Int. J Sci. Emerging Tech Vol-3 No 2 February, 2012

55

Pressure Transient Analysis of a Gas-

Condensate Well by Analytical and Numerical

Models (A Case Study in South of Iran) Amin Mirhaseli Igder

#1, Abdolnabi Hashemi*

2

Department of Petroleum Engineering

Petroleum University of Technology

Ahvaz, Iran 1igder@yahoo.com

Abstract In gas-condensate reservoirs when the pressure falls below the dewpoint pressure, liquid drop

out and condensate accumulates near the well. This

condensate buildup decreases the relative permeability

to gas, thereby causing a decline in the well

productivity. In this study a set of pressure transient

data obtained from an actual production well in a gas-

condensate reservoir in Iran has been used. The

objectives being analytical interpretation of the data,

and verifying the results with compositional simulation

results. At first the transient pressure test has been

analyzed using a standard well test package. The test is

then analyzed using a commercial compositional

simulator. The results of the compositional simulation

show that capillary number effects should be included

in order for history match. The challenge is then to find

the capillary number correlation parameters.

Keywords Well Test, Gas-Condensate, Analytical and Numerical Solution, Compositional Simulation, Relative

Permeability, Liquid Drop-out.

1. Introduction

For gas and gas-condensate reservoirs, the equation

governing pressure transmission in porous medium is

nonlinear in reality. Al Hussainy and Ramey [1] and

Al Hussainy et al. [2] showed that the flow equation

for real gases in porous media can be linearized using

the real gas pseudopressure:

This is known as single-phase pseudopressure and

this method works best for dry gases therefore, it can

be applied to gas-condensate wells producing above

the dewpoint pressure. Once the pressure falls below

the dewpoint pressure and a condensate bank is

formed around the wellbore, the single-phase method

does not work properly.

The two-phase steady-state theory to predict the

performance of single-well gas-condensate systems

was first proposed by ODell and Miller [3] and was later examined by Fussel [4]. The steady-state

saturation-pressure relationship predicted by ODell and Miller and Fussel was later reproduced by

Chopra and Carter and Jones and Raghavan [5]. The

steady-state model can be used to approximate the

actual reservoir pressure-saturation relationship by

assuming a hypothetical steady-state flow. The

pseudopressure computed by the steady-state model

is referred to as the steady-state pseudopressure [4].

The model assumes two flow regions around the

wellbore [4]: region 1: a near-wellbore region below

the dewpoint pressure where both gas and condensate

are present and mobile, region 2: an outer region

above the dewpoint pressure containing only single-

phase gas.

As shown in Figure 1 the three-zone flow model was

first introduced by Fevang [6]. Unlike the steady-

state model, the three-zone flow model considers the

existence of a transition zone where both gas and

condensate are present, but only gas is mobile [4].

Similar to the steady-state method, the three-zone

pseudopressure is only applied if the relative

permeability data are available and it can be

evaluated using the following integral [7] :

(

)

(

)

(

)

Figure1. Schematic near-wellbore region fluid

description [8]

Gringarten et al. [9] provided the first well test

evidence in the literature of the existence of a

velocity stripping zone. Previous well test

publications had only reported the existence of a

condensate bank (zones 2 to 3 in Figure 2) as a two-

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Int. J Sci. Emerging Tech Vol-3 No 2 February, 2012

56

region radial composite behavior (curve b in Figure

3). Jones and Raghavan [5] proposed that well tests

in gas-condensate wells below the dewpoint pressure

may be analyzed using either single-phase or two-

phase pseudo-pressures. Roussennac [10] compared

the accuracy between the steady-state method and the

three-zone method in analyzing the data.

Figure 2. Condensate saturation profile with

condensate drop-out and velocity stripping [11]

Figure 3. Pressure and derivative composite

behaviors: (a) three-region composite; (b) two-region

composite [11]

1.1 Parameters Affecting Flow in Gas-

Condensate Reservoirs

There are two competing phenomena which may

cause the effective gas permeability to be rate-

dependent [12]:

1. The relative permeability increase with velocity, which has been demonstrated in numerous

laboratory core flood experiments. This effect is

sometimes termed velocity stripping or positive coupling.

2. Inertial (non-Darcy) flow effects, which at high velocity reduce the gas permeability.

Since simultaneous flow of gas and condensate is

usually affected by the combined effect of these

phenomena (coupling and inertia), both of them

should be included in reservoir modeling. The

complications of transient test analysis in this type of

reservoir are caused by multiphase flow and change

in the composition of the flowing mixture.

