougher, 1977).
Original languageEnglish
Pages (from-to)25-28
Number of pages4
JournalFirst Break
Issue number2
StatePublished - 2005


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