Abstract This paper is a study aimed at the effect of Condensate blockage and tubing size on well deliverability. Gas sales contracts are usually based on the capacity of the system to deliver a specified rate over an agreed period of time. The results of this study are important to determine if a contract can be satisfied or in determining how it can be met. The EOS model is based on data collected from a gas condensate field, offshore Nigeria. This paper highlights the PVT properties most important in predicting gas condensate reservoir behaviour and the approach used in building the EOS model.

Proper EOS characterization is key in modeling the behavior of a gas condensate reservoir. As a starting point, the PVT report is obtained and a material balance analysis is carried out on the reported measured data. The reported data used in the equation of state (EOS) model are the Constant Volume Depletion (CVD), Constant Composition Expansion (CCE) and the hydrocarbon analysis during CVD. These are used in the study to do a material balance analysis based on existing correlations.

Apart from the subsurface samples, surface samples where obtained and physically recombined, a mathematical recombination was carried out as a quality check on the physical recombination. The material balance serves as a means of validating the PVT data before it is used for an EOS characterization. EOS characterization is carried out using the Soave-Redlich-Kwong (SRK) EOS which in this case is used to fit the measured PVT data through non-linear regression. The heavy fraction i.e. C7+ is split into SCN components from C7 to C30+ before the regression is carried out. In this study the fraction was split into thirty-four components. After a match is obtained, pseudoization is carried out to reduce the number of components in order to reduce

simulation run time. EOS characterization is carried out in phazecomp, a state of the art EOS modeling tool. The EOS is tuned so as to match measured data as contained in the PVT report.

This characterized fluid is then used as the basis for input into the single well numerical simulation model by which deliverability is studied. The effect of condensate blockage is studied with relative permeability as a variable to see if a desired rate can be maintained as is expected by gas sales contracts. If there is substantial blockage effect from the result of the simulation then it is an indication that a condensate bank forms in the near well bore region leading to loss in productivity. This becomes a useful way to decide what kind of mechanism will be employed for depletion, for example gas injection to keep the pressure above dew point pressure could prevent condensate blockage. The effect of tubing size on well deliverability is also studied so as to get an optimal tubing size to see out a gas contract which is a tubing size that makes it possible to satisfy contractual obligations.

Introduction Gas condensate’s may be thought of as an intermediate between oil and gas. Gas condensate reservoirs are predominantly gas in which oil is entraped. Development of gas condensate reservoirs requires a thorough study involving accurate PVT characterization using an EOS. This will enable determination of the fluid behaviour under different conditions of pressure and temperature. A major challenge in developing gas condensate reservoirs is the phenomenon known as condensate blockage or “banking”. Below the dew point pressure during the depletion of a gas condensate reservoir, “condensate” drops out in the near wellbore region forming a bank which can lead to loss in productivity. This is especially through in low permeability reservoirs. The bank becomes an impairment to inflow and ultimately leads to

SPE 140629

PVT Characterization of a Gas Condensate Reservoir and Investigation of factors affecting Deliverability Otavie Imo-Jack, SPE, The Shell Petroleum Development Company of Nigeria Copyright 2010, Society of Petroleum Engineers This paper was prepared for presentation at the 34th Annual SPE International Conference and Exhibition held in Tinapa – Calabar, Nigeria, 31 July–7 August 2010. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

2 O.O Imo-Jack SPE 140629

COMPONENT MOLE % SPECIFIC GRAVITY API GRAVITY MOL. WTN2 0.26CO2 1.32C1 79.85C2 5.36C3 4.03iC4 1.10nC4 1.51iC5 0.73nC5 0.57C6 0.80C7+ 4.47 0.774 51.3 129TOTAL 100.00

COMPOSITE MOLECULAR WEIGHT 25.8

GOR scf/bbl 13904 SSQFg 0.9279 7.487E-03

Measured Measured Reported Calc.Component MW SG Separator Separator Recomb Recomb Difference

Liq Comp Gas Comp Wellstr Wellstr % BetaH2S 34.1 0.00 0.00 0.00 0.00N2 28.0 0.04 0.36 0.34 0.34 0.9 0.94CO2 44.0 0.26 1.32 1.24 1.24 -0.3 0.92C1 16.0 9.24 85.53 79.67 80.03 -0.5 0.92C2 30.1 2.92 5.68 5.47 5.48 -0.2 0.92C3 44.1 5.89 3.80 3.96 3.95 0.2 0.92I-C4 58.1 0.5704 3.02 0.94 1.10 1.09 0.9 0.92N-C4 58.1 0.5906 5.44 1.19 1.52 1.50 1.6 0.92I-C5 72.2 0.6295 5.00 0.44 0.79 0.77 2.7 0.92N-C5 72.2 0.6359 5.07 0.26 0.63 0.61 3.7 0.92C6 84.1 0.7061 11.55 0.27 1.13 1.08 4.1 0.92C7+ 136.2 0.7912 51.57 0.21 4.15 3.91 5.7 0.92

Sum 100.00 100.00 100.0000Mw Average 97.4Sg Average 0.7912

a loss in productivity at the surface. This could then lead to deferments and ultimately inability to meet deliverability levels as specified in a gas sales contract. It could also lead to loss of revenue owing to reduced condensate at the surface. Typical recoveries for gas condensates are 60 to 80% for the gas and 20 to 40% for the liquid.

