spe-89905-pa.pdf---well test analysis of horizontal wells in gas-condensate reservoirs

Well-Test Analysis of Horizontal Wells inGas/Condensate Reservoirs

A. Hashemi, SPE, Imperial College London; L.M. Nicolas, SPE, Gaz de France; andA.C. Gringarten, SPE, Imperial College London

SummaryGas/condensate reservoirs usually exhibit complex flow behaviorsowing to the buildup of condensate banks around the wells whenthe bottomhole pressure drops below the dewpoint pressure. Theformation of this liquid saturation can lead to a severe loss of wellproductivity and, therefore, lower gas recovery. Several studieshave examined various ways to minimize the pressure drop inorder to reduce liquid dropout and related problems. One solutionimplemented over the past decade is the use of horizontal wells.

There is a lack of published knowledge on the flow behavior ofhorizontal wells in gas/condensate reservoirs. The limited studiesin this area (Muladi and Pinczewski 1999; Dehane et al. 2000;Harisch et al. 2001) focused on well performance rather than onwell-test behavior. There has been no evidence of condensatedropout effects in published horizontal-well-test data.

This paper presents preliminary results from a study aimed atestablishing an understanding of the near-wellbore well-test be-havior in horizontal wells in gas/condensate reservoirs, with afocus on the existence of different mobility zones caused by con-densate dropout.

We used a 3D fully compositional model to develop derivativeshapes to be expected from horizontal-well-test data in gas/condensate reservoirs below the dewpoint under various condi-tions. We then analyzed actual well-test data that exhibit suchderivative characteristics, using a uniform flux horizontal wellwith wellbore storage and skin model and appropriate reservoirboundaries. The condensate drop effects in the production testshave been accounted for through changes in the values of the totalskin effect. Finally, we used a compositional model to verify theresults obtained from conventional well-test analysis.

It was found that condensate deposit near the wellbore yields awell-test composite behavior similar to what is found in verticalwells, but superimposed on horizontal-well behavior, which makesit much more complex.

IntroductionMany studies (Fussel 1973; Barnum et al. 1995; Afidick et al.1994) have reported significant losses of well deliverability ingas/condensate reservoirs because of condensate blockage. Thelevel of productivity decline depends on several factors, includingcritical condensate saturation, relative permeabilities, non-Darcyflow, and high capillary number effects.

Retrograde condensation occurs when the flowing bottomholepressure falls below the dewpoint pressure (Kniazeff and Naville1965; Gringarten et al. 2000), creating three regions in the reser-voir with different liquid saturations. Away from the well, an outerregion has the initial liquid saturation; next, nearer the well, thereis a rapid increase in liquid saturation and a decrease in the gasmobility. Liquid in that region is immobile. Closer to the well, aninner region is formed in which liquid saturation is higher than acritical condensate saturation and both the oil and gas phases aremobile. Finally, in the immediate vicinity of the well, there is aregion with lower liquid saturation owing to capillary number

effects, which represents the ratio of viscous to capillary forces.Such a region has been inferred from a number of experimentalcore studies at low interfacial tension and high flow rates (Hen-derson et al. 1998; Ali et al. 1997). The existence of the fourthregion is important because it counters the reduction in productiv-ity caused by liquid dropout.

The various mobility zones described above can be identifiedby well-test analysis using a variety of analytical and numericalmodels. Well-test analysis is commonly used to identify and quan-tify near-wellbore effects, reservoir behavior (i.e., zones of differ-ent mobilities and storativities), and reservoir boundaries. Findingall this information from well tests in gas condensate reservoirs,however, is challenging, because of changes in the composition ofthe original reservoir fluid and the impact of wellbore dynamics.Nonetheless, gas/condensate flow behavior is now reasonably wellunderstood for vertical wells, in which the fluid flow toward thewell can be modeled with a simple radial-flow geometry. A num-ber of publications (Afidick et al. 1994; Daungkaew et al. 2002;Marhaendrajana et al. 1999; Saleh and Stewart 1992) have docu-mented vertical well tests in gas/condensate reservoirs that exhibitregions of decreasing gas mobility near the wellbore and includean increased gas mobility region in the immediate vicinity of thewellbore (the fourth region mentioned above) (Gringarten et al.2000; Daungkaew et al. 2002).

However, the situation is different in horizontal wells. Thepressure drawdown is less than in vertical wells under the sameconditions; therefore, liquid dropout in gas/condensate well tests isreduced, although it would still occur as the flowing bottomholepressure drops below the dewpoint. Among the limited publica-tions in this area, only the paper by Harisch et al. (2001) focuseson the multiphase effects on horizontal-well-test behavior. In thatpaper, the authors successfully history matched 1 year of produc-tion data obtained from permanent downhole gauges in a horizon-tal gas/condensate well. They used a numerical model that incor-porated Coats extended black-oil pressure/volume/ temperature(PVT) model (Coats 1985). A simulation with a dry gas, however,provided the same pressure responses for the same reservoir andhorizontal-well parameters. The authors concluded that multiphaseflow had no effects on their particular horizontal well test becausethe test was performed with drawdown pressures just below thedewpoint. The expected well test behavior when a horizontal welltest is conducted with drawdown pressures significantly below thedewpoint was not addressed.

