a new method to predict the performance of gas condensate reservoir

A NewMethod To Predict thePerformance of Gas-Condensate

ReservoirsAli Al-Shawaf, SPE, Saudi Aramco;Mohan Kelkar, SPE, University of Tulsa; and

Mohammad Sharifi, SPE, Amirkabir University of Technology

Summary

Gas-condensate reservoirs differ from dry-gas reservoirs. Theunderstanding of phase and fluid flow-behavior relationships isessential if we want to make accurate engineering computationsfor gas-condensate systems. Condensate dropout occurs in the res-ervoir as the pressure falls below the dewpoint, resulting in signif-icant gas-phase production decreases.

The goal of this study is to understand the multiphase-flowbehavior in gas-condensate reservoirs and, in particular, to focus onestimating gas-condensate-well deliverability. Our new methodanalytically generates the inflow-performance-relationship (IPR)curves of gas-condensate wells by incorporating the effect of con-densate banking as the pressure near the wellbore drops below thedewpoint. The only information needed to generate the IPR isthe rock relative permeability data and a constant-composition-expansion (CCE) experiment.

We have developed a concept of critical oil saturation near thewellbore by simulating both lean and rich condensate reservoirsand have observed that the loss in productivity caused by conden-sate accumulation can be closely tied to critical saturation. We areable to reasonably estimate re-evaporation of liquid accumulationby knowing the CCE data.

We validated our new method by comparing our analyticalresults with fine-scale-radial-simulation-model results. We dem-onstrated that our analytical tool can predict the IPR curve as afunction of reservoir pressure. We also developed a method forgenerating an IPR curve with field data and demonstrated itsapplication with field data. The method is easy to use and can beimplemented quickly. Another advantage of this method is that itdoes not require the knowledge of accurate production dataincluding the varying condensate/gas ratio (CGR).

Introduction

Well productivity is an important issue in the development of mostlow- and medium-permeability gas-condensate reservoirs. Liquidbuildup around the well can cause a significant reduction in produc-tivity, even in lean gas-condensate reservoirs in which the maximalliquid dropout in the CCE experiment is as low as 1% (Afidicket al. 1994). Subsequently, accurate forecasts of productivity can bedifficult because of the need to understand and account for the com-plex processes that occur in the near-well region.

The production performance of a gas-condensate well is easyto predict (similar to a dry-gas well) as long as the wells flowingbottomhole pressure (FBHP) is above the fluid dewpoint pressure.After the wells FBHP falls below the dewpoint, the well perform-ance starts to deviate from that of a dry-gas well. Condensatebegins to drop out first near the wellbore. Immobile initially, liq-uid condensate accumulates until the critical condensate satura-tion (the minimal mobile condensate saturation) is reached. Thisrich liquid zone grows outward deeper into the reservoir as deple-tion continues (Fevang and Whitson 1996).

The loss in productivity caused by liquid buildup is mostlyinfluenced by the value of gas relative permeability (Krg) near thewell compared with the value of Krg in the reservoir farther away.The loss in productivity is more sensitive to the relative perme-ability curves than to fluid pressure/volume/temperature (PVT)properties (Mott 1997).

The most-accurate way to calculate gas-condensate-well pro-ductivity is by fine-grid numerical simulation, either in single-well models with a fine grid near the well or in full-field modelswith use of local grid refinement. A large part of the pressuredrawdown occurs within 10 ft of the well, so that radial modelsare needed with the inner grid cell having dimensions of approxi-mately 1 ft (Mott 2003; Xiao and Al-Muraikhi 2004; Sharifi andAhmadi 2009).

Several investigators have estimated the productivity of gas-condensate reservoirs, but not one of these methods is simple to use.Some methods require the use of the modification of a finite-differ-ence simulation process, whereas other methods use simplified sim-ulation models (Guehria 2000; Xiao and Al-Muraikhi 2004; Ahmadiet al. 2014). Our objective is to develop a simple, yet accurate, ana-lytical procedure to estimate the productivity of gas-condensate res-ervoirs without running simulations. The only required data in ourmethod are the CCE data and the relative permeability curves. Aswith other simplified methods, our new technique allows well-per-formance evaluation quickly without reservoir simulations.

In this study, we propose a new methodology for predictinggas-condensate-reservoir performance with limited data (relativepermeability and PVT data). We know that the productivity index(J) for single-phase gas is always higher than the productivityindex (J*) for two-phase flow; therefore, the productivity ratio(J*/J) is always less than unity. By testing many cases, we foundthat productivity ratio (J*/J) is strongly correlated to Krg (So*) foreach relative permeability curve used. So* is the oil saturation atwhich oil becomes reasonably mobile. We define this critical satu-ration later. The main advantages of our method are being simple,direct, and yet reasonably able to capture the behavior of the res-ervoir for most of the cases. It can predict the behavior that thereservoir has before and after the average pressure is less than thedewpoint pressure. The procedure does not need knowledge of theproducing CGR. The application of the proposed method is di-vided into two cases. In the first case, the average reservoir pres-sure is above the dewpoint pressure (Pd); in the second case, theaverage reservoir pressure is below the Pd. For the first case, inwhich initial reservoir pressure is above the dewpoint, we foundthat the IPR curve can be explained by two straight linesone inwhich bottomhole pressure (BHP) is above and one in which BHPis below the dewpoint. Above the dewpoint, we can use a single-phase-flow equation; and below the dewpoint, we can modify theslope with the relative permeability of oil at residual oil saturation(ROS). We need only one set of observed production data to pre-dict the entire IPR curve.

For the case in which average reservoir pressure (current reser-voir pressure away from the wellbore) is below dewpoint, wehave only one curve below the dewpoint. We can predict the IPRunder these conditions if we have one set of production data avail-able or if we have the relative permeability and CCE data avail-able. We provide the details next.

CopyrightVC 2014 Society of Petroleum Engineers

This paper (SPE 161933) was accepted for presentation at the Abu Dhabi InternationalPetroleum Exhibition and Conference, Abu Dhabi, 1114 November 2012, and revised forpublication. Original manuscript received for review 7 January 2013. Revised manuscriptreceived for review 3 April 2013. Paper peer approved 30 January 2014.

REE161933 DOI: 10.2118/161933-PA Date: 30-April-14 Stage: Page: 177 Total Pages: 13

ID: jaganm Time: 16:01 I Path: S:/3B2/REE#/Vol00000/140011/APPFile/SA-REE#140011

May 2014 SPE Reservoir Evaluation & Engineering 177

A fine-grid radial compositional model was built in a commercialflow simulator to validate the results of our analytical approach.

