Well Testing Analysis

Previous Page The five different buildup examples shown in Figure 1.97 were presented by Economides (1988) and are briefly discussed below: SLOPE = 1300 psi/cycle SLOPE = 650 psi/cycle Figure 1.96 Estimating distance to a no-flow boundary. from which: Atx - YI. 45 hours Step 5. Calculate the distance L from the well to the fault by applying Equation 1.5.59: L_ /0.000148ftAf Example a illustrates the most common response—that of a homogeneous reservoir with wellbore storage and skin. Wellbo
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  Figure 1.96 Estimating distance to a no-flow boundary. from which: At x - YI. 45 hoursStep 5. Calculate the distance L from the well to the fault byapplying Equation 1.5.59: L _ /0.000148ftAf ~ V <i>m I 0.000148(30) (17.45)V (0.15) (0.6) (17 xlO- 6 ) Qualitative interpretation of buildup curves The Horner plot has been the most widely accepted meansfor analyzing pressure buildup data since its introduction in 1951. Another widely used aid in pressure transient analysisis the plot of change in pressure Ap versus time on a log-log scale. Economides (1988) pointed out that this log-log plotserves the following two purposes:(1) the data can be matched to type curves;(2) the type curves can illustrate the expected trends inpressure transient data for a large variety of well andreservoir systems.The visual impression afforded by the log-log presentationhas been greatly enhanced by the introduction of the pres-sure derivative which represents the changes of the slope ofbuildup data with respect to time. When the data producesa straight line on a semilog plot, the pressure derivative plotwill, therefore, be constant. That means the pressure deriva-tive plot will be flat for that portion of the data that can becorrectly analyzed as a straight line on the Horner plot.Many engineers rely on the log-log plot of Ap and itsderivative versus time to diagnose and select the properinterpretation model for a given set of pressure transientdata. Patterns visible in the log-log diagnostic and Hornerplots for five frequently encountered reservoir systems areillustrated graphically by Economides as shown in Figure1.97. The curves on the right represent buildup responsesfor five different patterns, a through e, with the curves onthe left representing the corresponding responses when thedata is plotted in the log-log format of Ap and (AtAp^) versus time. The five different buildup examples shown in Figure1.97 were presented by Economides (1988) and are brieflydiscussed below:Example a illustrates the most common response—thatof a homogeneous reservoir with wellbore storage andskin. Wellbore storage derivative transients are recog-nized as a hump in early time. The flat derivative portionin late time is easily analyzed as the Horner semilogstraight line.Example b shows the behavior of an infinite conductivity,which is characteristic of a well that penetrates a naturalfracture. The \ slopes in both the pressure change andits derivative result in two parallel lines during the flowregime, representing linear flow to the fracture.Example c shows the homogeneous reservoir with a sin-gle vertical planar barrier to flow or a fault. The level ofthe second-derivative plateau is twice the value of the levelof the first-derivative plateau, and the Horner plot showsthe familiar slope-doubling effect.Example d illustrates the effect of a closed drainagevolume. Unlike the drawdown pressure transient, thishas a unit-slope line in late time that is indicative ofpseudosteady-state flow; the buildup pressure derivativedrops to zero. The permeability and skin cannot be deter-mined from the Horner plot because no portion of the dataexhibits a flat derivative for this example. When transientdata resembles example d, the only way to determine thereservoir parameters is with a type curve match.Example e exhibits a valley in the pressure derivative thatis indicative of reservoir heterogeneity. In this case, thefeature results from dual-porosity behavior, for the caseof pseudosteady flow from matrix to fractures.Figure 1.97 clearly shows the value of the pressure/pressure derivative presentation. An important advantage ofthe log-log presentation is that the transient patterns havea standard appearance