Engineering gas condensate reservoirs is for the most part the same as engineering gas reservoirs. However, there are some exceptions to gas condensate reservoirs which include:

1. Sampling - Reservoir fluid compositions are important, initial composition is needed to define in-place reserves. Compositional variation is important to production economics and field development strategy.

2. PVT – Retrograde Condensation is important to well deliverability, pressure depletion performance and economics.

3. Reservoir Performance - The liquid yield decreases when reservoir pressure drops below the dew point ( GOR increases).

4. Well Deliverability – For moderate- and low- permeability reservoirs, reduced permeability due to near-wellbore condensate blockage may require additional wells and/or more expensive completions (stimulations).

5. Relative Permeability – Required to model well deliverability loss.

6. Gas Cycling – Potentially significant additional condensate recoveries, but with associated delay in gas sales (and/or required purchase of make-up gas)

Two major parts to a compositional study are the PVT data and the reservoir grid1. The standard PVT experiments carried out for a gas-condensate fluid includes Recombined well stream compositional analysis, Constant Composition Expansion(CCE) and Constant Volume Depletion, CVD2. During the matching of the measured PVT data with an EOS model, certain parameters rank higher in terms of the desired accuracy. The need to match these parameters accurately depends on the process being simulated. Thus while a good match of Z factor and compositional variation with pressure may be adequate to describe a gas condensate depletion, we may need to quantify phase behavior (vaporization, condensation, and near critical miscibility) which develops in gas cycling below the dew point. A good equation of state should be able to describe the properties of each component in the characterization. The two phase Z factor values, which are used in material balance equation below the dew point are non physical and are not required in traditional gas material balance.3 In this work an attempt has been made to give a physically consistent description of the PVT characteristics of the reservoir fluid. Also, an appropriate

grid suitable for studying the near-wellbore effect of banking has been adopted. The effect of tubing size on the well deliverability has also been investigated. This study is based on samples collected from a gas condensate field offshore Nigeria.

PVT data analysis The PVT data is based on analysis of recombined surface samples. Subsurface samples were also collected and the composition is shown in Table 1 below

Table 1: Subsurface Sample Composition

Seperator samples were collected and recombined to 13904 cubic feet of primary separator at 14.7psia and 60°F per stock tank barrel as contained in Table 2. The table contains the separator compositions of the oil and gas as well as the calculated wellstream composition.

Table 2: Recombined Surface Sample Compositions

SPE 140629 Modeling Gas Condensate Deliverability 3

Comp Sep Oil WellstreamMole% Mole% GPM Mole%

H2S 0.00 0.00 0.00N2 0.04 0.36 0.34CO2 0.26 1.32 1.24C1 9.24 85.53 79.67C2 2.92 5.68 5.47C3 5.89 3.80 1.044 3.96iC4 3.02 0.94 0.322 1.10nC4 5.44 1.19 0.374 1.52iC5 5.00 0.44 0.149 0.79nC5 5.07 0.26 0.096 0.63C6 11.55 0.27 0.111 1.13C7+ 51.57 0.21 0.100 4.15

100.00 100.00 2.196 100.00

Mole Fraction 0.068 0.932 1.000Comp. Mol wt 97.40 20.00 25.70

HEPTANES PLUS PROPERTIESAPI GRAVITY 47.3 51.1SP. GRAVITY 0.7912 0.72 0.7749MOL WEIGHT 136.2 108 130

Primary Separator Pressure(psig) 356Primary Separator Temperature(°F) 107

SEP GAS

The surface oil and gas are collected from the separator and the sampling GOR is recorded. The oil and gas collected are the recombined using this GOR to obtain the subsurface composition. This is usually done in the laboratory. The recombination can also be performed mathematically using a set of equations and these serves as a basis of quality checking the accuracy of the laboratory recombination. The surface samples are mathematically recombined to

the wellstream composition, zi. The following equation which is expressed in terms of gas mole fraction, yi and the liquid mole fraction, xi forms the basis of the mathematical recombination.

The Fg term can be expressed in terms of in terms of the specific gravity and mass of the surface oil as well as the solution gas-to-oil ratio.

Applying equations (1) and (2) above on the fluid sample leads to the results as displayed in Table 3.

Table 3: Comparison of calculated and reported wellstream

From the mathematical recombination results it can be seen that the difference between the reported and calculated reported well stream are generally below 1% for butane and lighter components, it however gets close to 6% for the heaviest fraction. The sum of squares (SSQ) was not regressed on as all calculations were based on the measured values. It is reasonable to say that the physical recombination process is acceptable.

The Hoffman et al4 method is another method employed in checking the recombined separator sample. They propose a method for correlating K values and the method has been widely adopted.

pK iFAA

i

)10(10 +=

Or

iFAApiK 10log +=----- (3)

Where,

)log(

11

11

scpcipFciTbiT

TbiTi −

−=

- ---------(4)

Tc =critical temperature; Pc =pressure; Tb = normal boiling point; Psc = pressure at standard conditions; and A1 and A0 = slope and intercept, respectively, of the plot log (KiP) vs. Fi.

Standing5 uses the Hoffman et al method to generate K-value equation for surface separator calculations (Psp < 1000 psia and Tsp < 200°F).

