WATER BREAKTHROUGH SIMULATION IN NATURALLY FRACTURED GAS RESERVOIRS WITH WATER DRIVE

466Journal of Hydrodynamics ,Ser. B,2005,17(4):466 - - 472China Ocean Press, Beijing - Printed in ChinaWATER BREA KTHROUGH SIMULATION IN NATURALLY FRACTUREDGAS RESERVOIRS WITH WATER DRIVEZHANG Lie-hui, FENG Guo-qing，LI xiao-ping， LI YunState Key Laboratory of Oil and Gas Reservoir Geology and Exploitation，Southwest Petroleum Institu-te, Chengdu 610500, China, E mail: zlhdyyzbn@ 163. com( Received Jan. 17, 2004)ABSTRACT: In the fractured water drive reservoirs of Chi-saturationna，because of the complex geological conditions, almost allK- formation permeabilitythe active water invasions appear to be water breakthrough- relative permeabilityalong fractures, especially along macrofractures. These sealproduction ratethe path of gas flow, thus the remaining gas in the pores mi-fluid potentialxes into water, and leads to gas- water interactive distribu-- porositytion in the fractured gas reservoir. These complicated frac-. viscositytured systems usually generate some abnormal flowing phe-nomena such as the crestal well produces water while thecapillary pressuredowndip well in the same gas reservoir produces gas, or thethe exchange termsame gas well produces water intermittently. It is very diffi-- fracture spacingcult to explain these phenomena using existing fracture mod-upstream weighting factorels because of their simple handling macrofractures withoutδ -- shape factorconsidering nonlinear flowing in the macrofractures and theξ -- inertial factorlow permeability matrix. Therefore, a nonlinear combined-flowing multimedia simulation model was scessfully devel-oped in this paper by introducing the equations of macrofrac-SUBSCRIPTStures and considering nonlinear flow in the macrofracturesmacmacrofractureand the matrix. This model was then applied to actual frac-tured bottom water gas fields. Sensitivity studies of gas pro-microfractureduction by water drainage in fractured gas reservoirs were- matrixcompleted and the effect of different water drainage intensityx---- x -directionand ways on actual gas production using this model were cal-y -directionculated. This model has been extensively used to predict thez -directionproduction performance in various fractured gas fields andl-一o，g,wproven to be reliable.1. INTRODUCTIONKEY WORDS:fractured gas reservoir, water break-Simulation of multiphase flow in heterogene-through，water invasion， numerical simulation， implicitous two porosity reservoirs such as naturally frac-treatmenttured system is a difficult problem from both a res-ervoir description standpoint as well as a numericalNOMENCLATUREone. The reservoir is represented by two collocated0l-time incrementcontinuums, i. e. a fracture continuum and a ma-T - fracture transmissibilitytrix continuum. The fracture continuum has highV。-- bulk volumeperr中国煤化工volume while the ma-YHCNMH G .Project supported by the Teaching and Research Award Program for Outstanding Y oung Teachers for Higher Edu-cation Institutions of Ministry of Education of China and the Fund of Ph. D. Student Supervisor of Ministry of Education ofChina (Grant No:20040615004).Biography :公HA教据.ie hui (1967-). Male, Ph. D. ，Professor467trix continuum has low permeability and high stor- considered the interaction between fluid flow andage volume.rock- mass deformation. Zhang-24] developed a su-Simulation of naturally fractured reservoirs per dual porosity model by introducing larger aper-has received much interest since the extension of ture fractures and a new combined fracture media ,Warren and Root's'1 model to multiphase systems which is used to quantitatively simulate waterby Kazemi et al.L241. Further developments were channeling through macrofracture. Based on the a-made by Iffly et al.t5]， Yamamoto et al.bove models, we have developed a two- phase ( gasKleppe and Morsef] ,Rossen-8J and Thomas et and water) and multiple fracture media simulatoral. [9] and others. These models include laboratory to simulate the fluid flow phenomena in naturallyinvestigations of oil and gas recovery from individ- fractured water drive gas reservoir by establishingual matrix blocks and simulation of single and mul-independently combined macrofracture equationstiphase flow in fractured reservoirs. Most of the and considering nonlinear flow in the combinedmultiphase models account emphatically for the macrofractures and the low