Timing of advanced water flooding in low permeability reservoirs

Available online at www.sciencedirect.comMININGScienceDirectSCIENCE ANDTECHNOLOGYEL SEVIERMining Science and Technology 19 (2009)0124 0128www.elsevier.com/locate/jcumtTiming of advanced water flooding in low permeability reservoirsXIE Xiao qing', JIANG Han-qiao', CHEN Min-feng', LIU Tong-jing', ZHANG Wei?'CMOE Key Laboratory ofPetroleum Engineering, China University of Petroleum, Beijing 102249, China'China Huayou Group Corporation, Beijing 100101, ChinaAbstract: It is very important to design the optimum starting time of water injection for the development of low permeability res-ervoirs. In this type of reservoir the starting time of water injection will be affected by a reservoir pressure-senstive effect. In orderto optimize the starting time of water injection in low permeability reservoirs, this effect of pressure change on rock permeability oflow permeability reservoirs was, at first, studied by physical simulation. It was shown that the rock permeability decreases expo-nentially with an increase in formation pressure. Secondly, we conducted a reservoir engineering study, 1om which we obtainedtainedanalytic relationships between formation pressure, oil production rate, water production rate and water injection rate. After ourphysical, theoretical and economical analyses, we proposed an approach which takes the pressure -sensitive effect into considerationand designed the optimum starting time of water injection, based on the principle of material balance. Finally, the correspondingsoftware was developed and applied to one block of the Jiangsu Oilfield. It is shown that water injection, in advance of production,can decrease the adverse impact of the pressure-sensitive efect on low permeability reservoir development. A water-flooding pro-ject should be preferably initiated in advance of production for no more than one year and the optimum ratio of formation pressureto initial formation pressure should be maintained at a level between 1.05 and 1.2.I Keywords: low permeability reservoir; water injection in advance of production; pressure-sensitive effect; starting time of waterinjection; deformation of porous medium1 Introductionlow permeability reservoirs.Combining physical simulation, analytical simula-During the process of reservoir development, for-tion and calculation software, the pressure-sensitivemation pressure will drop and the porous media of thebehaviour of low permeability reservoirs and its im-reservoir will deform, causing a pressure -sensitivepact on oil recovery was studied by us. A method iseffect. As a result, permeability and porosity will de-presented to determine the optimum timing of wa-crease, as well as oil well productivity. In order toter-flooding considering this pressure-sensitive effect.decrease the effect of pressure sensitivity, a method ofwater-flooding in advance of production is proposed2 Physical simulationsin view of this feature of elastic-plastic deformationof low permeability reservoirs. The pressure-sensitiveUsing typical cores from low permeability reser-effect has been widely studied by a number of re-voirs, the variation in permeability, given the condi-searchers through physical simulation experi-tion of various confinement pressures, was studied.mentsh . However, there are no study reports re-We conducted one-way pressuring and the circle ofgarding the relationship between pressure-sensitivepresuring and relief experiments. The major objec-effect and the timing of water floods. Some suggestedtive of the experiment was to investigate the impactapproaches were for the determination of tjming ofof pore structure and cage structural mechanics on ,water-flooding in advance of production, but thepermeability.pressure-sensitive effect had not been taken into con-The initial core confining pressure was 10 MPa.siderationoho. As a matter of fact, the timing of wa-The core was gradually pressurized from the initialter-flooding mainly depends on this pressure-sensi-value of 10 to 30 MPa and then slowly depressurizedtive effect. Because of this effect, it is required to im-and returmned to 10 MPa, with one datum recorded atplement water. flooding in advance of production forever中国煤化工Received 05 April 2008; accepted 11 July 2008TY.HCNMHGProjects 2003BA613-07-05 supported by the Program of National "Fifteen" Science and Tyatio FoundationCoresponding author. Tel: +86-10-89733096; E-mail addres: xiexiaoqing1205@163. comXIE Xiao-qingetal .Timing of advanced water fooding in low permeability resevoirs125The flowchart of the experiment is presented in Fig.enough, it will not fully recover, which means the1. During the experiment, a core was first placed in apermeability will suffer a great loss. The lower thehigh-pressure core holder. High pressure in the con-initial permeability, the greater the loss. If the coretainer was maintained with a hand-operated pump. Apermeability is high enough, it can almost resume itsconnection valve was opened to a pressure dampenerinitial value. In this case, the pressure-sensitive effectin order for the rock core to be maintained at a fun-will become weak as the initial