Interference Testing With Wellbore Storage And Skin Effect At The Produced Well

In the analysis of pulse-test theory, it has been shown that wellbore storage in the response well will cause the time lag to increase and the maximum pressure amplitude to decrease. Also it has been shown pressure amplitude to decrease. Also it has been shown that wellbore storage at the pulsing well reduces the maximum pressure amplitude of the pulse and increases the time lag. The net result is that the transmissibility is kh/mu, is underestimated, and the storativity, beta h, is overestimated. Although there is no general correlation to correct for wellbore storage at the pulsing well, wellbore storage in the response well can be eliminated by placing a bottomhole packer around the pressure bomb. pressure bomb. The object of this paper is to show how emperically developed equations can correct pulse-test results for the case with wellbore storage at the pulsing well. A group of correction equations were pulsing well. A group of correction equations were developed that would correct pulse-test results from an average 33% error to an average 3% error for values of transmissibility, and would correct the storativity from an average 14% error to an average 5% error. Introduction Two wells are used to conduct a pulse test. The two wells are termed the pulsing or active well and the responding or observation well. A series of flow disturbances is generated at the pulsing well and the pressure response is recorded at the responding well. pressure response is recorded at the responding well. Alternate periods of production and shut-in, or injection and shut-in are used to generate the flow disturbance. The pressure response is recorded using a highly sensitive differential pressure gauge. It has been shown that wellbore storage at the observation well will cause a delay in the time lag at which the maximum pressure is observed and a reduction in the maximum observed pressure response. Wellbore storage at the pulsing well can cause an underestimation of the transmissivity and an overestimation of the storativity when analyzing pulse-test data. pulse-test data. REVIEW OF LITERATURE Pulse Testing Pulse Testing Pulse testing was first introduced in 1966 by Johnson et al. Brigham developed some approximate equations that describe the theoretical rationale behind pulse testing. Vela and McKinley studied the effects of areal heterogeneities on pulse-test results. In 1970, Woods developed a pulse-test results. In 1970, Woods developed a mathematical model to study pulse-test results in a two-zone reservoir. In 1972, Odeh and McMillen presented a theoretical analysis of pulse presented a theoretical analysis of pulse propagation in linear cores saturated with air based on propagation in linear cores saturated with air based on solving the diffusivity equation for flow in porous media. In 1975, Prats and Scott showed the effects of wellbore storage at the response well on a pulse test. Jargon, in 1976, showed that wellbore storage at the pulsing well will cause an underestimation of transmissivity and an overestimation of storativity. Wellbore Storage The effect of wellbore storage was considered originally by van Everdinger and Hurst in 1949. In 1955, Gladfelter et al. presented a method for correcting pressure buildup data for wellbore storage. In 1970, Agarwal et al. examined the wellbore storage and skin-effect problem end presented dimensionless pressure vs dimensionless presented dimensionless pressure vs dimensionless time plots for a well in an infinitely large reservoir, producing at constant surface production rate. An investigation of the effect of wellbore storage and skin effect on transient flow was conducted using a finite-difference solution to the basic partial differential equation by Wattenbarger et al. in 1970. Ramey and Agarwal concluded (in 1972) that annulus unloading and wellbore storage to be an important physical effect that often controls the behavior of early pressure data taken during a well test.

Summary Pulse testing is used to determine the transmissivity and storativity of a reservoir. A pulse test is conducted by creating a series of flow-rate changes at an active (pulsing) well and observing the pressure response at a nearby observation (responding) well. Previous studies have shown that wellbore storage and skin effects should be accounted for when analyzing a pulse test. This study presents the data required for the analysis and design of pulse tests considering wellbore storage and skin effects at the pulsing or responding well, for tests run with unequal producing and shut-in periods. Before this study, data were limited to tests run with equal producing and shut-in periods. The use of unequal producing and shut-in periods is necessary to optimize test design and analysis. To reduce the amount of data required in this method, a new correlation is used and a set of regression coefficients is provided. A field example is included to illustrate how to use this method.