The capillary number model in the compositional

simulator was used to model velocity-dependent

relative permeabilities. This model reduces the

residual saturations and changes the relative

permeability from the user specified (immiscible)

saturation curves to an internally generated miscible

curve [13].

2. Reservoir Description

The SH gas-condensate field is located in southern

Iran (the original field name has been changed to

SH for confidentiality). Based on geological, seismic and well data, the field is an elongated

anticlinal structure and consists of three main

geological pay zones: Kangan, Upper Dalan and

Lower Dalan. To date a total number of 10 wells

have been drilled and completed in this structure.

These wells were completed on different reservoir

sections either as open holes or perforated liners.

Most of the reservoirs in the field are believed to be

carbonates.

The original fluid in this field is evaluated as a lean

gas condensate with an average CGR of 13.5

STB/MMSCF. PVT studies indicate a dewpoint

pressure of 4280 psia at a reservoir temperature of

184.5 F for the fluid samples taken from Kangan

formation. The average reservoir pressure in this

layer was 4117 psia. The basic reservoir parameters

used in this study are shown in Table 1.

Table 1. SH reservoir petrophysical and fluid

properties

3. Analytical Simulation

Pressure and rate history of the well test is shown in

Figure 4. The production test consists of four periods

of drawdowns and one buildup, referred to as DD1,

DD2, DD3 and BU1. The value of the dewpoint

pressure is shown in Figure 4 (4280psia). The

derivative curves of all three drawdown periods

exhibits completely erratic behavior which can be

explained by phase redistribution or flow rate

fluctuations around the wellbore, making them

interpretable (as shown in Figure 5). Buildup has the

longest duration. Hence, it was selected for analysis

using the well test interpreter. The log-log diagnostic

plot of this test period is also shown in Figure 6.

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Based on the shape of the derivative plot, a two-zone

radial composite model was used for analysis. The

wellbore storage dominated region and two radial

flow zones can be identified in Figure 6.

Semi-log, log-log and history plots (resulting

matches) of the final buildup test data are displayed

in Figures 7, 8 and 9 respectively. All of resulting

matches are very good. Match results are listed in

Table 2.

Figure 4. Pressure and rate history

Figure 5. Log-Log rate normalized pseudopressure

derivative plot of all the drawdown and buildup tests

Figure 6. Final buildup log-log diagnostic

pseudopressure derivative plot

Figure 7. Final buildup semi log plot (match results)

The estimated inner radii of zones 1 and 2 related to

the composite model are 98 and 340 ft, respectively,

which mean that the condensate bank radius is

estimated to be 340 ft. The rate dependent skin

coefficient of 1.29e-4 (1/(Mscf/day)) accounts for the

non-Darcy flow (inertia) effects near the wellbore.

Figure 8. Final buildup log-log plot (match results)

Figure 9. Test history plot (match results)

Table 2. Final buildup log-log match results

Estimated parameters from the history match, log-log

and semi-log plots (both match and model) are in

good agreement. Although the pressure history match

is not very good the third drawdown is somewhat

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good and the buildup match is perfect. The negative

skin factor reflects effective acid stimulation. Well

test analysis provided good estimation for the initial

reservoir pressure at the gauge depth in comparison

to real result.

4. Numerical Solution (Using

Compositional Simulator)

A key component in modeling gas-condensate

reservoirs is the development of a representative fluid

model. Therefore, commercial PVT analysis software

was used to simulate the experiments. The PVT data

used in the compositional model was based on the

samples collected from pay zone of the well SH. To

simulate the fluid samples of this pay zone, 3-

parameter Peng-Robinson (PR) equation of state was

used, and as shown in Figure 10 (parts a,b,c,d) very

good matches were obtained between calculated and

observed properties.

The next step is to build a static model to be

used as the basic reservoir structure. Rock and fluid

properties and completion production scenarios were

defined then. For compositional simulations capillary

numbers must be considered, otherwise pressure drop

and condensate dropout are overestimated and well

productivity is underestimated.

Finally a single three dimensional vertical well model

with radial grid blocks was defined. The model was

380ft in vertical direction and 3780 ft from the center

in radial direction and included 57 ft above and

below the pay zone. The grid model was divided into

90 cells in R- plane and 90 cells in Z direction (a total number of 8100 cells each having a height of 4.2

ft). All grid properties such as porosity, water

saturation and net to gross ratio were obtained from

petrophysical properties of the layer as listed in Table

1. The relative permeability data is also shown in

Figure 11.

