Pulse-Test Response of a Two-Zone Reservoir

1970 ◽  
Vol 10 (03) ◽  
pp. 245-256 ◽  
Author(s):  
E.G. Woods
Keyword(s):  
Flow Rate ◽  
Single Layer ◽  
Pressure Response ◽  
Test Results ◽  
Well Test ◽  
Reservoir Model ◽  
Reservoir Properties ◽  
Pulse Test ◽  
Pulse Testing ◽  
Single Well

Woods, E.G., Member AIME, Esso Production Research Co., Houston, Tex. Abstract A mathematical investigation of pressure response of two-zone reservoirs indicates apparent transmissibility (kh/ ) obtained by pulse testing is always equal to or greater than the total transmissibility of the zones, and that apparent storage (phi ch) is always equal to or less than the total storage of the zones. These apparent zone properties approach total properties as vertical fluid communication between zones increases. The presence of non uniform wellbore damage in the zones alters the division of flow between zones, and consequently, alters their apparent transmissibility ratio. In the absence of wellbore damage. the flow-rate ratio is a good estimator of the transmissibility ratio of the zones. A procedure is proposed for advantageously using differences in reservoir properties determined by single-well tests and pulse tests to describe flow properties of two-zone reservoirs. A numerical properties of two-zone reservoirs. A numerical example is included. Introduction Pulse tests, interference tests, and single-well pressure buildup or drawdown tests have been used pressure buildup or drawdown tests have been used to estimate reservoir properties. These pressure transient tests are normally analyzed with mathematical models which assume that the reservoir is a homogeneous single layer. Various techniques for analyzing single-well test data to obtain information about the properties of layered reservoirs have been shown by others to have limited applicability. This mathematical study was undertaken to determine what errors could be caused by interpreting pulse tests (in a multizone reservoir) with a single-layer model. Pulse testing is based on the measurement and interpretation of a pressure response in one well to a transient pressure disturbance introduced by varying flow rate at an adjacent well. The measured pressure response is usually a few hundredths of a pressure response is usually a few hundredths of a pound per square inch. Pulse-test terminology is pound per square inch. Pulse-test terminology is shown in Fig. 1; Johnson et al. give a complete description of pulse testing. Measured at the wellhead or in the wellbore, pressure response is a function of reservoir pressure response is a function of reservoir transmissibility (T=kh/mu) and diffusivity (n = k/phi cmu) in the region between the two wells; from these two quantities reservoir storage ( = /n=phi ch) can be derived. The analysis presented here discusses additional reservoir information made available by pulse testing and shows that single-well test and pulse-test results can be combined to give more information about a two-zone reservoir than either type of test alone. Also, procedures are given for estimating the magnitude of error if test results of a two-one reservoir are interpreted with the assumption that it is a one-zone, vertically homogeneous, reservoir. Discussions of theoretical work, field data requirements, interpretation procedure, and a numerical example follow. Details of the mathematical model are given in the Appendix. THEORETICAL STUDY - TWO-ZONE MODEL Reservoir Model - Assumptions and Boundary Conditions A reservoir model consisting of two zones penetrated by two wells, each of which is completed in both zones was assumed (Fig. 2). SPEJ p. 245

Determination of Reservoir Properties from Sinusoidal and Multirate Flow Tests in One or More Wells

1972 ◽  
Vol 12 (06) ◽  
pp. 499-507 ◽  
Author(s):  
C.H. Kuo
Keyword(s):  
Pressure Response ◽  
Theoretical Research ◽  
Variable Rate ◽  
Test Results ◽  
Well Test ◽  
Reservoir Properties ◽  
Flow Rates ◽  
Pulse Testing ◽  
Single Well ◽  
Theoretical Pressure

