Pressure Buildup for Wells Produced at a Constant Pressure

1981 ◽  
Vol 21 (01) ◽  
pp. 105-114 ◽  
Author(s):  
C.A. Ehlig-Economides ◽  
H.J. Ramey
Keyword(s):  
Constant Pressure ◽  
Variable Rate ◽  
Reservoir Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Pressure Flow ◽  
Value Analysis ◽  
Pressure Buildup ◽  
Constant Flow Rate ◽  
Constant Rate

Abstract Conventional well test analysis has been developed primarily for production at a constant flow rate. However, there are several common reservoir production conditions which result in flow at a constant pressure instead of a constant rate. In the field, wells are produced at constant pressure when fluids flow into a constant-pressure separator and during the rate decline period of reservoir depletion. In geothermal reservoirs, produced fluids may drive a backpressured turbine. Open wells, including artesian water wells, flow at constant atmospheric pressure.Most of the existing methods for pressure buildup analysis of wells with a constant-pressure flow history are empirical. Few are based on sound theory. Hence, there is a need for a thorough treatment of pressure buildup behavior following constant-pressure production.In this work, the method of superposition of continuously changing rates was used to generate an exact solution for pressure buildup following constant-pressure flow. The method is general. Storage and skin effects were incorporated into the theory, and both bounded and unbounded reservoirs were considered. Buildup solutions were graphed using conventional techniques for analysis. Horner's method for plotting buildup data after a variable-rate flow was found to be accurate in a majority of cases. Also, the method by Matthews et al. for determining the average reservoir pressure in a closed system was determined to be correct for buildup following constant-pressure flow. Introduction When a flowing well is shut in, the pressure in the wellbore increases with time as the pressures throughout the reservoir approach a static value. Analysis of the pressure increase, or pressure buildup, often provides useful information about the reservoir and the wellbore itself. Techniques exist for determination of wellbore storage, skin effect, reservoir permeability and porosity, and either the initial reservoir pressure or the volumetric average reservoir pressure at the time the well was shut in. Effects of fractures penetrated by or near the wellbore also can be detected, as well as nearby faults or reservoir drainage boundaries.Most of the techniques for pressure buildup analysis were developed for wells which, prior to shut-in, were produced at a constant rate. When the production rate before shut-in changes rapidly, conventional analysis is often suspect. If the exact rate history is known, the theory of superposition in time of constant-rate solution leads to the method derived by Horner which compensates for changing production rates. This method results in long calculations. However, in the same paper Horner proposed a simplified procedure in which the last established rate was assumed constant and the flow time was set equal to the cumulative production divided by the last established rate. Other methods for analysis of pressure buildup after a variable-rate production history were proposed by Odeh et al.A special case of variable-rate production results when a well is produced at constant pressure. The first published application of pressure buildup analysis for a well produced at constant pressure prior to shut-in was by Jacob and Lohman. Their graph of residual drawdown vs. total time divided by shut-in time results in a semilog straight line. SPEJ P. 105^

Determination of Average Reservoir Pressure from Pressure Buildup Tests

1972 ◽  
Author(s):  
Hossein Kazemi
Keyword(s):  
Reservoir Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Gas Well ◽  
Pressure Buildup ◽  
Production History ◽  
Calculated Average

Abstract Two simple and equivalent procedures are suggested for improving the calculated average reservoir pressure from pressure buildup tests of liquid or gas wells in developed reservoirs. These procedures are particularly useful in gas well test analysis irrespective of gas composition, in reservoirs with pressure-dependent permeability and porosity, and in oil reservoirs where substantial gas saturation has been developed. Long-term production history need not be known. Introduction For analyzing pressure buildup data with constant flowrate before shut in, two plotting procedures are mostly used: The Miller-Dyes-Hutchinson (MDH) plot (1,8) and the Horner plot (2,8). The Miller-Dyes-Hutchinson plot is a plot of pws vs log Δt. The Horner plot consists of plotting the bottom hole shut-in pressure, pws vs log [(tp + Δt)/Δt]. Δt is the shut-in time and tp is a pseudo-production time equal to the ratio of total produced fluid and the last stabilized flowrate prior to shut in. This method was first used by Theis (3) in the water industry.