The findings from Harisch et al. (2001) are not consistent withour own field data interpretations and compositional simulations.The issue in the above study seems to be the use of extendedblack-oil PVT instead of compositional modeling and the limita-tion of Coats black-oil PVT to only one C7+ fraction. Practicalexperience and theoretical studies have shown that more-detailedC7+ splitting yields noticeable differences in the oil viscosity be-tween compositional and black-oil simulations (Fevang and Whit-son 1996).

The present paper demonstrates how the horizontal-well flowregimes are affected by condensate accumulation and how thismodifies the derivative shapes.

Background and TheoryParameters Affecting Flow in Gas/Condensate Reservoirs. In agas/condensate reservoir, productivity above the dewpoint dependson the reservoir mobility (permeability times thickness divided byviscosity), as in a normal dry-gas reservoir. Below the dewpoint, it

Copyright 2006 Society of Petroleum Engineers

This paper (SPE 89905) was first presented at the 2004 SPE Annual Technical Conferenceand Exhibition, Houston, 2629 September, and revised for publication. Original manuscriptreceived for review 7 June 2004. Revised manuscript received 28 September 2005. Paperpeer approved 8 December 2005.

86 February 2006 SPE Reservoir Evaluation & Engineering

is controlled by the critical condensate saturation, the shape of thegas and condensate relative permeability curves, and the non-Darcy flow effects.

Near-Critical Relative Permeability. Most of the pressure dropfrom condensate blockage occurs within a few feet of the wellbore,where the gas phase is flowing at a high velocity. Within thisregion, pressure gradients in both flowing phases are large, and theinterfacial tension (IFT) between the gas and condensate is low.Experimental studies have shown that as a gas/condensate systemapproaches near-critical conditions, interfacial tensions decrease,and the relative permeability curves become progressivelystraighter (miscible) while the residual fluid saturations decrease(Henderson et al. 1998; Bardon and Longeron 1980).

However, IFT is not the only parameter that controls the rela-tive permeability profiles. An increase in relative permeabilitywith velocity has been demonstrated in numerous laboratory core-flood experiments (Ali et al. 1997; Henderson et al. 1997; Mottet al. 2000). Henderson et al. (1997), through steady-state relativepermeability measurements, confirmed the significant effect ofpositive coupling effect even at very high velocities, which iscontrary to the conventional view that relative permeability shoulddecrease with increasing velocity.

Because high velocities and low IFTs both cause increases inthe ratio of viscous to capillary forces, researchers have attemptedto model these phenomena in terms of a single parameter, namelythe capillary number (Nc). The capillary number is defined as

Nc =v

, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)

where is the gas viscosity, is the interstitial velocity, is theporosity, and is the IFT between the gas and liquid phases.

The capillary number is often used in compositional models tomodify the relative permeabilities at high velocities and/or lowIFT. The capillary number has two effects on the gas and oilrelative permeability curves: as the capillary number increases, itfirst reduces the residual saturations; then, it changes the relativepermeabilities from immiscible saturation curves to straight-linemiscible curves.

Non-Darcy Flow. Darcys law cannot describe fluid flow ac-curately when the flow rate is high. Forchheimer added a non-Darcy term into Darcys flow equation to express the relationshipbetween velocity and pressure drop in porous media:

dp

dl=

kv + v2 , . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)

where is the fluid density and is the non-Darcy coefficient,considered to be a characteristic of the rock. For single-phase fluidflow, the non-Darcy coefficient is usually determined from theanalysis of multirate pressure tests or is obtained from theoreticalor empirical correlations (Li and Engler 2001). In the case oftwo-phase flow, as in gas/condensate reservoirs, non-Darcy flowcreates additional condensate dropout because the inertial resis-tance to one phase is affected by the presence of a second phase.There is evidence in the literature that the non-Darcy coefficientincreases dramatically when liquid saturation increases (Wong1970). The non-Darcy coefficient in multiphase flow is usuallydetermined from empirical correlations (Li and Engler 2001).

It can be concluded that, in gas/condensate reservoirs, non-Darcy flow and near-critical relative permeabilities are two phe-nomena that are rate-dependent (Mott et al. 2000) but acting inopposite directions. Velocity-dependent relative permeability im-proves well productivity, while inertial flow lowers productivityby reducing the effective gas permeability.

Composite Well-Test Interpretation Models. Several authorshave published well-test data that show that mobility decreasesowing to condensate blockage (Afidick 1994; Jones et al. 1989;Barrios et al. 2003; Behrenbruch and Kozma 1984) or increasesowing to capillary number effects (Gringarten et al. 2000; Daung-kaew et al. 2002) can be observed and quantified by well-test analysis.

