Numerical Simulation and Analysis of Migration Law of Gas Mixture Using Carbon Dioxide as Cushion Ga

Journal of Harbin Institute of Technology( New Series), Vol 21, No 3, 2014Numerical Simulation and Analysis of Migration Law of Gas Mixture UsingCarbon Dioxide as Cushion gas in Underground gas Storage reservoirChuan-Kai Niu, yu-Fei TanSchool of Municipal Environment Engineering, Harbin Institute of Technology, Harbin 150090, ChinaAbstract: One of the major technical challenges in using carbon dioxide(CO, )as part of the cushion gas ofthe underground gasreservoir(UGSR) is the mixture of CO, and natural gas. To decrease the mixingextent and manage the migration of the mixedan understanding of the mechanism of CO, and natural gasmixing and the diffusion of the mixed gas in aquifer is necessary. In this paper, a numerical model based on thethree dimensional gas-water two-phase flow theory and gas diffusion theory is developed to understand thismechanism. This model is validated by the actual operational data in Dazhangtuo UGSR in Tianjin City, Chinae validated model, the mixed characteristic of CO, and natural gas and the migration mechanism of themixed zone in an underground porous reservoir is further studied. Particularly, the impacts of the followingfactors on the migration mechanism are studied the ratio of CO, injection, the reservoir porosity and the initialoperating pressure. Based on the results, the optimal CO, injection ratio and an optimal control strategy tomanage the migration of the mixed zone are obtained. These results provide technical guides for using CO, ascushion gas for UGSR in real projectKeywords: underground gas storage reservoir UGSR ) cushion gas; carbon dioxide; mixed zone; porousCLC number: TE82Document code. AArticle d:1005-9113(2014)03-0121-08iffusion In these models the coefficient for theIntroductionolecularsion term is much smaller than thecoefficient for the convection diffusion term So theseThe technology of using CO, as cushion gas for models cannot accurately predict the mixing extent ofUGSR has many advantages, including replacing the the two gases and the change of these concentrationslarge deposits of natural gas in UGSR, achievinIn this paper, a numerical model is proposed tocarbon sequestration, reducing the greenhouse effect, predict the mixture and diffusion of CO2 and natural gasand bringing high economic benefits, etc. According in aquifer UGSR, based on the three dimensional gasto the statistics from United States in 20102-4, the water two-phase flow theory and the gas diffusiontotal capacity of cushion gas in its running 411 UGSR theory. Firstly, the pressure equation and the saturationamounts to 117.67×10°m3.If20% of the cushiequation for the reservoir are discretized and solvedgases are replaced with CO2, as much as about 23. 54x using finite difference method, so the transient pressure10%m natural gas deposits can be further utilized, distribution and saturation in the reservoir are obtainedhich brings the significant social and economic Then implicit difference scheme is used to discretize thebenefitsgas diffusion equation, through which the concentrationThe major technical challenge of using Co, as the distribution of CO2 and natural gas of reservoir areushion gas in reservoirs is the mixed of CO, and derived based on thedistrilnatural gas. The studies have shown that the mixed of reservoir and saturation. The accuracy of the modeltwo gases will cause the increase of impurities in the further validated using the actual operation data fromeak shaving gand the deof the Dazhangtuo UGSR, China. Using the validated modelcalorific value 6-7. The mixed zone of co and natural the mixed characteristic of CO2 and natural gas and thegas was caused by both molecular diffusion and migration mechanism of the mixed zone in anconvection flow. However, the previous mathematic unde中国煤化工 r is further studiedmodels&-9 often neglected the influence of molecular PartiCNMHGollowing factors on theeceived 2013-11-27Sponsored by the National Natural Science Foundation of China( Grant No. 51276048CorrespondingauthorChuan-kaiNiu.E-mail:niuchuankai1228@163.com121Journal of Harbin Institute of Technology( New Series), Vol 21, No 3, 2014migration mechanism are studied: the ratio of CO2 production rate of mixed gas and water phaseinjection, the reservoir porosity and the initial wellhead( kg/(operation pressure. Based on the results, the optiminjection and negative while production and zero whileCO, injection ratio and an optimal control strategy to themanage the migration of the mixed zone are obtainee2. 2 Diffusion Equations of Mixed GasCO, as cushion gas for UGSR in real projecl or usinThese results will provide the technical guides foThe underground reservoir has good fractalharacters and the mixed gas diffusion follows Fickslaw. The total mass flow rate of the gas diffusion2 Development and Solution of Mathematical process contains convection and molecular diffusionModelConvective flow of fluid is the mass transfer caused byseepage flow of mixed gas, while molecular diffusion is2.1 Gas-Water Two-Phase Seepage Equationthe molecular motion from high concentration range toFollowing assumptions have been made to simplify low concentration range caused by concentrationthe mathematical model: (1) temperature is uniformly difference of mixed gas. Considering the effects ofdistributed in the horizontal direction: (2)natural gas dimension factor and coupling mass, diffusionoluble. Since the seepage is governed by gravityequations of mixed gas are expressed in Egs.