The technique of type-curve matching by eye judgement continues to be an extremely powerful tool in modern well test analysis. In practice, the method is restricted to cases involving steady flow rates and to include not more than three curve fitting parameters. In order to extend the type-curve method to more general problems of interest in the fields of petroleum problems of interest in the fields of petroleum engineering and hydrogeology, a computer aided curve matching procedure is proposed, which employs a multiparameter least square minimization procedure. Using this technique, the type-curve procedure. Using this technique, the type-curve method has been extended to problems involving arbitrarily varying flow rates in the presence of a boundary, well-bore storage and steady state skin. The proposed method has been verified against four hypothetical problems with known analytic solutions and has been applied to actual drawdown data collected from four geothermal well tests. The proposed method can easily be expanded to include such other type-curve situations as leaky multiple-aquifer systems, wells with horizontal or vertical fractures and wells with partial penetration. It is believed that this partial penetration. It is believed that this method is a very useful addition to the existing repertoire of well test analysis techniques. Introduction The technique of type-curve matching is extensively employed by petroleum engineers and hydrogeologists for analyzing well test data. Although this technique is extremely useful, it has a few inherent drawbacks. For example, the process of matching curves by eye judgement is process of matching curves by eye judgement is subject to individual bias. Moreover, most of the type-curves used in the literature relate to constant flow rate and when it is desired to include such additional features as well-bore storage, skin effects or boundaries, the result is the generation of too many families of type-curves, rendering the process of curve matching to be extremely cumbersome. To avoid some of these difficulties the method of ratios has been suggested by some. However, the ratio method uses only two or three data points for interpretation and as such is sensitive to the errors inherent in the data points chosen for interpretation. Under these circumstances, it is of great practical interest to develop computer assisted practical interest to develop computer assisted techniques of curve-fitting which will not only minimize the variabilities of personal judgements in the analysis but also extend the curve- matching technique to sufficiently general situations usually neglected while developing type-curves for eye-judgment applications. The purpose of this paper is to present a computer assisted curve-matching technique which permits the analysis of data from well tests with arbitrarily varying discharge, with or without effects of well-bore storage and skin. In addition, the method can also take into consideration the presence of a boundary (barrier or leaky), using the classical concept of the image well. Alternatively, the image well could be replaced by a second real well, enabling one to consider a production-production or production-injection doublet. The method is quite production-injection doublet. The method is quite powerful and can be extended to cases involving powerful and can be extended to cases involving leaky cap-rocks or the presence of fractures close to the well-bore.

A model recently presented by Cinco et al. for the transient pressure behavior of wells with finite conductivity vertical fractures was modified to include the effects of wellbore storage and fracture damage. An infinitesimal skin was considered around the fracture, and it was handled as a dimensionless factor defined as (pi/2)(wd/xf)[(k/kd) - 1]. It was found that the well behavior is importantly affected by the fracture damage. When plotted as a function of log pwD vs lot tD for short plotted as a function of log pwD vs lot tD for short times, results show flat, almost horizontal lines that later become concave upward curves asymptotically approaching the curve for undamaged fractures. This behavior is shown even by slightly damaged fractures. It also was found that important information about the fracture characteristics may not be determined when wellbore storage effects are present. present Introduction It has been shown that the increase in the productivity of a well created by hydraulic productivity of a well created by hydraulic fracturing depends on fracture characteristics, such as fracture conductivity, length, penetration, and also on a possible damage to the penetration, and also on a possible damage to the formation immediately surrounding the fracture. During the last few years, there has been a continuously increasing interest in the determination of the characteristics and orientation of fractures by means of transient pressure analysis. Most of these methods consider the fracture to be of infinite conductivity or of uniform flux; others consider finite conductivity fractures. Generally, these methods assume that there is no skin damage around the fracture. Evans proposed a pressure analysis technique considering fracture skin damage. He assumed the flow from the formation to the fracture to be linear, passing through two porous media in series, one being the damaged zone around the fracture and the other the undamaged formation. Ramey and Gringarten discussed the transient well behavior of vertically fractured wells with large wellbore storage, and suggested a matching technique for analyzing pressure data. Recently, Raghavan discussed pressure analysis techniques for vertically fractured wells, including the effects of wellbore storage and skin. He assumed the fracture to be of uniform flux, and presented general characteristics of the pressure transient behavior for these systems. The purpose of this study is to present solutions for the transient wellbore pressure behavior of a well crossed by a finite conductivity vertical fracture, considering the effect of a damaged zone around the fracture and wellbore storage. It is also intended to show the general flow characteristics of these fractured systems. MATHEMATICAL MODELS AND METHODS OF SOLUTION The transient flow toward a well with a finite conductivity vertical fracture surrounded by a damaged zone was studied by using a modified version of the model presented by Cinco et al. The following assumptions were considered.An infinite, homogeneous, isotropic reservoir of permeability k, porosity phi, and thickness h.The formation is produced through a vertically fractured well. The wellbore is intersected by a fully penetrating vertical fracture of permeability kf, porosity cf, width w, and permeability kf, porosity cf, width w, and half-length xf. All production of fluid is via the fracture.There is a zone of reduced permeability caused by fracturing fluid loss around the fracture. This region has a permeability ks and width ws.The porous medium contains a slightly compressible fluid of viscosity mu and compressibility c.All formation, fracture and fluid properties are independent of pressure.Gravity effects are negligible and pressure gradients are small everywhere.