Once a condensate bank has formed, the applicable interpreta-tion model is a radial composite model if single-phase pseudopres-sures are used. The radial composite model to represent zones ofdifferent fluids was first investigated by Van Pollen (1964). Itconsists of two or more circular zones surrounding the well, withdifferent mobilities and storativities in each zone. In the case ofgas/condensate reservoirs, the zones of the composite model cor-respond to the reservoir regions containing (1) the gas with theinitial condensate saturation, (2) the gas and condensate flowingtogether, and (3) the gas and condensate affected by capillarynumber effects. These yield different derivative radial-flow stabi-lization levels that make it possible to estimate the extent of thevarious zones. Fig. 1 shows generic shapes of log-log pressure andderivative curves for a vertical well below the dewpoint pressure ina gas/condensate reservoir. The different stabilization levels yieldthe mobilities and the radii of the various zones, assuming valuesof storativity ratios between consecutive regions (Gringarten et al.2000). Two skin values can also be obtained, a wellbore skin S(w)from the higher stabilization level and a total wellbore skin, S(w,t)from the lower level (Fig. 1). The wellbore skin includes the me-chanical skin and inertia effects. The difference between the well-bore skin and the total wellbore skin is the skin effect due tocondensate banking (Osorio et al. 2005). It can be shown that(Thomson et al. 1993):

Sw,t =1

kh12Sw + 1 kh12 ln r1rw . . . . . . (3)

Well-Test Interpretation Using Compositional Simula-tion. Well-test behaviors in gas/condensate reservoirs change withtime, from dry gas to condensate-dominated to boundary-dominated. Conventional well-test analysis can only account forthese continuous variations through a series of snapshots of thewell behavior at specific times. To investigate the possible causesof the various derivative shapes seen on the data, a series of ana-lytical and numerical tools must be used in forward-modelingmode, especially in the case of complex well or reservoir geometries.

Single-well numerical compositional simulations are particu-larly useful to study the evolution of the condensate bank withtime. For instance, one might expect that, in a buildup, the con-densate would revaporize and the oil saturation would decreaseowing to the increase in reservoir pressure. Actually, revaporiza-tion in buildups only occurs near the outer edge of the two-phaseregion and only in buildups that follow drawdowns at high pro-duction rates (Bozorgzadeh and Gringarten 2004). Elsewhere, theliquid saturation distribution remains equal to that at the instant ofshut-in (Bozorgzadeh and Gringarten 2004; Economides et al.1987; Raghavan et al. 1999). This is because of the hysteresis

Fig. 1Two- and three-mobility-zone radial composite well-testmodels for vertical wells.

87February 2006 SPE Reservoir Evaluation & Engineering

effects caused by excessive accumulation of condensate near thewellbore and changes in the composition of the reservoir fluid,while the dewpoint increases significantly as production continues(Economides et al. 1987).

Compositional simulation is also used to verify the results ofanalytical interpretations. Using the analytical well-test-interpreta-tion results as inputs, the compositional model must provide areasonable match not only on the pressure/rate history and theproducing gas/oil ratio (GOR), but also on the log-log plot of pseudo-pressure and derivatives of the main buildups and drawdowns.

Challenges in Gas/Condensate Well-Test Analysis. There aretwo main challenges in the interpretation of gas/condensate welltests. The first one is the relatively short duration of individualflow periods in production tests. Most production well tests are notlong to reach the derivative radial flow stabilization correspondingto the effective gas permeability. Only the stabilization corre-sponding to the gas condensate (and possibly the one correspond-ing to the velocity stripping) is apparent. In these cases, the corepermeability often has been shown to provide a good estimate ofthe effective gas permeability derivative radial-flow stabilization,at least in sandstone reservoirs (Daungkaew et al. 2002).

The other challenge is phase redistribution of the producingfluid in the wellbore. This affects drawdown or buildup shapesin a way that can make the data uninterpretable or cause it tobe misinterpreted.

Well-Test Analysis of Horizontal Wells. Horizontal-well testsare difficult to interpret even with single-phase fluids. This ismainly because of the three-dimensional nature of the flow geom-etry, the lack of symmetry, and the large number of parametersrequired for characterizing the flow.

When a horizontal well is put on production, three successiveflow regimes with different durations develop in the reservoir:early radial, linear, and pseudoradial flow (Fig. 2). The early radial(or cylindrical) flow occurs in the vertical plane, with the horizon-tal well as axis, creates the first stabilization in Fig. 2, and yieldskvkhL. If the horizontal-well length is significantly greater thanthe formation thickness, a linear flow may occur once the pressuretransient reaches the upper and lower impermeable boundaries,which yields a half-unit slope log-log straight line on the deriva-tive. Finally, a pseudoradial-flow regime develops in the horizon-tal plane as flowlines converge from all reservoir directions towardthe well, producing a final stabilization on the derivative. This, andthe corresponding Horner straight line, yields the horizontal per-meability. The three flow regimes described above may or may notdevelop or may overlap depending on the location of the well; thewell length; the location and type of the upper, lower, and lateralboundaries; and the reservoir and fluid properties.

In the case of gas/condensate reservoirs, the addition of con-densate dropout increases the flow-behavior complexity signifi-cantly by superimposing a composite behavior onto the normalhorizontal-well behavior. Because no analytical composite model

has been published for horizontal wells in the oil and gas literature,a numerical compositional simulator must be used to predict andanalyze the corresponding well-test behavior.

Compositional Simulation

In the following, we first investigate the condensate dropout effecton horizontal-well-test responses. This knowledge is then appliedto the analysis of actual field tests.