Transient Rate Decline Analysis for Wells Produced at Constant Pressure

1981 ◽  
Vol 21 (01) ◽  
pp. 98-104 ◽  
Author(s):  
C.A. Ehlig-Economides ◽  
H.J. Ramey
Keyword(s):  
Pressure Drop ◽  
Flow Rate ◽  
Constant Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Type Curve ◽  
Type Curves ◽  
Constant Rate ◽  
Cumulative Production

Abstract Although constant-rate production is assumed in the development of conventional well test analysis methods, constant-pressure production conditions are not uncommon. Conditions under which constant-pressure flow is maintained at a well include production into a constant-pressure separator or pipeline, steam production into a backpressured turbine, or open flow to the atmosphere.To perform conventional well test analysis on such wells, one common procedure is to flow the well at a constant rate for several days before performing the test. This procedure is not always effective, and often the delay could be avoided by performing transient rate tests instead. Practical methods for transient rate analysis of wells produced at constant pressure are presented in this paper. The most important test is the analysis of the rate response to a step change in producing pressure. This test allows type-curve analysis of the transient rate response without the complication of wellbore storage effects. Reservoir permeability, porosity, and the wellbore skin factor can be determined from the type-curve match. The reservoir limit test is also important. Exponential rate decline can be analyzed to determine the drainage area of a well and the shape factor.The effect of the pressure drop in the wellbore due to flowing friction is investigated. Constant wellhead-pressure flow causes a variable pressure at the sandface because the pressure drop from flowing friction is dependent on the transient rate. Finally, for testing of new wells, the effect of a limited initial flow rate due to critical flow phenomena is examined. Introduction Fundamental considerations suggest that conventional pressure drawdown and buildup analysis methods developed for constant-rate production should not be appropriate for a well produced at a constant pressure. However, a well produced at a constant pressure exhibits a transient rate decline which can be analyzed using techniques analogous to the methods for constant-rate flow. In this paper, analytical solutions for the transient rate decline for wells produced at constant pressure are used to determine practical well test analysis methods.Many of the basic analytical solutions for transient rate decline have been available for some time. The first solutions were published by Moore et al. and Hurst. Results were presented in graphical form for bounded and unbounded reservoirs in which the flow was radial and the single-phase fluid was slightly compressible. Tables of dimensionless flow rate vs. dimensionless time were provided later by Ferris et al. for the unbounded system and by Tsarevich and Kuranov for the closed-boundary circular reservoir. Tsarevich and Kuranov also provided tabulated solutions for the cumulative production from a closed-boundary reservoir. Van Everdingen and Hurst presented solutions and tables of the cumulative production for constant-pressure production. Fetkovich developed log-log type curves for transient rate vs. sine in the closed-boundary circular reservoir. Type curves for rate decline in closed-boundary reservoirs with pressure-sensitive rock and fluid properties were developed by Samaniego and Cinco. A method for determining the skin effect was given by Earlougher. Type curves for analysis of the transient rate response when the well penetrates a fracture were developed by Prats et al. and Locke and Sawyer. SPEJ P. 98^

Determining Average Reservoir Pressure From Pressure Buildup Tests

1974 ◽  
Vol 14 (01) ◽  
pp. 55-62 ◽  
Author(s):  
Hossein Kazemi
Keyword(s):  
Oil Reservoirs ◽  
Reservoir Engineering ◽  
Reservoir Pressure ◽  
Well Test ◽  
Gas Well ◽  
Pressure Buildup ◽  
Line Section ◽  
Straight Line ◽  
Buildup Curve