Literature Review

Fevang and Whitson (1996) proposed a method for modeling thedeliverability of gas-condensate wells. Well deliverability is cal-culated with a modified Evinger-Muskat pseudopressure approach(Evinger and Muskat 1942). The gas/oil ratio (GOR) needs to beknown accurately to use the pseudopressure integral method foreach reservoir pressure. Fevang and Whitson (1996) have devel-oped a method to calculate the pseudopressure integral in thepseudosteady-state gas-rate equation:

qg CPrPwf

KroBolo

Rs KrgBglg

!dp: 1

To apply their method, we need to break the pseudopressure inte-gral into three parts, corresponding to the three flow regions asdiscussed next:

Region 1: An inner near-wellbore region as shown in Fig. 1 inwhich both condensate and gas are mobile. It is the most importantregion for calculating gas-condensate-well productivity becausemost of the pressure drop occurs in Region 1. The flowing composi-tion (GOR) within Region 1 is constant throughout, and a semi-steady-state regime exists. This means that the single-phase gasentering Region 1 has the same composition as the produced well-stream mixture. The dewpoint of the producing wellstream mixtureequals the reservoir pressure at the outer edge of Region 1.

Region 2: This is the region in which the condensate satura-tion is building up. The condensate is immobile, and only gas isflowing. Condensate saturations in Region 2 are approximated bythe liquid-dropout curve from a constant-volume-depletion (CVD)experiment, corrected for water saturation.

Region 3: This is the region in which no condensate phaseexists (above the dewpoint). Region 3 exists only in a gas-conden-sate reservoir that is currently in a single phase. It contains a sin-gle-phase (original) reservoir gas.

One of the major findings in Fevang and Whitson (1996) is thatthe primary cause of reduced well deliverability within Region 1 isKrg as a function of the relative permeability ratio (Krg/Kro) Fevangand Whitsons approach is applicable for running coarse simulationstudies, in which the producing GOR is available from the priortimestep.

In addition to the existence of multiphase flow, high-velocityphenomena that include capillary number effect and non-Darcyflow also can affect the well performance. Usually, at high veloc-ity, non-Darcy flow has a negative effect, and the capillary num-ber has a positive effect on well productivity (Blom and Hagoort1998; Mott et al. 2000).

Guehria (2000) presented an approach to generate IPR curves fordepleting gas-condensate reservoirs without resorting to the use ofsimulation. The producing GOR (Rp) is calculated with an expres-

sion derived from the continuity equations of gas and condensate inRegion 1. But his approach requires an iterative scheme by assum-ing that Rp at a given reservoir pressure generates IPR curves forrich gas-condensate. Whereas, for lean gas-condensates, GOR val-ues from the reservoir material-balance (MB) model are adequate toachieve good results.

Later, Mott (2003) presented a technique that can be imple-mented in an Excel spreadsheet model for forecasting the per-formance of gas-condensate wells. The calculation uses an MBmodel for reservoir depletion and a two-phase pseudopressure in-tegral for well inflow performance. Motts method generates awells production GOR by modeling the growth of condensatebanking without a reservoir simulator.

All these methods do not provide a simple way of generatingIPR curves for condensate wells. The IPR curve as a function ofreservoir pressure is needed to accurately predict and optimize theperformance of the well.

Behavior of the Productivity Index inGas-Condensate Reservoirs

The pseudosteady-state rate equation for a gas well is given byFevang and Whitson (1996) and Kelkar (2008):

qsc 2p a TsckhmPr mPwf TPsc ln

rerw

0:75 S

; 2where a1 for the SI units, a1=2p 142 for field units,qsc gas flow, K permeability, h thickness, m (p) pseudo-pressure, T reservoir temperature, re drainage radius, and rwwellbore radius. We can use this equation to estimate the gas-pro-duction rate when the BHP is above the dewpoint of reservoir flu-ids. This means that this equation is applicable only for single-phase gas flow. As soon as the BHP drops below the dewpointpressure of reservoir fluid, condensate begins to drop out, firstnear the wellbore, and the well performance starts to deviate fromthat of a dry-gas well. Liquid condensate accumulates until thecritical condensate saturation (the minimal mobile-condensate sat-uration) is reached. This liquid-rich bank/zone grows outwarddeeper into the reservoir as depletion continues.

Liquid accumulation, or condensate banking, causes a reduc-tion in the gas relative permeability, and acts as a partial blockageto gas production, which leads to a potentially significant reduc-tion in well productivity. To quantify the impact of gas-condensa-tion phenomena, we have developed a method to generate the IPRof gas-condensate reservoirs with analytical procedures. The mainidea of our research is to combine fluid properties (CCE or CVDdata) with rock properties (relative permeability curves) to arriveat an analytical solution that is accurate enough to estimate theIPR curves of gas-condensate reservoirs.

Model Preparation. Fluid Description. Two different syntheticgas-condensate compositions were used to generate the rich, inter-mediate, and lean fluids represented in Fig. 2. The rich fluid is

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .

10.0

0.2

0.4

Liqu

id S

atur

atio

n

0.6

0.8

1.0Near Wellbore

Region 1Condensate

BuildupRegion 2

Single PhaseGas

Region 3Two-Phase Gas-Oil

Flow Only Gas Flowing

rw = 0.35 ft Swi = 0.25

10 100Radius, ft

1000 10000

Fig. 1Three regions of flow behavior in gas-condensate well.

10%

5%

10%

15%

Liqu

id D

ropo

ut (S

o)

20%

25%

30%

Rich Fluid Intermediate Fluid Lean Fluid

1000 2000 3000 4000Pressure, psi

5000 6000 7000

Fig. 2CCE data for synthetic gas-condensate compositions.



178 May 2014 SPE Reservoir Evaluation & Engineering

composed of three componentsmethane (C1) 89%, butane (C4)1.55%, and decane (C10) 9.45%. The composition of lean and in-termediate is the same, and we just use a 260F temperature forintermediate fluid and a 320F for lean gas. The four componentsare methane (C1) 60.5%, ethane (C2) 20%, propane (C3) 10%, anddecane (C10) 9.5%. The characteristics of the condensate mixturesare outlined in Table 1. The Peng-Robinson three-parameterequation of state (EOS) (PR3) was used to simulate phase behav-ior and laboratory experiments, such as CCE and CVD.

Reservoir Description. The Eclipse 300 compositional simula-tor was used for the simulation. A 1D radial compositional modelwith a single vertical layer and 36 grid cells in the radial directionis used as a test case, as shown in Fig. 3. Homogeneous propertiesare used in the fine-scale model, as described in Table 2.

A single producer well exists at the center of the reservoir. Themodel has been refined near the wellbore to accurately observethe condensate-dropout effect on the production. For that purpose,the size of the radial cells has been logarithmically distributedwith the innermost grid size at 0.25 ft, according to the followingequation:

ri1ri

rerw

1=N; 3

where N is the number of radial cells in the model. Besides, withvery small gridblocks around the well, the timesteps have beenrefined at initial times, which led to a very smooth saturation pro-file around the well. The fully implicit method was chosen for allthe runs.

Relative Permeability Curves. It already has been discussedin the literature that relative permeability curves affect the gasflow significantly in a gas-condensate reservoir after the pressurefalls below the dewpoint pressure. Accurate knowledge about rel-ative permeability curves in a gas-condensate reservoir is essen-tial. Unfortunately, the relative permeability curves are rarelyknown accurately. It would be worthwhile if we could investigatethe effect of different relative permeability curves and study theuncertainty they bring to the saturation buildup in gas-condensatereservoirs.