Well test interpretation for reservoirs with a single linear no-flow barrier

it has been long recognized that in some reservoirs the flow does not follow the expected radial cylindrical pattern. Spherical flow may take place in systems with wells completed in thick reservoirs where a short completion interval is open to flow yielding a unique and more complex early-time pressure behavior. Some of the main reasons for partial penetration are to avoid coning of water and minimize sand production. A similar early-time pressure behavior may be due to the presence of plugged perforations. Such well completions are referred to as limited-entry, restricted-entry or partially penetrating wells. A typical case of spherical propagation of pressure transients occurs during the repeat formation tester measurements. Such a test measures spot formation pressures and recovers formation fluid samples for gaining an insight into the reservoir flow mechanics. The purpose of this study is to identify on the pressure and pressure derivative curves the unique characteristics for different flow regimes resulting from these type of completions and to determine various reservoir parameters, such as vertical, horizontal permeability, and various skin factors. The interpretation is performed using Tiab’s Direct Synthesis (TDS) Technique, introduced by Tiab (1993), which uses analytical equations obtained from characteristic lines and points found on the log-log plot of pressure and pressure derivative to determine permeability, skin and wellbore storage without using type-curve matching. The extension of this methodology for the case under study includes wellbore storage and skin effects. It is applied to both drawdown and buildup tests. We found that a spherical or hemispherical flow regime occurs prior to the radial flow regime whenever the penetration ratio of about 20%. A half-slope line on the pressure derivative is the unique characteristic identifying the presence of the spherical/hemispherical flow. The typical half-slope line of theses flow regimes is used to estimate spherical permeability and spherical skin values. These parameters are then used to estimate vertical permeability, anisotropy index and skin. Results of TDS technique where successufully compared to those of conventional technique for field and simulated examples.

The early time buildup pressure response resulting from a surface shut-in of low to intermediate productivity wells can be dominated by wellbore storage (after production) and/or fluid segregation effects for extended time periods. The purpose of this paper is to periods. The purpose of this paper is to introduce a new downhole shut-off tool that reduces the wellbore volume during the shut-in period and allows the buildup pressure and period and allows the buildup pressure and temperature measurements to be made with surface recording downhole pressure/temperature instruments. Potential savings in well testing costs, minimizing afterflow and segregation effects and the possibility of acquiring early-time information on naturally fractured systems, nearby impediments, and hydraulic fractures, are motivating factors for conducting a buildup test by means of a subsurface shut-in. Shutting in the well near the formation face reduces the wellbore volume thus virtually eliminating the effects of fluid compressibility and fluid segregation. Introduction Several different types of downhole shut-in tools, have been used in the past. Most of these attempts had some difficulties because of temperature, differential pressure, chemical wad mechanical problems. Due to advances in material mad design problems. Due to advances in material mad design technology, a new tool was developed to overcome these problems. For the engineer faced with the problem of making decisions on stimulation at the problem of making decisions on stimulation at the wellsite, the use of the downhole shut-off tool with surface recording pressure temperature instruments in pre-frac and/or post-frac well testing offers a solution. The quality control of the data can be maintained and sufficient data can be gathered to allow evaluation at the wellsite. During the past twenty years, transient pressure analysts have been dealing with the pressure analysts have been dealing with the effects that change the pressure response of the well in the early part of a buildup before the "Horner straight line" develops. These effects on the pressure response include wellbore storage, phase segregation, various types of skin effect phase segregation, various types of skin effect such as perforations, partial penetration, fractures, washouts, inclined wellbore, aid non-Darcy flow, to name a few. To be able to evaluate the various skin effects including the fracture characteristics in low producing gas wells, the, downhole shut-in tool virtually eliminates the long duration of wellbore storage and/or phase segregation effects such that the effects of the skin can be evaluated. It can be readily seen that there is a tremendous advantage in shutting in the well near the formation to enhance gathering well test data that can be used to describe the reservoir near the wellbore. THEORY The idealized theory of pressure buildup assumes that after production and fluid phase segregation in the wellbore does not exist. Tn practice however, the well is normally shut-in at practice however, the well is normally shut-in at the wellhead allowing the after production and fluid phase segregation effects to dominate the pressure response of the well for a time period. pressure response of the well for a time period. Chen and Brigham state that the buildup time necessary to reach "Horner straight line" (after production has ceased dominating the pressure production has ceased dominating the pressure response) can be estimated by (1) where Vw = wellbore volume available for fluid compression (bbl) C = compressibility of the wellbore fluid (1/psi) S = skin factor (dimensionless) P. 335