Abstract Two simple and equivalent procedures are suggested for improving the calculated average reservoir pressure from pressure buildup tests of liquid or gas wells in developed reservoirs. These procedures are particularly useful in gas well test procedures are particularly useful in gas well test analysis, irrespective of gas composition, in reservoirs with pressure-dependent permeability and porosity, and in oil reservoirs where substantial gas porosity, and in oil reservoirs where substantial gas saturation has been developed. A knowledge of the long-term production history is definitely helpful in providing proper insight in the reservoir engineering providing proper insight in the reservoir engineering aspects of a reservoir, but such long-term production histories need not be known in applying the suggested procedures to pressure buildup analysis. Introduction For analyzing pressure buildup data with constant flow rate before shut-in, there are two plotting procedures that are used the most: the procedures that are used the most: the Miller-Dyes-Hutchinson (MDH) plot and the Horner plot. The MDH plot is a plot of p vs log Deltat, whereas the Horner plot is a plot of p vs log [(t + Deltat)/Deltat]. Deltat is the shut-in time and t is a pseudoproduction time equal to the ratio of total produced fluid to last stabilized flow rate before shut-in. This method was first used by Theis in the water industry. Miller-Dyes-Hutchinson presented a method for calculating the average reservoir pressure, T, in in 1950. This method requires pseudosteady state before shut-in and was at first restricted to a circular reservoir with a centrally located well. Pitzer extended the method to include other Pitzer extended the method to include other geometries. Much later, Dietz developed a simpler interpretation scheme using the same MDH plot: p is read on the extrapolated straight-line section of the pressure buildup curve at shut-in time, Deltat,(1) where C is the shape factor for the particular drainage area geometry and the well location; values for C are tabulated in Refs. 5 and 13. For a circular drainage area with a centrally located well, C = 31.6, and for a square, C = 30.9.Horner presented another approach, which depended on the knowledge of the initial reservoir pressure, pi. This method also was first developed pressure, pi. This method also was first developed for a centrally located well in a circular reservoir.Matthews-Brons-Hazebroek (MBH) introduced another average reservoir pressure determination technique, which has been used more often than other methods: first a Horner plot is made; then the proper straight-line section of the buildup curve is proper straight-line section of the buildup curve is extrapolated to [(t + Deltat)/Deltat] = 1 (this intercept is denoted p*); finally, p is calculated from(2) m is the absolute value of the slope of the straightline section of the Horner plot:(3) pDMBH (tDA) is the MBH dimensionless pressure pDMBH (tDA) is the MBH dimensionless pressure at tDA, and tDA is the dimensionless time:(4) tp k a pseudoproduction time in hours:(5) PDMBH tDA) for different geometries and different PDMBH tDA) for different geometries and different well locations are given in Refs. 6 and 13.The second term on the right-hand side of Eq. 2 is a correction term for finite reservoirs that is based on material balance. Thus, for an infinite reservoir, p = pi = p*, where pi is the initial reservoir pressure. SPEJ P. 55

Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests

2005 ◽  
Vol 8 (02) ◽  
pp. 113-121 ◽  
Author(s):  
Michael M. Levitan
Keyword(s):  
Test Data ◽  
Rate Data ◽  
Well Test ◽  
Pressure Data ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Deconvolution Algorithm ◽  
Constant Rate ◽  
Test Pressure ◽  
Real Test

