Analytical Treatment of Pressure-Transient Solutions for Gas Wells With Wellbore Storage and Skin Effects by the Green's Functions Method

SPE Journal ◽  
2016 ◽  
Vol 21 (05) ◽  
pp. 1858-1869 ◽  
Author(s):  
Emilio P. Sousa ◽  
Abelardo B. Barreto ◽  
Alvaro M. Peres
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Approximate Solutions ◽  
Test Problems ◽  
Well Testing ◽  
Well Test ◽  
Gas Reservoirs ◽  
Analytical Treatment ◽  
Wellbore Storage ◽  
Diffusivity Equation

Summary Even when written in terms of a pseudopressure function, the diffusivity equation for flow of gases through porous media is, rigorously speaking, nonlinear because the viscosity-compressibility product is pseudopressure-dependent. However, several techniques and analysis procedures neglect such nonlinearity. A new methodology for constructing solutions for gas reservoirs through the Green's functions (GF) technique was recently proposed in the literature. Such methodology handles the viscosity-compressibility product variation rigorously, and it was applied to solve several gas-well test problems successfully. However, wellbore storage and skin effects were not considered yet by this new approach. In this work, the GF technique is applied to obtain a new solution for an infinite, homogeneous, isotropic gas reservoir being produced through a single vertical well represented by a line-source with wellbore storage and skin. The solution, however, does not consider non-Darcy flow effects. Even though the wellbore storage introduces a new nonlinearity to an already nonlinear problem, this work presents two accurate approximate solutions compared with the results from a commercial numerical well-testing simulator. This work also shows that the wellbore pseudopressure dimensionless solution is a function of the correlating groups CDexp(2S) and tD/CD, exactly similar to the way that wellbore dimensionless liquid solutions are. Liquid and gas dimensionless solutions under these correlating groups are not equal, though.

Finite-Wellbore-Radius Solution for Gas Wells by Green's Functions

SPE Journal ◽  
2015 ◽  
Vol 20 (04) ◽  
pp. 842-855 ◽  
Author(s):  
Emilio P. Sousa ◽  
Abelardo B. Barreto ◽  
Alvaro M. Peres
Keyword(s):  
Line Source ◽  
Significant Loss ◽  
Computational Effort ◽  
Test Problems ◽  
Well Test ◽  
Gas Reservoirs ◽  
Gas Well ◽  
The Difference ◽  
Diffusivity Equation ◽  
Reservoir Simulator

Summary Even when written in terms of a pseudopressure function, the diffusivity equation for flow of gases through porous media is, rigorously speaking, nonlinear because the viscosity/compressibility product is pseudopressure-dependent. However, several techniques and analysis procedures neglect such nonlinearity. A new methodology for constructing solutions for gas reservoirs through the Green's-function (GF) technique was recently proposed in the literature. Such methodology handles the viscosity/compressibility product variation rigorously, and it was successfully applied to solve several gas-well-test problems. In those problems, the wellbore is always represented by a line source. This work extends the theory a little further by considering a finite-wellbore-radius (FWR) boundary condition for a single vertical well producing at constant rate from an isotropic homogeneous and infinite gas reservoir. The proposed solution does not consider non-Darcy-flow effects, wellbore storage, and skin. Results from our FWR solution are compared with a commercial finite-difference reservoir simulator that shows a very close agreement. We also compared the FWR solution to the correspondent line-source solution to study the difference between the two solutions. As expected, the pseudopressure solutions by use of line-source and FWR boundary conditions do not match at early times, but they do agree at long times, which is exactly how FWR and line-source well solutions for slightly compressible fluids behave. It seems that, even for gas-well problems, the wellbore can be satisfactorily represented by a line source without significant loss of generality. The line-source assumption greatly simplifies the mathematics and the computational effort. This aspect is especially attractive for complex nonlinear gas-well problems that remain to be solved by the GF approach.

In-Situ Poisson's Ratio Determination From Interference Transient Well Test

SPE Journal ◽  
2015 ◽  
Vol 20 (05) ◽  
pp. 1041-1052 ◽  
Author(s):  
Mojtaba P. Shahri ◽  
Stefan Z. Miska
Keyword(s):  
Fluid Flow ◽  
Stress Distribution ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Well Testing ◽  
Well Test ◽  
Induced Stress ◽  
Stress Changes ◽  
Diffusivity Equation