Different sets of relative permeability curves were used in thestudy. For two-phase relative permeability (oil and gas), thesecurves were generated on the basis of Corey equations, as illus-trated here:

Krg aSng 4

Kro b 1 Sg Sor1 Sor

m; 5

where n is the gas relative permeability exponent, m is the oil rela-tive permeability exponent, Sor is the ROS, a is endpoint gas rela-tive permeability, and b is endpoint oil relative permeability.Fractures (X-Curves) and intermediate and tight relative perme-ability curves were generated by changing n and m exponentsfrom 1 through 5 and changing Sor from 0 to 0.60. Fig. 4 showsthree sets of relative permeability curves. Corey-1 (X-curve) isgenerated on the basis of n 1, m 1, and Sor 0. Corey-14 isgenerated on the basis of n 3, m 4, and Sor 0.20. The thirdcurve, Corey-24 is generated on the basis of n 5, m 4, andSor 0.60.

Sensitivity Study. In this research, we have examined a largenumber (more than 20) of relative permeability curves. The sensi-tivity study also examined the effects of fluid richness on gas pro-ductivity with two fluid compositions (lean and rich fluids).

The results of the sensitivity study were checked with simula-tion results. The simulation runs were performed under a con-stant-rate mode of production with the fine compositional radialmodel. After testing this wide range of relative permeabilitycurves, we found that a very strong correlation exists between thewells productivity-index (PI) ratio and Krg (So*). Figs. 5 and 6show that for all 24 different cases of relative permeability and forboth rich and lean fluids, respectively, the relationship betweenthe PI ratio and Krg (So*) is linear with a strong correlation coeffi-cient. The value of So* is defined in a later section. The well PI ratiois defined as

PI ratio minimum wellPImaximum wellPI

: 6

Fig. 7 shows a typical example of the well PI as a function oftime for a producing well. For this case, we used a single-well

. . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . .

TABLE 1FLUID PROPERTIES

Parameters

Rich

Gas

Intermediate

Gas

Lean

Gas

Initial reservoir pressure (psia) 7,000 5,500 5,000

Dewpoint pressure (psia) 5,400 3,250 2,715

Reservoir temperature (F) 200 260 340Maximal liquid dropout (%) 26 20 8.5

0.00000 0.11686 0.23372 0.35057 0.46743

3000

3000 2000 1000 0 1000 2000 3000

2000

1000

0

1000

2000

3000

Dis

tanc

e Y,

ft

Distance X, ft

OilSat

Fig. 3The 36-cell fine radial model.

TABLE 2RESERVOIR PROPERTIES USED IN THE FINE

RADIAL MODEL

Porosity (%) 20

Absolute permeability (md) 10

Reservoir height (ft) 100

Irreducible water saturation (%) 0

Rock compressibility (psi1) 4.0106

0

0.10.20.30.40.5Kr0.60.70.80.9

1

00.1 0.2 0.3 0.4

Krg(Corey-1) Kro(Corey-1) Krg(Corey-14)Kro(Corey-14) Krg(Corey-24) Kro(Corey-24)

0.5Sg

0.6 0.7 0.8 0.9 1

Fig. 4Different sets of Corey relative permeability curves.




model that has rich gas-condensate. Initial reservoir pressure was7,000 psi, and the well was producing with a constant-rate con-straint of 20 MMscf/D. In this example, initial reservoir pressurewas above the dewpoint. We found that the PI ratio value is veryclose to that obtained from the corresponding relative permeabil-ity curve Krg (So*). This shows that, by using relative permeabilitydata, we are able to capture the behavior of the PI of a reservoirwithout performing any simulation. The abrupt fall of PI happensshortly after the FBHP falls below the Pd. After analyzing severalcases, we found that the PI ratio is very close to Krg (So*).

Fig. 7 shows that the well PI drops quickly and eventuallyincreases slightly before stabilizing. The slight increase in PI is aresult of the revaporization of oil and changing composition(leaner fluid). This type of PI behavior is observed in the fielddata in which, after the BHP drops below the dewpoint pressure,PI decreases suddenly before stabilizing. Similar behavior alsowas observed by Kamath (2007).

As we can see from Fig. 8, after oil saturation reaches a maxi-mal value, So drops gradually after a period of production, whichwill enhance the gas relative permeability and, therefore, the gasproductivity. Figs. 5 and 6 show clearly that for both rich and leanfluids, respectively, the relationship between the PI ratio and krg(So*) is linear with a strong correlation coefficient.

Another important outcome of this sensitivity analysis is thatthe loss in productivity is more sensitive to the relative permeabil-ity curves than to fluid PVT properties. Fig. 9 shows the well PIvs. time for the rich and lean fluids with the same relative perme-ability set. Fig. 9 demonstrates that the loss in productivity ismuch more dependent on relative permeability curves than on thefluid composition.

Fig. 10 summarizes the results of the sensitivity study per-formed on the rich and lean fluids with the wide range of relativepermeability curves. It appears that the loss is similar for bothrich and lean gases when the same relative permeability curvesare used. The slope is very close to a value of unity.

Generation of IPR Curves. IPR curves are very important topredict the performance of gas or oil wells; however, generatingIPR curves with a simulator is not straightforward because the

0.00 0.20 0.40

y = 1.4857x + 0.0153

R2 = 0.9445

0.60 0.80 1.00

K rg(S

o*)

0.00

0.20

0.40

0.60

0.80

1.00

PI Ratio

lean-Krg(So*) vs PI Ratio

Fig. 6Krg (So* ) vs. PI ratio for lean fluid.

0 5 10 15 20 25

100

200

300

400

500

600

Well

PI, M

scfd

/psi

0

Time, Years

Productivity Index (Fine Radial Model)

PI Ratio =Min Well PIMax Well PI

Fig. 7Well PI as a function of time.

0.00 0.20 0.40

y = 1.1827x + 0.0337

R2 = 0.9222

0.60 0.80 1.00

K rg(S

o*)

0.00

0.20

0.40

0.60

0.80

1.00

PI Ratio

Rich-Krg(So*) vs PI Ratio

Fig. 5Krg (So* ) vs. PI ratio for rich fluid.

0 5 10 15 20

Rich Fluid Lean Fluid

25 30Time, Years

Well

PI, M

scfd

/psi

35 40 45 500

50100150200250300350400450500

Fig. 9Well PI vs. time for the rich and lean fluids (same rela-tive permeability curves).

0 5 10 15 20 25

S o

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time, Years

Radial Cell-1 Radial Cell-5 Radial Cell-10Radial Cell-20 Radial Cell-30 Radial Cell-36

Fig. 8Oil-saturation profiles around the well as a function oftime.




IPR represents an instantaneous response of the reservoir at agiven reservoir pressure for a given BHP. This cannot be gener-ated in a single run, because if we change the BHP in a simulationrun, depending on how much oil or gas is produced, the averagepressure will change.

To generate IPR curves, we used a composite method. For dif-ferent initial reservoir pressures, we ran a simulator at a fixedBHP. We varied the BHP from high to low values. After we hadthe results for different BHPs, we combined the rates for differentBHPs for a fixed average pressure and constructed an IPR curve.We repeated this procedure for different average pressures so thatwe can construct the IPRs for different average pressures.

