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A Numerical Simulation Studyon Mixing of Inert CushionGas with Working Gas in anUnderground Gas StorageReservoirNilÜfer KilinÇer, Fevzi GÜmrahPublished online: 29 Oct 2010.

To cite this article: Nilfer Kiliner, Fevzi Gmrah (2000) A NumericalSimulation Study on Mixing of Inert Cushion Gas with Working Gas in anUnderground Gas Storage Reservoir, Energy Sources, 22:10, 869-879, DOI:10.1080/00908310051128219

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869

A Numerical Simulation Study on Mixing of InertCushion Gas with Working Gas in an Underground

Gas Storage Reservoir

NILÜFER KILINÇERFEVZI GÜMRAHPetroleum and Natural Gas Engineering DepartmentMiddle East Technical UniversityAnkara, Turkey

The cushion gas, providing the pressure energy necessary for withdrawal of working gas,makes up the largest part of the investment in underground gas storage projects. The sug-gested method of reducing this cost is the replacement of some part of the cushion gas withless expensive inert gas, such as nitrogen. In the replacement, there might be some prob-lems due to mixing between natural gas and inert gas. Turkey has sharply increasingdemand for natural gas. The constant imported gas and varying demand throughout theyear due to the distinct seasons in the region are the reasons for severe need for gas stor-age in Turkey. There are no underground storage units in Turkey, but two gas reservoirs inthe Thrace basin grant the potential for gas storage. From this point of view, the gas mix-ing problem is investigated for a typical gas reservoir by coupled use of a gas reservoirsimulator and a transport model. A two-dimensional (2-D), single-phase numerical gasreservoir simulator is developed to obtain the pressure distribution during production andinjection cycles. The velocity distribution is found by using these pressures. Then the two-dimensional transport model is used to calculate nitrogen concentrations around the injec-tion wells. Both models are used effectively for controlling the mixing problem in anunderground gas storage reservoir.

Keywords inert cushion gas, single phase numerical gas reservoir simulator, under-ground gas storage reservoir

The inventory represents the gas residing in the storage horizon. It is made up of two parts,cushion and working gas. The working gas is regularly bought and sold. The cushion gas, pro-viding the reservoir pressure necessary to conduct storage operations, represents a substantialcomponent of the investment (Moegen & Giouse, 1989). The replacement of some part of thecushion gas in an underground storage by inert gas has significant economic interest.

Nitrogen is the most acceptable inert gas for fully meeting underground gas storagerequirements, since it is widely available, cheap, and not corrosive (Berger & Arnoult, 1989).The inert gas must not be reactive with the products and materials with which it comes into

Energy Sources, 22:869–879, 2000

Copyright © 2000 Taylor & Francis

0272-6343 / 00 $12.00 1 .00

Received 16 July 1999, accepted 27 September 1999.The authors thank TPAO Production Group for supplying information about the gas field.Address correspondence to Fevzi Gümrah, Petroleum and Natural Gas Engineering Department,

Middle East Technical University, METU, 06531, Ankara, Turkey. E-mail: fevzi@metu.edu.tr

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contact: surface equipment, well completion, reservoir rocks. It must be pure substance andnot constitute an explosive mixture with natural gas. In general, nitrogen meets these require-ments.

Several projects involving the substitution of cushion gas already in place have been stud-ied by France, the United States, and Denmark. The injection of inert gas before natural gasinjection has been performed since 1979 on the storage of Saint Clair Sur Epte (France), andthe replacement of 20% part of cushion gas with nitrogen was achieved (Laille et al., 1989).In addition to this, at Tonder Aquifer in Denmark, again 20% of the cushion gas is recoveredwith the replacement of nitrogen (Labaune & Knudsen, 1987). Some simulation studies weredone by Laille in Cerville Velaine (France), and their studies also showed the possibility ofrecovering some portion of the cushion gas (Laille & Coulomb, 1986). This subject also wasstudied by Fasanino and Molinard (1988).