The Standing equations are:

)101 )10( AAsppK i

+=

---------(5) )11( TbTbF iii −= ----------(6)

)11)(log( cibiscci TTppib −= --------(7) )2)81015()4105.4(2.1)(0 pppA −×+−×+= -----------(8)

2)8105.3()4107.1(890.0)(1 pppA −×−−×−= -----------(9) pTcn 0016.00075.03.7

7++=

+ ------------(10) 2256.4324013,1777 +++

−+= cccnnb

-------- (11) 2777

971.085.59301 +++−+= ccbc nnT

-------------(12) All T are in °R except when calculating nc7+ (F).

)1()(1 −−−−−−−−−+= ixFyF gigiz

)2(/)/(000,133[1

1 −−−−−−−−+

=− sRMgF

oγ

4 O.O Imo-Jack SPE 140629

PRESSURE RELATIVE VOLUME DENSITY LIQUID VOLUME DEVIATION FACTOR DENSITY(PSIA) (V/VSAT) GM/CC) PERCENT Z LB/FT3

6000 0.8282 0.3172 1.082 19.802155500 0.8559 0.3069 1.025 19.159145190 0.8825 0.2977 0.997 18.58484810 0.9177 0.2863 0.961 17.873124515 0.9504 0.2764 0.934 17.255094130 0.9971 0.2635 0.896 16.449774110 1.0000 0.2627 0.00 0.895 16.399833975 1.0269 0.363890 1.0434 0.603755 1.0708 1.713565 1.1148 3.163230 1.1973 4.422960 1.3078 4.782660 1.4459 4.952375 1.6118 4.882095 1.8333 4.661830 2.1103 4.33

Measured CalculatedN2 0.26 0.25CO2 1.32 1.29H2S 0 0.00C1 79.85 79.21C2 5.36 5.30C3 4.03 3.98iC4 1.1 1.10nC4 1.51 1.54iC5 0.73 0.74nC5 0.57 0.59C6 0.8 0.99C7+ 4.47 5.01

100.00 100.00

PRESSURE LIQ. DROPOUT(psia) PERCENT(%) VAP Z 2PHASZE Z4110 0 0.895 0.8953600 3.84 0.857 0.8653100 6.57 0.842 0.8442600 8.18 0.843 0.8352100 8.81 0.851 0.8311600 9.11 0.866 0.831100 9.25 0.892 0.829

Table 4: CCE Data for Reservoir fluid @ 229°F Hoffman et al. found that for a reservoir gas condensate, the trend of log (KiP) vs. Fi is linear for components C1 through C3 at all pressures, while the function turns downward for heavier components at low pressures. It can be seen from figure 1 that though not all points fall on the straight line for the pure hydrocarbons they correlate fairly well for the reservoir fluid. C3 and C4 fall slightly away from the straight line, and the trend seems to improve for the pentanes and hexanes. The Heptanes plus turns downwards for the standing correlation while the measured value remains slightly higher.

C7+C6

nC5iC5

nC4iC4C3

C2

C1CO2

N2

-1.00.01.02.03.04.05.0

-4 -2 0 2 4Fi

log

KiP

Measured

Standing Correlation

Figure 1: Hoffman K-values for reservoir fluid Data from the constant composition experiment are also reported as contained in Table 4. Measurements reported are relative volume, density, liquid volume and gas deviation factor.

The data from the Constant Volume Depletion (CVD) is also reported as contained in Table 5 below. Reported data

Table 5: CVD Data for Reservoir fluid @229°F The CVD experiment gives an excellent representation of a gas condensate reservoir undergoing depletion. Assuming negligible rock and water compressibilities, data from this experiment can be used to estimate recoveries from a gas condensate reservoir undergoing depletion.

A forward and backward material balance can be carried out on the experimental data. The backward material balance is the most important. In this procedure, the released gases are added back to the oil. This back calculated compositions are then compared with measured data, generally less than 0.5% deviation for all components. The reported density of 41 lb/ft3 was used in the calculation. The backward material balance shows reasonable consistency as shown in Table 6.

Table 6: Backward material Balance Results The recovery factors from the CVD for the gas and condensate are shown in figure 2. It can be seen from this figure that recovery of the gas is close to 80%, while that of the condensate is between 40% and 50%. The lowest

SPE 140629 Modeling Gas Condensate Deliverability 5

Recovery factors from depletion, no water influx

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

01000200030004000500060007000abandonment pressure (psig)

Rec

over

y fa

ctor

s

Surface gas (volume)Surface oil (volume)C1C2C3C4'sC5'sC6C7+ (moles)

Calculated oil gas ratio - assumes surface oil = C6+

0

10

20

30

40

50

60

70

80

0 500 1000 1500 2000 2500 3000 3500 4000 4500

pressure (psia)

OG

R (b

bl/M

Msc

f)

Oil and Gas Densities calculated from material balance analysis of CVD data

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000 3500 4000 4500

pressure (psia)de

nsity

(Kg/

m3)

liquid density(kg/m3)gas density(kg/m3)

recovery is that of heptanes plus, which is expected as the condensate also consists of hexanes. In the case of the gas , the lighter components are mainly in the gaseous phase, hence the surface gas has the highest ultimate recovery.

Figure 2: Calculate recovery factors The Oil Gas Ratio (OGR) and density charts calculated from material balance are shown in figure 3 and figure 4 respectively. The OGR chart takes a hyperbolic shape with the OGR decreasing exponentially with pressure. This expected when the flowing bottomhole pressure drops below the dewpoint pressure as the gas making it to the surface is progressively poorer in its condensate content.