permeability matrix u-viscous, gravity and capillary forces, or a mixture sing a fully implicit formulation. The simulatorof them. In these models， usually the matrix can handle the reservoirs that contain arbitraryblocks are assumed as isolated block surrounded by combination of macrofractured, microfractured anda continuous fracture medium. The matrix blocks unfractured areas. In addition, our model has suc-act as sources or sinks to the fractures， which are ceeded in completing 24 single- well history matchthe main flow channel. This kind of models is with abnormal production phenomena for actualcalled dual porosity model. The other model is du- fractured water drive gas reservoirs. Sensitivityal- permeability model, also considering the matrix studies for water drainage production gas in the ac-to matrix flow.tual gas reservoir were carried out. The resultsIn recent years, the accurate modelling of ma- were used to direct actual production of the gastrix- fracture transfer has been the most important reservoir.aspect of the simulation of naturally fractured res-ervoirs. Numerous papers have appeared in the lit- 2. MODEL DESCRIPTIONeraturel0-16) discussing various approaches for im- 2. 1 Flow equationsproving the handling of the transfer in black-oilThe reservoir is assumed to be comprised of asimulation where the interaction between capillary continuous combined macrofracture system，a con-and gravity forces plays an important role. The tinuous microfracture system and continuous mamain deficiency of the original dual-porosity model trix blocks. The combined macrofracture system iswas the treatment of the gravity terms in the ex-formed by superimposing the larger-aperture frac-change terms. Several approaches have been protures on the local microfractures.The main flow inposed to account for gravity effects to enhance the the reservoir occurs along with the fractures withdual- porosity concept. A summary of the various local exchange of fluids between the matrix and theapproaches can be found in Gilman and Kazemilssurrounding fractures. But water breakthroughnd Fung and CollinsI1-11.1] and Yin[18] andcan be described by fluid flow through the com-ZhangL02. This area of research is reeiving more bined macrofracture grids. Each grid block is as-and more attention in recent years.sumed to have known properties, geometric shapes .However, people have paid lttle attention to and so on.the treatment of complex fluid flow in high perme-Following are the equations describing fluidability macrofracture and low permeability matrix. flow in the combined macrofracture, the microfrac-Conventional fractured gas reservoir models cannot ture and matrix are written in the differencereflect water breakthrough phenomena and explain forms.some abnormal production behaviors in naturallymhinndnor-fracture system:fractured water drive gas reservoir because of their中国煤化工simple handling macrofractures without consider- ( ATFCHCN MH G,0({+1)ing nonlinear flowing in the macrofractures and thelow permeability matrix. .Liu23] set up a fluid- solid coupled flow model(l*+")me + (I9+))mem= OB,for fractu布格据permeability oil reservoir, which468()2](1)and the gravity forces within the exchange termssimulate the behavior of a single matrix block sur-rounded by fractures that may contain several dif-For the microfracture system:ferent fluids. It can be calculated in the followingform,(OT ("t'2JφD)1+1)+ (T{+1Oφ{+1)) mic-me -I.me (or mic)→m=8λ mu (or mic)-m (中,m一 Plimrc(or mi) )(q{*+1)mie + (I+)mc-mVec[-m terms represent matrix/ frac- low velocity non- Darcian flow phenomena in theture fluid exchange and act as source or sink terms low permeabilitv matrix. so these models cannotin the microfracture ( or combined macrofracture) effec中国煤化工ure performance andwhich can be calculated as a function of viscous，matcYHCNMHGphenomenainsomecapillary and gravity forces.