Abstract This theoretical research deals with the use of periodic variable-rate flow tests for obtaining reservoir parameters. During the test period, the flow rate at a test well is varied periodically, either sinusoidally or in a repeated sequence of constant flow rates, while the accompanying resultant pressures are measured at the test well itself (single-well test) and/or at nearby responding wells (multiwell test). Theoretical pressure equations due to these periodic rates of fluid flow at a test well are derived. Methods of interpreting the test results are proposed. For the general periodic variable-rate flow tests, reservoir properties can be calculated from the slope and the intercept in a linear plot of the measured pressure responses vs a known time function. In cases where a sinusoidal rate is imposed at a test well, it is only necessary to measure the maximum pressure response amplitude and the phase lag in order to calculate the formation parameters. A single-well test yields the kh value and the skin factor. A multiwell test yields the average kh value and the storage capacity between wells. When the same wells are used, differences in the kh values from these tests would be indicative of reservoir heterogeneities. Since the tests can be carried out simultaneously, this combination provides more information about the reservoir than would be available from either test alone. A frequency analysis of the pressure responses also offers the possibility of determining the heterogeneity distribution within the reservoir. Introduction Pressure buildup analysis is one of the most common means of determining reservoir properties from well tests. The method is operationally simple, and the theory is well developed. Unfortunately, interpretation of pressure buildup test results is often difficult for reservoirs of very high or very low permeability. Another method involving use of two or more wells to evaluate reservoir properties is the interference test. This method, however, has not been used often because of the long interruption of normal field operations usually required to obtain useful data. To eliminate this drawback, a new method of interference testing, called pulse testing, recently was proposed by Johnson et al. The test utilizes a sensitive pressure gauge at a responding well to measure the response generated by a series of flow-rate changes at a test well. A key feature of these pulse test is that, because of the cyclic nature of the pressure response, the arrival of the response can be distinguished from the background pressure. Thus, the time required to obtain a diagnostic pressure response is very short (usually a few hours or less) compared with conventional interference testing. The field applications of this pulse-testing technique, made to determine the distribution of reservoir properties, also have been reported. This theoretical research investigates the use of periodically varying flow rates to obtain reservoir parameters. Two types of flow rates, sinusoidal and periodic multiple rates, are considered in this study. The pressure response can be measured simultaneously at both the test well and a nearby responding well. In this report, when the pressure response is measured at the test well, the test will be called a "single-well test"; if the pressure is measured at a responding well some distance away from the test well, the test will be termed a "multiwell test". Theoretical pressure response equations for these tests are derived in this report. Interpretation methods for evaluating the formation parameters are also developed. The advantages and the drawbacks of these tests will be discussed. THEORETICAL DEVELOPMENT In a manner analogous to that used in developing the theoretical pressure response for many other types of well tests, the reservoir is considered to be a homogeneous and isotropic porous medium. This reservoir has a finite thickness h. The porosity phi and the permeability k are assumed to be constants. A test well is located in this porous medium of infinite radial extent. SPEJ P. 499ˆ

How Areal Heterogeneities Affect Pulse-Test Results

1970 ◽  
Vol 10 (02) ◽  
pp. 181-191 ◽  
Author(s):  
Saul Vela ◽  
R.M. McKinley
Keyword(s):  
Time Lag ◽  
Pulse Amplitude ◽  
Test Results ◽  
Hydraulic Diffusivity ◽  
Pulse Test ◽  
Influence Area ◽  
Pulse Testing ◽  
And Storage ◽  
Degree Of Heterogeneity ◽  
Relative Variability