Flow rate history is the key information for reservoir surveillance and management, but it is not always available in practice due to expensive and unstable metering devices. This paper proposes an improved algorithm of reconstructing flow rate history from down-hole transient pressure data with wavelet transform (WT). The Haar wavelet can effectively identify flow events and distinguish pressure drawdowns from buildups, and the amplitude of WT coefficients of flow event is proportional to the flow rate change. The effects of data noise, wellbore storage and skin on flow event identification were investigated. The improved algorithm can reconstruct the flow rate history when the initial flow rate is unknown, and this improved algorithm was demonstrated with synthetic case studies and field application. [Received: November 25, 2015; Accepted: July 17, 2016]

In field data from slug test (decreasing flow rate) DSTS, an initial period of constant flow rate can often be observed. This may be a consequence of critical flow. "Critical flow" means that flow rate is independent of the pressure drop across the flow restriction. In the case of compressible fluid flow, this implies that the flow velocity is equal to the sonic velocity in the fluid. This was suggested by Ramey et al. in 1975. However, critical (constant-rate) flow was not included in their analysis of slug test DST flow period data. A new method which does consider an initial constant flow rate for a slug test was found. Graphs for the type-curve matching method are presented and field data are shown. Introduction Often in drill stem testing, the flow periods are characterized by a pressure trace which increases with increasing time, showing the accumulation of liquid in the drill string. In the expected case, the pressure-time trace is linear, showing constant-rate pressure-time trace is linear, showing constant-rate production. In other cases, the pressure-time trace production. In other cases, the pressure-time trace curves and is concave to the time axis. This shows a decreasing flow rate. In the case that formation pressure is too low to lift a column of reservoir pressure is too low to lift a column of reservoir liquid to the surface, the well may stop flowing before the tester valve is closed. This results because the head of liquid in the drill string becomes equal to initial formation pressure. This sort of test is similar to a pressure transient test called a "slug test" by Ferris and Knowles in 1954. The word "slug" refers to the maximum volume of liquid which may be produced by the time the well becomes static. produced by the time the well becomes static. A similar test involving the cooling of a batch of hot water was reported by Beck, Jaeger, and Newstead in 1956. Cooper et al., in 1967, reported the results of a field test in a static water well from which a float was suddenly removed, giving the appearance of the sudden removal of a quantity of water equal to that displaced by the float. Maier presented an approximate analysis of the equivalent DST presented an approximate analysis of the equivalent DST problem in 1970. problem in 1970.Van Poollen et al., in 1970, and Kohlhass, in 1972, applied the Cooper et al. solution to DST flow period data analysis. Although most current studies period data analysis. Although most current studies reference a study by Jaeger in 1956 which included a sandface resistance similar to the skin effect, most recent works do not include wellbore damage effects. A solution including the skin effect was presented by Ramey and Agarwal in 1972, although use of the solutions was not demonstrated. Papadopulos et al. presented extended results for the zero skin effect presented extended results for the zero skin effect case in 1973. The most complete discussion of DST applications of the slug test was presented in 1975. Three new slug test type-curves were developed for analysis of flow period data, and three field cases were analyzed. This study was included in the Earlougher monograph in 1977, and large-scale type-curves were printed with that monograph. printed with that monograph. Finally, Fenske showed that pressure buildup data for a well produced a short time (with wellbore storage) would follow the slug test type-curves. This is a potent observation. It means that the slug test type-curves may work for the initial shut-in, as well as for flow period data. This establishes the importance of slug test type-curves for DST work whether the test would normally be classified a "slug test" or not. Although not within the scope of this study, slug test type-curves may be used to match the initial shut-in for a DST following a very short initial flow to provide permeability, skin effect, and extrapolated initial pressure. One of the most important observations made from attempts to match field data with slug test type-curves is that there is often an initial constant-rate flow period before the rate begins to decline. Reference period before the rate begins to decline. Reference 1 pointed out this phenomena was related to conventional DST results for liquid flow wherein flow rate was constant for both flow periods: "Before proceeding with the presentation of the 'slug test', it should be pointed out that the conventional DST… contains the seed of a paradox.