Model Setup. A single horizontal-well model was set up in 3Dwith the compositional simulator Eclipse-300 from Geoquest-Schlumberger. Cartesian coordinates were used to represent a syn-thetic single-layer homogeneous reservoir of 100 ft thickness with20,475 grids (453513) and a horizontal well of 750 ft lengthlocated at the center. The well is parallel to the x direction andperforated over its entire length. The grid size increases logarith-mically away from the well to allow accurate modeling of near-wellbore gas/condensate behavior (Fig. 3). The grid dimensionsare listed in Table 1, and the basic reservoir rock and fluid prop-erties are in Table 2. The model does not account for wellborestorage or skin. Frictional losses in the wellbore and capillarypressures are also neglected.

PVT Modeling. The PVT data used in the compositional modelwere based on recombined separator samples collected from wellCDW2 in the CDFi structure. CDFi is the modified name of aNorth Sea gas/condensate reservoir, which will be described laterin this paper. The heavier fractions of the fluid samples (i.e., C7+)were lumped into fewer pseudocomponents to reduce the numberof components from the initial 24 and decrease CPU and timedemands (Table 3). The laboratory experiments conducted on therecombined fluid samples include hydrocarbon analysis, constantcomposition expansion (CCE), constant volume depletion (CVD),and separator flash test.

The PVTi package from Geoquest-Schlumberger was used tosimulate the experiments. All experimental results were matchedsimultaneously to develop a representative equation of state(EOS). The modified Peng-Robinson (PR) EOS was used to gen-erate the full range of PVT properties needed for input into thesimulator. EOS matching with 13 components provided goodagreement for the dewpoint pressure (3,235 psia measured vs.3,250 psia calculated) and for the maximum condensate liquiddropout in the CVD experiment (1.9% measured and calculated).Figs. 4 and 5 show comparisons of liquid dropout between EOS-predicted and CVD-/CCE-measured data, respectively.

Relative Permeability. Relative permeability characteristics wereestimated from the standard Corey expressions (Ali et al. 1997).The relative permeability curves and the Corey function param-eters are shown in Fig. 6.

Fig. 2Different flow regimes in horizontal wells and corre-sponding derivatives.

Fig. 3Schematic of the well reservoir model used in compo-sitional simulation.


Fig. 4Comparison between simulated and observed CVD ex-periments.

Fig. 5Comparison between simulated and observed CCE ex-periments.


Eclipse 300 interpolates the gas relative permeability curvesbetween a base and a miscible fluid relative permeability curve toaccount for the relative permeability dependency on velocity andIFT. The base relative permeability curve is the measured curve atthe lowest possible velocity level and the highest realistic IFTvalue (Jamiolahmady et al. 2003). The miscible or straight-linerelative permeability is calculated and accounts for inertial effects.The interpolation is weighted by capillary number dependent func-tions according to correlations developed by Henderson et al. (1998).

Simulation Results. An anisotropic simulation model with a hori-zontal permeability of 10 md and a vertical-to-horizontal perme-ability ratio of 0.1 was selected. This ratio of horizontal to verticalpermeability is typical for sandstone reservoirs. The simulationruns were designed to generate the derivative shapes that could beexpected in horizontal-well tests in gas/condensate reservoirs be-low the dewpoint pressure under various conditions. In all cases,the initial reservoir pressure was set just above the dewpoint pres-sure so that a liquid-phase condensate forms at the start of pro-duction. An example of pressure/rate history for a simulation runis shown in Fig. 7.

It consists of 10 periods of alternating drawdowns and build-ups, labeled DD1, BU2, DD3, BU4, etc. Because the pressuredrawdown is small in horizontal wells, the gas-flow rates (50MMscf/D) and the durations of the drawdown periods (exceptDD1) were selected large enough so that condensate could accu-mulate and be detected on the derivative during the different hori-zontal-well flow regimes. The first drawdown was at very lowflow rate (1 MMscf/D) and of short duration (40 days) to demon-strate a homogeneous well-test behavior near the dewpoint pres-sure for comparison. The model was run for a total of 8.4 years andwas assumed to produce at constant rate. All the drawdown and

buildup flow periods (except BU2) are below the dewpoint pres-sure, as shown in Fig. 7. Consequently, a condensate bank isexpected to be developed. This is verified in Fig. 8, where thecondensate saturation is plotted vs. radial distance at differentproduction times.

Fig. 9 shows a diagnostic log-log plot of rate-normalizedpseudopressures and derivatives for the different flow periodsfrom Fig. 7. As can be seen in this figure, a composite behaviordue to condensate banking (BU4, BU6, BU8, and BU10) is super-imposed on the horizontal-well homogeneous behavior (DD1 andBU2). From the derivative shapes, it is obvious that when theflowing bottomhole pressure drops below the dewpoint, a near-wellbore zone with a reduced mobility is created. This behavior isfirst characterized by an upward shift of the early radial-flow de-rivative stabilization, as in BU4. As production time increases,more condensate is accumulated, and eventually, the compositebehavior appears on the linear and pseudoradial flow regimes(BU6, BU8, and BU10).

Fig. 9 also shows an increase in the skin factor as producingtime increases. This is indicated by the different levels of thepressure curves. Because we did not take into account the me-chanical skin in the simulation, and because the gas-flow rate is thesame in the various flow periods, this increase in skin is due to thecondensate drop only.

