TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis work addresses the behavior and analysis procedures for injectivity tests on horizontal wells completed in an oilbearing reservoir. In general, pressure and pressure derivative behave quite similar to the single-phase solution calculated with oil properties, thus flow regimes can be identified by loglog plots. However, skin factor and effective well length estimates are severely affected if one neglects the effect caused by the contrast in fluid mobility. A simple approximate analytical solution for the wellbore pressure is derived in this work. The accuracy of this solution is verified by comparison of results obtained from a reservoir simulator using hybrid grids and local grid refinement. The analytical solution, supported by simulator results, indicates that the injected water going through a damaged zone has a strong and distinctive effect on both pressure and pressure derivative behavior at early times. It is also shown that, if relative permeability data are available, an equivalent single-phase data can be constructed from the measured wellbore pressures. These equivalent single-phase data can be analyzed by standard single-phase flow techniques for horizontal wells, providing reliable estimates for effective permeability, skin factor and effective wellbore length.

Summary Although the Thompson-Reynolds steady-state theory has proved useful for explaining the relation between reservoir physics and the pressure/pressure derivative response for both injection and falloff tests, until now, we have been unable to apply this method to construct analytical solutions for the falloff response. In this work, we remedy this deficiency by constructing approximate analytical solutions for the pressure falloff response subsequent to water injection at a vertical or horizontal well. By comparison with a finite-difference simulator using grid refinement and a hybrid grid, it is shown that our multiphase-flow solutions are accurate. The falloff solution can be written as the sum of the single-phase falloff solution based on oil properties at initial water saturation plus a multiphase flow term, which reflects the deviation of the total mobility (in the region contacted by injected water) from oil mobility at initial water saturation. The multiphase term is presented as an integral in the vertical well case and a sum of one to three integrals in the horizontal well case. For the purpose of constructing an accurate estimate of the falloff multiphase pressure change term, one can use a series of 1D Buckley-Leverett solutions (one for each integral in the multiphase term) and assume that, throughout the falloff period, the total mobility profile in the reservoir is equal to the total mobility profile that existed at the instant of shut-in. Evaluation of each integral in the multiphase term requires the 1D mobility profile constructed from the Buckley-Leverett solution and a corresponding 1D flow rate profile during falloff. For linear single-phase flow, it is shown that rate superposition applies and we use this concept in a reasonable but ad hoc way to estimate the rate profiles needed to compute the multiphase pressure term. It is shown that even in cases where falloff data allow one to accurately estimate the properties of the oil zone, knowledge of the multiphase term is critical in order to obtain an accurate estimate of the mechanical skin factor.

A new method for determining hydraulic properties from slug test well data in a confined aquifer is presented. The new procedure is based on an exact equation which converts measured slug test head data to equivalent head data that would be obtained due to a constant discharge of a well with well bore storage and skin effects. A related procedure yields equivalent head derivative data (time rate of change of head) that would be obtained for the classical constant discharge with well bore storage and skin problem without applying numerical differentiation. After the constant discharge head data and its derivative data are generated by our procedure, these converted data can be analyzed by using existing well bore storage and skin type curves for the appropriate aquifer/well model. Therefore slug test type curves are no longer needed. For cases in which the relative change in the water level is not significant during the slug test, most of the converted data will fall on the unit slope line of the conventional well bore storage and skin type curves and it will be difficult to obtain a unique type curve match of converted head data. For such cases, it is shown that a discharge normalization procedure can be applied to improve the reliability of the analysis. A field case illustrating the reliability of the new method is presented.

We propose a novel well-test for in-situ estimation of relative permeabilities under two-phase (oil/water) flow conditions. The test consists of three periods: injection of water into an oil reservoir operating above bubblepoint pressure, a falloff test, and a producing period. The producing period is critical because it yields production data that reflect changes in sandface mobility and thus is highly sensitive to the parameters used to model relative permeability curves, whereas our results indicate that injection/falloff pressure data by themselves are not as reliable for defining relative permeability curves. We have developed optimization code based on the Levenberg-Marquardt algorithm and coupled it with a commercial reservoir simulator to obtain a procedure for data analysis wherein the reservoir simulator is used as the forward model. By matching data by minimization of a weighted least-squares objective function, we generate estimates of absolute permeability, relative permeability, and the well skin factor. We show the method can be applied with either power-law models or B-splines. We introduce a variable transformation that can be used to ensure that the estimated relative permeabilities are monotonic and concave up when B-splines are used. Power-Law ParameterizationThe standard representation of power-law relative permeability curves is as follows:

Summary This work presents an analytical solution for the pseudopressure function that represents the reservoir and wellbore responses resulting from production at a constant oil rate in a solution-gas-drive reservoir. The solution can also be reduced to obtain the analytical solution for the corresponding single-phase-flow problem. The general analytical solution suggests a new definition for the dimensionless flow rate. The analytical solution is used to construct new type curves for analysis of interference tests conducted under multiphase-flow conditions. It is shown that if we ignore multiphase-flow effects and analyze interference data with the line-source-solution type curve, then the estimates of the permeability and porosity-compressibility product obtained may be in error by 20 to 40%. porosity-compressibility product obtained may be in error by 20 to 40%. Introduction Most theoretical work on well testing is based on a linearization of the partial differential equation that describes fluid flow in a porous medium. Our work presents a unification of the porous medium. Our work presents a unification of the well-test-analysis theory for nonlinear-radial-flow problems and extends the work of Refs. 1 through 5 to interference testing. Well-testing theory is based on approximate solutions of partial differential equations that describe fluid flow. The slightly compressible fluid of constant viscosity approximation, the ideal gas approximation, and Perrine's multiphase-flow approximation are well known and widely applied. The usual form of linearization assumes a weak dependence of fluid and rock properties on pressure and/or assumes small gradients in pressure, saturation, or pressure and/or assumes small gradients in pressure, saturation, or related properties, so second-order terms can be neglected. A major advance in dealing with nonlinear problems is Al Hussainy et al.'s real-gas-pseudopressure function, which accounts for the variation in gas properties in the transmissibility flow term and does not neglect second-degree pressure-gradient terms. Following the ideas of Evinger and Muskat, Refs. 9 through 12 applied the pseudopressure approach to solution-gas-drive reservoirs. Perrine suggested that conventional semilog analysis of well-test pressure data could be used if single-phase mobility were replaced by the sum of the mobilities of each phase and the compressibility term were volumetrically averaged. Martin showed that Perrine's approach can be theoretically justified if the effect of saturation gradients is negligible. Chu et al. examined the effect of saturation gradients for oil/water systems and showed that Perrine's procedure does not apply when more than one phase is Perrine's procedure does not apply when more than one phase is mobile and if saturation gradients are significant. Thus, Perrine's procedure is inappropriate for solution-gas-drive reservoirs, procedure is inappropriate for solution-gas-drive reservoirs, especially during the transient period when large saturation gradients exist. To use pseudopressure methods to analyze multiphase-flow well-test pressure data, relative permeability curves must be available, whereas new methods do not require a prior knowledge of relative permeability data. Instead, they compute effective phase or relative permeabilities as functions of pressure directly from well-test pressure data, and under ideal conditions, these permeabilities pressure data, and under ideal conditions, these permeabilities can also be approximately computed as functions of oil saturation directly from measurements of wellbore pressure and phase flow rates. Here, our objectives are to provide a fundamental theoretical basis for well-test analysis of nonlinear problems, especially for solution-gas-drive reservoirs, and to present procedures for the analysis of pressure data obtained from an observation well under multiphase-flow conditions.