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

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.

Pressure Buildup Equations for Spherical Flow Regime Problems

1974 ◽  
Vol 14 (06) ◽  
pp. 545-555 ◽  
Author(s):  
W.E. Culham
Keyword(s):  
Flow Regime ◽  
Transition Period ◽  
Oil Wells ◽  
Reservoir Pressure ◽  
Pressure Data ◽  
Pressure Buildup ◽  
Practical Utility ◽  
Straight Line ◽  
Practical Guidelines ◽  
Buildup Curve

Abstract Pressure buildup and flow tests conducted in wells that do not completely penetrate the producing formation or that produce from only a small portion of the total productive interval can generate noncylindrical flow regimes and require special interpretation procedures. Frequently a spherical flow regime is representative, and a new equation based on the continuous point-source solution to the diffusivity equation in spherical coordinates is presented for analyzing tests of this nature. The practical utility of the equation is demonstrated by practical utility of the equation is demonstrated by analyzing tests involving restricted producing intervals that cannot be treated with existing analytic methods.Practical guidelines for applying the proposed equation are developed by analyzing pressure data generated by a numerical simulator and more complex analytic solutions for variety of special completion situations. Equations for determining static reservoir pressure, formation permeability, and skin factors pressure, formation permeability, and skin factors are derived and their validity verified under theoretical test conditions. The equations presented should have a variety of applications, but are particularly suited for analyzing pressure data from particularly suited for analyzing pressure data from drillstem tests with short flow periods. Introduction The fundamental equation for analyzing pressure buildup tests of oil wells was presented by Horner in 1951. This equation is based on the "line source" solution to the boundary value problem describing the pressure distribution resulting from the cylindrical flow of a slightly compressible fluid in an infinite reservoir. To achieve cylindrical flow the wellbore of a well must completely penetrate the producing formation. Although this restriction is often satisfied, in many tests it is not; for example, oil wells producing through perforated casing may have only a small portion of the total production interval perforated, or in the case of production interval perforated, or in the case of drillstem tests only a small interval (often 10 to 15 ft) of a thick (hundreds of feet) homogeneous formation may be selected for testing. Tests involving restricted producing intervals of this type have a characteristic buildup curve as described by Nisle and by Brons. These authors demonstrated that Horner's conventional equation could also be used for restricted producing interval problems, provided the correct portion of the buildup problems, provided the correct portion of the buildup curve is used. They showed that during a short period after starting production (or equivalently period after starting production (or equivalently after shut-in) the well behaves as if the total sand thickness were equal to the interval open to flow. That is, Horner's equations apply if the total sand thickness, h, is replaced by the producing interval thickness, h. They also showed that after a transition period the late part of the buildup curve could be used in the conventional manner to calculate formation permeability and static reservoir pressure. Kazemi and Seth extended the work of pressure. Kazemi and Seth extended the work of Nisle by including the effect of anisotropy; they also presented an equation, based on an analytic solution developed by Hantush, for estimating the shut-in time required for the development of the second straight-line portion in a conventional plot --i.e., p vs In (t + Deltat/Deltat. The first straight-line part o the buildup curve usually lasts only a few part o the buildup curve usually lasts only a few minutes and may often be obscured by afterflow, whereas the latter straight-line portion may take several hours to develop and may not even occur for practical shut-in times if the formation is thick and the producing time is relatively short. This paper demonstrates that the transition period paper demonstrates that the transition period between the two cylindrical flow periods can be analyzed with the spherical* flow equations presented here. In addition, practical guidelines presented here. In addition, practical guidelines cue developed for their application.Moran and Finklea first suggested that a pressure buildup equation based on spherical now pressure buildup equation based on spherical now was necessary to correctly analyze pressure data obtained from wireline formation testers. In many respects this study is similar; in fact, the basic pressure buildup equation (although it was derived pressure buildup equation (although it was derived from a different starting equation) presented here was used by Moran and Finklea in analyzing wireline formation test data. SPEJ P. 545

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^

Effect of Flow Time Duration on Buildup Pattern for Reservoirs With Heterogeneous Properties

1984 ◽  
Vol 24 (03) ◽  
pp. 294-306 ◽  
Author(s):  
Tatiana D. Streltsova ◽  
Richard M. McKinley
Keyword(s):  
Flow Time ◽  
Well Testing ◽  
Well Test ◽  
Time Duration ◽  
Semilog Plot ◽  
Heterogeneous Reservoir ◽  
Straight Line ◽  
Buildup Curve ◽  
Straight Lines ◽  
Exploration Well