Figure 3: Calculated Oil-gas ratios The decrease is initially rapid but takes a gentler slope after the maximum liquid dropout is attained at about 2500 psia. It should be noted that surface oil is assumed to be C6+. While the gas density decreases linearly with

pressure decline below the dewpoint, the liquid density increases with pressure decline until just above 2000 psia when it begins to drop. From these plots the PVT data can be regarded as “reasonable”. It is seen from the oil gas ratio chart as expected, that the OGR reduces continuously with pressure reduction below the dew point.

Figure 4: Oil and gas densities versus pressures From figure 4, it can be seen that the gas density reduces almost linearly with pressure depletion, oil density increases with pressure reduction at a point, probably the maximum liquid dropout. There might be some swelling effect at that point as the oil density reduces with pressure reduction.

Matching PVT data to EOS A cubic equation of state (EOS) is a simple equation relating pressure, volume and temperature (PVT). Volumetric behavior is calculated by solving a cubic equation. This equation is expressed in terms of Z=PV/RT and can be written as:

012

23 AZAZAZ +++ --------------------------------- (13)

Many EOS’s have been proposed since Van der Waals original EOS in 1873. The Soave-Redlich-Kwong (SRK) EOS is used in this work. This EOS evolved as a result of the need to improve vapor-liquid equilibrium (VLE) predictions of the Redlich-Kwong EOS. It is known that the SRK EOS and offers an excellent predictive tool for systems requiring accurate predictions of vapor liquid equilibrium and vapor properties. The RK EOS can be written as:

)( bvva

bvRTp +−−= ----------------------------(14)

6 O.O Imo-Jack SPE 140629

With the EOS constants defined as:

)(22

rTcpcTRo

aa Ω=

where ;4278.0=Ω oa

cpcRTo

bb Ω=

where ;08664.0=Ω ob

After validating the PVT data, the next step was to use this data in developing an Equation-Of-State (EOS) model. The procedure is for the EOS calculated data to be fit with measured data using non linear regression procedures. It should be noted that a successful EOS characterization is a trial and error process. Considerable effort was made in matching the Reservoir fluid but with care not to regress on the physical properties of the pure components (C5-). The EOS characterization was carried out in Phazecomp, state-of-art EOS modeling software. A set of parameters was regressed upon, fixed to maintain consistent results and then the others tuned. A detailed description of the regression parameters, their significance in the modeling process and the order in which they are tuned, is now presented. SORREIDE: This correlation was developed based on analysis of 843 TBP fractions from 68 Reservoir C7+ samples. The equation which relates specific gravity to molecular weight is given as:

13.0)66(2855.0 −+= iMfCiγ ----------(15)

Where fC typically has a value between 0.27 and 0.31

and is determined for a specific C7+ sample by satisfying the following equation.

)/(1

77)7

(

iiMizN

i

cMczc

γγ

=Σ

++=+

--------(16)

For this EOS characterization, it was regressed between these two extremes to arrive at a value of 2.91648e-01. This value was found by creating a new fluid comprising of only the C7+ fraction and regressing on Cf to match the API gravity, Molecular weight and liquid specific gravity of this fraction. This is due to the fact that the report contains measurements of these properties for the oil and matching these measurements becomes a valid way of finding this parameter which relates molecular weight and specific gravity of the liquid fraction.

TWU DAMPING FACTOR: This factor is used to dampen the influence of Specific gravity on the Twu

correlation of molecular weights with boiling points and specific gravities. The default correlation (TWUMW=1) uses the specific gravity of each component, which may result from the Soreide correlation, to determine the relationship between the molecular weight and boiling point. When TWUMW=0, a normal paraffin-like relationship is assumed between molecular weight and boiling point. This may not be realistic for most reservoir fluids but it becomes very close to the Katz-Firoozabadi8 relationship, which is often assumed by PVT laboratories. A value of TWUMW between 0 and 1 interpolates between these two extremes. In the case of the reservoir fluid the search went to the default correlation (TWUMW=1).

The Twu Molecular weight- Boiling point Correlations are given as:

2)21

21(lnln

MfMf

MM P −

+= ------------------- (17)

]5.0

328086.0175691.0[ MbT

xMMf γγ Δ⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+−+Δ= ,--------(18)

5.0328086.0012342.0

bTx −= ,

and )](5exp[ γγγ −=Δ pM

GAMMA DISTRIBUTION MODEL: This three- parameter gamma distribution is a more general model for describing molar distribution. The gamma probability density function is:

)(

]/)[exp1)()(

ααβ

βηαη

Γ

−−−−=

MMMp --------------(19)

Where =Γ gamma function and β is given by

α

ηβ += 7CM

The three parameters in the gamma distribution are α, η, and

+7CM .

The parameter α defines the form of the distribution, and its value usually ranges from 0.5 to 2.5 for reservoir fluids; α =1 gives an exponential distribution. In the case of heavy oils, bitumen, and petroleum residues the upper limit for α is between 25 and 30 and this approaches a log-normal distribution. Figure 3.5 is indicative of the various distribution shapes with respect to α. The parameter η can be physically interpreted as the minimum molecular weight found in the C7+ fraction. The relationship between α and η is

SPE 140629 Modeling Gas Condensate Deliverability 7

)7.0/41(1

110

αη

+−≈ ----------------------- (20)

For reservoir fluids C7+ fractions.

For this reservoir fluid characterization a shape factor of 1 and Gamma bounding MW factor of 90 are applied.

Figure 5 : Gamma distributions for petroleum residue (after Brule et al. 6).

