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SPE 103255
Optimizing the Productivity of Gas/Condensate WellsC. Shi, R.N. Horne, and K. Li, Stanford U.
Copyright 2006, Society of Petroleum Engineers
This paper was prepared for presentation at the 2006 SPE Annual Technical Conference andExhibition held in San Antonio, Texas, U.S.A., 2427 September 2006.
This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than300 words; illustrations may not be copied. The abstract must contain conspicuous
acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
AbstractGas-condensate reservoirs exhibit complex phase and flow
behaviors due to the appearance of condensate banking in the
near-well region. A good understanding of how the condensateaccumulation influences the productivity and the composition
configuration in the liquid phase is very important to optimize
the producing strategy, to reduce the impact of condensate
banking, and to improve the ultimate gas recovery.
This study addressed several issues related to the behavior of
the composition variation, condensate saturation build-up and
condensate recovery during the gas-condensate producingprocess. A key factor that controls the gas-condensate well
deliverability is the relative permeability, which is influenced
directly by the condensate accumulation. The accumulatedcondensate bank not only reduces both the gas and liquid
relative permeability, but also changes the phase composition
of the reservoir fluid, hence reshapes the phase diagram of
reservoir fluid and varies the fluid properties. Different
producing strategies may impact the compositionconfiguration for both flowing and static phases and the
amount of the liquid trapped in the reservoir, which in turn
may influence the well productivity and hence the ultimate gas
and liquid recovery from the reservoir. Changing the manner
in which the well is brought into flowing condition can affectthe liquid dropout composition and can therefore change the
degree of productivity loss.
In this study, compositional simulations of multicomponent
gas-condensate fluids were conducted at field scale to
investigate the composition and condensate saturation
variations. Different producing strategies have been compared,and the optimum producing sequences are suggested for
maximum gas recovery. A core flooding experiment with two-
component synthetic gas-condensate was designed andconstructed to model gas-condensate production behavior
from pressure above the dew-point to below. Experimental
observations of gas-condensate production confirm the
dramatic changes in the liquid composition seen in the
simulations.
IntroductionLiquid forms in a gas-condensate reservoir when the bottom-
hole pressure drops below the dew-point pressure. The
accumulated condensate in the vicinity of the well bore causea blockage effect and reduces the effective permeability
appreciably, and also causes the loss of heavy components atsurface. These effects depend on a number of reservoir andwell parameters.
The productivity loss caused by the condensate buildup is
striking. In some cases, the decline can be as high as a factor
of two to four, according to the case studies of Afidick et al.and Barnum et al.2. Even in very lean gas-condensate
reservoirs with a maximum liquid drop out of only 1%, the
productivity may be reduced by a factor of about two as thepressure drops below the dew-point pressure1. In order to
predict well deliverability and calculate gas and liquid
recovery, it is necessary to have a detailed knowledge of liquid
banking in gas-condensate fields.
Fevang and Whitson3 addressed the well deliverability
problem in their gas-condensate modeling, where they
observed that well deliverability impairment resulting from
near well-bore condensate blockage depends on PVTabsolute and relative permeabilities, and how the well is being
produced.
The relative permeability effect has been reported in field
observations. Variations of reservoir fluid PVT properties a
discovered condition have been observed and discussed formany reservoirs around the world (for example reference 4 for
mid-eastern reservoirs and reference 5 for North Seareservoirs). Lee6 also presented an example to show the
variation of composition and saturation of the gas-condensate
system due to the influences of capillary and gravitationaforces.
Roussennac7illustrated the phase change during the depletionin his numerical simulation. According to Roussennac, during
the drawdown period, with the liquid building up in the well
grid cell, the overall mixture in that cell becomes richer in
heavy components, and the fluid behavior changes from theinitial gas-condensate reservoir to that of a volatile/black oil
reservoir.
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2 SPE 103255
The well producing scheme may impose significant impacts
on PVT properties. However, the manner by which the
producing scheme influences the PVT properties has not yetbeen sufficiently addressed. This study aims to investigate the
producing strategy and its influences on productivity and
composition.