However, the important question concerning the behavior of storage containing inert gasas a part of the cushion focuses mostly on the mixing between natural gas and inert gas.Turkey is newly faced with the wide usage of natural gas and has increasing demand for gas.Also, natural gas is imported from abroad. However, there are no underground gas storageunits in Turkey. A candidate gas reservoir for underground gas storage is being studied forstorage purpose. In this study, the mixing problem is investigated by coupled use of two mod-els, a numerical gas reservoir simulator and a transport model.

Numerical Gas Reservoir Simulator

The 2-D gas flow equation in a porous medium is

(1)

The definition of transmissibility (Ts) is

(2)

The 2-D finite-difference equation, linearized by simple iteration of the transmissibilities,is

(3)

where i = 1, 2, . . . , Nx; j = 1, 2, . . . , Ny. In Eq. (3), the superscripts m and m 1 1 refer to theold and new iteration levels, respectively. Equation (3) is solved for unknown pressures byusing the pointwise successive overrelaxation method (PSOR) (Kilinçer, 1999).

Transport Model

The 2-D transport model computes the changes in concentration over time caused by theprocesses of convective transport, dispersion, and mixing from fluid sources. Pressuresobtained from the developed numerical gas reservoir simulator are used to calculate the veloc-

5 u Vb

a c D t i, j

1Bg i, j

n1 1 21

Bg i, j

n

1 Tx i, j 1 1 2

n1 1 m

P i, j 1 1n 1 1 m 1 1

2 P i, jn1 1 m1 1

2 Tf i, j 2 1 2

n1 1 m

P i, jn1 1 m1 1

2 P i, j 2 1n 1 1 m 1 1

1 qsci, j

Tx i 1 1 2, j

n1 1 m

P i 1 1, jn1 1 m1 1

2 P i, jn 1 1 m 1 1

2 Tx i 2 1 2, j

n 1 1 m

P i, jn 1 1 m 1 1

2 P i 2 1, jn1 1 m 1 1

Ts 5 b c ksAs

l gBg D s

q

qx b c

q scAxkx

a c l gBg qPqx

D x 1q

qy b c

q scAyky

a c l gBg qPqy

D y 1qsc

a c q sc 5

Vb

a c q

qt

u q sc

a cBg

870 N. Kilinçer and F. Gümrah

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ities. The model, simulating the transport of the substance in a miscible process, was devel-oped by Konikow and Bredehoeft (1978). The pressures obtained from Eq. (3) are used to cal-culate the gas velocity at each grid point from Eq. (4) (Shaw, 1988):

(4)

The equation describing the 2-D transport and dispersion of injected inert gas is (Konikow &Bredehoeft, 1978)

(5)

Equation (5) is solved by using the method of characteristics (Shaw, 1988).

Conversion of a Gas Reservoir as a Storage Medium

The candidate gas field in Turkey is considered as a case study. The reservoir properties and asketch of the thickness distribution of the reservoir are given in Table 1 and Figure 1a, respec-tively. The field is newly discovered and it is at the initial stage of production. It is also plannedthat the gas field will be considered as an underground gas storage reservoir in the near future.Therefore, it was decided to conduct a preliminary simulation study for the conversion, whichis based on the following four scenarios: (1) depletion of the natural gas reservoir, (2) injectionof nitrogen to recover some portion of cushion gas, (3) injection of natural gas for storage, (4)production of natural gas during the heating season. The above procedures are summarized inTable 2. The production and injection wells on the field are shown in Figure 1b.