Important Observations From the Simulation Study. Wewanted to develop simple relationships for generating the IPRcurves under the field conditions. We used some important obser-vations from our simulation study to develop our procedure:

As previously discussed, we observed that the relative per-meability curves have a bigger impact on the loss of productivitythan the type of fluid that is produced.

The loss of productivity is significant and almost instantane-ous after the pressure drops below the dewpoint. After that point,the PI recovers because of the revaporization of the liquid and thechanging composition (with leaner fluid).

The oil-saturation profile near the wellbore is a strong func-tion of the average reservoir pressure (Dyung et al. 1987). Conse-quently, for a given reservoir pressure, the oil-saturation profiledoes not change significantly for different BHPs, which is shownin the next section.

Relative change in well performance before and after thedewpoint depends only on relative permeability, but, overall, wellperformance depends on other reservoir properties (i.e., perme-ability). This is incorporated in PI calculations automatically(Eqs. 2 and 16).

Development of New Approach

New Analytical Approach for Estimating Gas-Condensate-Well Productivity. When we plotted IPR curves (i.e., for inter-mediate fluid with Pd 3,250 psi), as a function of both pressureand pseudopressure, we noticed that plotting the pseudopressurevs. the gas rate resulted in two clear straight lines for every reser-voir pressure (Fig. 11). This is consistent with our observationthat below the dewpoint, the oil saturation does not change signifi-cantly for a given reservoir pressure. Fig. 12 represents the nor-mal depiction of IPR curves. Notice a peculiar behavior of IPRcurves when plotted as a function of pseudopressure. The linesare parallel above the dewpoint as expected because the produc-tivity does not change. Below the dewpoint, for different reservoirpressures, the lines are parallel for a certain pressure range; how-ever, as the reservoir pressure depletes, the slope becomes gentler.This is an indication of improved productivity. This is a result ofthe re-evaporation of the liquid phase and changing composition(with leaner fluid) as the pressure declines. This type of trend isdifficult to capture with the pressure data.

As soon as reservoir pressure drops below the dewpoint (Pd),which is 3,250 psi in this example, there will be a productivity lossthat is characterized by the straight line below Pd in the pseudopres-sure plot, shown in Fig. 11. To illustrate our method, we will takePr 5,400 psi as an example for illustration (Fig. 13).

0 20 40qg, MMscfd

60 800

1000

2000

3000

BHP,

ps

i

4000

5000

6000

Pr (5400 psi) Pr (5000 psi) Pr (4000 psi)Pr (3000 psi) Pr (2000 psi) Pr (1000 psi)

Fig. 12BHP-vs.-gas-rate IPR plot.

0 10 20 30 40qg, MMscfd

50 60 70 800.0E+08

2.0E+08

4.0E+08

6.0E+08

m(P

), psi2

/cp 8.0E+08

1.0E+09

1.2E+09m(P) vs qg, Pr = 5400 psi

Slope = (1/j)

Slope = (1/j*)

Pd = 3250 psi

Fig. 13IPR for Pr5 5,400 psi.

0.00 0.20 0.40

R2 = 0.9621

0.60 0.80 1.00

Ric

h PI

Rat

io

0.00

0.20

0.40

0.60

0.80

1.00

Lean PI Ratio

Rich vs Lean PI Ratio

Fig. 10Rich vs. lean PI ratio.

0 10 20 30 40qg, MMscfd

50 60 70 800.E+00

2.E+08

4.E+08

6.E+08

m(P

), psi2

/cp 8.E+08

1.E+09

1.E+09

Pr (5400 psi) Pr (5000 psi) Pr (4000 psi)Pr (3000 psi) Pr (2000 psi) Pr (1000 psi)

Fig. 11Pseudopressure vs. gas-rate plot.




The pseudopressure plot in Fig. 13 clearly shows that there aretwo distinct PIs. The first PI (J) is constant for a single-phase gasflow (in which FBHP is above Pd), and the second PI (J*) is for atwo-phase flow (in which FBHP is below Pd). Referring to thepreceding pseudosteady-state gas-rate equation (Eq. 2), one cansee that

qsc 2p aTscKhmpr mpwf TPsc ln

rerw

0:75 S

:

The PI in terms of pseudopressure is given by

J qscmPr mPwf : 7

Looking at Fig. 13, we can define the slopes as

slope of the line abovePd being 1=J 8

and

slope of the line belowPd being 1=J: 9

After analyzing several cases, we found that the PI ratio can bedetermined by dividing the slope abovePd by the slope below Pd as

slope of the line abovePdslope of the line belowPd

1J

1J

JJ PI ratio:

10Because the PI (J) for a single-phase gas is always higher than thePI (J*) for a two-phase flow, the PI ratio (J*/J) is always less thanunity. By conducting many numerical experiments, we found thatthe PI ratio (J*/J) is strongly correlated to Krg (So*) for each rela-tive permeability curve used (i.e., Figs. 5 and 6). The applicationof the proposed method is divided into two cases. The first case iswhen the average reservoir pressure is above the Pd, and the sec-ond case is when the average reservoir pressure is below the Pd.

General ProcedureAverage Reservoir Pressure Is Abovethe Pd. In this case in which the average reservoir pressure isabove the Pd, the pseudosteady-state gas-rate equation (Eq. 2) isused to estimate the gas rate when the BHP>Pd. When the BHPdrops below the Pd, we need to estimate (J*) first to be able to cal-culate the gas rate analytically. Because, in this case, initial reser-voir pressure is above the Pd, we can estimate the PI (J), which willbe constant for all BHPs above the Pd. The procedure is as follows:

1. Estimate the PI above dewpoint with Eq. 7.2. Calculate J* with our knowledge of Krg (So*) and J from the

previous section as

J

J PI ratio KrgSo: 11

3. Generate the IPR curve below Pd and calculate the flow rate.After estimating J*, which has a constant but higher slope than

J, as shown before on the pseudopressure plot, we can use J* toestimate the gas rate for all BHPs below the Pd. With the follow-ing equation, we assume

y mx b 12

and

mPwf 1J

q b: 13

We can use our knowledge of the rate and FBHP at the Pdwith the pseudosteady-state gas-rate equation (Eq. 2) above dew-point. Then, the intercept b can be calculated as

b mPd qdJ

; 14

where b in field units is in (psi2/cp).Now, our straight-line pseudopressure equation is complete to

estimate the gas rate for any FBHP less than the Pd as

q b mPwf J; 15

where q is in (Mscf/D), b and mPwf are in (psi2/cp), and J* is in[(Mscf/D)/psia2/cp].

