Deliverability of wells in carbonate gas condensate reservoirs and the capillary number effect

Pet sci.(2009)6:51-56DOI0.1007/s12182-00900099Deliverability of wells in carbonate gas condensatereservoirs and the capillary number effectLi Yong, Hu Yongle, li Baozhu and xia jingResearch Institute of Petroleum Exploration and Development, Petro China, Beijing 100083, ChinaAbstract: With the development of the Tazhong No I carbonate gas condensate reservoir in China, ithas become more and more important to study the characteristics of gas condensate well deliverabilitA single-well radial simulator for dual-permeability reservoirs was established to study the influences offluid properties, permeability, and pressure drawdown on well deliverability with and without the capillarynumber effect. The simulation shows that well deliverability basically maintains its initial value and is notaffected by the capillary number when the formation pressure is higher than dew-point pressure. However,well deliverability drops rapidly when the formation pressure is lower than dew-point pressure. Even ifthe condensate dropout is very low, well deliverability without the capillary number effect reduces to 50percent of its initial value when reservoir pressure declines to 95 percent of dew-point pressure, but welldeliverability is significantly improved if the capillary number effect exists. The capillary number effect ismost significant when reservoir pressure is just lower than dew point pressure, then the effect decreasesthe reduction of well deliverability is mainly caused by the reduction of gas relative permeability of thematrix system near the wellboreKey words: Carbonate reservoir, gas condensate, capillary number effect, well deliverability, dual-osity medi1Introduction2005: Bengherbia and Tiab 2002: Blom and hagoort. 1998aFevang and Whitson, 1996; Tong et al, 2006). With theUnderground flow in gas condensate reservoirs usually development of the Tazhong No. 1 carbonate gas condensateexists as a single-phase gas flow under initial reservoir reservoir in China, it has become increasingly importantconditions when reservoir pressure is above the upper to investigate this type of gas condensate reservoir. Thedew-point pressure. However, with the depletion of gas characteristics of well deliverability were investigated andcondensate reservoirs, a relatively high liquid saturation will the capillary number effect was also studied using a finebuild up in the vicinity of the wellbore when the bottom- grid single-well radial compositional simulator for dualhole flowing pressure is below the dew-point pressure of the permeability reservoirscorresponding reservoir fluid. This is, known as condensateblocking(Boom et al, 1995). Condensate blocking will lead 2 Capillary number effect modelto a reduction in gas relative permeability, thus resulting inloss of well deliverability(Fussell, 1973). For example, inThe gas velocity is relatively high near the wellbore in gasthe Arun gas condensate reservoir, the largest liquid holdup condensate reservoirs, and the gas phase can carry part of theof the retrograde condensate reservoir was about 1%, but the condensate dropout to the surface. So oil saturation near thewell deliverability had been reduced nearly by half of the wellbore reduces with increasing gas relative permeabilityinitial value as the reservoir pressure dropped down below and weakening impairment by condensate blockage. Thisdew-point pressure(Mott et al, 2000a). However, for some phenomenon can be expressed by the capillary number effectgas condensate wells, significant loss in well deliverability model. There are many definitions of capillary number so far, butwould not occur as reservoir pressure falls down below dew- the conventional definition is written as follows( Qin et al, 2004)point pressure. This is due to the synthetic effect of lownterfacial tension of gas condensate reservoirs and high-N=gHgvelocity fluid flow near the wellbore. This synthetic effect canbe represented by the capillary number. In-depth research has where Ncp is the capillary number; Ug is the gas velocity in thebeen concentrated on conventional sandstone gas condensate direction of flow, m/s: u is the gas viscosity mPa: and o isreservoirs in this field, but few on carbonate gas condensate the gas-oil surface中国煤化工reservoirs(Asar and Handy, 1988; Ayyalasomayajula