BINARY INTERACTION PARAMETERS (BIP): The binary interaction parameters used were those recommended for the SRK EOS. The table below has the recommended BIP’s for the Peng-Robinson and Soave-Redlich- Kwong EOS. The BIP’s regressed on for this characterization is those of methane with the C7 to the C30+ fraction.

Table 7: BIP’s of fluid Components

The Cheuch-Prausnitz9 modified equation for BIP’s of C1 through C7+ pairs is given as:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+−=

B

cjvciv

cjvcivAijK

31

31

61

61

21 ,------------------- (21)

With A=0.18 and B=6 for a PR EOS. In this case where the SRK EOS is used for the EOS and A was regressed upon between values of -2 and +2 and the lower limit of 2 was found.

BOILING POINT: The recommended correlation for calculating the critical properties of all C7+ fractions are

MMMcT

4.187743475.0ln052.8612.163 −++= ρ ’-----(22)

22.398746.208

5019.213408.0lnMM

cP −++−= ρ ’ --------- (23)

With Tc=critical temperature and Pc=critical Pressure. Instead of regressing on the critical properties (Tc and Pc) separately, the boiling point (Tb) was regressed on. The critical properties of the plus fractions being the most uncertain, the boiling point of C29 and C30+ were regressed upon. REGRESSION RESULTS 1. GAS Z-FACTOR: This is the only factor that still needs accurate determination in a gas condensate as well as gas reservoirs. There are two reasons why this is so: (i) To get an accurate and consistent estimate of the initial gas (and condensate) in place (ii) To accurately predict the gas (and condensate) recovery as a function of pressure during depletion drive.

8 O.O Imo-Jack SPE 140629

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Pressure (psia)

Gas

Vis

cosi

ty (c

p)

Experimental Calculated

Figure 6: Z-factor regression result

The match of the gas Z factor is shown in the figure 6 above. The Z factor seems to be overpredicted but the match is increasingly closer at lower pressures, suggesting the gas may be slightly leaner than anticipated. Overall, it is a “decent” match with an error margin of 3.78 %. 2. COMPOSITIONAL VARIATION DURING DEPLETION: The distinguishing characteristic of a gas condensate reservoir is the added value from condensate production in addition to gas. It is the importance of this parameter that leads to the matching of C6+ variation with pressure as shown in the plot below. As the FBHP drops below the dewpoint, the amount of C6+ decreases with continued pressure decline. This reduces the quality of the surface gas as the amount of condensate recoverable at the surface continues to reduce. Figure 7 shows the match of the EOS calculated and the measured condensate recovery.

Figure 7: y-C6+ variation with Pressure match

The match of the y-C6+ match is quite good with five of the seven points (calculated) not falling exactly on the EOS predictions. The error is 3.09 % but the spread of this error makes it quite a good match, a good prediction of the condensate recovery should be expected. 3. DEW POINT PRESSURE: The dew point pressure is the pressure where an incipient liquid phase condenses from a gas phase. It is at this pressure that condensate accumulation starts in the reservoir. The effect of the dew point pressure would vary from reservoir to reservoir but in most cases, it is not important. For this sample the dew point pressure of 4110 psia was closely matched with an EOS prediction of 4109.7 psia which represents 0.007% error. 4. GAS VISCOSITY: The gas viscosity is usually within 0.02 and 0.03 cp for all pressure conditions. For near critical gas condensates or high pressure gases, the viscosity may initially be 0.05 cp. What is important for viscosities is that a consistent value be used in all engineering applications. The gas viscosity output is shown in figure 8 below:

Figure 8: Gas viscosity match 5. LIQUID DROPOUT: The liquid dropout is considered by many engineers as a measure of the richness of the condensate. Generally speaking, the liquid dropout is not as important as the condensate yield in determining the richness of the condensate. Particularly, this parameter is not very important in modeling condensate blockage except at low pressure in the Constant Composition Expansion (CCE) experiment. The match from CVD experiment is as shown below and the EOS seems to under predict liquid volumes from the experiment. It seems a bit unusual that the experiment was still recording increasing liquid volumes at pressures below 1000 psia.

SPE 140629 Modeling Gas Condensate Deliverability 9

0

1

2

3

4

5

6

7

8

9

10

0 500 1000 1500 2000 2500 3000 3500 4000 4500Pressure (psia)

Liqu

id d

ropo

ut (%

)

Experimental Calculated

Figure 9: Liquid dropout match 6.OIL VISCOSITY: Oil viscosity is important in the proper modeling of “condensate blockage”. Oil viscosity is usually low for reservoir condensates in the range of 0.1 to 1 cp in the near well-bore region. Measurements of these viscosities are generally not made in routine laboratory tests and it may be difficult to obtain measurements for lean condensates (due to small volumes of condensates). Viscosity correlations are typically unreliable for predicting low oil viscosities and some approach is needed to ensure accurate and consistent modeling of this important property.

The Orrick and Erbar 7 method is employed here in

calculating the low temperature oil viscosity. This method employs a group contribution technique to estimate A and B in Eq. (3.24)

T

BA

ML

L +=ρ

ηln ---------------------------------(24)

Where =Lη liquid viscosity, cP

=Lρ Liquid density at 20oC, g/cm3 =M Molecular weight =T Temperature, K

The oil viscosity is not regressed on during the initial regression step. It is however regressed on after the initial match and during this step; it is the only property regressed on. Using the Orrick and Erbar method, viscosities of all C7+ are calculated at atmospheric pressure and reservoir temperature. The critical Z factor of each component is then regressed on to match the viscosities to those calculated by Orrick and Erbar method. The results show the matches were between 0.00 and 0.02 % error margin. The EOS then matches the Orrick and Erbar viscosities and this is shown in the next section after the lumping.