Abstract Reservoir transmissibility and storage values can be obtained from pressure pulses induced in one well and measured at a second well. Such pulse-test values are generally calculated from pulse-test values are generally calculated from equations which assume the formation is homogeneous. This paper examines the effects of areally distributed heterogeneities on pulse-test values. An influence area is first developed for a pulse-tested well pair; only those heterogeneities pulse-tested well pair; only those heterogeneities within this area significantly affect pulse-test results. Next, for three limiting cases, the manner in which a pulse test averages heterogeneities within the influence area is described. These are the cases for which one of the three formation properties - hydraulic diffusivity, transmissibility properties - hydraulic diffusivity, transmissibility and storage - is constant throughout the influence area. Finally, a method called directional correction is developed that when applied to pulse-test values of transmissibility and storage restores some, if not most, of the true degree of heterogeneity to these values. Accuracy of the method depends upon the relative variability of the true values. Introduction The pulse-testing method of Johnson et al. uses a sequence of rate changes at one well to create a low-level pressure interference response at an adjacent well. This response is readily analyzed for reservoir properties if one assumes an infinite, homogeneous reservoir model. The field data of McKinley et al. show that, despite the use of a simple analytical model, pulse-test values are sensitive to between-well pulse-test values are sensitive to between-well formation properties. Calculated values for transmissibility and storage exhibit considerable variation with direction around a central pulsing well. These values cannot, however, reflect the exact degree of heterogeneity since flow about the pulsing well is usually nonradial. pulsing well is usually nonradial. This paper examines the effects of certain idealized types of areal heterogeneities on pulse-test values calculated from the simple model. In pulse-test values calculated from the simple model. In particular, an influence area for a pulse-tested well particular, an influence area for a pulse-tested well pair is first developed. This area is defined as that pair is first developed. This area is defined as that areal portion of the formation whose properties determine the numerical value, obtained from pulse testing the well pair. Its size depends on the length of the pulse and the hydraulic diffusivity of the formation. We then determine the type of average values yielded by a pulse test when heterogeneities are distributed randomly throughout the influence area. Results of these studies provide a simple correction scheme that restores some of the true degree of heterogeneity to pulse-test values of transmissibility and storage. Accuracy of the method depends on the relative variability of the latter two reservoir parameters. PULSE-TEST TERMINOLOGY AND ANALYSIS PULSE-TEST TERMINOLOGY AND ANALYSIS A typical rate-change sequence at the pulsing well appears at the bottom of Fig. 1. The pulse rate is q reservoir B/D and the pulse length is delta t minutes. The time between pulses is R delta t minutes. Each such pulse cycle induces at the responding well the pressure response (pulse) shown at the top of Fig. 1. According to the analysis method of Johnson et al., each pressure pulse is characterized by two quantities - a time lag, tL minutes, and a pulse amplitude, delta p psi. How these values are pulse amplitude, delta p psi. How these values are determined from the pressure response is apparent from Fig. 1. For an infinite, homogeneous formation, the time lag, tL, the R-value and the well spacing, rws, are sufficient to determine the hydraulic diffusivity, of the formation. These values, coupled with pulse amplitude, p, and pulse rate, q, determine formation transmissibility, =kh/ . Formation storage, = ch, is obtained from the ratio = / . Charts to facilitate this analysis are given by Brigham for R=1. SPEJ P. 181

A Method To Account for Afterflow at the Pulsing Well During Pulse Tests

1983 ◽  
Vol 23 (03) ◽  
pp. 519-520
Author(s):  
Hubert Winston
Keyword(s):  
Computer Simulations ◽  
Flow Rate ◽  
Storage Capacity ◽  
Pulse Length ◽  
Test Area ◽  
Pilot Test ◽  
Test Results ◽  
Pulse Test ◽  
Wellbore Storage ◽  
And Storage

Abstract The nature of wellbore storage is such that afterflow during a pulse test can affect the reservoir pressure performance and can lead to the calculation of erroneous performance and can lead to the calculation of erroneous values for formation transmissibility and storage. This is most likely to occur when the wells of interest are close together or when after flow persists for a long time relative to the pulse length. This article describes a technique that was developed to account for the effects of after flow at the pulsing well during pulse testing of a small production pilot. The technique is not general because it requires that a computer-generated simulation of each pulse test be made. An application of the method is given. Introduction In carrying out a pulse test, we introduce a pressure disturbance into a reservoir by alternately increasing and decreasing the flow rate at the pulsing well in a known manner. The pressure at the responding well is monitored, and, if the wells are in pressure communication, the pressure distrubance eventually will affect the pressure at the responding well. Since the form and the duration of the flow, rate disturbance are known, and since the mathematics that describe the pressure behavior of fluid-beefing reservoirs are well understood, the pulse test pressure response can be predicted. Several methods are available to calculate values for formation transmissibility and storage within a pulse-tested reservoir. Although all real reservoirs are heterogeneous, the models for deriving these techniques assume that the reservoir is ideal. When the wells of interest are far apart or when the duration of after flow is short relative to the pulse length, the effects of wellbore storage on the pulse test results will be slight. If, on the other hand, the pulsing well and the responding well are close together or if after flow persists for a tong time, the effects of wellbore storage on the pulse test results may be substantial. The work described here began during the analysis phase of a series of pulse tests that were run in a small phase of a series of pulse tests that were run in a small pilot test area. Computer simulations of the tests showed pilot test area. Computer simulations of the tests showed that the method of Mondragon and Menzie would not compensate adequately for the strong effects of after flow on test results. Description of the Method Since a series of injection/falloff tests had been run in the pilot area, it was possible to obtain values for the ratio of formation transmissibility to the wellbore storage capacity, /F, at each well by type-curve matching techniques. Using this parameter, we can determine the after flow vs. time profiles that would occur during the pulsing-well shut-in periods and incorporate them into a computer simulation of each pulse test. A typical pulsing well-flow profile showing after flow during the shut-in period is profile showing after flow during the shut-in period is illustrated in Fig. 1. Given that the pulsing wells were observed to go on vacuum soon after shut-in and given that the wellbore storage capacity for these wells during the on-vacuum condition should be approximately two orders of magnitude larger than it would be during injection SPEJ p. 519

