Interpretation of Pressure Buildup Curve in Layered Reservoirs With Afterflow

Determining Average Reservoir Pressure From Pressure Buildup Tests

Society of Petroleum Engineers Journal ◽

10.2118/4052-pa ◽

1974 ◽

Vol 14 (01) ◽

pp. 55-62 ◽

Cited By ~ 8

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

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Pressure Buildup Equations for Spherical Flow Regime Problems

Society of Petroleum Engineers Journal ◽

10.2118/4053-pa ◽

1974 ◽

Vol 14 (06) ◽

pp. 545-555 ◽

Cited By ~ 14

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

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Visualization of Fluid Flow Through Cracks and Microannuli in Cement Sheaths

SPE Journal ◽

10.2118/180019-pa ◽

2018 ◽

Vol 23 (04) ◽

pp. 1067-1074 ◽

Cited By ~ 7

Author(s):

Ragnhild Skorpa ◽

Torbjørn Vrålstad

Keyword(s):

Fluid Flow ◽

Effective Permeability ◽

Cfd Simulation ◽

Simulation Software ◽

Pressure Buildup ◽

Buildup Curve ◽

Flow Through ◽

Cement Sheath ◽

Pressure Driven Flow ◽

Pressure Driven

Summary Cement-sheath integrity is important for maintaining zonal isolation in the well. The annular-cement sheath is considered to be one of the most-important well-barrier elements, both during production and after well abandonment. It is well-known, however, that cement sheaths degrade over time (e.g., from repeated temperature and pressure variations during production), but the link between leak rate and the cause of cement-sheath degradation has not yet been established. In this paper, we have studied fluid flow through degraded cement sheaths. The degree of degradation of the cement sheaths varied from systematically connected cracks to real microannuli. The leak paths, created by thermal-cycling experiments, were imported into a computational-fluid-dynamics (CFD) simulation software. The pressure drop over the cement sheath was used as a boundary condition, and the resulting pressure-driven flow was studied using methane gas as the model fluid. The Forchheimer equation was used to estimate the effective permeability of the cement sheaths with defects. Our results show that the pressure-driven flow is complex and greatly affected by the geometry of the flow paths. A nonlinear pressure-buildup curve was observed for all experimental cases, indicating that Darcy's law was not validated. For homogeneous microannuli, the pressure-buildup curve was linear. The estimated effective permeability for all cases was observed to be orders of magnitude larger than that of a good cement sheath.

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