permeability in-damental constant confining pressure. An air sourcecreases.was connected to keep the inlet pressure of the core2.3 Relationship between permeability and con-maintained at a steady level. The next step was tofining pressureopen the export valve and use a suction ball to createa sustained air bubble in the soap bubble flow meter.With the circle of pressuring and depressuring ex-The time how long it takes for definite gas volume toperiment, the relation between permeability and con-pass the flow meter was continuously recorded atfining pressure can be investigated. An exponentialleast three times with a second counter. Then the ex-relation between permeability and confining pressureperiment pressurization and relaxation of pressurein the circle of pressuring and relief of core No.1 iswas carried out.shown in Fig. 2.0.9Pressuring1.8+.7 tRelief“72?9占1.6一 101520253035>CFig.2 Relation between permeability and confining pressureDuring the pressuring period, the permeability de-Fig. 1 Experimental flowchartcreases gradually, while during the depressuring pe-1. Air source; 2. Air source valve; 3. Pressure control valve; 4. Pressureriod, the permeability increases gradually._gauge; 5. Air inlet valve; 6. Core holder, 7. Soap bubble flow meter;8. Confining pressure pump; 9. Pressure gauge; 10. Confining pressureAccording to the permeability variation curvesvalve; 11. Pressure transducer; 12. Pressure dampener,from different cores, the extent of the permeabilitydecline during the pressurizing process increases and2.1 Analysis of experimental resultsthe pemeability reversion degree reduces during theThe pressure sensitive effect experiment with dif-depressuring process with a decrease in the initialferent cores was completed and the results are shownpermeability.in Table 1.The permeability variation curves from differentcores in the pressurizing process show their nonlinearTable 1 Results of pessre-sensitive experimentfeatures. Exponential relations were found by curveInitialCyelical damageIreversible Depressur- Pressuringfitting.evaluationdamage. zing damageCore BbiliDegree of DamageimproveSince the variation in stress can be simulated using(103 um') damage rate (%)(%) mentrat (%)the confining pressure, the relationship between per-1.943 Weak9.66 .6.799.54meability and variation in stress of low permeabilityreservoirs was established from our experimental re-0.729 Strong 19.6512.478.2019.65sults. Replacing variation in stress with variation in0.30414.0910.1722.83formnation pressure, this relationship was thus ob-0.095 Strong 39.6027.1617.0839.60tained.0.119 Strong 36.60 24.3716.1436.606.426Weak7.49K= Ke(h-P)(1)7 93.195 Weak4.514.06where K is the permeability when initial formationNote: Pressuring; damage rate of rock: Dk;= (Kr K2)K; de~pressure drops to P (10- um), Ko the permneabilityundJer the condition of initial formation pressure (10-3pressurizing improvement rate of rock: Dkz= (K;-K2VKz,where K is the initial permeability, K2 the final pressurizingμm), ak the permeability variation factor (1/MPa)permeability and K3 the final depressurizing permeability.and P the initial formation pressure (MPa).2Relationship between initial permeability2.4中国煤化工re eftet on welland range of decline in permeabilityThe higher the initial permeability, the smaller theBaC NMH G.ction rnate for IDextent of permeability. If the core permeability is lowradial flow can be obtained as:126Mining Science and TechnologyVol.19 No.12xrhKK。dP3.2 Computation process2=B从。(2)1) Water saturation is calculated at each of the nthwhere 0。is the oil production rate (m'/d), B thetime step (s.")metric conversion factor (D), r the well bore radiusAccording to the pore volume balance:(m), h the net pay thickness (m), K。the oil rela-V"s." +Opu" +V"S"CLP" =V"S。"(5)tive permneability (f) and 从。 the oil viscosity(mPas).S"+l=1-S。(6)Substituting Eq.(1) into Eq(2) can yield:where Pp is the pore volume (m) and C。is the oilK.ea(_-)dp=&.土(3)compressibility (1/MPa).The initial value is the initial water saturation. Thewater saturation of each of the nth time step (sw" ), 2rhKwheren=B^旦. By integrating, Eq.(3) can becan be obtained.2) The water cut f。" and water cut f。" areexpressed as:calculated as follows:ζK.c1M0-)aP=[品_出k."/Pn___不.2rh rf"=.wr"/Hhw+k."/H%(7)where P.q is the bottom hole pressure (MPa), Pthe average formation pressure (MPa), r the wellf,"=1-f."(8)bore radius (m) and F the average oil drainage ra-3) The permeability at the nth time step K" isdius (m).calculated according Eq.(1):The relationship between the oil production rateand the formation pressure can be written as:K"=K° exp(- -a%(P, +0p"))(9)K。h4) The pressure variation per time step is calcu-[ e~(A-R-) -e*(0-月](4)lated.an In(F/r)LThe material balance equation is:Similarly, we can obtain Q. ,Q and 口，whereN.B。=NB.C(P-P)+(W;-W,)B.(10)Q。is the water production rate (m'/d), Qi the liq-where Np is the cumulative oil production (m), B。