Depletion of Natural Gas Reservoir

Before converting the gas reservoir into a storage environment, it is decided to produce nat-ural gas from three wells (M1, M2, M3) until the abandonment pressure of 1,000 psia isreached. The production rates are 80 MMscf/day for well M1, 10 MMscf/day for well M2,and 6 MMscf/day for well M3.

q C D z

qt5

q

qx D zDi, j

qCqy

2q

qx D zCui, j 2

C9 Wu

ui, j 52 ks q g

l g u Ñ P i, j 2 c g D z

Gas-to-Gas Mixing Problem in Gas Reservoirs 871

Table 1Reservoir properties

Average porosity 21%(range = 15–25)

Matrix permeability Average = 35 mD(range = 12–200 mD)

Original average reservoir pressure 2100 psia at 1,150 mReservoir temperature 65°CThickness Average = 62.5 m

(range = 30–70 m)Reservoir depth Average depth = 1,150 m

(range = 1,110–1,475 m)Lithology LimestoneType of structure Anticline

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872 N. Kilinçer and F. Gümrah

Replacement of Cushion Gas with Nitrogen

Then, the nitrogen is injected into four wells (N1, N2, N3, N4) for 210 days (0.58 year) toraise the average reservoir pressure from 1,000 psia to 1,200 psia. The injection rate is calcu-lated by using Beggs’s correlation (Beggs, 1984). The resulting plot for tubing size of 2 in.is presented in Figure 2. The injection rate is found to be 13 MMscf/day. In order to controlthe spreading of nitrogen around the injection wells, the concentrations are monitored by run-ning the transport model for each 30-day period throughout 210 days. The constraint is cho-sen as the concentration of nitrogen (1,000 ppm) cannot reach to half the distance between theproduction and injection wells. In order to observe the distance to which the nitrogen con-centration reaches, the cross sections A–A9 and B–B9 shown in Figure 2 are taken. The dis-tance of A–A9 is 3,225 m and that of B–B9 is 2,175 m. The injection of nitrogen is ceased whenthe average reservoir pressure reaches 1,200 psia. The total amount of injected nitrogen is10,920 MMscf. An amount equal to 22.6% of the cushion gas is replaced with nitrogen. Thenitrogen concentration at the end of 210 days (when nitrogen injection ceased) did not exceed21% (677 m) of the distance of cross section A–A9 . The nitrogen concentration map and crosssection A–A9 is shown in Figures 3a and 3b.

38

Figure 1. (a) Sketch of the thickness distribution of the reservoir. (b) Well locations and crosssections (A–A 9 and B–B 9 ).

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Gas-to-Gas Mixing Problem in Gas Reservoirs 873

Injection of Natural Gas for Storage

Natural gas is injected from three wells, M1, M2, M3, at a rate of 13 MMscf/day. The injec-tion is continued until the original average reservoir pressure of 2,100 psia is reached. Toreduce the injection time and to operate the storage system effectively, the three wells (M4,M5, M6) are put into operation (Figure 1b). Then natural gas is injected at a rate of 13

Table 2Injection and production periods of natural gas and nitrogen

Production Injection period period (days) (days) Inert gas (nitrogen ) Natural gas (methane)

Active Active injection production or Produced

wells with Injected injection wells or injected Number rates amount Number with rates amount of wells (MMscf/day) (MMscf) of wells (MMscf/day ) (MMscf)

0–5,281 — — — — 3 M1 = 80, 506,976M2 = 10, M3 = 6

— 5,281–5,491 4 N1 = N2 = 10,920 — — —(210 days) N3 = N4 = 13

— 5,491–8,401 — — — 6 M1 = M2 = 226,980(2,910 days) M3 = M4 =

M5 = M6 = 13Case 1 — — — — 6 M1 = M2 = 11,7008,401–8,551 M3 = M4 =(150 days) M5 = M6 = 13Case 2 — — — — 6 M1 = M2 = 95,4008,401–8,551 M3 = M4 =(150 days) M5 = M6 = 106

Figure 2. Bottomhole well pressure versus gas rate.

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MMscf/day from six wells. The pressure distribution is obtained from the 2-D reservoir sim-ulator and the nitrogen concentration is monitored using the transport model. The injection ofnatural gas causes the squeezing of nitrogen around the nitrogen injection wells. After 360days of natural gas injection, the nitrogen concentration is continued to extend to 25% (806m) of the distance A–A9 . Since nitrogen concentration around the nitrogen injection wells ishigher than that of the center of the reservoir, the mixing continues from the higher concen-tration through the lower concentration due to dispersion. The concentration of nitrogen after2,880 days of natural gas injection (when natural gas injection is ceased) reached 35% (1129m) of the distance of A–A 9 (Figures 4a and 4b).