as long as the data is plotted withsquare log cycles. The visual patterns in semilog plots areamplified by adjusting the range of the vertical axis. Withoutadjustment, many or all of the data may appear to lie on oneline and subtle changes can be overlooked.Some of the pressure derivative patterns shown are sim-ilar to those characteristics of other models. For example,the pressure derivative doubling associated with a fault(example c) can also indicate transient interporosity flowin a dual-porosity system. The sudden drop in the pres-sure derivative in buildup data can indicate either a closedouter boundary or constant-pressure outer boundary result-ing from a gas cap, an aquifer, or pattern injection wells.The valley in the pressure derivative (example e) could indi-cate a layered system instead of dual porosity. For thesecases and others, the analyst should consult geological, seis- mic, or core analysis data to decide which model to use inan interpretation. With additional data, a more conclusiveinterpretation for a given transient data set may be found.An important place to use the pressure/pressure deriva-tive diagnosis is on the well site. If the objective of the test is todetermine permeability and skin, the test can be terminatedonce the derivative plateau is identified. If heterogeneitiesor boundary effects are detected in the transient, the testcan be run longer to record the entire pressure/pressurederivative response pattern needed for the analysis. 1.6 Interference and Pulse Tests When the flow rate is changed and the pressure response isrecorded in the same well, the test is called a single-well test. Examples of single-well tests are drawdown, buildup,injectivity, falloff and step-rate tests. When the flow rate ischanged in one well and the pressure response is recordedin another well, the test is called a multiple-well test. SLOPE = 650 psi/cycleSLOPE = 1300 psi/cycle Previous Page  aWell with WellboreStorage and Skin in a Homogeneous ReservoirbWell with InfiniteConductivity VerticalFracture in a Homogeneous ReservoircWell with WellboreStorage and skin in a Homogeneous Reservoirwith One Sealing FaultdWell with WellboreStorage and skin in a Homogeneous Reservoirwith Closed OuterBoundaryeWell with WellboreStorage and skin in a Dual Porosity Systemwith Pseudo-SteadyState Flow from Matrix to Fractures Figure 1.97 Qualitative interpretation of buildup curves (After Economides, 1988). Log - LogDiagnostic PlotHomer Plot WELLBORE'STORAGE RADIAL FLOWLINEAR FLOW-TRANSITIONRADIALFLOW .WELLBORESTORAGERADIALFLOWSEALINGFAULTWELLBORESTORAGENOTLOWBOUNDARYRADIAL FLOW(TOTAL SYSTEM)RADIAL FLOW(IN FISSURES)WELLBORE' STORAGEPSEUDO-STEADY STATEFLOW FROM MATRIXTOHS6URES  Figure 1.98 Rate history and pressure response of a two-well interference test conducted by placing the active well on production at constant rate. Examples of multiple-well tests are interference and pulsetests.Single-well tests provide valuable reservoir and well char-acteristics that include  flow  capacity kh, wellbore conditions, and fracture length as examples of these important prop-erties. However, these tests do not provide the directional nature of reservoir properties (such as permeability in the A:, y, and z direction) and have inabilities to indicate the degreeof communication between the test wells and adjacent wells. Multiple-well tests are run to determine: ã the presence or lack of communication between the test well and surrounding wells; ã the mobility-thickness product kh/'\i\ ã the porosity-compressibility-thickness product (f)C t h; ã the fracture orientation if intersecting one of the test wells; ã the permeability in the direction of the major and minoraxes. The multiple-well test requires at least one active (produc-ing or injecting) well and at least one pressure observation well, as shown schematically in Figure 1.98. In an interfer- ence test, all the test wells are shut-in until their wellborepressures stabilize. The active well is then allowed to pro- duce or inject at constant rate and the pressure response in the observation well(s) is observed. Figure 1.98 indicates this concept with one active well and one observation well. As the figure indicates, when the active well starts to pro- duce, the pressure in the shut-in