This paper presents the first study of transient drawdown and buildup pseudopressure behaviour of a gas well located in multilayered infinite acting reservoirs wehre wellbore storage, skin and turbulence intensity effects were taken into account A mathematical model was developed to investigate the pseudopressure function and it's derivative for different situations of wellbore and reservoir characteristics. It was found that pseudopressure function ΨD, for all cases considered in this study, is characterized by a unit slope line (during early time) followed by a transition period and then a pseudoradial flow period during late time. The pseudopressure derivative function (Ψ’D*tPD) is characterized by a unit slope line, a curvature and then a constant value. The effect of the contrast in kh product on ΨD and Ψ’D*tPD was found to be significant compared to the effect of both skin factors and ϕh products. Type curves were developed for buildup and drawdown testing analysis. The drawdown type-curves can be used to analyze buildup test data as long as the duration of buildup test is less than the producing time before shuting-in the well. The fractional production rate from different layers can be evaluated using the mathematical model presented in this study. The results of a flow meter survey can be used to eva-luate the contrast in kh product of different layers.

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract The purpose of this study is to obtain a set of expressions and procedures that can be used to determine the reservoir parameters from pressure buildup curves for an infinite pressure buildup curves for an infinite two-layered oil reservoir. Equations were derived that define the pressure behavior at the wellbore. Pressure drop equations were derived for the upper and lower zones using Hartsock's method. From these pressure drop equations, other equations were derived that describe theoretical buildup for this system when the well is shut in. From these equations it is possible to determine the initial pressure of one zone the other initial pressure or the difference between the two initial pressures of the respective zones are known. The effective permeabilities can also be computed under the permeabilities can also be computed under the above conditions; that is, if the initial pressure in either zone is known or if the pressure in either zone is known or if the difference in pressure between the two zones is known. Hartsock used only the pressure drop of the upper zone for these derivations and determinations, but this study shows that from the pressure drop and shut-in pressure equations, equations can be derived to determine the skin factors for the upper and lower zones. This study also shows under what conditions an infinite two-layered oil reservoir is similar to a single-layered reservoir. Hartsock and Lefkovits et al. methods have been used to show the effects of permeability and thickness ratios on pressure buildup permeability and thickness ratios on pressure buildup curves. Also studied were the effects of skin and wellbore storage using the equations derived for an infinite two-layered reservoir with boundary conditions at the wellbore outlined by Lefkovits et al. Introduction The pressure buildup analysis considered in this study is that of an infinite two-layered reservoir without crossflow. So far, equations have not been developed to obtain the pressures, permeabilities and skin factors for the permeabilities and skin factors for the individual zones of two- or more-layered reservoirs. Lefkovits et al. studied the behavior of bounded reservoirs composed of stratified layers. Their work showed that the time necessary to reach pseudo-steady state is much longer for a two-layer reservoir than for a single-layer reservoir.