Compositional simulations of a multicomponent gas-condensate system and a binary-component gas-condensate
system were conducted here. To confirm the compositionalvariations resulting from producing strategy, a core flood
experiment has also been designed and constructed to
investigate the gas-condensate flow behavior in porous media.
The simulation models, the experimental apparatus and theprocedures are described here. Following that, the simulation
results and the experimental results are presented. Finally,
some conclusions are drawn.
Simulation models
Multicomponent simulation model
The primary objective of the simulation was to understand the
impact of producing scheme on the condensate banking and
compositional variations. A hypothetic cylindrical reservoir
model, with radius of 5200 ft and permeability-thickness of 20
md50 ft has been chosen, and a simulator E300 (2005a,Eclipse) with fully implicit (FULLIMP) method was used to
simulate the performance under different producing strategies.
The multicomponent fluid properties are shown in Table 1.Additional laboratory liquid dropout data were used to
correlate with equation of state (EOS) phase-behavior
calculation. The PVT program used in this study was PVTi byGeoquest. The Modified Peng-Robinson EOS was used to
perform the fluid characterization. Figure 1 shows the liquiddropout calculation from a tuned EOS, which matches well
with the measured data. Figure 2 shows the phase envelope for
this multicomponent gas-condensate system. The EOSpredictions were then used as the input to the simulator.
Table 1: Fluid composition of gas-condensate
Component
N2CO2C1C2C3
iC4nC4iC5nC5C6C7C8C9
C10+C10+MW
C10+density (g/cm3)
Fluid (mol%)
0.00850.0065
0.8358
0.0595
0.0291
0.00450.0111
0.0036
0.0048
0.00600.0080
0.0076
0.00470.0103
183
0.8120
0.5 1 1.5 2 2.5 3
x 107
0
0.5
1
1.5
2
2.5
3
3.5
4
Pressure (MPa)
Liqu
idd
ropout
liquid dropout (simulated)
liquid dropout (experimental)
Figure 1: Liquid dropout from constant volume depletion (CVD)experiment.
Figure 2: Phase diagram of a multicomponent condensatesystem.
In the simulations, small radii around the well-bore were
chosen to allow for accurate pressure drop calculation in the
near well-bore region.
In porous media, PVT properties are controlled by the in-situreservoir temperature, pressure and the porous media
properties. In this study, no temperature change has been
considered. Hence, the PVT properties are determined by the
in-situ reservoir pressure and the way the heavy components
accumulate. In order to investigate how the producing strategyinfluences the condensate blockage and hence, the final gas
recovery, two sets of simulations were conducted, one with
fixed bottom-hole pressure (BHP) strategy with different BHPsettings and the other with varying BHP as a function of time,.
Binary-component simulation model
To investigate the composition and saturation change resultingfrom the producing scheme, a binary-component gas-
condensate system was selected to conduct the core flooding
experiment. Figure 3 shows the phase diagram of the C1/C4(85%/15%) synthetic gas-condensate system. This system haslow critical temperature (Tc = -13.2 C) and critical pressure
(pc= 1760 psi), which makes the experiment easy to perform
under room temperature and within relatively low pressure
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4 SPE 103255
These four sampling points are shown in Figure 3. All gas
samples were collected in the sampling bags and sent to the
gas chromatograph for composition analysis.
Results and Discussion
Experiment results
Figure 5 shows the gas chromatograph results for all the gassamples. Notice that the first batch of gas samples, which were
collected before the flow test, show slightly differentcomposition for the same component (C1 or C4) at different
sample ports and these compositions also differ slightly from
the initial compositions. The samples taken at the sample port
2 and 6 are the only two samples exactly equal to the initialcompositions. Sample 1, 3 and 4 show higher C4percentage
and sample 5 shows lower C4 percentages compared to the
initial 19% C4percentage. This may be due to the fact that the
core was presaturated with pure methane at pressure 1,800 psi.