Operation of a Storage Field

The heating season is taken as 150 days. The natural gas is produced from each of six wells(M1, M2, M3, M4, M5, M6) at a rate of 13 MMscf/day. The new pressure distribution isobtained from the reservoir simulator and then it is found from the transport model that thenitrogen concentration distribution does not change significantly during the production of nat-

874 N. Kilinçer and F. Gümrah

Figure 3. (a) Nitrogen concentration distribution after 210 days of nitrogen injection (Cmax =1,000,000 ppm). (b) Nitrogen concentration profile , along cross section A–A 9 after 210 days ofnitrogen injection (LA–A 9 = 3,225 m).

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ural gas. This means that natural gas can be safely produced without producing nitrogen fromthe reservoir. After 150 days of production from these six wells at 13 MMscf/day, there wasno change in nitrogen concentration when compared to the results of natural gas injectionafter 2,880 days. In order to observe the effect of production rate on nitrogen concentration,the rate was increased to 106 MMscf/day. Again there was no significant change in the arrivaldistance of nitrogen between injection and production wells (Figures 5a and 5b). The reasonmight be the short production duration for lowering the pressure at the center of the reservoir.It can be concluded that the operation is again on the safe side during natural gas production.In order to observe the movement of nitrogen concentrations toward the natural gas produc-tion wells, an extreme case run is done. In this run, production time is increased to 2125 days(5.8 years). Natural gas is produced again from six wells at a rate of 106 MMscf/day. After2,125 days of natural gas production, the increase in nitrogen concentration is observedaround the natural gas production wells as shown in Figures 6a and 6b. Similar results are alsoobtained for the B–B9 cross section.

In this study, the molecular diffusion coefficient Do is taken as 4.13 3 10 2 8 m2 for theCH4–N2 binary system (Sigmund, 1976) during natural gas injection and 3.307 3 10 2 7 m2 for

Gas-to-Gas Mixing Problem in Gas Reservoirs 875

Figure 4. (a) Nitrogen concentration distribution after 2,880 days of natural gas injection (injectionwells M1, M2, M3, M4, M5, M6) (Cmax = 1,000,000 ppm). (b) Nitrogen concentration profile alongcross section A–A 9 after 2,880 days of natural gas injection .

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the N2–CH4 binary system (Newberg & Foh, 1988) for nitrogen injection and natural gas pro-duction. The dispersivity is used as 315 m (Fetter, 1993).

Conclusions

The need for understanding the flow and displacement processes as affected by mixing anddispersion in a porous system is important, both in design and operation of gas storage reser-voirs. In this study, the mixing problem is investigated by the combined use of a developednumerical gas reservoir simulator and a transport model. The following conclusions weredrawn from this study.

1. The developed numerical gas reservoir simulator is an efficient predictive tool fordeveloping a gas reservoir, determining the best production and injection scheme toimplement the operations properly and economically. Also, it is useful in controllingconversion operations.

876 N. Kilinçer and F. Gümrah

Figure 5. (a) Nitrogen concentration distribution after 150 days of natural gas production (Cmax =1,000,000 ppm) (production rate = 106 MMscf/day). (b) Nitrogen concentration profile along crosssection A–A 9 after 150 days of natural gas production .

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2. A transport model is used to obtain the changes in concentration over time caused bythe processes of convective transport, dispersion, and mixing from fluid sources. Thecombined use of the developed numerical gas reservoir simulator and a transportmodel provided the control of the spreading of nitrogen concentrations during theperiods of injection of nitrogen as cushion substitute, injection of natural gas for stor-age purposes, and production of natural gas in the heating period.