General ProcedureAverage Reservoir Pressure Is LessThan the Pd. In this case, the pseudopressure vs. rate plot, IPR,will have only one straight line. Fig. 11 shows three examples ofIPR lines in which initial reservoir pressure is below the Pd. To beable to generate the IPR curves for cases in which initial reservoirpressure is below the Pd, the following procedure should befollowed:

1. Estimate the PI (J).If an IPR curve for the case in which reservoir pressure is

above the Pd is available, the PI (J) of this case could be used toestimate J* as a function of pressure with CCE data, as will beexplained in the next step. For cases in which IPR curves abovethe Pd are not available, the PI (J) could be estimated with a pseu-dosteady-state gas-rate equation,

J qscmPr mPwf 2p aTscKh

TPsc Inrerw

0:75 S

: 16

2. Estimate the PI (J*).As we stated earlier, the PI ratio (J*/J) is correlated to krg (So*),

but in these cases in which initial reservoir pressure is below Pd,liquid revaporization plays a very important role in determiningthe productivity of gas-condensate reservoirs. By examining theCCE data, as shown in Fig. 2, we can see that, as soon as the pres-sure drops below the Pd, liquid saturation reaches a maximalvalue (Max_SoCCE) around the Pd quickly. Although the rate ofaccumulating condensate bank to its maximal saturation could beaffected by many variables (e.g., rate, pressure drop, and fluidcomposition), in general, the pressure drop near the wellbore islarge, and the volume near the wellbore is small. The combinationof a higher pressure gradient and a smaller volume results in arapid accumulation of condensate as soon as the pressure dropsbelow the dewpoint. As the pressure declines further, the liquidsaturation gradually declines. Our idea of using CCE data in gen-erating the IPR curves is really to account for this phenomenon ofliquid vaporization and changing composition (with leaner fluid)as pressure drops below the Pd (Dyung et al.1987). We found thatthe use of a fixed value of Krg (So*) or Krg (Max_SoCCE) will under-estimate the gas productivity for cases in which initial reservoirpressure is below the Pd.

Therefore, for any reservoir pressure below Pd, the Krg needsto be estimated at the corresponding pressure and oil saturationfrom the CCE data according to the following equation:

J

JPr PI ratio KrgSoCCE 17

3. Estimate the gas rate.Finally, the gas rate can be estimated directly from the follow-

ing equation:

q mPr mPwf J 18

The preceding outlined procedure for generating IPR curvesassumes that SorMax_SoCCE, but this is not always the case inreal field applications. Because Sor is a rock property whereasMax_SoCCE is a fluid property, we expect them to be different inmost of the cases in field applications.

. . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . .




For that purpose, we have analyzed several cases in which Sorcould be equal to, less than, or greater than Max_SoCCE. On the ba-sis of our evaluation, we believe that the maximum of the two val-ues should be used to correctly capture the fluid behavior aroundthe wellbore and thereby accurately estimate the gas productivity.

The procedure to estimate PI (J*) here is exactly the same asthe preceding procedure outlined for the case in which SorMax_SoCCE, but with some modifications, as given by Table 3.This procedure is used for flowing pressure less than the dew-point. In effect, what we are saying in this table is that, if we havereservoir pressure above the dewpoint, then to calculate the IPRcurve for the BHP below the dewpoint, we can use a constantslope (J*) on the basis of the Krg estimate, as stated in Table 3.Subsequently, after the reservoir pressure drops below dewpoint,we will need to use Krg as a function of average reservoir pressure.

Importance of Threshold Oil Saturation (So*). We found that anaccurate estimation of gas productivity depends not only on Sor butalso on the threshold oil saturation (So*) for reservoirs with tight oilrelative-permeability curves. Fig. 14 shows an oil relative-perme-ability curve that was generated on the basis of Sor 0.20 and ahigh value of oil exponent (m 4). This higher value of the oil rela-tive permeability exponent makes the oil relative permeability verylow and eventually makes oil practically immobile until its satura-tion exceeds the threshold value (So*), which is, in this case, 0.48, asshown in Fig. 14. After testing several tight relative permeabilitycurves, we found that, for practical applications, we can determinethat the threshold (So*) corresponds to Kro 1% of the maximalvalue of oil relative permeability.

Therefore, in generating IPR curves, it is more important toknow So* than Sor. We define So* as a minimal saturation needed tomake oil mobile (i.e., Kro is at least 1% of the endpoint value). Itis a strong function of the curvature of the relative permeabilitycurve. Therefore, all we need to do is use Table 3 as it is, butreplace Sor with So*, as shown in Table 4.

Cases in Which So*>Max_SoCCE. This is probably the mostcommon case in the field. Even for rich condensates, it is not un-usual to find that the minimal mobile oil saturation is greater thanmaximal oil saturation in the CCE experiment. The rich conden-sate fluid with maximal liquid dropout (26%) is being used forthis case in which it is less than So* 0.48, as shown previously inFig. 14. Referring to Table 4, we can see that in this case the PIratio is determined by Krg (So*).

Initial Reservoir Pressure Is Above the Pd. Fig. 15 showsthe So distribution around the wellbore as a function of the BHP.We would like to examine this figure carefully. As soon as the

BHP drops below Pd, which is 5,400 psi for this fluid, liquid startsdropping out close to the wellbore first. The radius of oil bankingexpands inside the reservoir, and oil saturation away from thewellbore increases as BHP decreases. We can see that, at a BHPof 3,000 psi, So reaches a maximal value of approximately 0.62,and this value almost stays constant even though the BHP dropsto 1,000 psi and then to atmospheric conditions.

What we want to highlight here is that when reservoir pressureis above the Pd, the oil saturation near the wellbore remains rea-sonably constant, irrespective of the BHP. Because, in this case,the threshold (So*) is higher than Max_SoCCE, the value of So*

should be used to obtain the corresponding krg and therefore esti-mate the well productivity for the cases in which reservoir pres-sure is above Pd. By following the general procedure outlinedpreviously for the case in which the initial reservoir pressure isabove the Pd, we can generate the IPR curve, as shown in Figs.16 and 17. It can be seen that, as long as the BHP is above thedewpoint (Pd 5,400 psi) that corresponds to a gas rate below 40MMscf/D, our method can exactly predict the behavior of the sim-ulation model. Below the dewpoint pressure, although there is asmall difference, our method can reproduce the simulation behav-ior with reasonable accuracy. Just keep in mind that the onlychange you would make for this case in which the threshold(So*)>Max_SoCCE is to use the larger value of the two, which, inthis case, is the So*,

J

J PI ratio KrgSo: 19. . . . . . . . . . . . . . . . . . . . .

TABLE 4GENERAL PROCEDURE FOR ESTIMATING PI

RATIO FOR TIGHT ROCKS

Case

Cases in

Which Pr Above Pd

Cases in

Which Pr Below Pd

So* Max_SoCCE J*/JKrg (So* ) JJPr KrgSoCCESo* Max_SoCCE J*/JKrg (So* )

TABLE 3GENERAL PROCEDURE FOR ESTIMATING

PI RATIO

Case

Cases in

Which Pr Above Pd

Cases in

Which Pr Below Pd

SorMax_SoCCE J*/JKrg (Sor) JJPr KrgSoCCE

SorMax_SoCCE J*/JKrg (Sor)

0 0.1 0.2 0.3 0.4Sg

0.5 0.6 0.7 0.8 0.9 10

0.10.20.30.40.50.60.70.80.9

1

K r

Krg(Corey-14) Kro(Corey-14)

So* = 0.48 Sor = 0.20

Fig. 14Illustration of threshold (So* ) in tight relative permeabil-ity curves.