et alThe capillary nuCNMHGto modify gasrelative permeabi8b: Mott et al*Correspondingauthor.email:hyl@petrochina.com.cn2000b), which can be expressed by the model developed byReceived February 26, 2008Whitson et al(1999). The gas relative permeability, whenPet. Sci(20065156capillary number effect exists, can be described as follows: 3 Simulation model and related descriptionkrg=f,krel +(1-Sr)A compositional radial model was used to predict thesingle-well performance in dual-permeability carbonate gaswhere krg is the capillary number modified gas relative condensate reservoirs and the capillary number effect waspermeability; krn is the user-input immiscible, rock relative also taken into account. The grids of the model are builtpermeability at low capillary number; krem is a straight-line with 25(X direction) x 10(r direction)x 2(Z direction)miscible relative permeability at high capillary number value; 500 nodes. The Z direction grid is divided into two layersfi is a transition function depending on the gas capillary representing the matrix block system grid and the fracturenumber, and can be given bysystem grid, respectively. One producer is located at thecenter of the model. In order to capture the flow performancefr(3) near the wellbore, the grid is composed of logarithmicallyN)+1distributed radial nodes(du et al, 2004). In other wordsthe cell block in the center(near the wellbore) is the finestithand cell size increases with a logarithmic relationshipThe innermost node size is only 0.36 m, while that of theoutermost node is 340 m wide, The thickness of the matrix(4) layer is 30 m and its porosity is 0. 1; while the thicknessof the fracture layer is 10 m, and its porosity is 0.01. Althe models have the same outside boundary of 1, 300 mTo reduce the complexity of three-phase interaction in thewhere K is the rock permeability, 10 um; is the porosity; model, there is no aquifer in these models. Initial reservoiao is a constant depending only on rock properties; n is a pressure is a little larger than the dew-point pressure of thecoefficient;a and n are usually defaulted to be 0.65 and reservoir fuid. Table I shows the components of each samplerespectively.and their propertiesTable 1 Components of each sample and their propertiesComponents, mol%Maximum liquidWellyield in constantnameC, C i-C4 n-C4 i-Cs n-Csm3/m3elll86.341.420.560.210.360.230.250.500.580.650430.341.58555well288422.210.720.200.350.150.170.250.210.330.290.271.368.344311well393.840.910.190.030.070.030.040.050.070.100.090.090.641.14Gas well deliverability at different reservoir pressures was where (Ncp) is the relative productivity index with thethen calculated. It is defined in terms of the productivity index, capillary number effectwhere is the productivity index of gas wells, m/(dMPa Fs) productivity index with and without capillary number effewhich is defined as the ratio of gas flow rate to pressure dropIn Eq(7), A stands for the difference between relatiPr-p4 Results and discussionthe gas flow rate, m/d; P, is the current reservoir pressure, 4.1 Effect of fluid characteristicsMPa; and pwf is the bottomhole flopressure, MPaThe concept of relative productivity index was proposedFor gas condensate reservoirs, the larger the initial gas-for the sake of comparison between different cases and the oil ratio in the production well, the smaller the volume ofrelative productivity index is defined as followsetrograde condensed liquid, as shown in Table 1. Figshows the reduction in relative productivity index for a well(6) producing at different initial gas-oil ratios, where P Pp isthe ratio of reservoir pressure to dew-point pressure. In thehere J, is the relative productivity index;J, is the simulation, the initial reservoir pressure is slightly higher thanproductivity index at reservoir pressure p, m/(d- MPa); and the dew-point pressure of the gas, that means pi/pp>1.WhenJa is the productivity index at initial reservoir pressure p, Prpp>l, the relative productivity index is approximatelyI/(d- MPa)equal to unity, pr中国煤化工 s at the initialA parameter A/, is defined to investigate the capillary value; when p/.number effect on the productivity indexthe well initial gasCNMHGnS the smallerthe maximumliquid yield, and the greater the well deliverability reduction△J=J(Na)-J(7) For Well 3, the maximum liquid yield in a CVD expePet. sci.(2009)6:51-56is only 1. 