Figure 10. Match of PVT experiment, well SL-1(a.

liquid saturation from CVD, b. moles recovery from

CVD, c. relative volume from CCE, d. liquid

saturation from CCE)

Figure 11. Relative permeability curves of SH field

It is essential to refine the model around the

production well especially for capillary number

analysis; otherwise the model cannot cover the full

physics of occurring phenomena around the

producing well. This causes the velocities across cells

to approach each other which results in better

performance of the model. For minimum fluctuation

in the wellbore pressure data and allowing more

detailed evaluation of near wellbore behavior local

grid refinement is also necessary. A logarithmic trend

was used for this purpose.

4.1 Model Verification

In order to verify the model output and numerical

dispersion effects, the model performance should be

investigated with a simulated well test scenario. As

shown in Figure 12 the simulated well test analysis

shows that the numerical model provides good

agreement with the reservoir parameters obtained

from the interpretation of the simulated well test. For

instance permeability input of the simulator was 25

md and the well test interpreter shows a value of 24.3

md or the simulator input for skin is zero and that of

the well test interpretation is about 0.14.

Figure 12. Log-Log pseudopressure derivative plot

(match results) of drawdown test for model

verifications

Next we have to define the actual well test

scenario using the compositional model. In other

words, this time the flowing and shut-in periods and

production rates and pressures are assumed exactly

the same as the real test.

Simulation was run considering capillary

number effects. Figure 13 also displays the effect of

exclusion of capillary number effects in the

simulation.

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Figure 13. Real pressure and the resulted pressure

from the compositional simulation without capillary

number effects for first interpretation

Figure 14. Real pressure and the resulted pressure

from the compositional simulation with capillary

number effects for first interpretation

In this case by sensitivity analysis of capillary

number parameters good match was achieved in lean

gas condensate reservoir (as shown in Table 3).

Table 3. Capillary number parameters

As in Figure 13 the simulation results did

not match the real pressure data, especially in high

gas rate drawdown periods in which the flowing

bottom hole pressure falls below the dewpoint

pressure. Therefore inclusion of capillary number in

the model, results in increase of the flowing bottom

hole pressure which results in good matches (Figure

14).

As can be seen in Figure 15 the rate

normalized log-log plot of pseudopressure and

derivative plot corresponding to simulated case and

actual derivative are compared. Match is moderately

good at middle times and as expected, but not good at

early times since the wellbore storage effects are not

accounted for in the compositional model.

Furthermore, the simulated case well matches the real

derivative at late times. Match results are listed in

Table 2.

Figure 16 shows the condensate saturation

profile versus distance from the well at the start of

the buildup period. Condensate bank radius can be

calculated from this figure. The velocity stripping

zone can also be easily identified in the figure. Figure

17 is the graphical depiction of the process of finding

the best reservoir parameters.

Figure 15. Final buildup log-log pseudopressure

derivative curves of the real data and compositional

simulation results with capillary number effects

corresponding to first interpretation

Figure 16. Radial distribution of condensate

saturation

Figure 17. Graphically sequence to find the best reservoir parameters.

Conclusions

1. Condensate saturation profile resulted from the compositional simulation underestimates the

condensate bank radius in this lean gas condensate

reservoir compared to the well test analysis

results.

2. A good match was obtained by sensitivity analysis of capillary number parameters, in this lean gas-

condensate reservoir.

3. The buildup log-log plot obtained from the compositional simulator shows that the simulated

case matches the actual derivative reasonably at

middle times and more accurately at late times,

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60

yet not at early times, since currently available

compositional simulators cannot properly

simulate wellbore storage and skin effects.

4. The capillary number effects must be included in the lean gas-condensate reservoir compositional

simulation, although the flowing bottom hole

pressure in the buildup period does not change

significantly with and without inclusion of

capillary number effects.

Nomenclature

BU build up

Bg gas formation volume factor

CCE constant composition expansion

CVD constant volume depletion

Cg isothermal gas compressibility

Cs wellbore storage coefficient

Ct total compressibility

D non-Darcy skin factor

DD drawdown

ft foot

k permeability

k2 permeability of zone 2 in radial composite

model

M parameter controls the variability of the

critical oil/gas saturation

krg gas relative permeability

kro oil relative permeability

m(p) pseudopressure

n1,n2 controls the weighting between the miscible

and immiscible relative permeability curves

Ncb the threshold value of capillary number

NTG net to gross ratio

p system pressure

pdew dewpoint pressure

PR Peng Robinson

RCP2 the ratio of zone 2 storativity to zone 1

storativity

RI2 inner radius of zone 2 in radial composite

model

S skin factor

scf standard cubic feet

Acknowledgements

The authors would like to express their gratitude to

the management of Iranian Central Oil Field

Company and South Zagros Oil and Gas Production

Company for supporting this study and permission to

publish this paper.

References

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