Summary Poisson's ratio is usually determined with well logging, fracturing data, and core samples. However, these methods provide us with a Poisson's ratio that is representative of only near-wellbore regions. In this paper, a technique is proposed by extending currently used pressure-transient-testing concepts to include reservoir stresses. More specifically, the interference well test is generalized to find not only conventional flow parameters such as reservoir transmissivity and storage capacity, but also the average in-situ Poisson's ratio. This is accomplished with the generalized diffusivity equation, which takes into account flow-induced stress changes. First, a generalized diffusivity equation is formulated by considering a deformable porous medium. The main goal of the generalized diffusivity equation is to extend current well-testing methods to include both fluid-flow and rock-mechanics aspects, and to present a way to determine the rock-mechanics-related property, Poisson's ratio, from the interference-well test. The line-source solution to the diffusivity equation is used to modify the current interference well-test technique. A synthetic example is presented to show the main steps of the proposed transient well-testing analysis technique. In addition, application of the proposed method is illustrated with interference-well-test field data. With a Monte Carlo simulation, effects of uncertainty in the input data on the prediction of Poisson's ratio are investigated, as well. In addition, a coupled fluid-flow/geomechanical simulation is performed to show the validity of the proposed formulation and corresponding improvement over the current analytical approach. One can put in practice an average in-situ value in different applications requiring accurate value of Poisson's ratio on the reservoir scale. Some examples of these include in-situ-stress-field determination, stress distribution and rock-mass deformation, and the next generation of coupled fluid-flow/geomechanical simulators. By use of Poisson's ratio that could capture flow-induced stress changes, we would be able to find the stress distribution caused by production/injection within the reservoir more precisely as well.

scholarly journals Wellbore Storage Effects in Geothermal Wells

1980 ◽  
Vol 20 (06) ◽  
pp. 555-566 ◽  
Author(s):  
Constance W. Miller
Keyword(s):  
Flow Rate ◽  
Oil And Gas ◽  
Early Time ◽  
Geothermal Field ◽  
Effect Of Temperature ◽  
Well Testing ◽  
Well Test ◽  
Gas Field ◽  
Temperature Changes ◽  
Wellbore Storage

Abstract The early-time response in the well testing of a homogeneous reservoir customarily is expected to give a unit slope when the logarithm of pressure is plotted vs. the logarithm of time. It is shown that this response is a special case and that another nondimensional parameter must be defined to describe the set of curves that could take place for each value of the wellbore storage coefficient C . In addition, the effect of temperature changes along the bore is shown to increase the time when wellbore storage is important. Introduction The petroleum industry's technique of assessing oil and gas reservoirs by well testing has been extended to the geothermal field by a number of workers. However, at least two important differences between a geothermal field and an oil or gas field must be considered in analyzing geothermal well test data. First the kh/mu value of a geothermal field is usually much larger than that of an oil or gas field because the reservoir thickness h is greater in a geothermal field and the viscosity mu is smaller (k is the permeability). Second, heat loss in the wellbore, which can be ignored in oil and gas fields, is significant in geothermal bores.The concept of wellbore storage - which has been considered quite extensively and refined in such detailed studies as those of Agarwal et al., Wattenberger and Ramey, and Ramey - usually is treated as a boundary condition on the reservoir flow. The boundary condition used is (1) where dp w/dt is the flowing pressure change with time in the wellbore. However, dp w/dt is not necessarily independent of position in the well. When dp w/dt is dependent on the measurement point, a plot of log (p sf) vs. log (t) will not result in a unit slope at early times. This study will consider wellbore storage by looking at the flow in the well itself while treating the reservoir as simple homogeneous radial flow into the well.Heat loss from the well and temperature changes along the bore also have been ignored because oil and gas news can be treated as isothermal. Heat transfer from the well and heating of the fluid in the well is usually a very slow process. When very long times are considered, these temperature effects can become important. Once the early transient behavior is over and a semilog straight line of p sf vs. log(t) is expected in the pseudosteady region, temperature changes in the well can alter the slope of that line so that the slope would no longer be q mu/4 pi kh. The duration and importance of any temperature changes will be considered.A numerical model of transient two-phase flow in the wellbore with heat and mass transfer has been developed. It is used to investigate (1) the early-time interaction of the well flow with that of the reservoir and (2) the longer-time effect of temperature changes on the well test data. Concept of Wellbore Storage Wellbore storage is the capacity of the well to absorb or supply any part of a mass flow rate change out of a well/reservoir system. For a change in flow rate at the surface of the well, the sandface mass flow rate usually is expressed as (2) SPEJ P. 555＾

The Use of Source and Green's Functions in Solving Unsteady-Flow Problems in Reservoirs

1973 ◽  
Vol 13 (05) ◽  
pp. 285-296 ◽  
Author(s):  
Alain C. Gringarten ◽  
Henry J. Ramey
Keyword(s):  
General Theory ◽  
Unsteady Flow ◽  
Point Source ◽  
Green's Functions ◽  
Green’S Functions ◽  
Fluid Viscosity ◽  
Flow Problems ◽  
Principal Axes ◽  
Product Method ◽  
Diffusivity Equation