Pseudoization Having achieved a reasonable match of the EOS, the next step is to lump the components in such a way that the match is retained and computing space is minimized. Thus the 34-component EOS is pseudoized to obtain a 9-component EOS. Different lumping schemes were tried to see which produced the best results and the results are shown below. The approach used was to lump less of the lighter liquid fractions ( C6 – C10) or less of the heavier liquid fractions ( C23 – C29) and observe the error margins of the most important measurements. The results are summarized in table 8 to 10 below.

Table 8: Pseudoization Scheme 1

Table 9: Pseudoization Scheme 2

10 O.O Imo-Jack SPE 140629

Table 10: Pseudoization Scheme 3 It can seen that the best result is obtained from table 8 and this is the lumping scheme used in the final characterization. Generally, it is seen that better results are obtained if fewer components of the lighter plus fractions (C6-C10) are lumped together. The various schemes can be compared by looking at the percentage errors between the extended and combined Eos’s for the various lumping schemes. And this is summarized by the chart in figure 10.

Figure 10: Lumping scheme Performance So in the final analysis, this pseudoized EOS is compared with the extended EOS. The idea is that the pseudoized EOS should be able to produce the same result as the extended EOS as this helps the engineer maintain the characterization and reduce the resources (computing) that would have been used with the extended EOS. The trend of the lumping scheme performance is shown in Figure 10 Using the most accurate of the lumping schemes, the pseudoized EOS gives a “close to accurate” match of the extended EOS shows the extended match for some of the measurements whose initial matches were earlier discussed. These matches are shown in Figures 11 to 13

Figure 11: y-c6+ pseudoization

Figure 12: Liquid dropout pseudoization

Figure 13: Gas Z factor pseudoization

It is seen from the plots presented above that the pseudoized EOS approximates, to a high degree of accuracy, the initial extended EOS characterization. The

SPE 140629 Modeling Gas Condensate Deliverability 11

Component Mol Wt A B Tc (K) Pc (bar) AF Tb (F) Sp Gr------------ --------- -------------------------------------- ---------------------------C1N2 16.094 0.427 0.087 190.3 45.936 0.011 -258 0.14C2CO2 32.646 0.427 0.087 296.8 50.551 0.107 -136 0.314C3-4 49.682 0.427 0.087 389.6 40.169 0.169 -16.3 0.538C5 72.15 0.427 0.087 464.6 33.764 0.239 89.26 0.634C6-7 88.211 0.427 0.087 530.3 32.828 0.252 170.9 0.721C8-10 119.091 0.427 0.087 602.5 27.376 0.341 285 0.774C11-19 177.51 0.427 0.087 700.9 19.966 0.522 462.8 0.824C20-29 288.5 0.427 0.087 821.7 13.203 0.841 705.7 0.875C30+ 414.299 0.427 0.087 910.3 9.7691 1.166 895.6 0.91

properties of the final characterization are shown in Table 11 below

Table 11: Final EOS characterization properties It is this pseudoized 9-component EOS that is exported to the simulator and used as the basis for PVT interractions during the reservoir simulation phase of the condensate study. Upscaling The reservoir model was imported into eclipse reservoir simulator and visualized using floviz (a post processor in the eclipse suite) to investigate the presence of sealing fault(s), so this could be accounted for during the upscaling process. The model was converted into sensorTM which is a dynamic reservoir simulator with functionality for compositional simulation. Figure 14: Floviz visualization of reservoir model. Figure 14 is the model from floviz, analysis of the model showed no sealing faults and so only one region was defined for the reservoir model. The original model contained 41310 grid cells (30X51X27), and the upscaling was done to fall within the 6000 grid cells the package allows. The Cartesian model was built to have

2700 grid cells (10x10x27). The upscaled model has no water- oil contact. This was because the fine model had an edge aquifer but hydrocarbon extended through the 27 layers in the area of completion. The Cartesian model is drained by 4 wells. Average properties (porosities, permeabilities etc) were used over every layer and the following relationship was used in converting the Cartesian model to a radial model.

4

2 yyNxxNer

ΔΔ=π ------------------------------ (25)

where re = drainage radius of reservoir. Nx = number of cells in x direction Ny = number of cells in y direction ∆x = x direction gridblock thickness ∆y = y direction gridblock thickness The above relationship gives the radius of the reservoir which is used in the radial model with dimensions 30-1-27 (r-θ-z). The initialization shows that the model was about 250 psia undersaturated and calculated GOR is 13545 scf/Stb psia while recombination GOR is 13904 scf/Stb.Initialization results are shown in Table 12.

Table 12: Initialization results

RADIAL MODEL The single well radial model is used because it has sufficient resolution in the near wellbore region to show the effect of blockage. This is against the full field model (fine or upscaled) which does not have the necessary resolution for the study of blockage effect. An exception is of course the use of local grid refinement (LGR) in the case of the original full field model.