Abstract For a heterogeneous reservoir, the shape of a buildup curve is strongly dependent on the length of the preceding flow period. Therefore, in exploration well testing, where the flow period is usually short, modification of the pressure buildup pattern caused by insufficient flow time can lead to erroneous interpretation of well behavior. Buildup pattern, as a function of flow time, is discussed here for various types of pattern, as a function of flow time, is discussed here for various types of ideal heterogeneities such as linear reservoir discontinuities, natural fractures, vertical stratification, pressure support, and lateral permeability loss. A relationship is provided for the dimensionless flow permeability loss. A relationship is provided for the dimensionless flow time required to produce a certain buildup pattern. The effect of flow time on quantitative assessment of reservoir parameters is determined aswell. Introduction Well test analysis traditionally has been based on techniques developed for either drawdown calculations or buildup calculations after long flow periods. In exploration well testing, however, flow times prior to buildup periods. In exploration well testing, however, flow times prior to buildup tests are usually short. For a well in a reservoir with homogeneous properties and of infinite extent, the shape of neither the drawdown curve properties and of infinite extent, the shape of neither the drawdown curve nor the ensuing buildup curve is affected by flow time duration. Both are straight lines of a certain slope on a semilog plot of pressure vs. time. However, this is not the case for a reservoir with heterogeneous properties. For a heterogeneous reservoir in which a well shows a drawdown properties. For a heterogeneous reservoir in which a well shows a drawdown curve with multiple slopes on a semilog plot as production progresses, the drawdown as well as the buildup patterns become essentially dependent or the producing time. Moreover, for a given flow time, the drawdown curve and the following buildup curve may have different shapes. In well test analyses where the shape of pressure curves is used to evaluate reservoir properties, recognition of the pressure pattern alterations caused by properties, recognition of the pressure pattern alterations caused by insufficient flow time becomes important. In the case of a linear discontinuity such as a sealing fault, for example, it has been found that the buildup data on a Homer plot would show the second, double-slope straight-line characteristic of the fault only if the radius of investigation, before the well is shut in exceeds at least four times the distance, to the fault, = . Even this criterion is optimistic from a practical point of view. All buildup data exhibiting this characteristic double slope will be at relatively long shut-in times for which the Homer time ratio ( + ) is less than1.5. Since actual data seldom extend into this range, longer flow time swill be necessary. In what follows, the modification of buildup pattern caused by insufficient flow time is considered along with the specification of both the flow time and buildup time necessary to recognize a heterogeneity from its characteristic buildup pattern . The heterogeneities considered aresingle no-flow and constant pressure boundaries,single boundary with permeability and storage contrasts,multiple boundaries,radial loss in permeability,vertical stratification, andnatural fractures. Reservoir Limited by One or More Boundaries Linear No-Flow Boundary. Drawdown at a well producing a reservoir limited by an impermeable barrier, such as a sealing fault, according to the method of images that duplicates such a boundary mathematically, is and ............................(1) where ( ) is the exponential integral function, is the distance from the well to the fault, and = is the dimensionless flow lime. The characteristic drawdown pattern for a well near a sealing boundary, described by Eq. 1 and illustrated by the insert in Fig. 1, depicts on a semilog plot a curve consisting of two straight lines joined by a smooth transition. The first straight line represents the well response before the fault exerts any influence. The slope of this straightline, is inversely proportional to the reservoir transmissibility. This line is referred to as the middle-time region (MTR) line. The second straight line, formed after a smooth transitional period, represents the well behavior as affected by the fault. Its slope is twice that of the first straight line. The intersection of the two straight lines occurs at a nondimensional time ............................(2) The transition region between these two straight lines lasts, however, for more than one log cycle. The slope of the drawdown curve, ............................(3) SPEJ p. 294

Preparation of bottom waters to maintain reservoir pressure of low permeable oil reservoirs

2019 ◽  
pp. 22-28
Author(s):  
V.D. Nazarov ◽  
◽  
M.V. Nazarov ◽  
M.V. Astashina ◽  
K.L. Chertes ◽  
...  
Keyword(s):  
Oil Reservoirs ◽  
Reservoir Pressure ◽  
Bottom Waters

Evaluating the Performance of Horizontal Multi-Frac Wells in a Depleted Gas Condensate Reservoir in Sultanate of Oman

2022 ◽  
Author(s):  
Josef R. Shaoul ◽  
Jason Park ◽  
Andrew Boucher ◽  
Inna Tkachuk ◽  
Cornelis Veeken ◽  
...  
Keyword(s):  
Horizontal Well ◽  
Horizontal Wells ◽  
Gas Condensate ◽  
Integrated Analysis ◽  
Single Fracture ◽  
Reservoir Pressure ◽  
Well Test ◽  
Vertical Wells ◽  
Fracture Conductivity ◽  
Half Length

Abstract The Saih Rawl gas condensate field has been producing for 20 years from multiple fractured vertical wells covering a very thick gross interval with varying reservoir permeability. After many years of production, the remaining reserves are mainly in the lowest permeability upper units. A pilot program using horizontal multi-frac wells was started in 2015, and five wells were drilled, stimulated and tested over a four-year period. The number of stages per horizontal well ranged from 6 to 14, but in all cases production was much less than expected based on the number of stages and the production from offset vertical wells producing from the same reservoir units with a single fracture. The scope of this paper is to describe the work that was performed to understand the reason for the lower than expected performance of the horizontal wells, how to improve the performance, and the implementation of those ideas in two additional horizontal wells completed in 2020. The study workflow was to perform an integrated analysis of fracturing, production and well test data, in order to history match all available data with a consistent reservoir description (permeability and fracture properties). Fracturing data included diagnostic injections (breakdown, step-rate test and minifrac) and main fracture treatments, where net pressure matching was performed. After closure analysis (ACA) was not possible in most cases due to low reservoir pressure and absence of downhole gauges. Post-fracture well test and production matching was performed using 3D reservoir simulation models including local grid refinement to capture fracture dimensions and conductivity. Based on simulation results, the effective propped fracture half-length seen in the post-frac production was extremely small, on the order of tens of meters, in some of the wells. In other wells, the effective fracture half-length was consistent with the created propped half-length, but the fracture conductivity was extremely small (finite conductivity fracture). The problems with the propped fractures appear to be related to a combination of poor proppant pack cleanup, low proppant concentration and small proppant diameter, compounded by low reservoir pressure which has a negative impact on proppant regained permeability after fracturing with crosslinked gel. Key conclusions from this study are that 1) using the same fracture design in a horizontal well with transverse fractures will not give the same result as in a vertical well in the same reservoir, 2) the effect of depletion on proppant pack cleanup in high temperature tight gas reservoirs appears to be very strong, requiring an adjustment in fracture design and proppant selection to achieve reasonable fracture conductivity, and 3) achieving sufficient effective propped length and height is key to economic production.

Sign in / Sign up

Export Citation Format

Share Document