0.1 1 10

BHP(5000 psi) BHP(3000 psi) BHP(1000 psi) BHP(15 psi)

Radius, ft100 1000

0

0.1

0.2

0.3

So0.4

0.5

0.6

0.7

Fig. 15Oil-saturation distribution as a function of BHP forPr56,900 psi.




Initial Reservoir Pressure Is Below the Pd. Now, we willillustrate an example for the case in which initial reservoir pres-sure is below Pd. To correctly generate the slope of the IPR curveon the pseudopressure plot, we need to account for revaporization.Again, we need to use the fine grid model to capture the conden-sate behavior near the wellbore.

By examining three figures, Figs. 18 through 20, that showthe So distribution for saturated reservoirs, one will notice that Sodecreases gradually as a function of reservoir pressure from

approximately 0.62, when Pr 6,900 psi (Fig. 15) to almost 0.30when Pr 1,000 psi (Fig. 20). Looking at Fig. 20, we can seethat, for low pressure (BHP 1,000 psi), condensate saturationaround wellbore is negligible and is smaller compared with thesaturation far away from the wellbore. We conclude from thesefigures that oil revaporization and changing fluid compositionclose to the wellbore are strong functions of decreasing reservoirpressure that results in lower saturation.

For each saturated reservoir pressure, we can see that So buildsup to a uniform value close to the wellbore. This uniform Soremains almost constant as BHP decreases when reservoir pres-sure remains constant. Therefore, a valid assumption for the appli-cation of our method is to assume a uniform So for every saturated(average) pressure under consideration. Fig. 20 shows an exampleof an extreme case in which all the oil evaporates at a very lowflowing pressure.

After we have understood gas-condensate behavior around thewellbore, we can see that we really need to use a method that canmimic condensate revaporization as reservoir pressure depletes.The best tool to use is the CCE or CVD data for each condensatefluid being used (Dyung et al. 1987). The CCE data of the richfluid are shown previously in Fig. 2. Following Fevang and Whit-son (1996), we will assume that CCE provides the best descriptionof fluid near the wellbore (i.e., we can use CCE data to predict therevaporization of oil). The reason we choose CCE is because theaccumulation near the wellbore is minimal, which means thatnear the wellbore region, whatever flows from the reservoir willflow into the wellbore without any change in the composition.

Because in this case the threshold (So*) is greater than Max_SoCCE, our approach is to develop a linear relationship betweenthe So* and the CCE data, as shown in Fig. 21. In other words, weassume that relative gas permeability should be evaluated at a

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

Fine Radial ModelAnalytical Solution

qg, MMscfd

0.0E+00

2.0E+08

4.0E+08

6.0E+08m(P

), (ps

ia2/c

p)

8.0E+08

1.0E+09

1.2E+09

1.4E+09

1.6E+09

Fig. 17Pseudopressure vs. gas-rate plot for Pr5 6,900 psi.

0.1 1 10

BHP(3,000 psi) BHP(1,000 psi) BHP(15 psi)

Radius, ft100 1,000

0

0.1

0.2

0.3So

0.4

0.5

0.6

0.7

Fig. 18Oil-saturation distribution as a function of BHP forPr5 5,000 psi.

0.1 1 10

BHP(15 psi)

Radius, ft100 1,000

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

So


0 10 20 30 40 50 60 70

Fine Radial Model Analytical Solution

qg, MMscfd

0

1000

2000

3000

4000

BHP,

ps

i 5000

6000

7000

8000

Fig. 16IPR curve for Pr5 6,900 psi.

0.1 1 10

BHP(1,000 psi) BHP(15 psi)

Radius, ft100 1,000

0

0.1

0.2

0.3So

0.4

0.5

0.6





value between So* and Max_SoCCE. So, for any pressure, we can goto the figure and choose corresponding saturation and relative per-meability. A careful examination of Fig. 15 and Figs. 18 through20 tells us that an actual liquid dropout around the wellbore ismuch greater than Max_SoCCE and is closer to the threshold So*.We have seen after testing several cases under this category thatthe use of Krg (Max_SoCCE) will overestimate the gas rate becauseit will not account for the relative permeability of the oil phase;however, we use CCE data to account for changes in oil saturationas the reservoir pressure declines.

It is very clear that condensate banking (accumulation) is tiedup with two factors. The first factor is fluid properties (maximal Sofrom CCE), and the second factor is rock properties (immobile So).Accordingly, we have asked ourselves this question: Althoughwe know that the actual liquid dropout around the wellbore ismuch greater than Max_SoCCE, how can we still use the CCEdata along with relative permeability curves to arrive at a robust an-alytical procedure that is accurate enough to estimate the wellproductivity?

Other researchers have shown that relative permeability has afirst-order effect on condensate banking rather than the PVT prop-erties (Mott 1997). As we have concluded from the results of thesensitivity study, different fluids will have a similar productivityloss for the same relative permeability curve used, confirming tous that it is the relative permeability that is the most important indetermining the productivity loss.

We used engineering approximation to model the behaviorbelow the dewpoint pressure. As we have stated before, we aregoing to assume that the area around the wellbore behaves simi-larly to the CCE data for every designated saturated pressure. Fol-lowing the general procedure outlined previously for the case inwhich (the Initial Reservoir Pressure Is Below the Pd subsection),we are going to explain our approach at Pr 4,000 psi. After esti-mating the PI (J), as shown in Step 1 of the procedure, we canestimate PI (J*) as the following:

J

JPr KrgSoCCE: 20

At Pr 4,000 psi, we should estimate So from the linear rela-tion between the So* and CCE data, as shown in Fig. 21. The nextstep is to go back to relative permeability curves to estimate Krgat the corresponding So from this linear relation. After that, J* canbe calculated directly from Eq. 20. The last step before generatingthe IPR curve is to estimate the gas rate directly from Eq. 18. Justkeep in mind that in this case the pseudopressure vs. rate plot willhave only one straight line because this is what we expect to seein saturated reservoirs. The IPR curve is shown in Fig. 22 alongwith the pseudopressure plot in Fig. 23. The complete IPR curvesof this case are shown in Fig. 24.

Fig. 25 shows the well PI producing at a constant-rate control.We used rich fluid, and relative permeability parameters aren 3, m 4, Sor 0.2, a 0.9, and oil endpoint relativepermeability 0.58.

We found that the PI ratio from flow-simulation data is

minimum wellPI

maximum wellPI 0:09: 21

On the basis of the relative permeability data, we haveKrg(So*) 0.08. As was expected, by use of our new method, weare able to capture the change in PI below the dewpoint.

On the basis of the PI ratio, we can define the productivity lossas

productivity loss 1 minimum wellPImaximum wellPI

: 22

Therefore, in this example, the productivity loss is 0.91. Thismeans that this well will experience a 91% productivity loss assoon as BHP reaches the Pd. Looking at Fig. 25, we can see thatthe well restores some of its productivity after approximately 5years of production. Fig. 26 shows the saturation profiles as afunction of time, which shows the re-evaporation process.

. . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . .

. . . . . . . . .

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000P, psi

CCE

KrgSo* = 0.48

Rich Fluid

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

So

Fig. 21Developing linear relation between So* and CCE data.