The effect of the quadratic gradient term on variable-rate well-tests

This study develops a novel, two‐dimensional analytical model to study capillary effects on Earth tidal responses of groundwater in unconfined aquifers. It differs from the previous model by accounting for effects of finite aquifer thickness, anisotropy and wellbore storage. We test the present model against the previous model and numerical simulations and apply it to the field data. Several significant results are obtained: (a) At high conductivity ( m/s), the effect of capillary zones dominates tidal responses of groundwater and causes higher amplitude ratio and smaller phase shift compared with that predicted by the unconfined aquifer model without a capillary zone. At low conductivity ( m/s), the effect of capillary zones on the tidal responses diminishes. (b) The impact of the finite thickness on the tidal response is regulated by the anisotropy. If the anisotropic ratio is small (), the impact of thickness may be negligible; at high anisotropic ratio (), however, the amplitude ratio decreases and the phase shift increases, and the response differs substantially from that of the previous model, which is caused by a change in the flow pattern. (c) Wellbore storage have significant impacts on the tidal response at low conductivity ( 10−5 m/s) but negligible impact at higher conductivity. (d) The present model marginally improved the fit by the half‐space model to the field data from a well in SW China, showing that the remaining misfit to the field data by models with capillarity cannot be due to finite aquifer thickness, anisotropy, or wellbore storage.

A nonlinear regression technique based on the method of least squares is developed for pulse lest analysis. The values of the transmissivity, kh// µ and storativity h Φc, that minimize the sum of squares of differences between observed and calculated pressures are determined. The equations that represent the conditions for minimum are solved by an iterative procedure based Oil a combination of the Newton-Raphson and the Regula-falsi methods. The pressure at any point is estimated using the line-source solution and the principle of superposition. The method can be used for the analysis of pulse testing of equal and unequal periods as well as cases that could not be analyzed by the tangent construction method of the conventional pulse testing methods. Such cases include situations of unequal pulse ratio and variable flow rate in the different cycles. The method is applicable for the general case of multiple-rate interference testing with pulse testing as a special case. The developed method was tested using simulated data. The method was found to converge rapidly. Excellent agreement was found between the assumed and estimated parameters for the different cases tested. Introduction Pulse testing is being widely considered as a method for obtaining interwell reservoir properties such as porosity and permeability(1–3). In pulse testing, the rate at an active welt is periodically changed between flowing and shut-in conditions while the pressure response at an observation well is recorded. The data is then analyzed graphically by drawing tangents to the pressure-time curve and determining the time lag and the pressure response amplitude of the different odd and even cycles. A set of correlations published by Kamal and Brigham(3) is then used to estimate the transmissivity, kh/ µ and storativity h Φc. Recently, Ogbe and Brigham(4) presented a method to correct for the skin and wellbore storage effects. They also found it necessary to correct the previously published Kamal-Brigham correlation curves. Moreover, the use of these correlations is limited to cases of constant pulse ratio, constant flow rate and constant cycle length of the different cycles. Cases where the lengths of the pulse and/or shut-in periods or flow rates are different in the different cycles cannot be analyzed by the conventional tangent construction method. Furthermore, the conventional graphical method cannot be used in a computer-based systematic analysis which is most desirable. Some attempts were made to apply the methods of regression analysis for the determination of reservoir characteristics from well test data (5–7). These methods, however, are coupled with numerical reservoir simulators that solve the diffusivity equation. For a presumably homogeneous reservoir for which an analytical solution exists, such methods are unnecessarily complicated. In a previous work, the method of least squares was applied for interference test analysis in the cases of constant rate and two rate tests(8). In this work, the method of least squares is used to develop a procedure for the analysis of the general case of multiplerate interference testing which includes pulse testing as a special case.

This paper introduces new techniques for restoring disrupted data by wellbore storage. The proposed techniques are applicable for reservoirs depleted by horizontal wells and hydraulic fractures. Several analytical models describe early time data have been generated. The relationships of the peak points (humps) with the pressure, pressure derivative and production time have been mathematically formulated in this study for different wellbore storage coefficients. Two complete sets of type curves have been generated for horizontal wells and fractured formations considering different skin factors and wellbore storage coefficients. The study has shown that early radial flow for short wellbores is more affected by wellbore storage while for long horizontal wells; early linear flow is the most affected flow regime. The study emphasises the applicability of early time data for characterising formations that could be controlled by wellbore storage effect by proposing different relationships between wellbore storage dominated flow and other flow regimes. [Received: October 2, 2016; Accepted: December 7, 2016]