The simulation model was run with and without capillary num-ber to understand the effect of Nc on the derivative. As can be seenin Fig. 10, the early-time mobility in BU4, which follows theextended drawdown DD3, is much lower without Nc effects thanwith Nc effects. As a result, the skin due to the condensate bank isless with Nc effects. The derivative for BU4 exhibits three stabi-lizations at early times (Fig. 11), as in the case of a vertical well,corresponding (as time increases) to values of kvkhL for

Fig. 7Rate and pressure history example for the simulationruns.

Fig. 8Condensate distribution in the reservoir over the entirerate history in Fig. 7 (model with Nc).

Fig. 9Log-log diagnostic of the main flow periods consideredin Fig. 7.

Fig. 6Gas/oil relative permeability curves used in the syn-thetic model.


capillarity number effects, condensate banking, and initial gas inplace, respectively. In our case study, assuming a constant effec-tive well length of 750 ft and a horizontal permeability of 10 md,the corresponding values are 2, 1.83, and 3.16 md, respectively(Fig. 11).

The simulation study thus confirms that condensate depositnear the wellbore yields a well-test composite behavior and anincrease in the value of the skin factor. The composite behavior issimilar to that in vertical wells but superimposed on horizontal,rather than vertical, well behavior, which makes it more complex.

Well-Test AnalysisIn this section, we discuss the interpretation of well-test data ob-tained from one drillstem test (DST) and two production tests fromthree horizontal wells in a North Sea gas/condensate reservoir. Theoriginal field name has been changed to CDFi for confidential-ity. The tests exhibit condensate banking behavior similar to thosepredicted in the previous section from compositional simulations.

Reservoir Description. The CDFi structure is an elongated east/west-trending anticline with an extent of 5 km by 1 km (Fig. 12).It lies at depths of approximately 7,400 to 7,500 ft true verticaldepth subsea (TVDSS). The producing interval is approximately100 ft thick. The proven reservoir in this field is made of tworelatively thin Early Westphalian age sandstones (Unit 1 and Unit2), overlaying a thin Numurian clastic sequence and a carbonateplatform of Dinantian age. The volumetric average core porosityand permeability of each sand unit are shown in Table 4. Based ongeological information from the analysis of cuttings, cores and logdata, Unit 1 sand is interpreted as having good reservoir develop-ment across the entire structure. This unit is expected to comprisemedium to conglomeratic sandstone throughout with a high pro-portion of kaolin, while the shallowest sand (Unit 2) is developedas a channel system having a more variable reservoir quality.Although a relatively thin mudstone is detected between Unit 1

and Unit 2 that may cause vertical isolations, it is speculated thatthe two zones communicate across the field owing to the presenceof considerable faults.

The reservoir fluid in the CDFi structure is a lean gas/condensate fluid with a condensate/gas ratio between 24 and 33STB/MMscf. The PVT characteristics of the reservoir fluid werediscussed earlier. The initial reservoir pressure was estimated to be3,570 psia at a field datum of 7,415 ft TVDSS.

A total number of seven horizontal or slanted wells have beendrilled and completed in this reservoir to-date. The completiontype is complex: the wells were often completed with a combina-tion of barefoot, slotted liners, and perforations. Only well CDW3was completed as barefoot.

The tests selected for interpretation are from wells CDW1,CDW2, and CDW3.

Well-Test Analysis of Well CDW1. Well CDW1 is a horizontalwell, completed with a slotted liner and perforations. The slottedliner covers 941 ft of Unit 1b in the interval between 8,442 and9,383 ft measured depth (MD) (7,415 to 8,904 ft TVDSS), as wellas 315 ft of Unit 2a between a depth of 9,383 and 9,698 ft MD(7,372 to 7,402 ft TVDSS). The total drilled interval open to flowis therefore 1,256 ft. Unfortunately, no production log is availableto detect the net producing interval in this well. The deviationangle varies between 78 and 95. The upper producing interval,Unit 2b, is from a 128-ft perforated section in 512-in. casing at anangle of 74. The reservoir section plot for Well CDW1 is shownin Fig. 13.

The producing interval was tested in three stages. A DST wasperformed in July 1999, followed by two production tests in Marchand October 2000. The pressure and rate histories of the DST areshown in Fig. 14. The entire DST was divided into 38 separateflow periods, each one corresponding to a constant rate. The flow-ing bottomhole pressure was below the dewpoint during the draw-down periods, but the downhole shut-in pressure was above thedewpoint in the main shut-in periods (BU29 and BU38).

Fig. 10Log-log plot for BU4. Fig. 11Three derivative stabilizations for BU4.

Fig. 12Structural map of the CDFi field.


The first production test was carried out in March 2000, ap-proximately 4 months after the beginning of production. The sec-ond production test was performed in October 2000. The well wasproduced at an average rate of 13 MMscf/D of gas and 300 STB/Dof condensate before the first production test and at 10.5 MMscf/Dand 200 STB/D between the first and second production tests. Theproduction tests were conducted at bottomhole pressures below thedewpoint pressure. Both tests consisted of two drawdown and twobuildup periods. The pressure and rate histories for the first andsecond production tests are shown in Figs. 15 and 16, respectively.