Methods To Obtain Quick Estimates of Formation Parameters in Interference Tests Derived From Features of the Line-Source Solution—Theory and Application

2013 ◽  
Vol 16 (01) ◽  
pp. 29-39
Author(s):  
Pierre-David Maizeret
Keyword(s):  
Line Source ◽  
Time Lag ◽  
Early Time ◽  
Integral Function ◽  
Pressure Response ◽  
Well Test ◽  
Diagnostic Plot ◽  
Single Well ◽  
Interference Test ◽  
Interference Tests

Summary Interference testing is the oldest, but still the most effective, way of establishing communication between wells and determining the interwell-reservoir transmissibility. Yet these tests are not run frequently because often the results are difficult to analyze as a result of unforeseen complications. This paper presents practical methods derived from the properties of the line-source solution that is used to design and interpret effective interference tests. In single-well transient tests, early-time features of the exponential integral function occur too early to be observed. However, these features appear much later in an interference test and can be used in an observation well to estimate the storativity and transmissibility ratios of the reservoir. The pressure response and the log derivative of the pressure intersect on the log-log diagnostic plot, and the pressure response itself exhibits an inflection point. With these characteristics, simple geometrical methods are proposed to estimate reservoir parameters. Moreover, a new expression of the “lag time,” or delay in the response, is formulated. The particular case of falloff or buildup is studied in detail, because the time lag in the reservoir response can bring extra information. A field example is included to demonstrate the application of these methods to actual data and their usefulness to a practicing well-test engineer.

Modeling the Interfering Effects of Gas Condensate and Geological Heterogeneities on Transient Pressure Response

SPE Journal ◽  
2013 ◽  
Vol 18 (04) ◽  
pp. 656-669 ◽  
Author(s):  
H.. Hamdi ◽  
M.. Jamiolahmady ◽  
P.W.M.. W.M. Corbett
Keyword(s):  
Present Report ◽  
Early Time ◽  
Pressure Response ◽  
Gas Condensate ◽  
Well Test ◽  
Transient Pressure ◽  
Sensitivity Coefficients ◽  
Vertical Permeability ◽  
Single Well ◽  
The Impact

Summary Numerous publications have investigated the effect of gas condensate fluid on the transient pressure well-test (WT) response. However, to the best of our knowledge, its combined effect with geology has rarely been studied. Our findings in the present report demonstrate that geology can complicate the WT response and make it difficult for interpretation. In this study, the impact of geological heterogeneities on the WT response of a commingled braided fluvial gas condensate reservoir has been investigated. Numerical WT data were generated for a single-well model with a commercial compositional reservoir simulator. Several sensitivity simulations were performed to explore the effects of correlation length, vertical permeability, production rate, and drawdown time on the pseudopressure-derivative curves. The WT weighting kernel function and the calculated well-pressure sensitivity coefficients were implemented to demonstrate different trends of drawdown and buildup responses encountered in this study. The results clarified the idea that some geological heterogeneities and production parameters can alter pressure distribution and condensate saturation and mask the native model WT signatures. In this exercise, it was demonstrated that ramp effect, a geologically complex phenomenon in high-net/gross commingled reservoirs, is affected by the condensate formation. This interfering phenomenon is reflected on the derivative curves and is magnified in the presence of the shorter correlation lengths, the lower vertical communications, and the higher production rates. We also examined the stepwise stripping of the reservoir heterogeneity, demonstrating the significant impact of some facies on the buildup and drawdown transient pressure response. The time-dependent sensitivity coefficients were calculated to show that the drawdown test is sensitive to effective permeability in near-wellbore regions, in which condensate is prone to build up with time. In the buildup, on the other hand, the condensate saturation is almost invariant with time and affects the early-time region. This work leads toward better understanding of the influence of geology in gas condensate WT interpretation of fluvial reservoirs.