‘ The exchange terms reservoirs. Therefore， the paper has improved thecontrol the movement of fluids between the matrix linear Darcian flow equation by comprehensively u-and the microfracture (or the combined macrofrac- sing the laboratory results and theoretical researchture) wihi布 数据id cell, and the exchange terms achievements.469For the combined macrofracture system or 4.IMPLICIT TREATMENT OF FLOW EQUA-fracturing system，many formula for high-velocityTION OF THE RESERVOIR .nonlinear flow were drawn based on a handful ofSmall grid spacing around the combined mac-laboratory experiments and theories. One of such rofracture are usually required to properly accountformula of binomial high- velocity nonlinear flow for saturation changes in the vicinity of the com-model is extensively used,bined macrofracture. In order to maintain the sta-bility of the finite differential equations, an implic-it treatment of the nonlinear terms in the macro--VP= u/k元+ 500(9) fracture, microfracture and the matrix equations isused.For gas and water phase, we can obtain gen-In the gas reservoir model, the primary varia-eral flow equation as follows.bles are gas pressure and gas saturation. The mod-el equations may be expressed in vector forms as-VP = u/(k,)v + ζ?(10)Rm(Pm,Sam ,P,Therefore，we can obtain a flow equation inRme(P.,Spm,Pmie.,Sgmic,Pwe.Sgmac)|= 0 (14)the same form with Darcian equation，Rm(P.Sm.PmireSmienPmeSmwc-VP1= u/(k'k,)u(11)where the elements of the vectors are given by thematrix, microfracture and combined macrofracturewhereequations written in residual form.k’= u/(u/k + 5pruvken)The non-linear set of equations expressed byEq. (14) can be solved by Newton Raphson’:For the low permeability matrix， recent exmethod applied simultaneously to the set of thetensive experiment results show that there existremarkable low-velocity non- Darcian flow andequations. The following is solved at each iterationpseduo- starting pressure gradient phenomena. Formulti-phase fluid flow， a pseduo-Darcian flow e-pox,rRmquation was proposed and is used successfully.Jm-mic Jm-mie7 'That is,Jmie-m J mtcJ mic-macJnac-m J mec-mic J meRm0=-!t(VP,一。n)(12)(15)μwhere Jm，Jmie and J m are respectively the Jacobianwhere Yo1 is pseudo-starting pressure gradient.Combination of Eq. (11) and Eq. (12) resultsmatrices for the matrix，microfracture and macro-in the following comprehensive nonlinear flow e-fracture models. Jmr -mi and J mwic -m represent the cou-pling between the matrix and microfracture, Jm-mequation,and J mc -. for the matrix and macrofracture, Jand Jfor microfracture and combined macro-VPI-a3Y。= u/{[βk +(1一β)员']ka}初(13fracture.The unknown vectors arewhere Eq. (13) represents linear Darcian flow if aequals0 and β equals 1, it represents high- velocity8Xmic = (8Pmc,8Sgmic)T, 8Xmw = (δP me,8Sw )T,non- Darcian flow if both a and βare 0, it represents .low- velocity non- Darcian flow if both a and β equal.x中国煤化工.MYHCNMH Gwhere δ indicates change over iteration.Equation (16) are solved simultaneously inthe same manner as presented by Vinsome-25].470through the whole production history.5.2 The effect of ways and intensity of water5. RESULTS AND DISCUSSIONSdrainage production gas on actual gas pro-The model presented in this paper was valida-ductionted by its application to field data from 24 abnor-Based on matched geological model for Areamal phenomena wells. After getting satisfactory 5，this section establishes an ideal model with 15Xresults，the model was used to investigate the 15X 15-grid system and 50m equal spacing in x andeffect of water drainage ways and intensity on gas y direction. We assume that there are 2 wells in therecovery. .reservoir with daily gas production rate of 1 X5.1 History match and prediction for actual gas 105 m2 and 5X 105 m2 respectivlely, and the gas res-producers with abnormal production phe-ervoir is fully flooded after three years of produc-nomena in Area 5，Zigong，Chination.Area 5 is a complicated fracture gas reservoirwith highly developed macrofracture， located inZigong，China. The gas reservoir is characterizedby low porosities (about 1% for the matrix, 0. 8%Hisory MalhPeditionfor the fracture) and low permeabilities，common-. 120|ly around 0.026md for the matrix and 2 md for the80|fracture. Because of its complex geological condi-40|tions，almost all the water invasions appear to be19641972198019881996water channeling along macrofractures.' T hesecomplicated fractured systems usually resulted insome abnormal flowing phenomena such as the cr-estal well produces water while the downdip wellδin the same gas reservoir produces gas， or thesame gas well produces water intermittently.History MathPrdictionTherefore，in order to clearly understand30CalauaedWaer Poution Ratethese abnormal production phenomena， we havedone 24 single-well history matching and predic-案。