BLOCKAGE EFFECT In a gas condensate well, when FBHP drops below the dewpoint it causes a significant condensate saturation buildup near the wellbore, resulting in lower gas permeability. This reduced gas permeability gives rise to a phenomenon known as “condensate blockage” and it can lower a well’s PI by 50% to 200% (equivalent to a skin of 5 to 20). Corey type relative permeability curves were used for this work. Since the actual rock curves are not available for this reservoir, Corey type relative permeability curves with n=1, 1.5 and 3 were used. The curve with n=3 is assumed to represent the “immiscible” curves. The curve with a corey exponent of 1 represents a “miscible” condition. The curve with a Corey exponent of 1.5

CIIP(MMSTB) GIIP(BSCF) Eclipse Sensor Eclipse Sensor 104.7 105.9 1412.9 1435.4

12 O.O Imo-Jack SPE 140629

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represents an interpolated value between the “immiscible” and “miscible” curves and represents a more realistic case of the actual relative permeability curves. This is because it takes into account the capillary number improvement at high relative permeabilities which are encountered close to the wellbore. The capillary number (Nc) is a dimensionless number which measures the ratio between viscous and capillary forces. Mathematically, it is defined as

IFTityvisvelocityCN cos*= -------------------------(26)

or CPviscousPCN /)(Δ= Velocity as defined above is the superficial pore velocity (equals Darcy velocity/Porosity/ (1-Swc)). It is advised to have data in consistent units and SI units are recommended with velocity in m/s, viscosity in Pa.s, IFT in N/m. The relperm curves for the different corey exponents are shown in the curve below. Figure 15 shows the relperm curves for different exponents with the straight line representing the miscible case.

Figure 15: Relperm curves for different corey exponents The Fevang-Whitson model describes the change in capillary number with relperm. The model needs only two empirical parameters to define this relationship The interpolation is between rock and miscible (straight line) rel perms at fixed values of Krg/Kro

miscrgkfrockrgfkrgK ,)1(, −+= ---------------- (27)

1)(

1

+= n

CNf

α ----------------------------------- (28)

Usually α is between 3000 and 5000, while n is approximately 0.7.In this case the interpolation has not been carried out since the actual rock curves are not available. As seen in the figure below, the relperms have an insignificant effect on the deliverability.

Figure 16: Blockage effect on deliverability There is little pressure drop around the wellbore and the total Kh is quite high, in excess of 40,000 md-ft . The pressure profile is shown in figure 17 below.

Figure 17: Pressure profile along radial well The pressure drop between the FBHP and the average reservoir pressure is about 3 psi (~0.2 bar) and so virtually all the pressure drop is taking place in the tubing. The reservoir has average porosity of 0.23.

SPE 140629 Modeling Gas Condensate Deliverability 13

The Krg vs. Krg/Kro relationship for the three cases of relperm curves are shown in figure 18. It can be seen that the near well (r=1) relperms for the case run with a corey exponent of 3 falls on the curves with n=3. This serves as quality check for the simulator generated relperm table.

Figure 18: Relperms curves with near-well relperm data Taking a close look at the near-well relperms for the most pessimistic case (Corey exponent of 3) as shown above and it is seen that the initial Krg/Kro is greater than 10, which is a high number for a case with significant condensate blockage effect. The figure further suggests the leanness of the gas as this number is quite large even for the most pessimistic case.

Figure 19: Simulated Recovery factors Figure 19 above shows the recovery factors from the single well simulation, it’s performance was simulated using a Corey exponent of 1.5. The gas ultimate recovery factor is about 83.3%, and this is achieved just after about a 20 year period. The condensate ultimate recovery stands at 46.6% and this is achieved at about the same time as the gas. The results are quite close to the recovery factors calculated by material balance equations and shown in

figure 2. It is seen that while the ultimate condensate recovery stands at about same for both cases, the gas increased by some 5%, probably owing to the influence of pore compressibilities which are not considered in the material balance model. It can be inferred from the results that blockage has no significant impact on the ultimate recovery. The productivity index is an important parameter to observe while studying the effect of blockage. Blockage constitutes a serious problem if there is a reduction of >50% in the well’s productivity index (PI). The Productivity index, J, is given as

bswreroo

khJ+−

=]75.0)/[ln(2.141 βμ

------------ (28)

Where Sb is the blockage skin which stated mathematically is:

)/ln()11

( wrbrrgbKbS −= ----------------------- (29)

The productivity index profile for the well over the 28 year production period is shown in Figure 20 below. It is seen that change is about 15%. Figure 20: PI profile over time

Tubing Size Impact The gas tubing or VFP (vertical flow performance) rate equation defines the relationship between surface gas rate and pressure drawdown (bottomhole flowing pressure minus tubing flowing pressure). This relationship is also called “tubing performance” or tubing “backpressure curve”. The most important variable defining a well’s tubing performance under steady state conditions is the tubing diameter.