To estimate the main reservoir parameters and the reservoirvolume and to investigate the long production-time effects on thenear-wellbore properties, the DST and both production tests wereanalyzed as a single test using the entire rate history. The DSTgauge depth was selected as the datum level, and the downholepressures in the production tests were corrected for gauge-depthdifferences by applying the gas pressure gradient. A total of 67flow periods were used to represent rate variations during the DST,the production tests and the periods between the DST and the firstproduction test, and between the two production tests. A rate-normalized log-log plot of pressure and derivative data for themain buildup and drawdown periods is shown in Fig. 17. Thecorresponding superposition plot is shown in Fig. 18. From thesefigures, it can be stated that (1) wellbore storage and skin dominatethe early-time responses, and (2) the durations of all flow periodsare too short to reach the pseudoradial-flow stabilization at latetimes. Only the early radial-flow derivative stabilization corre-sponding to vertical radial flow around the horizontal well can beseen in the log-log plot. It can be stated further that (3) the skineffect increases with production time, and (4) the early radial-flowderivative stabilizations during the production-test flow periods(BU 48, 50, and 67) are shifted upward compared to the corre-sponding stabilizations in the DST (BU 29 and BU38). This indi-cates a reduction in mobility near the wellbore, most likely causedby an increasing condensate-bank radius. The assumption that acondensate bank had formed is reasonable because the tests havebeen conducted below the dewpoint. Finally, we can state that (5)there is evidence of reservoir pressure depletion from the super-position plot of the main buildup periods.

Because the various flow periods in the tests are not longenough to reach the pseudoradial-flow regime, it is difficult to

estimate the vertical and horizontal permeabilities from the log-logdiagnostic plot without an initial estimate of horizontal permeabil-ity from other sources. Successful interpretation has been achievedby estimating horizontal permeability from a volumetric averageof the available core data (Daungkaew et al. 2002).

A uniform flux horizontal well in a reservoir of infinite lateralextent with homogeneous behavior was first used to obtain themain reservoir parameters from the last buildup period of the DST(BU 38). The model yields kh2.4 md, a vertical-to-horizontalpermeability ratio of 0.2, and an effective producing length of 410ft. The effective length calculated from the analysis is less than thetotal drilled length. This is consistent with the interpretation ofother wells in the same field and with common experience withhorizontal wells, which indicates that producing lengths are oftenmuch less than the drilled lengths (Lenn et al. 1998).

This model, however, fails to simulate the entire test. A closedrectangular boundary was then added that yields a good match ofthe pressure history over the total production time, with a calcu-lated drainage area of approximately 238 acres. The calculateddrainage shape is that of an elongated rectangle, with the lengthparallel to the well and the width perpendicular to the well. Theinterpretation model and the estimated reservoir volume are sup-ported by geological description. The distances to the no-flowboundaries are also in good agreement with the seismic interpre-tation (Fig. 19).

Results from the models with infinite lateral extent and closedrectangular boundaries are compared in Figs. 20 through 22.

Because no composite model exists for horizontal wells, thecondensate bank in Well CDW1 cannot be treated explicitly, as inthe case of vertical wells. Its effects were therefore accounted forthrough changes in the values of the total wellbore skin effect. Asummary of the analysis results for different flow periods is givenin Table 5.

As can be seen in this table, the total wellbore skin has in-creased from 1.6 in BU38 (DST) to 4.4 in the last BU of the secondproduction test (i.e., BU67). This increase in the total skin is mostlikely caused by buildup of the condensate bank over the produc-ing history. However, because this value has been obtained with ahomogeneous model, it should be verified through compositionalsimulation of the test.

Fig. 13Section plot of Well CDW1.

Fig. 14Pressure/rate history of the DST, Well CDW1.

Fig. 15Pressure/rate history for the first production test, WellCDW1.

Fig. 16Pressure/rate history for the second production test,Well CDW1.


The change in shape of the derivative in production-test flowperiods with respect to the derivative stabilizations in the DST andthe corresponding increase in the value of total wellbore skin withproduction time are consistent with the composite well-test behav-ior predicted by compositional simulation (Fig. 9). The presence ofa decreasing gas mobility zone is clearly seen in this well. Becausewellbore storage effects dominate at early times, the enhancedpermeability region due to Nc effects is not obvious in the log-logdiagnostic plots but probably does exist. This is supported by theplot of skin vs. flow rate, which does not show the increasingtrend normally expected in gas wells because of non-Darcy flow(Fig. 23), thus suggesting that non-Darcy effects are being com-pensated for by Nc effects (Daungkaew et al. 2002).

To confirm this behavior, two additional wells were analyzed.A summary of their interpretation follows.

Well-Test Analyses of Wells CDW2 and CDW3. The data forone DST and two production tests conducted in Wells CDW2 andCDW3 are prepared and analyzed as for Well CDW1. The infor-mation for the individual tests is summarized in Tables 6 and 7,and the reservoir cross-section plots are shown in Figs. 24 and 25,respectively.

The interpretation presented several challenges. Phase redistri-bution (Fig. 26) dominates at early times. So do wellbore storageeffects, owing to large volumes between the gauges and the hori-zontal wellbores (in the production tests of Well CDW3, the pres-sure gauge was set 500 ft vertically above midperforations). Fur-thermore, the wells are not perfectly horizontal (undulations), andthe wellbores usually intersect different formations with possiblelayering effects (Fig. 25).

Fig. 17Log-log diagnostic plot, Well CDW1.

Fig. 18Superposition plot, Well CDW1.

Fig. 19Schematic of the reservoir boundaries and drainagearea of Well CDW1.