0 5 10 15 20

Fine Radical Model Analytical Solution

qg, MMscfd

0

1,000

2,000

3,000

4,0004,500

500

1,500

2,500

3,500

BHP,

psi

Fig. 22IPR curve for Pr54,000 psi.

0 5 10 15 20


qg, MMscfd

0.0E+001.0E+082.0E+083.0E+084.0E+085.0E+086.0E+087.0E+088.0E+089.0E+08

m(P

), (ps

ia2/c

p)

Fig. 23Pseudopressure vs. gas-rate plot for Pr54,000 psi.

0 10 20 30 40 50 60 70


qg, MMscfd

0

1,000

2,000

3,000

4,000

BHP,

psi 5,000

6,000

7,000

8,000

Fig. 24IPR curves for rich gas (Corey-14).




In summary, in the proposed method, with accurate relativepermeability and CCE data, one can predict the change in per-formance of the reservoir above and below the dewpoint withoutconducting any flow simulation. We should explain that we havenot included non-Darcy and capillary effects in our analysis. Onthe basis of a very limited number of runs (which are not includedhere), we believe that our method should reasonably work whenboth the effects are present.

Validation by Field Applications

In this section, we will show the application of our method for afield case. Both compositional-model data and relative permeabil-ity curves were provided for a field case. A nine-component com-positional model is used with the PR3 to simulate phase behaviorand laboratory experiments (CCE tests), as shown in Fig. 27.Tables 5 and 6 show fluid properties and composition for the fieldcase, respectively.

The relative permeability curves are shown in Fig. 28. As iscommon in field applications, what matters here is the thresholdSo*. Although Sor 0.20, the threshold So* 0.32, which corre-sponds approximately to Kro 1% as a practical value. As wehave stated before, an accurate estimation of gas productivity inthis case depends on the value of Krg estimated at the thresholdSo*, which equals 0.32 in this case.

In this section, we illustrate the application of our methodfrom the production-operations view in the field. We are going toshow that our method can be used to generate IPR curves on thebasis of production-test data in the same way as the Vogel, Fetko-vich, and other IPR correlations.

Assume that we are working in a production environment in afield in which we have no knowledge about relative permeabilitycurves. The only thing that we have is some production data.Because initial reservoir pressure is above the Pd, we know that thepseudopressure vs. gas-rate plot will have two straight lines, asexplained earlier. Therefore, to generate the IPR curve for a given

0 10 20 30 40 50

Productivity Index (Fine Radial Model)

Time, Years

050

100150200250300350400450500

PI, M

scfd

/psi

Fig. 25Well PI as a function of time.

0 10 20 30 40 50

Radial Cell 1Radial Cell 20



Time, Years

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

S o

Fig. 26Oil-saturation profiles around the well as a function oftime.

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000Pressure, psi

0%

1%

1%

2%

2%

3%

3%

4%

Liqu

id D

ropo

ut (S

o)

Liquid Dropout Curve (CCE)

Fig. 27CCE data for field-case fluid.

TABLE 5FLUID PROPERTIES FOR THE FIELD CASE

Initial reservoir pressure (psia) 9,000

Dewpoint pressure (psia) 8,424

Reservoir temperature (F) 305Maximal liquid dropout (%) 3

TABLE 6FLUID COMPOSITION FOR THE FIELD CASE

Component Composition (Fraction)

H2S 0

CO2 0.0279

N2 0.0345

C1 0.7798

C2C3 0.1172

C4C6 0.0215

C7C9 0.0132

C10C19 0.00445

C20 0.00145

0 0.1 0.2 0.3 0.4Sg

0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

K r

Krg-Field Case Kro-Field Case

Krg(So*) = 0.31

Sor = 0.2So* = 0.32

Fig. 28Relative permeability set of the field case.




reservoir pressure, all we need is two test points. One point shouldbe above the Pd, and the other point should be below the Pd.

Fig. 29 shows an example of data from two production tests. Toexplain how our method will work, we have chosen one of the testdata to be at the Pd. Otherwise, any available test data above the Pdwill suffice. We will illustrate our method by the following procedure.

Summary of New PI-Generation Procedure. Estimate the PI(J) by using Pr and the test data at the Pd with the previously citedEq. 7:

J qscmPr mPwf :

Or another way to estimate J is to plot the test points above thePd on the pseudopressure plot, as shown in Fig. 30, and then J canbe calculated from the previously cited Eq. 8:

slope 1J:

2. Using J, you should be able to generate the first portion ofthe IPR curve with Eq. 7.

3. In the same way as conducted previously, we need to plotthe test points below the Pd on the pseudopressure plot, as shownin Fig. 31. Then, J* can be calculated from the slope as in the pre-viously cited Eq. 9:

slope 1J

:

4. The intercept of the straight line (b) should be estimated aswith the previously cited Eq. 14:

b mPd qdJ

:

5. Finally, we can estimate the gas rate for any BHP less thanthe Pd with the previously cited Eq. 15:

q b mPwf J:Results. The generated IPR curve and the pseudopressure plotare shown in Figs. 32 and 33, respectively. We have shown thatone can use our method to generate the IPR curves on the basis ofavailable test data without any basic knowledge about the relativepermeability curves. Before we proceed to an example in whichinitial reservoir pressure is below the Pd, we would like to high-light one important observation. We found that the PI ratio equals0.30 with the preceding Eq. 10 as noted in Eq. 23:

slope of the line above Pdslope of the line belowPd

1J

1J

JJ

productivity ratio 0:30: 23We would have expected this value to be equal to Krg (So*).

From Fig. 28, we can see that So* 0.32 and Krg (So*) 0.31. Wecan easily quantify the productivity loss after we have an ideaabout the PI ratio or Krg (So*) with Eq. 22 as the following:

productivity loss 1 productivity ratio:

Therefore, in this, after the FBHP drops below the Pd, the wellwill lose 70% of its productivity. We would like to highlight twomajor points here:

Having two tests of production data clearly helped us tocharacterize one value of relative permeability, which is Krg at(So*). By knowing Krg (So*), one can easily use relative permeability

0 10 20 30 40 50 60 70

Production Test Data, (Pr = 8,900 psi)

qg, MMscfd

01,0002,0003,0004,000BH

P, p

si

5,0006,0007,0008,0009,000

10,000

Fig. 29Production data of two tests.

0 2 4 6 8 10 12 14 16 18

Test Data Above Pd

qg, MMscfd

2.20E+092.22E+092.24E+092.26E+092.28E+092.30E+092.32E+092.34E+092.36E+092.38E+09

m(P

), (ps

ia2/c

p)


0 10 20 30 40 50 60 70

Test Data Below Pd

qg, MMscfd

0.E+00

5.E+08

1.E+09

2.E+09

2.E+09

3.E+09

m(P

), (ps

ia2/c

p)


0 10 20 30 40 50 60 70 80 90 100


qg, MMscfd

0

1,000

2,000

3,000

4,000BH

P, p

si

5,000

6,000

7,000

8,000

9,000

10,000

Fig. 32IPR curve for Pr58,900 psi.




curves (if available) to estimate (So*) or maximal oil saturationaround the well.