theuid production rate (m'/d) and Q the water injec-oil formation volume factor (f), N the initial oil intion rate (m'/d).place (m'), Boi the initial oil volume factor (), C thetotal compressibility (1/MPa), P: the initial formation3 Design for optimum timingpressure (MPa), P the current formation pressure(MPa), W; the cumulative water injection (m'), Wp the3.1 Design and calculation procedurescumulative water production (m) and Bw the initiala) According to basic parameters of both actualoil formation volume factor ().Establish the iteration for (n+1)th and nth timereservoir engineering and economic analysis, the wellsteps:spacing density and the number of oil producers andwater injectors are determined using a trial and errorN"'B。=BW.f-QP-*+)+(**"-w."*)B. (1)method.b) Any oilfeld development process can be dividedN,"B.=NB.C,(R-PI+(W" -W,")B。(12)into two phases. The first phase is the water floodingEq.(11)-Eq.(12):in advance of production and the second is the con-ventional water-flooding. The total development timeN."*B。=-NB.CPt + (W"*-oW")B. (13)can be divided into n time steps, where n should be aslarge as possible for greater accuracy. Considering thewhere:pressure-sensitive effect and according to the materialbalance equation, production targets are calculatedsw" = mQn"(OP°-ZsP -P")/OP. (14)for each time step. ,c) Referring to economical parameters supplied,ON,'中国煤化工; + P)DPp.°the net present value is calculated from the initialtime of water-flooding and the optimum timing of theCNMHG(15)water-flooding project can then be obtained.XIE Xiao qing ctaleconomic beneft is maximized. Early water-floodingsw* =m.Qm 9j.(P."+ZOP +OP*)OP.。projects will yield high oil recovery at higher costsand vice versa, late water flooding projects will re-duce the costs, but a lower oil recovery will bewhere Poo is the initial producing pressure dropachieved. Hence, there is an optimal timing to maxi-(MPa), OPm0 the initial difference between reservoirmize the economic benefit.As shown in Fig. 3, the x axis represents the injec-pressure and injection pressure (MPa), Qm° the ini-tion time, where negative values refer to advancedtial water injection rate (m/d), Qn the initial oilwater-flooding in advance of production; 0 refers tosynchronous injection and production and positiveproduction rate (m'/d), 4 is ith time step(d), fw thevalues refer to late water-flooding. The y axis repre-sents the net present value. From this graph, it is seenwater cut (①and f。the oil cut ().that by postponing the water injection initiation, theAccording to Eqs.(13), (14), (15) and (16)，pres-net present value increases at frst and then decreases.sure differences can be obtained:There is a maximum point of net present value andIfβ =Qp&°^Pg;(m.L.°B. -m2o&'f。B。the corresponding injection time at this maximum-m2Q9B.f.")point is the optimum time for water-looding.1500pB=-:亡0P(OP.9B.m.Lmf"宜1000+OP °m.Qn°B. +OP2°m.Qms +B.f.")B=P.°^P.°NB.C. +P.&*m.Q2m°B.,+QP2°m,Qm .18,.J.," + OP.°B.mQ2o&S"430 -10 10 3050thenOP*1=(B +B2)/B(17)Water flood timning (month)5) The water injection rate and oil producing rate atFig. 3 Relationship between water-flood timingthe nth time step are calculated.and net present valueThe water injection rate at the th time step is:As shown in Fig. 4, the optimum starting time ofK"(P°-Z4p,)water-flooding in advance of production is usually(18)less than one year and the corresponding pressureK°polevel is between 1.05 and 1.2 (0. The lower the for-mation permeability, the stronger the pressure-sensi-The oil production rate at the nth time step is:tive effect and correspondingly the earlier the startingtime of water flooding. While with the increase ofK"(P.°+Z4p)f"effective thickness, the pore volume becomes larger,(19)a larger water injection volume is needed and conse-quently, the water-flooding should be initiated earlier.where K° is the initial permeability (10- μm)+5m二h10mandK”the permeability at the nth time step.6) The net present value is calculated as:NPV=之(CI-C0),0+i)*where NPV is the net present value (10* yuan); io thei0203040~5discount rate (f); (CI CO), the net cash flow in yearPermeability (10*2m2)th (10* yuan); CI the cash inflow (10* yuan) and cothe cash outflow ( 10* yuan).Fig. 4 Relationship between permeability, net pay thicknessIn summary, given the arbitrary injection time ,and optimum time of water floodingthe production target at the nth time step can be ob-As shown in Fig. 5, the optimum time of water-tained. Furthermore, the oil recovery and net presentflooding is directly proportional to the permeabilityvalue at each time step can be obtained as well.varia中国煤化工-nsitive effct be-3.3 Calculation results analysiscomey variation factorYHC N M H Gilooding initiationFrom an economic viewpoint, the optimum timewill be earler.for water-flooding is the injection time when the$128Mining Science and TechnologyVol.19 No.1an increase in effective thickness and the permeabil-9外ity variation factor, an earlier initiation time of wa-ter-flooding is required.6tReferences0.02 0.04 0.06 0.080.1 0.121] Liu X, Lu W, Deng x, Christian M. Simulation of ran-Permeability variation factor (0dom crack generation in concrete members with uniformstress fields. Journal of China University of Mining &Fig. 5 Relationship between perimeability variation factorTechnology, 2006, 16(4):519- -522.and optimum time of water-flooding2] WuJ, Cao D Y. 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