Dynamic determination reserves of the underground gas storage

Journal of Harbin Institute of Technology( New Series), Vol. Il, No 5, 2004Dynamic determination reserves of the underground gas storageTAN YIfei谭羽非(1. Institute of Engineering Mechanics China Seismological Bureaus Postdoctoral Program, Harbin 150001, China, E-mail: Tanyufei2002@ 16of Municipal and Environmental Engineering, Harbin Institute of Technology, Harbin 150001, China)Abstract: One of the key problems in the use of underground gas storage is frequent leakage. It can lead to theual gas storage amount being less than that accounted for. Combining numerical simulation and parameter au-to fit, this paper ascertains the dynamic variation of the pressure in the storage reservoir, adjusts the actualjecting and producing gas to fit the accounted pressure with the tested pressure, obtains the gas leakage of thestorage, and then determines the difference between accounted amount and leakage amount. The result is theactual reserves of the storage. The simulation result shows that the method presented can provide a theoreticfoundation for estimating the leakage amount, thereby ensuring the actual reserves, searching the leakage routeand reducing leakage by adjusting the storage methodKey words: underground gas storage; reserves; fraction step solution; numerical simulation; parameter autoit: leakage problemCLC number TU996. 7. TE822 Document code: AArticle ld:10059113(2004)05051603Leakage problems frequently occur when we makeuse of water driving gas fields near the city to store nat- 1 Establishment and Solution of the mathematicural gas. Leakage is caused by the two followingModelpects: firstly, when the gas is produced, the pressurein the storage area descends and the water at the bottomFlowing equation:rushes in, causing the natural gas to flow through thv(a,vp)+8,HQv/V=route of least resistance. This allows some gas into thwater stratum to be bondage saturation gas, and thusH(2+(c+6)2)ide leakage occursondly, when the gas is injec- where d, is potential function VPI= VppigVZ,theted into storage areas, even though the pressure onlykk, (s)reaches its highest permission value( original stratumg, gas w, water; arressure), the outside gas must be injected into thethe permeability rate; k is the relative permeabilitystorage area with higher pressure, which may force therate, u,, B, are respectively the viscidity and volume co-gas out through the stratum covered with natural gas efficient of the fluid, Qw=QP. is the volume flux inand thus the outside leakage occurs. These causesmake the actual gas storage amount often less than thatstandard state. c.c, are the condensation coefficient ofaccounted for( the sum of injecting-producing gas and the rock and fluidunderlay stratum gas). For instance, the Leroy UnderAt the well points 8= I and at the non-wellground Natural Gas Storage in Wyoming had a serious points 8a =0eakage problem during its operation between 1975 andSaturation balance equation of gas and liquid:1982, and finally had to stop productionS。+S(2)Combining numerical simulation and parameter au- Force balance equation of the capillary:to fit, this paper ascertains the dynamic variation of the(S)=中。-△rZ(3)pressure in the storage reservoir, adjusts the actual inInitial condition: original distribution of the pres-cting and producing gas to fit the accounted pressure sure and state saturations at the beginning of simulationith the tested pressure, registers the gas leakage from operationthe storage area. and then determines the differencecondition. make the storage boundary asbetween accounted amount and leakage amount in the中国煤化工 it closedactual reservesTHCNMHGReceived 200-03-12Sponsored by the Postdoctoral Found Foundation of Heilongjiang Province( Grant No. LRB-KY01026)516·Journal of Harbin Institute of Technology( New Series), Vol. 11, No 5, 2004District C in field M is the water driving gas reser-The established three-dimensional seepage models voir and its area is (2.8 x4.5)km23). It is built into(1)-(3)are a group of three-dimension partial dif- a natural gas storage after it is turned into exhaustedferential equations which have two ranks and are non- storage by producing 70% of the original reservoirlinear singular and non-stable constants. The un- The exhausted pressure is 2. 84 MPa, and after contin-knowns are Pr, Pw,Se, S and their solutionery uously injecting 2. 75 x 10m' of cushion gas the stordifficult. The method of fissionable fractionas a- age begins to run. There are six injecting-producingdopted to work out the model[21wells and four observation wells. The injecting-producing cycle of the storage is one year, and each produ2 Dynamic Determination of the Actual Reserves cing and injecting period is 170 days in which there are12 days the wells are closed. Because the storage con-The gas and water pressure Pe, Pw in the storage tinuously runs for five years, the injecting-producingare related with the physical characteristic parameters speed remains constant. The injecting-producing aof the original storage and with the injecting-producing mount of the six wells are respectively W, W2: Q=5.0amount and time, so the dynamic change of the stored x10*(m/d):W4, Ws: Q=7. 