Summary Pressure/rate deconvolution is a long-standing problem of well-test analysis that has been the subject of research by a number of authors. A variety of different deconvolution algorithms have been proposed in the literature. However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, vonSchroeter et al.1,2 published a deconvolution algorithm that has been shown to work even when a reasonable level of noise is present in the test pressure and rate data. In our independent evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Some degree of inconsistency is normally present in real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate the application of pressure/rate deconvolution analysis to several real test examples. Introduction The well bottomhole-pressure behavior in response to a constant-rate flow test is a characteristic response function of the reservoir/well system. The constant-rate pressure-transient response depends on such reservoir and well properties as permeability, large-scale reservoir heterogeneities, and well damage (skin factor). It also depends on the reservoir flow geometry defined by the geometry of well completion and by reservoir boundaries. Hence, these reservoir and well characteristics are reflected in the system's constant-rate drawdown pressure-transient response, and some of these reservoir and well characteristics may potentially be recovered from the response function by conventional methods of well-test analysis. Direct measurement of constant-rate transient-pressure response does not normally yield good-quality data because of our inability to accurately control rates and because the well pressure is very sensitive to rate variations. For this reason, typical well tests are not single-rate, but variable-rate, tests. A well-test sequence normally includes several flow periods. During one or more of these flow periods, the well is shut in. Often, only the pressure data acquired during shut-in periods have the quality required for pressure-transient analysis. The pressure behavior during the individual flow period of a multirate test sequence depends on the flow history before this flow period. Hence, it is not the same as a constant-rate system-response function. The well-test-analysis theory that evolved over the past 50 years has been built around the idea of applying a special time transform to the test pressure data so that the pressure behavior during individual flow periods would be similar in some way to constant-rate drawdown-pressure behavior. The superposition-time transform commonly used for this purpose does not completely remove all effects of previous rate variation. There are sometimes residual superposition effects left, and this often complicates test analysis. An alternative approach is to convert the pressure data acquired during a variable-rate test to equivalent pressure data that would have been obtained if the well flowed at constant rate for the duration of the whole test. This is the pressure/rate deconvolution problem. Pressure/rate deconvolution has been a subject of research by a number of authors over the past 40 years. Pressure/rate deconvolution reduces to the solution of an integral equation. The kernel and the right side of the equation are given by the rate and the pressure data acquired during a test. This problem is ill conditioned, meaning that small changes in input (test pressure and rates) lead to large changes in output result—a deconvolved constant-rate pressure response. The ill-conditioned nature of the pressure/rate deconvolution problem, combined with errors always present in the test rate and pressure data, makes the problem highly unstable. A variety of different deconvolution algorithms have been proposed in the literature.3–8 However, none of them is robust enough to be implemented in the commercial well-test-analysis software used most widely in the industry. Recently, von Schroeter et al.1,2 published a deconvolution algorithm that has been shown to work when a reasonable level of noise is present in test pressure and rate data. In our independent implementation and evaluation of the algorithm, we have found that it works well on consistent sets of pressure and rate data. It fails, however, when used with inconsistent data. Examples of such inconsistencies include wellbore storage or skin factor changing during a well-test sequence. Some degree of inconsistency is almost always present in real test data. Therefore, the deconvolution algorithm in the form described in the references cited cannot work reliably with real test data. In this paper, we describe the enhancements of the deconvolution algorithm that allow it to be used reliably with real test data. We demonstrate application of the pressure/rate deconvolution analysis to several real test examples.

scholarly journals Well Test and Short Term Multiple Rate Flow Tests Analyses to Successfully Hydraulic Fracturing Program of Block X

2018 ◽  
Vol 1 (1) ◽  
Author(s):  
Muhammad Dimas Adiguna ◽  
Muhammad Taufiq Fathaddin ◽  
Hari Karyadi Oetomo
Keyword(s):  
Secondary Data ◽  
Test Method ◽  
Well Test ◽  
Short Term ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Pressure Buildup ◽  
Skin Factor ◽  
Oil Flow ◽  
Rate Test

<p>Well test analysis was conducted to determine the characteristics of reservoir rocks. From the well test analysis it is obtained information such as permeability and skin factor. The skin factor is a quantity indicating the presence of disturbance in the formation as a result of drilling operations, production operations, perforating casing, gravel pack installation, remedial well work, acidizing operation, and hydraulic fracture operation. The objective of this research is to determine the relationship of multi rate test method of Jones, Blount, and Glaze and the comparison result among pressure buildup test and pressure drawdown test analyses, using Kappa software or manually calculation. Therefore, in this paper will study the method of Jones, Blount, and Glaze and the well test analyses to determine further work of the wells on block X. The data used in this paper is secondary data, namely the results of well test from three wells.Applying drawdown test analysis of A, Y, and Z wells yield skin factor values of 3.37; 27.10; and -1.39. Where in buildup pressure Horner method analysis of A, Y, and Z wells yield skin factor values of 16.10; 11.18; and -2.07. In the method of type curve derivatives the drawdown analysis of A, Y, and Z wells yield skin factor values of 7.04; 11.18; and 4.20. The analysis of pressure buildup, of A, Y, and Z wells yield skin factor value of 25.11; 14.47; and 1.93. In the analysis using <br /> Kappa software of A, Y, and Z wells yield skin factor values of 5.56; 10.2; and 2.00. The skin results of these wells indicate the formation damages. The Short Term Multiple Rate Flow Tests analysis using Jones, Blount, and Glaze method from the plots of Δp/q versus oil flow rate (q) are b’ high and b’/b low. These indicate that the three wells are encountering formation damages. The Jones, Blount, and Glaze method as well as the pressure buildup and pressure drawdown test analyses in block X indicate that these wells require to be stimulated.</p>