3. In underground gas storage reservoirs, some part of the cushion can be replaced byinert gas to minimize cushion cost. In this study, 22.6% of the cushion is replaced withnitrogen. This replacement may bring considerable savings in investment.

Nomenclature

A area, L2

Bg gas volume formation factor, L3/L3

C concentration, M/L3

Gas-to-Gas Mixing Problem in Gas Reservoirs 877

Figure 6. (a) Nitrogen concentration distribution after 2,125 days of natural gas production (Cmax =1,000,000 ppm) (production rate = 106 MMscf/day). (b) Nitrogen concentration profile along crosssection A–A 9 after 2,125 days of natural gas production .

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C9 concentration of inert gas in a source or sink fluid, M/L3

D longitudinal or transverse dispersion coefficient, or apparent diffusion coefficient, L2/tk permeability, L2

P gas pressure, M/Lt2

t time, tTs transmissibility to gas in s direction, (L3/t)/(M/Lt2)u interstitial velocity, L/tv Darcy velocity vector, L/tVb bulk volume, L3

W volume flux per unit area (positive sign for production, negative sign for injection), L/tg gas gradient, M/L2t2

D t time increment, tD z reservoir thickness, Lm g gas viscosity, M/Ltr density, M/L3

f porosity, fraction

Superscripts

n time stepm iteration level

Subscripts

i x-direction spatial indexj y-direction spatial indexs spatial, x, ysc standard conditions, 60°F and 14.7 psiax x directiony y direction

Unit Conversions

a c volume conversion factor, field units = 5.614583 , SI units = 1b c transmissibility conversion factor, field units = 1.127, SI units = 0.000000864

References

Beggs, H. D. 1991. Production optimzation using NODAL analysis, pp. 146–148. OGCI Pub-lications. Oil & Gas Consultants International, Inc., Tulsa, OK.

Berger, L. C., and J. P. Arnoult. 1989. Production of inert gas for partial replacement of nat-ural gas trapped in an underground aquifer storage reservoir, SPE 19089. Presented at theSPE Gas Technology Symp., Dallas, TX, June 7–9.

Fasanino, F., and J. E. Molinard. 1988. Mixing in underground gas storage. Proc. NATOAdvanced Study Institute on Underground Storage of Natural Gas Theory and Practice,Ankara, Turkey, pp. 301–325.

Fetter, C. W. 1993. Contaminant hydrogeology, pp. 71–73. Englewood Cliffs, NJ: Prentice-Hall.

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Kilinçer, N. 1999. Mixing of inert cushion gas with natural gas in underground gas storagereservoirs: A numerical simulation study. M.Sc. thesis, Middle East Technical University,Ankara, Turkey.

Konikow, L. F., and J. D. Bredehoeft. 1978. Computer model of two dimensional solute trans-port and dispersion in ground water, MOC-2D. U.S. Geol. Surv.,http://wwwpah2o.er.usgs.gov/projects/frhr/goode91.html.

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Laille, J. P., and C. Coulomb. 1986. Underground storage in Cerville-Velaine, France: A casehistory in conversion and inert gas injection as cushion substitute, SPE 15588. Presentedat SPE 61st Annual Technical Conference and Exhibition, New Orleans, LA, October5–8.

Laille, J. P., J. E. Molinard, and A. Wents. 1989. Inert gas injection as part of the undergroundstorage of Saint-Clair-Sur-Epte, France, SPE 17740. Presented at SPE 64th Annual Tech-nical Conference and Exhibition, San Antonio, TX, October 8–11.

Moegen, H., and H. Giouse. 1989. Long-term study of cushion gas replacement by inert gas,SPE 19754. Presented at SPE 64th Annual Technical Conference and Exhibition, SanAntonio, TX, October 8–11.

Newberg, M. A., and S. E. Foh. 1988. Measurement of longitudinal dispersion coefficients forgas flowing through porous media, SPE 17731. Presented at SPE Gas Technology Sym-posium, Dallas, TX, June 13–15.

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Gas-to-Gas Mixing Problem in Gas Reservoirs 879

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