5x*(m/d):Wsamount can be reflected by the pressure change of the W6: Q=9.4x10(m /d)observation well and injecting-producing well. If thereThe measured boundary conditions duringis leakage, the calculated pressure error of the well isning arevery great compared with the actual pressure. Otherwise,the error is small. The calculation steps of actualreserves are as follows1)Original condition pan 148=02)Boundary condition ap/an I1)According to the known dynamic and static paAccording to the actual storage area, the simula-rameters, simulates the pressure with time changes tion area is carved up into block center grid systemwhen the injecting-producing amount satisfies the peak with AX= AY= 100 m, AZ=5 m of space step and28×45×4gids. The values of Z(P),C(P)2)The grid nodes of the observation well where B, (P), capillary pressure, curve of relatively permea-the difference between calculated and measured pres-sures Ap= max(peol Pct is the area where the maxi-bility rate, grid configuration, static and dynamic pa-rameters of the storage and the boundary treatment aremum leakage exists.howed in ref3)Using least squares method, sum up the squareUsing MATLAB calculation software, it compilesof the difference between calculated pressure and meas- the calculation program. Fig. I shows the pressure vari-ured pressure to be an object functionation of the observation wel122 with the time change2(4) obtained by numerical simulation. Fig. 2 is the compar-ison curve of the simulated and measured pressure of4)Put the injecting-producing gas amount that is the observation well22 with the time variation. Tab. Iadjusted again and again into the math model, and compares the relative errors between the pressures bework out the pressure in storage, then calculate expres- fore and after the injecting-producing gas amount beingsion(4), making the object function have the least adjusted, where we can find that the most leakage oc-value E minE. The difference between the injecting- curs in the area of W33 and the pressure variation ofproducing amount after being adjusted and the actual a- the observation well is relative with that of injectingmount is the leakage of the storageroducing well with only about 0. 5% of overall averageQt=∑∑(Qmm-Qm-n)+relative error after the amount is adjustedQetnroduct),where k is the number of well, iis the number of injec-ting day, andi is the number of producing day6.0q is the actual injecting-producing amount, qthe calculating injecting-producing amount.中国煤化工(5)the actual reserves amount Qct:O(6)CNMHwhere Qdesign is the accounted amount of gas storageI/years3 Simulation InstanceFig 1 Pressure variation with the time in Well225l7Journal of harbin Institute of Technology( New Series), Vol. 11, No. 5, 2004storage,the paper confirms the pressure variation instorage at arbitrary injecting-producing circulation, anfinds that the leakage direction can be judged throughcomparing the calculated pressure with that measuredpressure in the observation well. Further, adjusting theactual injecting-producing gas amount to let the calculated and measured pressure be directly related to eachother, we can determine the actual reserves amountnamIc2) The uneven injecting-producing running stateactual pressuremay intensify the leakage, so the injecting-producingFig 2 Comparison of the simulated and measured pressure gas amount in each well should be scientifically alloca-in Weln22ted to reduce the leakage according to the static andTaRelative error cordynamic fields of parameters on the basis of satisfyingthe modulation of city gas peakRelative Error with theRelative Error with the3)a decrease in the pressure difference by pro-actual Injecting-producing calculation Injecting-producing ducing gas is more than an increase by injecting thegas amount/%same amount of gas. According to theoretical analysis0.55is because Kp(s,)>Krl(S) and Pe(Se)>P.(S.). That is to say, the variation of the relative in2.550.4filtration rate and capillary pressure when producing isgreater than that when injecting. So, producing speedW443.67and amount should be strictly controlled in order to avoid too much pressure decreasing, too rapidly prickingforwards the bottom water and too wide scope the preswhere the relative errore=-×100%sure funnel spreads toPThe overall leakage after 5 years of injecting-prcReferencesducing running can be worked out by formula (5):Q-≈1.347×10°m[1 TAN Yufei, LIAN Leming, YAN Mingqing. Simulationsearch of underground gas storage reservoir in foreigFurther by formula (6), the actual reserves amountcountry[ J]. Natural Gas Industry, 1998(6): 23( in Chi-Qnese)Qn=8.15×103-1.347×103=6803×10(m3)[2 LV Tao, SHI Jimin, LIN Zhenbao Decompostion Algo-As so far. the actual reserves amount is 6. 803xrithm in Area[M]. Beijing: Science Press, 1992(in10m'after 5 years of equal quantity injecting-produ[3] YOUSSEF T. Hamade"Experimental study of formationcing cyclebehavior om imdergpimd storage"[A]. SPE 7164[C]51.]:[s.n.],1992Conclusions[4] TAN Yufei. Simulation Research of Underground GasStorage Reservoir in Depleted Gas Field[ D].Harbin1)By setting up the dynamic injecting-producingHarbin Institute of Technology, 1998math model of water- driven underground natural ga中国煤化工CNMHG万捋数据