Well Test Analysis for a Well in a Constant Pressure Square

1972 ◽  
Author(s):  
Anil Kumar ◽  
H. J. Ramey
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Initial Pressure ◽  
Fluid Injection ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Water Influx ◽  
Mean Pressure ◽  
Well Tests

Abstract Very little information exists for analyzing well tests wherein a part of the drainage boundary is under pressure support from water influx or fluid injection. An idealization is the behavior of a well in the center of a square whose outer boundary remains at constant pressure. A study of this system indicated important differences from the behavior of a well in a closed outer boundary square, the conventional system. At infinite shut in, the constant- pressure boundary case well will reach the initial pressure of the system, rather than a mean pressure resulting from depletion. But it is possible to compute the mean pressure in the constant-pressure case at any time during shut in. Interpretative graphs for analyzing drawdown and buildup pressures are presented and discussed. This case is also of interest in analysis of well tests obtained from developed five-spot fluid injection patterns. Introduction Well-test analysis has become a widely used tool for reservoir engineers in the last twenty years. The initial theory was reported by Horner1 for unsteady flow of single phase fluids of small but constant compressibility to a well producing at a constant rate in -infinite and closed boundary reservoirs. Extension of the theory to the finite reservoir case involves specification of the outer boundary condition. The two most commonly observed conditions are: (1) no flow at the outer boundary corresponding to a closed or depletion reservoir, and (2) constant pressure at the outer boundary corresponding to complete water-drive.

Similar Constructive Method of Solution for the Nonlinear Percolation Model in Composite Reservoir

2014 ◽  
Vol 670-671 ◽  
pp. 678-682
Author(s):  
Feng Jiu Zhang ◽  
Xi Tao Bao ◽  
Shun Chu Li ◽  
Dong Dong Gui ◽  
Xiao Xu Dong
Keyword(s):  
Constant Pressure ◽  
Outer Boundary ◽  
Percolation Model ◽  
Constructive Method ◽  
Well Test ◽  
Analysis Software ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Method Of Solution ◽  
Quadratic Gradient

This paper presents a percolation model for the composite reservoir, in which quadratic-gradient effect, well-bore storage, effective radius and three types of outer boundary conditions: constant pressure boundary, closed boundary and infinity boundary are considered. With Laplace transformation, the percolation model was linearized by the substitution of variables and obtained a boundary value problem of the composite modified zero-order Bessel equation. Using the Similar Constructive Method this method, we can gain the distributions of dimensionless reservoir pressure for the composite reservoirs in Laplace space. The similar structures of the solutions are convenient for analyzing the influence of reservoir parameters on pressure and providing significant convenience to the programming of well-test analysis software.

scholarly journals ANALISIS PRESSURE BUILD-UP RESERVOIR GAS KONDENSAT DALAM FORMASI KARBONAT

PETRO ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 153
Author(s):  
Jodica Jodica ◽  
Onnie Ridaliani ◽  
Ghanima Yasmaniar
Keyword(s):  
Initial Pressure ◽  
Flow Region ◽  
Homogeneous System ◽  
Carbonate Reservoir ◽  
Gas Condensate ◽  
Reservoir Pressure ◽  
Well Test ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Carbonate Formation