tion with abnormal production phenomena in the988reservoirs.Hsory MachPredictconThe production schedule was entered in termsRaeof monthly average gas output rate for each well.We completed production history match for 24wells，with satisfactory results. Figure 1 shows199%6the history match of water production rate, shut-inwell and bottomhole pressure for a typical produc-tion well of 24 wells from startup through Dec. Fig. 1 History match map of Well w1071994. History match for different kinds of wellsrepresent various kinds of abnormal production 5.2. 1.The effect of water drainage ways on pro-phenomena. For example， the crestal well pro-duction behavior .duces water, but the downdip well in the same gasWater drainage ways，which are extensivelyreservoir produces gas, or the same gas well pro-used in Sichuan, China, include internal drainage,duces water intermittently. Subsequent field dataexternal drainage and combination of the two. OIwere not used in the history match in order to pro- th中国煤化工°means that watervide a measure of reliability of our model predic- drairYHCNMH(he water- blocked re-tions. The only model update performed was togions uver tne gas- waier contact， while externalenter the actual monthly well gas output rate.one indicates water drainage wells are located inWater production rate, shut-in well and bot-the water regions below the gas water contact.tomhole pressure data were compared between cal-However，only the internal and the combined wayculated and督題1 field results, with satisfaction,471are most effectively used in water flooded gas res- Table 1 Different water drainage schemeservoir.' Therefore, we designed three water drain-WaterWater drainage ratesage schemes with daily water drainage rates are de-Schemedrainagetermined by actual water drainage capacity for eachWel 1Well 2scheme (Table 1). The results calculated by ourmodel were shown in Fig. 2. It can be seen that:AInternal150(1) External water drainage can slow downInternal andpressure draw-down scale of the reservoir, reduc-B200externaling water invasion rate to some extent，but thedraw -down scale is relatively small. In addition,B:100300because external water drainage cannot directly reduce water invasion rate of water flooded regions,net water invasion rate increases inside the reser- 5.2. 2 The effect of water drainage intensity onvoir.production behavior(2) Although formation pressure caused bySimulation has been completed by using theinternal drainage draws down more quickly than internal way. The daily water drainage rates arethat caused by external one，internal drainage can 200m3 ，400m and 800m3 respectively. The resultsdirectly reduce water invasion rate into the reser-are showed in Fig.3. It can be seen that:voir. As a result, this way can reduce net water(1) Gas production rate and formation pres-invasion rate inside the reservoir effectively.sure draw- down scale increases with the increase of(3) Because net water invasion rate caused by water drainage intensity.internal way is small, corresponding daily produc-(2) During the initial period of water drain-tion gas rate and gas recovery of the reservoir is age, net water invasion rate and water gas ratiohigh while water- gas ratio is low.grows with water drainage intensity.As a result, internal way is more reasonableAs a result, the key to stabilize gas produc-and effective than external one for controlling wation capacity of the reservoir is to ensure that wa-ter flooded area and the improvement of gas pro- ter drainage intensity is higher than water invasionduction capacity in the reservoir.rate. This was supported by actual gas productionbehavior of the reservoir.元422居x500，800T20054000 800 T2xSQW/10'm216C sQW10*m'40086 400800 1200 30 400 800 1200SQW/10*m'SQG/10*m*Fig. 2 Efect of different water drainage ways on gasFig.3 Efect of different water drainge intensity ongasproduction中国煤化工YHCNMH G472processes in naturally fractured reservoirs[J]. SPE6. CONCLUSIONSRes. Eng. ，1991，11: 477-484.(1) A numerical non-linear combined flowing[11] FUNG LARRYS. K. and COLLINSD. A. An evalu-ation of the improved dual porosity model for the sim-model that properly simulates water breakthroughulation of gravity effects in naturally fractured reser-in naturally fractured gas reservoir is developed. Avoirs[J]. JCPT, 1991, 30(3): 61-67.fully implicit technique is applied. The numerical[12] SAIDI A. M. Simulation of Naturally Fractured Reser-model has been shown to be reliable and applicablevoirs[A]. SPE 12270[C]. 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