When the upstream pressure drops, more gas condensate drops
out into the core, and the accumulated condensate liquid,which is richer in heavier component, can not flow until the
condensate saturation reaches the threshold saturation on the
relative permeability curve. Hence the flowing phase consists
of lighter component; this is confirmed by the composition
decrement in C4component in the second and the third flowtest.
When the core system pressure drops below the pressure
corresponding to the maximum liquid drop-out point, thecondensate starts to revaporize. A higher percentage of heavier
component was expected to be seen at this stage. This is
confirmed by the composition results from the last batchsamples (batch 4), where the sampling pressure was only 61.5
psi and the C4composition is as high as 57.5%. At this pointin the experiment, the accumulated heavy component was
revaporized and recovered.
0
10
20
30
40
50
60
70
1 2 3 4 5 6
Port
C4(%)
Batch 1
Batch 2
Batch 3
Batch 4
Flow direction
original
composition
0
10
20
30
40
50
60
70
1 2 3 4 5 6
Port
C4(%)
Batch 1
Batch 2
Batch 3
Batch 4
Flow direction
original
composition
Figure 5: Gas sample results for the mole fraction of C 4 in theflowing phase.
Multicomponent simulation results
In the field scale simulation results, Figure 6 shows the
condensate saturation profiles vs. radius rfor different times.
The region of interest here is the two-phase zone. As expected
as the production proceeds, the pressure-drop expands to
regions further away from the producing well. Once thepressure drops below the local dew-point pressure, condensate
drops into the reservoir and accumulates until the accumulated
liquid saturation reaches the relative permeability threshold
From the figure, we can also see that the near well region has
the greatest liquid accumulation resulting from the early liquiddrop-out.
Figure 7 shows mole fractions of C7for the liquid phase. The
trend is similar to that of saturation profiles, noticing that the
heavy component (C7, in this case) accumulation is more
prominent in the near well region.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1 1 10 100 1000 10000
Radius r (ft)
S
c(fraction)
t = 0.5 day t = 1.5 days t = 102 days t = 206 days t = 345 days
t = 575 days t = 670 days t = 755 days t = 840 days t = 900 days
t = 940 days t = 980 days t = 990 days t = 1000 days
increasing producing time
Figure 6: Saturation profiles at different times.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.1 1 10 100 1000 10000
Radius r (ft)
C7
inliquidphase(fra
ction)
t = 0.5 day t = 1.5 days t = 102 days t = 206 days t = 345 days
t = 575 days t = 670 days t = 755 days t = 840 days t = 900 days
t = 940 days t = 980 days t = 990 days t = 1000 days
increasing producing time
Figure 7: Mole fraction profiles of C7in liquid phase.
a) Strategy of fixed BHP
In a PVT cell, the liquid drop-out from the gas-condensate
system can be revaporized if we either lower the BHP orincrease the BHP. However, in a porous medium, the
liquid drop-out is immobile unless the liquid accumulation
reaches the critical condensate saturation value on the
relative permeability curve. The accumulated condensate isgenerally made up of heavier components and hence
changes the local phase composition. Whether the
condensate build-up can be revaporized is mainlydetermined by the local fluid composition. Figure 8 shows
the saturation profile for different well BHPs. We can see
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SPE 103255 5
that the liquid saturation still accumulates as the BHP
drops, and no revaporization appears to happen for this
particular fluid system.
As the BHP drops, more C7, one of the heavy components,
drops to the liquid phase (Figure 9). Although the total gas
production (Figure 10) increases as the BHP decreases, the
well productivity (Figure 11) drops dramatically as liquidsaturation builds up.
Figure 12 and Figure 13 show that as the BHP decreases,
the two-phase region expands, and more heavy-
component will be left in the reservoir.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 100 200 300 400 500 600 700 800 900 1000
Time (days)
SC
(fraction)
BHP = 2000 psi BHP = 500 psi BHP = 1000 psi BHP = 1500 psi
BHP = 2500 psi BHP = 3000 psi BHP = 3500 psi BHP = 4000 psi
decreasing BHP
Figure 8: Condensate saturation profile for different BHP.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0 100 200 300 400 500 600 700 800 900 1000
Time (days)
C7inliquidphase(fracti
on
BHP = 2000 psi BHP = 500 psi BHP = 1000 psi BHP = 1500 psi
BHP = 2500 psi BHP = 3000 psi BHP = 3500 psi BHP = 4000 psi
decreasing BHP
Figure 9: Mole fraction profiles of C7in liquid phase.