High Efficient Viscoelastic Damper for Heavy Trucks

2012 ◽  
Vol 215-216 ◽  
pp. 318-321 ◽  
Author(s):  
Sai Fei Zhang ◽  
Xiao Ling Liu ◽  
Yong Liu
Keyword(s):  
Flow Rate ◽  
Viscous Damping ◽  
Calculation Formula ◽  
Performance Curve ◽  
Test Results ◽  
Viscoelastic Damper ◽  
Damping Force ◽  
Heavy Trucks ◽  
High Efficient ◽  
Damper Design

In this paper, a new viscoelastic damper design for heavy trucks is presented and a calculation formula of viscous damping force considering the effect of Viscoelastic Fluids (VF) flow rate is carried out. By numerically simulating this equation, curves of the viscoelastic damper performance curve is obtained, and the results show that theoretical calculation result and the test results are well consistent, with the exception at the start point. Theoretical curves are more plumpness in compared with test curves.

Getting Your Perforations in a Line Can Mean More-Productive Fracturing

2021 ◽  
Vol 73 (07) ◽  
pp. 18-21
Author(s):  
Stephen Rassenfoss
Keyword(s):  
Hydraulic Fracturing ◽  
Flow Rate ◽  
Test Results ◽  
Choked Flow ◽  
Target Angle ◽  
High Side ◽  
Treat All ◽  
Estimated Ultimate Recovery

Want more production from a shale well? Consider lining up the perforations. A handful of speakers at the recent SPE Hydraulic Fracturing Technology Conference talked about improved fracturing results with oriented perforating—shooting the holes at the same place in the casing, often the top. This breaks from designs that arranged the holes in a helical pattern with each charge angled 60° from the previous one. “We did see indications we are getting better production from oriented perforating,” said Blake Horton, senior completions engineer for Ovintiv (SPE 204177). Production gains were also reported by ConocoPhillips which compared production from similar wells with and without oriented perforating. The analysis was designed to filter out differences in the geology, drilling, and completions. It concluded the value of the added production far exceeded the $20,000-per-well cost of installing the assembly, including a weight bar to tilt the perforating guns into position. “That’s less than the undiscounted value of 400 barrels of oil. An internal study indicated that ConocoPhillips improved estimated ultimate recovery (EUR) by a minimum of 5% when using high-side-oriented perforating,” said Dave Cramer, senior engineering fellow at ConocoPhillips and an early advocate for the method. “For an initial choked flow rate of 1,000 B/D, the payout on investment is 10 days or less,” he said. Ovintiv declined to provide a number, but Horton said ConocoPhillips’ estimate is within Ovintiv’s range based on similar comparisons of wells with and without oriented perforating. That number is at the low end of the estimates offered in discussions about oriented perforating performance at the conference. Higher estimates are questioned by those who doubt the test results can be sustained when the method is scaled up. What was certain is the number of users is rising and includes names such as Shell and Chevron. “We found that oriented perforating definitely helps to treat all the clusters,” said Jon Snyder, a staff completion engineer for ConocoPhillips who presented the paper, adding, “by oriented perforating we mean that when we are perforating, we aim for the high side of the wellbore” (SPE 204203). When Horton polled the audience at a recent talk, more than half of the respondents said they were using gun systems designed to orient the perforating charges at a target angle. “A year from now, few people will not be doing oriented perforating; the advantages of it are clear,” Cramer said. He has been promoting the idea within the company for years with mixed acceptance.

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