14%, but the well deliverability decreases sharplywith decreasing pressure at the initial GOr of 5,900 m/msimilar to the arun gas condensate field(Mott et al, 2000a)4311mmand the well deliverability reduces by 50 percent when the5900m3m3reservoir pressure is 95 percent of dew-point pressure, then itdecreases slowly with pressure and even has an upward trendunder the effect of various factors There is a little differenceof productivity index between the reservoir fluids with initGoR of 4.311 m/m' and that of 5.900 m/m,, but both ofthem have a relatively large difference with that of 2, 555 m/Figs. I and 2 indicate that the reduction in relativeproductivity index decreases significantly when the capillarypnumber effect exists. Fig. 3 shows the capillary number effecton relative productivity index. The capillary number effectFig. 3 The capillary number effect on relative productivity indexbecomes important when reservoir pressure reaches dew-dditionally, Figs. 4 and 5 show the oil saturation andpoint pressure, and the capillary number effect on relative gas permeability distribution in the matrix block and fractureproductivity index was significant only when the reservoir network in Well 1. Oil saturation in the matrix block near thepressure is slightly lower than the dew-point pressure of the wellbore is higher than that in the fracture network,whichcorresponding gas. With decreasing reservoir pressure, the leads to a significant reduction in gas relative permeabilitycapillary number effect on relative productivity index drops of the matrix block. The gas relative permeability of thegradually Capillary number is related to fluid viscosity, fluid fracture network changes little because of lower oil saturationflow velocity and interfacial tension, the larger the initial in the fracture network near the wellbore. Therefore, theGOR, the greater the capillary number effect. That is, the deliverability loss of wells in carbonate gas condensatedeliverability of gas wells can be improved further with the reservoirs is mainly caused by the reduction in gas relativeexistence of the capillary number effectpermeability of the matrix block.as-oil ratio2555mm35900m3m3Matrix oil saturation1.0(a)Fig. 1 Relative productivity index without capillary number effectGasoil ratio2555m3m3中国煤化工0.6CNMHGp ipFig. 4 Oil saturation distribution in the matrix block (a)and in the fractureFig. 2 Relative productivity index with capillary number effectsystem(b)at final simulation step( GOR is 2, 555 m/m)Pet. sci.(2009)6:51-56simulation is terminated ) The maximum oil saturation canreflect the impairment by condensate blocking and its effecton gas relative permeability. When p /pp is equal to 0.957,the maximum oil saturation in the matrix block of kmd is lower than that of the others while the maximum oilsaturation of the fracture system is higher than those of theole in well production at the early stage, and the smallerthe matrixsignificant the role of thefracture system and the smaller the impairment by condensateblocking. Therefore, the loss of relative productivity index ofK=l md reservoir is lower than those of the others Whereasat the final simulation time. the maximum oil saturation of0090154202815039705200the matrix and the fracture systems of the low-permeabilityreservoir is larger than those of the others. That is, the gasrelative permeability loss near the wellbore in this reservoiris the largest, which leads to the largest reduction in relativeoductivity indexThe capillary number effect on deliverability of gas wellswas studied and shown in Fig. 7. It can be concluded that thesmaller the permeabilities of the matrix block and the fracturesystem, the larger the capillary number effect on the wellrelative productivity index except for the low permeabilitycarbonate gas condensate reservoirs, for which the capillarynumber effect is the smallest2Km=imD, KF100mDK=10mD,Fig. 5 Gas relative permeability distribution in the matrix block(a) and in >0.6the fracture system(b) at final simulation step(GOR is 2, 555 m/m)4.2 Effect of permeabilityThe effect of permeability on well deliverability is morecomplicated because of severe heterogeneity of carbonategas condensate reservoirs. Four scenarios with a ratio offracture permeability to matrix permeability of 100: 1 wereestablished using PVt data of Well 2. The values of matrixFig. 