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
45000000
50000000
0 100 200 300 400 500 600 700 800 900
Time (days)
W
GPT(mscf)
BHP = 2000 psi BHP = 500 psi BHP = 1000 psi BHP = 1500 psi
BHP = 2500 psi BHP = 3000 psi BHP = 3500 psi BHP = 4000 psi
decreasing BHP
Figure 10: Total gas production profile for different BHP.
0
20
40
60
80
100
120
140
160
180
200
0 100 200 300 400 500 600 700 800 900
Time (days)
WPIG(mscf/day-p
si)
BHP = 2000 psi BHP = 500 psi BHP = 1000 psi BHP = 1500 ps
BHP = 2500 psi BHP = 3000 psi BHP = 3500 psi BHP = 4000 ps
decreasing BHP
single phase
two phases
Figure 11: Well productivity index (WPIG) profiles for differenBHP.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1 1 10 100 1000 10000
Radius r (ft)
Sc
(fraction)
BHP = 2000 psi BHP = 500 psi BHP = 1000 psi BHP = 1500 psi
BHP = 2500 psi BHP = 3000 psi BHP = 3500 psi BHP = 4000 psi
decreasing BHP
Figure 12: Comparison of condensate saturation profiles fordifferent BHP at t = 1000 days.
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6 SPE 103255
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1 1 10 100 1000 10000
Radius r (ft)
C7
inliq
uidphase(fraction
BHP = 2000 psi BHP = 500 psi BHP = 1000 psi BHP = 1500 psi
BHP = 2500 psi BHP = 3000 psi BHP = 3500 psi BHP = 4000 psi
decreasing BHP
Figure 13: Comparison of mole fraction profiles of C7 in liquidphase at t = 1000 days.
In this case, we can decrease the BHP to achieve greater
pressure difference; hence temporarily to produce more gasfrom the reservoir. However, lowering the BHP will cause the
expansion of the two-phase region, and the accumulation ofmore heavy-component in the reservoir. Hence, lowering the
BHP may not be a good strategy for maximizing total fluidrecovery.
b) Strategy of BHP ramping as a function of time.
Instead of setting BHP at a fixed value, we can also control theBHP such that it ramps as a function of the producing time.
For all simulation tests in this case, the initial reservoir
pressure and the final well bottom-hole pressure control werethe same.
Figure 14 shows the ramping strategies used in this study.
Increasing the ramping time, the gas production rate increasesat the late producing life, although the initial production rate islow due to the smaller pressure difference (Figure 15). The
well loses some gas production in total when the ramping time
increases (Figure 16). However, the well productivity index
reduction is delayed from the high productivity of single-phase flow to low productivity of two-phase flow (Figure 17).
The accumulation of condensate saturation (Figure 18) and
heavy component (Figure 19) are also delayed.
1500
2000
2500
3000
3500
4000
4500
5000
5500
0 100 200 300 400 500 600 700 800 900 1000
Time (days)
WBHP(psi)
Increase ramping time
Figure 14: BHP ramps as functions of time.
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
0 100 200 300 400 500 600 700 800 900
Time (days)
WGPR(mscf/day)
Increase ramping time
Figure 15: Gas production rate profiles for different rampingstrategies.
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
40000000
45000000
0 100 200 300 400 500 600 700 800 900
Time (days)
WGPT(mscf)
Increase ramping time
Figure 16: Total gas production profiles for different rampingstrategies.