14 O.O Imo-Jack SPE 140629

The gas tubing equation is given as:

5.0)22( tpwpCgq −= ------------------- (30)

The basic form of this equation is often applicable even for rich gas condensate, though it may be difficult to predict in advance the tubing constant, C, with standard (dry gas) equations. The reservoir studied does not contribute any significant deliverability shortfall due to “near well” blockage. The expectation (as can be seen from figure 21) is that the tubing sizes will have a major effect on deliverability. Tubing tables were generated and these tables served as input in the simulator to study the effect of tubing size on delTubing tables were generated for three tubing sizes: 3.5”, 4.5” and 7”. Each of these cases was run with the same production constraints for the single well radial model and results show significant differences in the deliverability Figure 21: Tubing size effect on well deliverability It is seen that the 7” tubing gives the best results for deliverability. In general, the trend shows that the larger the tubing, the better the deliverability. It is important to quantify the incremental gains and choose an optimal size. Conclusions The quality check shows the PVT data is acceptable, and the EOS gives a good representation of the PVT data. Also, the final EOS is physically consistent and can accurately describe reservoir performance under natural depletion or gas cycling. There would be no need to

undertake a study to obtain accurate rock curves in this reservoir for the purpose of studying near wellbore condensate blockage.Condensate banking is not a major issue in the near-wellbore area of this reservoir and thus has no significant effect on deliverability or the ultimate recovery.This is not suprising considering the reservoir has an average permeability of 2000md. The tubing size for completion of wells in this reservoir need to be optimally selected after carrying out some sensitivity. Generally it may be optimal to initially complete with a large tubing but a smaller sized tubing may be better after water breakthrough. This reservoir can be developed withoutout necessarily putting a gas injection scheme in place.

Nomenclature a = numerical constant(s) used in equations; dimensional equation-of-state (EOS) constant describing molecular attractive forces, psia/ (ft3-lbm-mol) 2 A = numerical constant(s) used in equations; dimensionless EOS constant describing molecular attractive forces b = dimensionless EOS constant describing molecular repulsive forces L3/n, ft3/lbm mol bi = Hoffman et al. K-value correlation parameter for Component i Fi = Characterization factor in Hoffman et al. K-value correlation Ki = yi/xi = equilibrium ratio (k value) of Component i nc7+ = C7+ approximate Carbon number in Standing’s low-pressure k-value correlation P = Pressure, m/Lt2, psia Pc = critical Pressure, m/Lt2, psia Psc = Pressure at standard conditions, m/Lt2, psia Psp = Separator Pressure, m/Lt2, psia T = Temperature, T, °F or °R Tb = normal boiling point at 1 atm, T, °R Tr = reduced temperature T, °R Tc = Critical temperature, T, °R R = Universal Gas Constant = 10.73146 psia-ft3/°R-lbm mol V= molar volume, L3/n, ft3/lbm mol Z = Compressibility or “deviation”, factor Ωa°, Ωb° = numerical constants in Cubic EOS’s Ωa, Ωa = Constant’s in Cubic EOS’s γi = specific gravity, air=1 or water=1 Cf = Soreide specific gravity correlation characterization factor. M = molecular weight, m/n, lbm/lbm mol Mp = molecular weight of paraffin hydrocarbons, m/n, lbm/lbm mol γc7+ = C7+ specific gravity, water=1 zc7+ = C7+ mole fraction in overall mixture N = total number of components fM = parameter in Twu correlation for molecular weight

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SPE 140629 Modeling Gas Condensate Deliverability 15

∆γM = parameter in Twu correlation for molecular weight η = gamma distribution model parameter m/n, lbm/lbm mol. Γ = gamma function α = gamma distribution model parameter β = parameter in the gamma distribution model kij = EOS binary interaction parameter vc = critical molar volume, L3/n, ft3/lbm mol ρ = mass density, m/ L3,lbm/ ft3 or g/cm3 krg = gas relative permeability krg,rock = rock gas relative permeability krg,misc = miscible gas relative permeability f = interpolation parameter Nc = dimensionless viscous to capillary number qg = total surface gas rate, L3/t, scf/D C = tubing constant, scf/D/psi Pw = bottomhole pressure Pt = tubing head pressure, psi Kh = permeability thickness, md-ft μo = oil viscosity, cp Bo = Oil volume factor, rb/stb Sb = Blockage skin factor Krgb = Average blockage gas relative permeability re = reservoir radius, feet re = well radius, feet.

References 1. Douglas E. Kenyon and G. Alda Behie: “Third SPE Comparative Solution Project: Gas Cycling of Retrograde Condensate Reservoirs,” paper SPE 12278 JPT (August 1997) 1. 2. Curtis H. Whitson and Michael R. Brule: “Phase Behavior” AIME, SPE Monograph Series 2000. 3. Curtis H. Whitson, Øivind Fevang and Tao Yang: “Gas Condensate PVT- What’s Really Important and Why?” IBC Conference “Optimization of Gas Condensate Fields”, London, Jan. 28-29, 1999. 4. Hoffman, A.E, Crump J.S., and Hacot, C.R.: “Equilibrium constants for a gas condensate system,” Trans, AIME (1953) 198, 1. 5. Standing, M.B.: “ A set of Equations for Computing Equilibrium ratios of a crude oil/ Natural Gas System at Pressures less than 1000 psia” JPT (September 1979) 1193. 6. Brule, M.R., Kumar, K.H., and Watansiri, S.: “Characterization Methods Improve Phase-Behavior Predictions,” Oil & Gas J. (11 February 1985) 87. 7. Reid, R.C, Prausnitz J.M, Poling B.E.: “The Properties of Gases & Liquids” 1987 McGraw-Hill Book Company, 456 8. Firoozabadi, A., Hekim, Y., and Katz D.L.: “Reservoir Depletion Calculations for Gas Condensates using Extended Analyses in the Peng-Robinson Equation of State,” Cdn. J. Chem. Eng. (Oct. 1978) 56, 610-15. 9. Coats, K.H. and Smart, G.T.: “Application of a Regression-Based EOS PVT Program to Laboratory Data,” SPERE (May 1986) 277