6 Relative productivity index versus p/pp for differentpermeability were set 1, 5, 10 and 50 mD, respectivelypermeability scenariosand other parameters maintained the same value. Fig. 6shows the relative productivity index curves, where Km isthe matrix permeability and k is the fracture permeabiliIt can be concluded that the smaller the matrix and fractureK=10mD,K=1000mDpermeabilities, the larger loss the well deliverability. WhenK=50mD, K=5000mDthe matrix permeability and fracture permeability increase tospecific values, variation of permeability has slight infiuence.Additionally, when the reservoir pressure is slightly belowew-point pressure, the reduction in relative productivityindex of a low-permeability reservoir (Km=l mD)is lessthan those of the others the conclusion that the smaller thereservoir permeability, the smaller the productivity index中国煤化工loss, may be drawn only when ppp is less than 0.9. Table 2YHCNMHGpresents oil saturation of different systems(matrix systemand fracture system) at different simulation time-steps(theFig. 7 The capillary number effect on relative productivity index attime-step when ppp is equal to 0.957 and the time-step whendifferent permeabilityPet. sci.(2009)6:51-56Table 2 Oil saturation comparison of different systems at different simulation timesMaximum oil saturationMaximum oil saturation at final simulationSwhen p pp=0.957,%Matrix blockFracture networkMatrix blockFracture networkK=lmd. K=100mD0.4300.501K=SmD, K=500mD0.313Km=lOmD, K=1000mD0.438Km=50mD, K=5000mD0.3760.0330.01234.3 Effect of pressure drawdownDifferent gas production rates were set from PVt data ofWell 2, to study the influence of pressure drawdown on well=20x10′mddeliverability. The well gas production rate(O)specifiedwere5×10,10×10,15×10,and20×104md, respectivelyGreater gas production rate corresponded with higher 2pressure drawdown on relative productivity index without orwith the capillary number effect. Fig 8 shows that the loss ofwell deliverability (i.e, relative productivity index)increasesth increasing pressure drawFigs. 9 and 10indicate that the higher the pressure drawdown rate, the moresignificant the capillary number effect on relative productivitypFig. 10 The capillary number effect on relative productivity index atQ=5×10m3ddifferent pressure drawdown rate1.0Q=15×10m3dQ=20x10m3d5 Conclusions1)The above-mentioned analysis indicates that condensateblockage has a significant effect on well deliverability and ifthe capillary number effect does not exist, the impairment bycondensate blocking will be exaggerated2) Well deliverability will basically maintain its initialvalue when reservoir pressure is higher than dew-pointpressure. However, it will drop rapidly just when reservoirpressure is smaller than dew-point pressure, even if thep, ipmaximum liquid yield in a CVD experiment is only aboutone percent, well deliverability also decreases to 50 percentFig. 8 Relative productivity index curves at different pressurof its initial value at the early production phase, then itdrawdown rates without capillary number effectdecreases little or even has an upward trend. The loss of welldeliverability is mainly caused by the reduction of gas relativeQ=5×10mdpermeability of the matrix systemQ2=10×10my3) Well deliverability can be significantly improved if theQ=15×10mdcapillary number effect exists. The capillary number effect isinsignificant when reservoir pressure is higher than dew-pointpressure, and the capillary number effect is most significantjust when the formation pressure is smaller than dew-pointpressure, then the effect drops with the depletion of thereservoil4) Under the same conditions, the higher initial gasoil ratio (i. e, the larger maximum liquid yield in a CVDexperiment)will let中国煤化工 lity loss:Alsothe lower permealthe higher well gasCNMHigher pressureFig.9 Relative productivity index curves at different pressure deliverabilitydrawdown rate) will result in significant reduction in wedrawdown rates when capillary number effect existsPet. sci.(2009)6:51-565) The lower the permeability of matrix and fracture421-429(SPE51367)system, the larger the capillary number effect on well relative Boom w, wit K, Schulte A M, et al. Experimental evidence for improvedproductivity index, except for low permeability carbonatecondensate mobility at near wellbore conditions. 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