0
20
40
60
80
100
120
140
160
180
200
0 100 200 300 400 500 600 700 800 900
Time (days)
W
PIG(mscf/day-psi)
Increase ramping time
Figure 17: Well productivity index profiles for different rampingstrategies.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 100 200 300 400 500 600 700 800 900
Time (days)
Sc
(fraction)
Increase ramping time
Figure 18: Condensate saturation profiles for different rampingstrategies.
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SPE 103255 7
0
0.01
0.02
0.03
0.04
0.05
0.06
0 100 200 300 400 500 600 700 800 900 1000
Time (days)
C7
inliquidphase(fraction)
Increase ramping time
Figure 19: mole fraction profiles for C7in liquid phase at differentramping strategies.
From Figures 20 and 21, we can see that by increasing theramping time, the two-phase region can be effectively shrunkby a factor as much as 10, and less heavy-component can beleft in the reservoir. This is very meaningful from the point ofthe long-term field development since it has been reportedfrom many field cases that the heavy components are difficult
to recover once they have been left in the reservoir.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.1 1 10 100 1000 10000
Radius r (ft)
Sc
(fraction)
ramp = 0 ramp = 1000 ramp = 100 ramp = 200 ramp = 300 ramp = 400
ramp = 500 ramp = 600 ramp = 700 ramp = 800 ramp = 900
Producer
Increase ramping time
Figure 20: Saturation profiles for different ramping strategies att = 1000 days.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.1 1 10 100 1000 10000
Radius r (ft)
C7inliquidphase(fraction
ramp = 0 ramp = 1000 ramp = 100 ramp = 200 ramp = 300 ramp = 400
ramp = 500 ramp = 600 ramp = 700 ramp = 800 ramp = 900
Producer
Increase ramping time
Figure 21: Mole fraction profiles of C7in liquid phase for differentramping strategies at t = 1000 days.
Two-component simulation results
Figures 22 to 29 show the simulation results for the binary-component methane/butane system. These are a representationof flow in the experiment described earlier. The generaconclusions for the BHP strategy are the same for bothmulticomponent and binary-component systems. That is, thetotal gas production increases as a result of greater pressure
difference between the reservoir and the well, but at the sametime, lower BHP also brings more heavy-component into thereservoir and generates a larger two-phase region. For thiparticular binary combination of C1 and C4, the saturationprofile (Figure 22) shows decreases after the accumulatedcondensate saturation reaches a maximum value. Noticing thathis maximum condensate saturation (Scam =0.53) is greaterthan the critical condensate saturation (Sac=0.25) from therelative permeability curve. The mole fraction of C4 in theliquid phase also drops as the well continues producing. Thereason is that some revaporization of the in-place liquid phasetakes place; thus the two-phase zone varies as the well keepsproducing.
Figure 25 shows that the well gas productivity dropssignificantly from single-phase flow to two-phase flow and thelower the BHP, the greater the drop in gas productivity.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30
Distance (cm)
Sc
t = 0.005h t = 0.01h t = 0.015h t = 0.02h
t = 0.025h t = 0.035h t = 0.055h t = 20h
flow direction
Figure 22: Saturation vs. distance for binary-componencondensate system at BHP = 75 atm.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 5 10 15 20 25 30
Distance (cm)
C4inliquidphase
t = 0.005h t = 0.01h t = 0.015h t = 0.02h
t = 0.025h t = 0.035h t = 0.055h t = 20h
flow direction
Figure 23: Mole fraction of C4 vs. distance at BHP = 75 atm.
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8 SPE 103255
0
10000000
20000000
30000000
40000000
50000000
60000000
0 5 10 15 20 25
Time (hour)
WGPT(scc)
BHP = 75 atm BHP = 25 atm BHP = 35 atm BHP = 45 atm
BHP = 55 atm BHP = 65 atm BHP = 85 atm BHP = 95 atm
BHP = 105 atm BHP = 115 atm
decreasing BHP
Figure 24: Total gas production profiles for different BHP.