Abstract Although it is an old method, the use of Green's functions to solve unsteady flow problems in reservoir engineering is not widely practiced. The reason is that it is difficult to find the appropriate Green's junction. In this study, tables of instantaneous Green's and source functions were prepared that can be used with the Newman's prepared that can be used with the Newman's product method to generate solutions for a wide product method to generate solutions for a wide variety of reservoir flow problems. New solutions for infinite conductivity sources were also prepared. Introduction The transient flow of a slightly compressible fluid in a homogeneous and anisotropic porous medium D, bounded by a surface Se (Fig. 1), is described by the diffusivity equational derived from the continuity equation and Darcy's law? Assuming constant permeabilities, porosity, and fluid viscosity and small pressure gradients everywhere, and neglecting the effect of gravity, the diffusivity equation can be written as ..(1) where x, y and z are the principal axes of permeability, and the coefficients Nx, Ny, Nz are permeability, and the coefficients Nx, Ny, Nz are the principal diffusivities. When Nx = Ny = Nr (cylindrical systems), the diffusivity equation can be written as ........................(2) The diffusivity constants are given by ...........(3) Many techniques have been used for solving Eqs. 1 and 2. Most of these were first used for solving heat conduction problems and have since been applied by different authors to petroleum engineering. In the literature, most problems were solved either with Laplace transforms or Fourier transforms. One useful method employs Lord Kelvin's instantaneous point source solution. Another method that is of value although very rarely used is the Green's function method. This study presents the point source solution as part of a more general theory of Green's functions. part of a more general theory of Green's functions. This theory is applied in combination with other techniques to yield immediate solutions to difficult flow problems, some of which either have not been published or have been solved by long analytical published or have been solved by long analytical methods or sophisticated numerical techniques only. SPEJ P. 285

Annulus Unloading Rates as Influenced by Wellbore Storage and Skin Effect

1972 ◽  
Vol 12 (05) ◽  
pp. 453-462 ◽  
Author(s):  
Henry J. Ramey ◽  
Ram G. Agarwal
Keyword(s):  
Test Data ◽  
Skin Effect ◽  
Transient Flow ◽  
Test Problems ◽  
Well Test ◽  
Pressure Drops ◽  
Wellbore Storage ◽  
Unloading Rate ◽  
Short Time ◽  
Storage Type

Abstract The modern trend in well testing (buildup or drawdown) bas been toward acquisition and analysis of short-time data. Pressure data early in a test are usually distorted by several factors that mask the conventional straight line. Some of the factors are wellbore storage and various skin effects such as those due to perforations, partial penetration, non-Darcy flow, or well stimulation effects. Recently, Agarwal et al. presented a fundamental study of the importance of wellbore storage with a skin effect to short-time transient flow. This paper further extends the concept of analyzing short-time well test data to include solutions of certain drillstem test problems and of cases wherein the storage constant, CD, undergoes an abrupt change from one constant value to another. An example of the latter case is change in storage type from compression to liquid level variations when tubinghead pressure drops to atmospheric Arks production. The purpose of the present paper is to: production. The purpose of the present paper is to:present tabular and graphical results for the sandface flow rate, qsf, and the annulus unloading rate, qa, as a fraction of the constant surface rate, q, andillustrate several practical well test situations that require such a solution. Results include a range of values of the storage constant, CD, and the skin effect, s, useful for well test problems. problems. Annulus unloading or storage bas been shown to be an important physical effect that often controls early well test behavior. As a result of this study, it appears that interpretations of short-time well test data can be made with a greater reliability, and solutions to other storage-dominated problems can be obtained easily. Techniques presented in this paper should enable the users to analyze certain short-time well test data that could otherwise be regarded as useless. Introduction In a recent paper, Agarwal et al. presented a study of the importance of wellbore storage with a skin effect to short-time transient flow. They also presented an analytical expression for the fraction presented an analytical expression for the fraction of the constant surface rate, q, produced from the annulus Although the rigorous solution (inversion integral) and long- and short-time approximate forms were discussed, neither tabular nor graphical results ofdpwD the annulus unloading rate, CD, were given.dtD It now appears that such solutions are useful in certain drillstem test problems and in cases wherein the storage constant, CD, changes during a well test. An example is change in storage type from compression to liquid level change when tubinghead pressure drops to atmospheric during production. pressure drops to atmospheric during production. The purpose of this study is to (1) present tabular and graphical results for the sandface flow rate and the annulus unloading rate and (2) illustrate several practical well test situations that require the practical well test situations that require the solutions. THE CLASSIC WELLBORE STORAGE PROBLEM The problem to be considered is one of flow of a slightly compressible fluid in an ideal radial flow system. SPEJ P. 453

scholarly journals FEATURES INTERPRETATIONS OF HORIZONTAL OIL WELL BUILD-UP TEST IN OIL AND GAS RESERVOIRS

2015 ◽  
pp. 45-47
Author(s):  
M. D. Zejnal'-Abidin ◽  
S. K. Sohoshko ◽  
A. V. Sarancha ◽  
N. P. Kocherga
Keyword(s):  
Oil And Gas ◽  
Oil Wells ◽  
Oil Well ◽  
Well Testing ◽  
Test Interpretation ◽  
Well Test ◽  
Anisotropy Coefficient ◽  
Gas Reservoirs ◽  
Vertical Permeability ◽  
Oil And Gas Reservoirs

The article describes the features of well test interpretation in horizontal oil wells in the development of oil and gas reservoirs. The results obtained provided a method of estimating the vertical permeability and the anisotropy coefficient according well testing of horizontal oil wells.

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