<p><em>Different flow region will form in the reservoir when the gas condensate fluid flows with a bottom</em><em> </em><em>hole</em><em> </em><em>pressure</em><em> </em><em>below</em><em> </em><em>the</em><em> </em><em>dew</em><em> </em><em>point</em><em> </em><em>pressure.</em><em> </em><em>This</em><em> </em><em>flow</em><em> </em><em>region</em><em> </em><em>can</em><em> </em><em>be</em><em> </em><em>identified</em><em> </em><em>by</em><em> </em><em>the</em><em> </em><em>pressure build-up test analysis. This analysis can be done well on reservoir with homogeneous system and becomes</em><em> </em><em>more</em><em> </em><em>complex</em><em> </em><em>on</em><em> </em><em>reservoir</em><em> </em><em>with</em><em> </em><em>heterogeneous</em><em> </em><em>system.</em><em> </em><em>The</em><em> </em><em>purpose</em><em> </em><em>of</em><em> </em><em>this</em><em> </em><em>study</em><em> </em><em>is</em><em> </em><em>to</em><em> </em><em>find informations and characteristics about carbonate reservoir with gas condensate. Reservoir parameters that can be obtained are initial reservoir pressure (</em><em>pi</em><em>), </em><em>permeability (k), skin factor (s), reservoir boundary (boundary), drainage area, and average reservoir pressure ( </em><em>pr </em><em>). "JD-1" exploratory well penetrated the carbonate formation with the gas condensate hydrocarbon content. The well test analysis conducted is pressure analysis with pressure build-up testing and theanalysis results show a reservoir with a two-layer model, permeability value of 154 md, skin 13.8, initial pressure 3286.3 psia, and average reservoir pressure of 3285.7</em><em> </em><em>psia</em><em>.</em></p><p><em> </em></p><p> </p>

scholarly journals Bilinear pressure diffusion and termination of bilinear flow in a vertically fractured well injecting at constant pressure

Solid Earth ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 1423-1440
Author(s):  
Patricio-Ignacio Pérez Donoso ◽  
Adrián-Enrique Ortiz Rojas ◽  
Ernesto Meneses Rioseco
Keyword(s):  
Hydraulic Conductivity ◽  
Flow Regime ◽  
Flow Rate ◽  
Transient Flow ◽  
Constant Pressure ◽  
Well Test ◽  
Production Well ◽  
Well Test Analysis ◽  
Fracture Length ◽  
Fourth Root

Abstract. This work studies intensively the flow in fractures with finite hydraulic conductivity intersected by a well injecting or producing at constant pressure, either during an injection or production well test or the operation of a production well. Previous investigations showed that for a certain time the reciprocal of flow rate is proportional to the fourth root of time, which is characteristic of the flow regime known as bilinear flow. Using a 2D numerical model, we demonstrated that during the bilinear flow regime the transient propagation of isobars along the fracture is proportional to the fourth root of time. Moreover, we present relations to calculate the termination time of bilinear flow under constant injection or production well pressure as well as an expression for the bilinear hydraulic diffusivity of fractures with finite hydraulic conductivity. To determine the termination of bilinear flow regime, two different methods were used: (a) numerically measuring the transient flow rate in the well and (b) analyzing the propagation of isobars along the fracture. Numerical results show that for low dimensionless fracture conductivities the transition from bilinear flow to another flow regime (e.g., pseudo-radial flow) occurs before the pressure front reaches the fracture tip, and for high dimensionless fracture conductivities it occurs when the pressure front arrives at the fracture tip. Hence, this work complements and advances previous research on the interpretation and evaluation of well test analysis under different reservoir conditions. Our results aim to improve the understanding of the hydraulic diffusion in fractured geologic media, and as a result they can be utilized for the interpretation of hydraulic tests, for example to estimate the fracture length. Highlights. The reciprocal of flow rate is proportional to the fourth root of time. The migration of isobars in the fracture is proportional to the fourth root of time. For low dimensionless fracture conductivities, bilinear flow ends before the pressure front reaches the fracture tip. For high dimensionless fracture conductivities, bilinear flow ends when the pressure front reaches the fracture tip. Isobars accelerate when they approach the fracture tip.

Sign in / Sign up

Export Citation Format

Share Document