0
200000
400000
600000
800000
1000000
1200000
1400000
1600000
0.001 0.01 0.1 1 10 100
Time (hour)
WPIG(scc/hour-atm)
BHP = 75 atm BHP = 25 atm BHP = 35 atm BHP = 45 atm
BHP = 55 atm BHP = 65 atm BHP = 85 atm BHP = 95 atm
BHP = 105 atm BHP = 115 atm
increasing BHP
singlephase
region
twophasesregion
Figure 25: Well gas productivity profiles for different BHP.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.001 0.01 0.1 1 10 100
Time (hour)
Sc
(fraction)
BHP = 75 atm BHP = 25 atm BHP = 35 atm BHP = 45 atm
BHP = 55 atm BHP = 65 atm BHP = 85 atm BHP = 95 atmBHP = 105 atm BHP = 115 atm
increasing BHP
Figure 26: Condensate saturation vs. time for different BHP.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.001 0.01 0.1 1 10 100
Time (hour)
C4
inliquidphase
BHP = 75 atm BHP = 25 atm BHP = 35 atm BHP = 45 atm
BHP = 55 atm BHP = 65 atm BHP = 85 atm BHP = 95 atm
BHP = 105 atm BHP = 115 atm
decreasing BHP
Figure 27: Mole fraction of C4vs. time for different BHP.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30
Distance (cm)
Sc
BHP = 75 atm BHP = 25 atm BHP = 45 atm
BHP = 65 atm BHP = 85 atm BHP = 105 atm
flow direction
decreasing BHP
Figure 28: Saturation vs. distance for different BHP at t = 20h.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30
Distance (cm)
C4
inliquidphase(fraction
BHP = 75 atm BHP = 25 atm BHP = 45 atm
BHP = 65 atm BHP = 85 atm BHP = 105 atm
flow direction
decreasing BHP
Figure 29: Mole fraction of C4vs. distance for different BHP at t =20h.
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SPE 103255 9
In summary from the simulation results, we can conclude that
there is no standard way to optimize the producing strategy.
Using low BHP or rapid ramping time for BHP, we canachieve high total gas production temporarily, however, to
minimize the condensate banking blockage and hence to
enhance the ultimate gas and liquid recovery, higher BHP or
slower ramping time for BHP may be a better strategy. The
optimal approach is likely to be dependent on the originalcomposition.
Conclusions1. In gas-condensate flow, local composition changes
due to relative permeability effects.
2. Composition and condensate saturation changesignificantly as a function of producing sequence.
The higher the BHP, the less the condensate banking
and a smaller amount of heavy-component is trapped
in the reservoir; increasing ramping time of BHP will
also help to alleviate the condensate banking andheavy-component trapping.
3. Gas productivity can be maximized with properproducing strategy. The total gas production can be
achieved by lowering the BHP or dropping the BHP
quickly instead of ramping slowly to a preset BHP
value.
4. Productivity loss can be reduced by optimizing theproducing sequence.
5. The condensate drop-out will hinder the flow
capability, due to relative permeability effects.
NomenclatureN2 nitrogen
CO2 carbon dioxideC1 methane
C2 ethaneC3 propane
iC4 i-butane
nC4 n-butaneiC5 i-pentane
nC5 n-pentane
C6 hexaneC7 heptane
C8 octane
C9 nonaneC10+ decene
MW molecular weight
CVD constant volume depletion
BHP bottom-hole pressureScc critical condensate saturationSc condensate saturation
WPIG gas productivity index of a well (mscf/day-psi or
scc/hour-atm)
WGPT well total gas production (mscf or scc)Tc critical temperature (K or C)
pc critical pressure (psi or atm)
AcknowledgementsWe would like to express our appreciation to Saudi Aramaco
and the members of SUPRI-D (Research Consortium onInnovation in Well Testing) for financial support and usefu
discussions.
References
1. Afidick, D., Kaczorowski, N.J., and Bette, S., 1994Production Performance of a Retrograde Gas: A Case Study
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SI metric conversion Factorsatm 1.013250 * E+05 = Paft3 1.589873 E-01 = m3
F (F-32)/1.8 = C
in.3 1.638706 E+01 = cm3
psi 6.894757 E+00 = kPa