(5)andand capillary pressure and it also considers the (6)213, in which A and B represent CO, and naturalcompressibility of rock and fluid, and the anisotropy of gas respectively.the rock theage can be described by theKKextended darcy la10-111Q、"J+·( hMS D,VC)Gas phaase(MCAS2中)VH6·4=HBa7dpBPPV·HMCn=VWater phaseky+v·( HMRS ODa(MBcrs, d)KKH6·qm=HasHSqB=H(6)P+SCBwhere Dar, is fractal diffusion coefficient of CO, in thehere K is absolute permeability of mixed gas( um)medium of natural gas(m2/s)K, and Ke are relative permeability of mixed gas anddiffusion coefficient of natural gas the medium of CO 2water phase; u, and Po are dynamic viscosity of mixed (m2 /s):M, and Ma are molecular weight of CO,andhase(Pa·s); s and slatural gas; CA and CB are molar concentration of COare gas anwater saturation; is effective porosity; 8 is a function 2. 3 Auxiliary Equationsof gas source and8= 1 at the wellhead and 8=0 not atthe wellhead H is dimension factor; C, and C,areSaturation equlum equationisothermal compressibility of mixed gas and waterphase, which can be calculated as in Eq (3), and BThe constraint equation of capillary pressurewhich is a function of fluid saturation is as followsd B are volume coefficients of mixed gas and waterf(s)phase, which can be calculated as in Eq (4)Now, it can complete the variable resolution ofPg, pS, Ca and CB using the coupled eqp, dpof Eqs. (1, 2, 5-8). Moreover, the coefficient of eachVB;B。(4)parameter in the equations needs to be calculated basedon the auxiliary equations, in which the detailedwhere V and Pp are the volume(m)and density of derivation processes are shown in Ref[ 14mixed gas(kg/m')under formation condition; Vn andBe=B(PR); B=B(Pw): Cr=CE(pPs are the volume(m')and density of mixed gaC =C(p):P =P (S);K=K(s,);u(p).(kg/m)under standard condition; V and p are the中国煤化工 Boundary Conditions(m') and density of water( kg/m')underformation condition; Vs and purs are the volume(m)CNMH Gon is used at the outeroundary of Ugsr as followsand density of water( kg/m')underHowever, the second boundary condition is givenand water phase( Pa); q, and q are unitat the head of the injection-production well of UGSR122Journal of Harbin Institute of Technology( New Series), Vol 21, No 3, 2014follows in which n is normal directionReservoir pressure equation and saturationlation are discretized using finite element methodnf(x,y,2,t)and the discrete form of the equations is as followsThe boundary condition of the UGSR in thesandwich is given as follows[N]lp}"-[G]{S△t[E]"-[0])p}"+(△t:[R11)[F])S=[o]*p"+[F]"SThe initial pressure and initial saturation of UGSRhich are certain functions are given as followswhere [K],[R] and [E] are rigidity matrix; [G]P(x,y,z,0)=φ(x,y,z)(12) [N,[ F] and [O] are coefficient matrix(13)Based on the calculation method of the binaryThe initial pressure gradient in the reservoir of the spread system, gas diffusion equations are discretizedUGSR is given as followsand solved using finite difference method where thedpfractal diffusion coefficient inorous: mealculated as in Eq (19)182 5 Solution of Numerical modelDuring the operation of UGSRs in aquifer with3-d-0 a(19)cushion gas, the edge and bottom water are not usually where D is diffusion coefficient of CO, or natural gasto contact with the mixed zone. Therefore, the pressurein the homogeneous Euclidean space(m/s),andfields and concentration fields of natural gas andcushion gas are respectively solved in the pure naturalrepresent CO2 and natural gas respectively; 6 isdiffusion attenuation index and e=1/H-2gas field and pure cushion gas field, while the coupled called Hurst coefficient is a characteristic parameterpressure fields and concentration fields in the mixture reflected diffusion slowing-down effect of moleculargas field are solved using the iterative methodBrownian motion in different fractal structuresaturationcapillary pressure Eg(8)into gas-water two-phaseTaking CO, for example, first of all, Eq (5)canseepage Egs.(1-2)and then eliminating the variablesbe converted into the following formP and s, the simultaneous equations of p and S,areCa dca dc=obtained as followspaH+sC(15)KKKK apKK/herb=MKKM,s, idzSHp(CP'-S, CP-1)3+(1-S)CrNon-isometric 8 points implicit scheme of Ec(20)is discretized using finite difference method asThe reservoir space of UGSR is a type of porfollows. Where, T is time stepmedia with fractal characteristics[ I5 The relative+-cth-+-cthhctermeability of gas phase which are not fixed values in2u 2the above equations are changing with the difference ofore fractal dimension and porosity of porous mediaex ca+li +e 2. i)The relative permeability of gask is calculatedhshas in Eg (17)16-1K=Cl d,A2(1-2A(d-2)d-A2-A2=+2A3-24-A4)(17)H中国煤化工where d is pore fractal dimension of porous media; rCNMHGand rma are minimum pore size and maximum pore size(μm);λ is aperture ratio of porous media,andA(21)r/r C is a constant related with the structure ofSimilarly, the diffusion equation of natural gas isreservoir spacediscretized. Firstly, it is assumed the initial123Journal of Harbin Institute of Technology( New Series), Vol 21, No 3, 2014concentration of reservoir, the pressure field and( CAi+I, CRi+I)as the input conditions. The iterationssaturation field at the next time step are calculated are completed once meeting the conditions of I Pntlaccording to the equations of the discrete pressure andPRi+1I