Although this field case has very lean gas with a maximalliquid dropout of only 3%, as shown in Fig. 27, the loss in produc-tivity is significant (70%). This clearly tells us that the most-im-portant parameter in determining the productivity loss is the gas/oil relative permeability curves, expressed in terms of Krg esti-mated at residual (or threshold) oil saturation.

We can easily generate the IPR curves for reservoir pressureabove the dewpoint pressure. The slope of IPR curves above andbelow the dewpoint will remain the same, except that the curvewill shift downward as the reservoir pressure declines. If the res-ervoir pressure is below the dewpoint, to generate the entire IPRcurve, we will need just one observation.

The PI (J*) can be calculated directly on the basis of the testdata and reservoir pressure with the previously cited Eq. 16:

J qscmpr mpwf :

After that, the gas rate can be directly estimated from the pre-viously cited Eq. 18:

q mPr mPwf J:

If we want to predict the future IPR on the basis of the currentIPR curve, we will need to have information about relative perme-ability and CCE data. The complete IPR curves of this case areshown in Fig. 34 in which the generated IPR curves are validatedwith the results of the fine-radial-compositional model.

With our methodology, we examined 10 years of the produc-tion history of a gas-condensate well with known CCE and rela-

tive permeability data. We used the initial production data andcalculated the future IPR curves with our methodology. We showthe future IPR curves in Fig. 35. Superimposed on those curves,we also show the actual production data as a function of time asthe reservoir pressure has declined. The match between predictedrates and observed rates is good, validating our procedure.

Conclusions

In this paper, a new analytical procedure is proposed to estimate thewell deliverability of gas-condensate reservoirs. Our new methodgenerates IPR curves of gas-condensate wells by incorporating theeffect of condensate banking as the pressure near the wellbore dropsbelow the dewpoint. Other than basic reservoir properties, the onlyinformation needed to generate the IPR is the rock relative perme-ability data and the CCE-experiment data. In addition to predictingthe IPR curve under current conditions, our method also can predictfuture IPR curves if the CCE data are available.

We found that the most important parameter in determiningproductivity loss is the gas relative permeability at immobile oilsaturation. We observed that at low reservoir pressures, some ofthe accumulated liquid near the wellbore revaporizes. This reva-porization can be captured with CCE data. In our method, we pro-pose two ways of predicting the IPR curves: Forward approach: With the basic reservoir properties, relative

permeability data, and CCE information, we can predict theIPR curves for the entire pressure range. A comparison withsimulation results validates our approach.

Backward approach: With field data to predict the IPR curvesfor the entire pressure range, this method does not require reser-voir data; instead, similar to the Vogel method, it uses point in-formation from the IPR curve and predicts the IPR curve for theentire BHP range. Both synthetic and field data are used to vali-date our second approach.

Nomenclature

h formation thickness, ftJ PI, [(Mscf/D)/psia2/cp]K absolute rock permeability, md

Krg gas relative permeabilityKro oil relative permeability

m ( p) pseudopressure function, (psi2/cp)Pd dewpoint pressure, psiaPr average reservoir pressure, psiaPsc pressure at standard condition, psiaPwf flowing BHP, psiaqsc gas-flow rate at standard conditions, Mscf/Dre external reservoir radius, ftRp producing GOR, scf/STBrw wellbore radius, ft

0 20 40 60 80 100


qg, MMscfd

0.00E+00

5.00E+08

1.00E+09

1.50E+09

2.00E+09

2.50E+09m

(P), (

psia2

/cp)

Fig. 33Pseudopressure vs. gas-rate plot for Pr5 8,900 psi.0 20 40 60 80 100


qg, MMscfd

0

1,000

2,000

3,000

4,000BH

P, p

si

5,000

6,000

7,000

8,000

9,000

10,000

Fig. 34IPR curves for the field case.

0 20 40 60 80 100

Analytical Solution

Field Observed Data

qg, MMscfd

0

1,000

2,000

3,000

4,000BH

P, p

si

5,000

6,000

7,000

8,000

9,000

10,000

Fig. 35Validation of the new method with field data.




Sg gas saturation, fractionSo oil saturation, fractionSo* threshold oil saturation, fractionSor ROS, fractionSwi connate water saturationT reservoir temperature, R

Tsc temperature at standard condition, R

Acknowledgments

The first author would like to acknowledge the support from theReservoir Description and Simulation Department at Saudi Ara-mco. All the authors thank the University of Tulsa for computa-tional and other administrative support.

References

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10.2118/28749-MS.

Ahmadi, M., Hashemi. A., and Sharifi. M. 2014. Comparison of Simulation

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Ali M. Al-Shawaf is the lead simulation engineer for offshoregas fields in Saudi Aramcos Reservoir Description and Simula-tion Department. He started his career as a production fieldengineer with Saudi Aramco; then, he joined the ReservoirSimulation Division, in which he conducted several full-fieldsimulation models in onshore and offshore development andincrement fields. In May 2012, Al-Shawaf completed his mas-ters thesis program at the University of Tulsa through which hedeveloped a new method to predict the performance of gas-condensatewells. He has authored or coauthored several tech-nical papers and has participated in several technical confer-ences and symposiums regionally and internationally. Al-Shawafis an active member of the SPE, in which he serves on severalcommittees for SPE technical conferences and workshops. Heearned a BS degree from King Fahad University of Petroleum &Minerals, Dhahran, Saudi Arabia, and an MS degree from theUniversity of Tulsa, both in petroleumengineering.

Mohan Kelkar is the director of the Tulsa University Center forReservoir Studies. He is currently working with several medium-and small-sized oil and gas companies in relation to reservoircharacterization and optimization of tight gas reservoirs. Kel-kar has published more than 50 refereed publications and hasmade more than 100 technical presentations. He is a coau-thor of the book Applied Geostatistics for Reservoir Characteri-zation, published by the SPE in 2002, and the book GasProduction Engineering, published in 2008 by PennWell Books.Kelkar earned a BS degree in chemical engineering from theUniversity of Bombay. He earned MS and PhD degrees in pe-troleum engineering and chemical engineering, respectively,from the University of Pittsburgh, USA.

Mohammad Sharifi is assistant professor of the Petroleum Engi-neering Department at the Amirkabir University of Technology.He has authored/coauthored several technical papers thathave been presented at international conferences or pub-lished in journals. Sharifis main research is in the area of bridg-ing static to dynamic models through efficient upgridding andupscaling techniques and the simulation of gas-condensateand naturally fractured reservoirs. He is currently working ondeveloping a fast dynamic method for ranking multiple reser-voir realization models. Sharifi earned BS, MEng, and MSdegrees from the Petroleum University of Technology (PUT),the University of Calgary, and PUT, respectively, all in reservoirengineering. He earned his PhD degree in petroleum engi-neering from the University of Tulsa (2012).

SI Metric Conversion Factors

ft 3.048* E01mft3 2.831685 E02m3

bbl 1.589 873 E01m3psi 6.894757 E00 kPa

ft3/D 2.831685 E02m3/dcp 1.0* E03 PaS

R (R460) C*Conversion factor is exact.




a new method to predict the performance of gas condensate reservoir

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