Fig. 20Log-log match, Flow Period 38, Well CDW1.

Fig. 21Simulation of the entire pressure history with variousinterpretation models. Fig. 22Horner match, Flow Period 38.


Considering these limitations, the tests have been analyzed withmodels that fit the data best and are consistent with the otherinformation available in the wells and the reservoir. The interpre-tations attribute the derivative shape changes to the existence of acondensate bank. Figs. 27 and 28 show the log-log plots of therate-normalized pseudopressures and derivatives for the mainbuildup periods of the DSTs and the production tests in WellsCDW2 and CDW3, respectively. These figures indicate that thewell-test behaviors for the tests conducted below the dewpoint areconsistent with what has been observed in Well CDW1 and pre-dicted from the compositional simulation.

The study of the well tests thus confirms that a compositewell-test behavior develops when the flowing bottomhole pressurein a horizontal well drops below the dewpoint. The existence of a

reducing gas mobility zone is identified in all wells. The existenceof an enhanced mobility zone due to Nc effects, however, is notclear because of wellbore effects.

Compositional Simulationof Well Tests in Well CDW1In this section, we use a numerical compositional model to simu-late the DST and the two production tests in Well CDW1. Contraryto conventional well-test analysis, compositional simulations takeinto account the changes in the composition of the initial gas/condensate fluid over the entire production period. This approachthus can validate results obtained from conventional well-testanalysis and provide detailed information on the different near-wellbore effects caused by condensate dropout.


A single 3D horizontal-well model with 20,757 (373317)Cartesian gridblocks was used for the compositional simulation.The well is fully penetrating in the x direction. The distances to theno-flow boundaries (Fig. 29) and the basic reservoir parameterswere as obtained from well-test analysis. Wellbore storage andfrictional losses in the wellbore were not simulated. The reservoirdepth, gas/water contact (GWC), and water saturation were ob-tained from the field history report. The PVT characteristics of thereservoir fluid were as discussed earlier. The entire productionhistory was used. The non-Darcy coefficient was determined fromwell-test analysis.

Because special core analysis was not available for this well,the relative permeability characteristics were estimated using theCorey function. Sensitivity runs were made on the Corey param-eters to define a consistent set of relative permeability curves(Fig. 30) that could provide calculated oil-production rates equal tothe observed field oil rate at a specific gas-flow rate, in addition toa good match with the flowing bottomhole pressure. The capillarynumber was also included in the model.

History Match. The model was initially run to ensure that thesimulation response matched the entire pressure history from theDST to the second production tests. Because the main drawdownflow periods of the DST are conducted slightly below the dewpointand for very short times, pressure drawdowns are governed bynon-Darcy flow and mechanical skin only. A mechanical (damage)skin of 0.4 in the simulation model provided a reasonable match onthe DST. This value was kept constant on all simulations to seewhether it matched the corresponding drawdown flow periods inthe production tests.

The good DST match shown as a broken line in Fig. 31 sug-gests that the horizontal and vertical permeabilities, the effectivewell length, and the non-Darcy flow coefficient estimated fromconventional well-test analysis are reasonably accurate. Beyondthe DST, however, the match becomes worse because the modelunderestimated the bottomhole pressure and, therefore, the reser-voir volume has to be adjusted upward. A better overall historymatch (solid line in Fig. 31) is obtained with a drainage area of254.5 acres, which is 6.75% greater than the value from well-test

Fig. 23Skin vs. flow rate, Well CDW1.



analysis. These differences most likely result from differences inthe PVT used by the simulator and the well-test software.

Log-Log Match. A rate-normalized log-log plot of single-phasepseudopressures and derivatives for the different flow periods(Fig. 32) shows that almost all the simulated cases match thecorresponding actual derivatives at late times. As expected, thematches are not as good at early times because the compositionalmodel does not account for wellbore storage effects.

Fig. 33 shows the condensate saturation profile vs. radial dis-tance at the heel of the well in the y direction for the different flowperiods of the DST and the production tests in Well CDW1 at thestart of each shut-in period. This condensate saturation remainsconstant during buildup and is equal to the condensate saturation atthe end of the precedent drawdown (Bozorgzadeh and Gringart-en 2004).

Fig. 33 allows calculation of the condensate bank radius, whichcould not be obtained from conventional analysis because a com-posite model is not available. During the DST (BU29 and BU38),the pressure drawdown is low, and the condensate bank radius isless than 3 ft. The condensate saturation is less than the criticalcondensate saturation, even very near the wellbore. As productiontime increases, the oil saturation increases gradually. In the firstproduction test (BU48 and BU50), three regions are obvious: (1)an inner region in which both gas and oil phases are flowing but atdifferent rates and where oil saturation increases gradually; (2) anintermediate region in which only the gas phase is flowing and theoil phase is present but is immobile, and where oil saturationincreases dramatically; and (3) an outer region, in which only thegas phase is present. The radius of the condensate bank in BU50is approximately 500 ft. The condensate bank expands further asproduction time increases and eventually reaches the boundary ofthe reservoir. In BU67 (the final BU of the second production test),all the reservoir volume in the direction parallel to the wellbore isinvaded by the condensate, and only the first and second regionscan be identified on the condensate saturation profile.