observation well begins torespond after some time lag that depends on the reservoirrock and fluid properties.Pulse testing is a form of interference testing. The pro- ducer or injector is referred to as the pulser or the active Figure 1.99 Illustration of rate history and pressureresponse for a pulse test (After Earlougher, R. Advancesin Well Test Analysis) (Permission to publish by the SPE, copyrightSPE 1 1977). well and the observation well is called the responder. Thetests are conducted by sending a series of short-rate pulsesfrom the active well (producer or injector) to a shut-in obser-vation well(s). Pulses generally are alternating periods of production (or injection) and shut-in, with the same rateduring each production (injection) period, as illustrated inFigure 1.99 for a two-well system. Kamal (1983) provided an excellent review of interfer- ence and pulse testing and summarized various methods thatare used to analyze test data. These methods for analyzing interference and pulse tests are presented below. 1.6.1 Interference testing in homogeneous isotropicreservoirs A reservoir is classified as homogeneous when the poros-ity and thickness do not change significantly with location.An isotropic reservoir indicates that the permeability is the same throughout the system. In these types of reser-voirs, the type curve matching approach is perhaps the most convenient to use when analyzing interference test data in a homogeneous reservoir system. As given previously by Equation 1.2.66, the pressure drop at any distance r from anactive well (i.e., distance between an active well and a shut-inobservation well) is expressed as: A ->(r,/) = A>=|___JEI|—^- j Earlougher (1977) expressed the above expression in adimensionless form as: Pi-P(r f t) Ul.2QBn _ 1 \(-l\ ( *№% \ (lV] kh 2 [V 4 / V0.0002637*f/ V*W J From the definitions of the dimensionless parameters PD, fo, and ro, the above equations can be expressed in a TimeTimeTime pressure response in the observation well FmaoFPee Lag TimeTime Re a Av W Re aPsnW Pee a Ovo W  dimensionless form as: *. = >[=£] [1.6.1] with the dimensionless parameters as defined by: = [P 1 -PJrJ)]Hh PD ~ U1.2QBnrr D = — r w _ 0.0002637fr where: p(r, t) — pressure at distance r and time t, psi r = distance between the active well and a shut-inobservation well t = time, hours p\ = reservoir pressure k = permeability, mdEarlougher expressed in Equation 1.6.1 a type curve formas shown previously in Figure 1.47 and reproduced for convenience as Figure 1.100. To analyze an interference test by type curve matching,plot the observation well(s) pressure change Ap versus timeon tracing paper laid over Figure 1.100 using the matchingprocedure described previously. When the data is matched tothe curve, any convenient match point is selected and matchpoint values from the tracing paper and the underlying typecurve grid are read. The following expressions can then be applied to estimate the average reservoir properties: k = ri4i.2QfiMirfoi [162] L * JLA/>J MP O0002637 m T t 1 c^ UJLfo/vgj MP where: r = distance between the active and observation wells, ft k = permeability, mdSabet (1991) presented an excellent discussion on the useof the type curve approach in analyzing interference test databy making use of test data given by Strobel et al. (1976). Thedata, as given by Sabet, is used in the following example to illustrate the type curve matching procedure: Example 1.42 An interference test was conducted in a dry gas reservoir using two observation wells, designatedas Well 1 and Well 3, and an active well, designated as Well 2. The interference test data is listed below:ã Well 2 is the producer, Q g = 12.4 MMscf/day;ã Well 1 is located 8 miles east of Well 2, i.e., r 12 = 8 miles;ã Well 3 is located 2 miles west of Well 2, i.e., r 23 = 2 miles. Flow rate Time Observed pressure (psia) Q t Welll Well 3 (MMscf/day) (hr) P 1 Ap 1 p 3 Ap 3 0.0 24 2912.045 0.000 2908.51 0.00 12.4 0 2912.045 0.000 2908.51 0.00 Figure 1.100 Dimensionless pressure for a single well in an infinite system, no wellborn storage, no skin.Exponential-integral solution (After Earlougher, R. Advances in Well Test Analysis) (Permission to publish by the SPE,copyright SPE, 1977).

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