A good match is obtained in Fig. 31 over the entire set ofdrawdowns without modifying the wellbore skin or the producingwell length. As the total skin increases with time according to Fig.17, it can be concluded that the increase in skin is caused bycondensate dropout only. This can also be verified approximatelyby calculating skin values from the observed condensate-bank ra-dius (Fig. 33) and the change in mobility at early times (Fig. 17)using the Hawkins relationship (1956). Results are shown in Table 8for different flow periods.

ConclusionsTo the authors knowledge, the present study is the first one de-tailing near-wellbore effects in well tests of horizontal wells ingas/condensate reservoirs below the dewpoint.

From compositional simulations, we found that the condensatedeposition creates a composite well-test behavior similar to what isobtained in vertical wells, but superimposed on a horizontal-wellbehavior. Such a behavior was confirmed with actual well-test dataon three horizontal wells from a gas/condensate reservoir in theNorth Sea.

Analysis of these well tests by conventional interpretation tech-niques and by compositional simulation leads to the followingconclusions:1. Actual well-test behaviors were consistent with the behaviors

predicted from compositional simulations.2. Only the derivative stabilizations corresponding to the reduced

mobility zones caused by condensate deposit could be identifiedon the log-log diagnostic plots at early times. A derivative sta-bilization caused by capillary number effects could not be iden-tified on the data because of dominating wellbore storage effects.

3. Capillary number effects probably did exist because a plot ofskin vs. flow rate did not show the increasing trend caused bynon-Darcy flow expected in gas wells. This was probably due to


Fig. 26Effects of wellbore phase redistribution, Well CDW3.

Fig. 27Log-log diagnostic plot, Well CDW2. Fig. 28Log-log diagnostic plot, Well CDW3.


non-Darcy effects being compensated by capillary number ef-fects (Daungkaew et al. 2002).

4. Analyses of buildups in production tests yield larger skins thanin the DSTs. This should result from the condensate bank in-creasing over the test duration because the production tests wereperformed at pressures significantly below the dewpoint pressure.

5. Because of the complex PVT behavior in gas/condensate sys-tems, both analytical well-test analyses and compositional simu-lations are required to analyze well tests in horizontal wells.

NomenclatureC wellbore storage coefficient

D(x) gridblock dimension in x directionD(y) gridblock dimension in y directionD(z) gridblock dimension in z direction

h reservoir thicknessk permeability

kh horizontal permeabilitykr relative permeability

krg gas relative permeabilitykro oil relative permeabilitykv vertical permeability

Lw horizontal-well lengthm(p) single-phase pseudopressure function

Nc capillary numberp pressure

pdew dewpoint pressurepi initial pressure

Qg gas flow rateQo oil flow rate

rw wellbore radiusS(t) total skin

S(w) mechanical skinSc completion skinSg gas saturation

Sorg residual oil saturation by gasSwc connate-water saturationzw vertical distance between horizontal drainhole and

no-flow boundaries (well eccentricity) viscosity density interstitial velocity porosity interfacial tension

AcknowledgmentsWe gratefully acknowledge the financial support for this project aspart of a Joint Industry Project funded by the U.K. Dept. of Tradeand Industry, Anadarko, Burlington Resources, BHP Billiton, Bri-tannia Operator Ltd., ConocoPhillips, Gaz de France, and Total.Partial support of Abdolnabi Hashemis PhD studies by the Natl.Iranian Oil Company (NIOC) is also acknowledged.

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Fig. 29The model configuration for simulation Well CDW1.

Fig. 30Relative permeability curves used for compositionalsimulation of Well CDW1.

Fig. 31Comparison of pressure matches using different res-ervoir volumes.


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SI Metric Conversion Factorsacre 4.046 873 E+03 m2

bbl 1.589 873 E01 m3

ft 3.048* E01 mft3 2.831 685 E02 m3

in. 2.54* E+00 cmmile 1.609 344* E+00 km

psi 6.894 757 E+00 kPa

*Conversion factor is exact.

Abdolnabi Hashemi is a PhD student at Imperial College Lon-don. e-mail: [email protected]. Previously, he workedfor the Natl. Iranian Oil Co. (NIOC) for 10 years as a seniordrilling engineer and drilling programs project leader. He holdsa BS degree from the Petroleum U. of Technology-Ahvaz (Iran)and an MS degree with distinction from Imperial College Lon-don, both in petroleum engineering. Laurent Nicolas is the co-ordinator for subsurface research activities in Gaz de France.e-mail: [email protected]. He is a gradu-ate of the Ecole Polytechnique and holds an MS degree inreservoir engineering from IFP in France. Alain C. Gringarten isa professor of petroleum engineering and Director of the Cen-tre for Petroleum Studies at Imperial College London. e-mail:[email protected]. Before joining Imperial in 1997,he held a variety of senior technical and management posi-tions with Scientific Software-Intercomp, Schlumberger, andthe French Geological Survey in Orlans, France. Gringarten isa recognized expert in well-test analysis and was the recipientof SPEs 2005 Cedric K. Ferguson Certificate, 2003 John FranklinCarll Award, and 2001 Formation Evaluation Award. A mem-ber of SPE since 1969, he was elected a Distinguished Memberin 2002. He holds MS and PhD degrees in petroleum engineer-ing from Stanford U. and an engineering degree from EcoleCentrale, Paris.


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