two tracer test method for quantification of residual oil

8/9/2019 Two Tracer Test Method for Quantification of Residual Oil

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Society of Petroleum Engineers

SPE 252 1

Two Tracer Test Method for Quantification of Residual Oilin Fractured Porous MediaB.P. Grigorievich, Moscow State Oil 8 Gas Academy, and J .S. Archer, Imperial College

SPE Members

Copyright 1993, Society of Petroleum Engineers. Inc.

This paper was prepa red for presentation at the SPE Interna tional Sympos ium on Oilfield Chemistry held in New Orleans, LA. U.S.A.. March 2-5, 1993

This paper was selected for presentation by an SPE Program Comm ittee following review of information contained in an abstract submitted by the author@). Contents of the pape r.as presented, have not been reviewed by the Society of Petroleum Engin eers and are su bject to correction by the author s). The m aterial, as presen ted, does not necessarily reflectany position of the Society of Petroleum E ngine ers, its officers, or m embers. Pap ers presen ted at SPE meetings are su bject to publication review by Editorial Com mittees of the Societyof Petroleum Eng ineers. Permission to copy is restricted o an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledg-ment of where and by whom the paper is presented . Write Libra rian, SPE , P.O . Box 833836, Richardson, TX 750833836 U.S.A. Telex, 163245 SPEUT.

The metho d for identification of residual oil from the dataof flow of two tracers with different solubility in oil isdeveloped for fractured-porous mervo irs.

The solubility of tracer in the immobile phase (oil,retrograde condensate) leads the lag of the tracer frontpropagation behind the displacement front.The ratio of thetracer front velocity and the velocity of total flux is determ ined

by the saturation of imm obile phase. It allows us to determin ethe saturation of the residual hydrocarbon phase from the dataof flow of two tracers with the different magnitude of theconstant of tracer distribution between the water (gas) and oil(condensate).

A new equations for flow of two tracers in fractured-porous media re derived. Both diffusive and convectivemechanisms of the tracer mass transfer between blocks andfractures are taken into account. The hydraulic interactionbetween fluxes in cracks and in m atrix is described as well.Problem of one-dimensional flow leads to the linear system ofhyperbolic equations. Analytical solution for 1D problem ofinjection of water (gas) with the two tracers is obtained.Results of theoretical prediction oftr cers wave propagationare in a good agreement with the data of laboratoryexperiments.

Exact explicit formulae for propagation of theconcentration wave of two tracers allows us to solve aninverse problem. Method for improved characterization offractured-wrous media from data of twotracers concentrationson the ex of re se ~o irs developed Measurement of the firsttracer concentration allows us to determine the followingproperties of fractured-porousmedia: fractional flow function(fraction of the flux via fracturesin the total flux); fraction ofporous space of cracks in the total space of fractured-porousmedia; coefficient of mass transfer between fractures andmatrix. Information about the concentration of the secondtracer permits us to determine the saturation of the immo bilephase separately in fractures and in blocks.

INTRODUCTION

The problem of identification of the residual oil afterwaterflooding is important for making a decision about thetertiary EOR methods application.

A method of two tracers test is used to determine thesaturation of residual oil in porous media [I]. The first traceris dissolved in the water phase only, the second tracer couldedissolved in water and oil both. The first tracer moves with

the velocity of flow in porous media. The velocity of thesecond tracer is lower comparing with the velocity of the f i t

one (chrom atography effect). The delay of the second tracercomparing with the first one allows us to determine thesaturation of oil in the porous m edia.

In fractured-porous media the fast breakthroug h of theinjected water via fractures and capillary imbibition in matrixform the contrast saturations of residual oil in blocks and infissures [2] Distribution of the residual o il between blocksand fractures can be determined by two tracer methodapplication.

In the paper presented we investigate how to determinesaturation of residual oil in blocks and in fractures andproperties of fractured-porous media from the two tracer testanalyses data.

Analogous problem arises with the gas recycling in gascondensate fractured-porous reservoirs. Saturation of thehydrocarbon liquid (retrograde condensate, residual oil) inmatrix and in fractures are different. Measurements ofconcentration of two co mponen ts with the different solubilityin hydrocarbon liquid allows us to determine saturations inblocks and in matrix. If the initial reservoir fluid containedsour componen ts (carbon dioxide, nitrogen) theycan be usedas a natural tracers lean gas canbe injected into the reservoirwithout additives. f the reservoir fluid contained hydrocarboncomponents only sour components could be used as anariilicial tracers.


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TWO TRACER TESTMETHOD FOR QUATIFICATiON OF RESIDUAL OIL INFR CTURED OROUS MEDIA

SPE 025201

W.ith the waterflwd mineral salts could be used as anatural tracers.

Describe the process of two tracers flow in fractured-

porous media inthe framework of double-porosity approach[3.4]. Introdu ce concentratio ns of the first tracerci of the

second onex il saturations si, porositiesmi low velocitiesWi. self perme abilities of the porou s media ki. relative phasespermeabilities for the, water phase KHi (Fig 2). Index i=l Wrelates to the system of fractures, index i=Y tothe system,of matrix.

We assume that wateris incompressible. T he addition ofthe low con centrated tracers does not change water density.So pressuresin blocks and in cracksare equal.

Flow in fractured-porous media can be described as aflow in porous me dia with self permeabilities and porosities incracks and in blocks (Fig 3). Flow is described by the motionequation in block s and in cracks separately.On he boundarybetween blocks and fissures conditions of continuity ofpressure and of a mass fluxare satisfied. This problem can be

solved for heterogeneous porous media with periodicalvariation of coefficients by the method ofan asymptoticaveraging [5.q. As a result of averaging for small blockswith permeabilitiesk kl


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The second tracer can be dissolved in the liquidhydrocarbon phase. K- equilibrium constant, equa l to the ratioof concentrations in oil and in water. The mass of secondtracer in blocks in every unit volume of the mediais equalto (1- X y2 (1 - -) Ky2 s2]. in crack sit is Xml [yl (1 - sl) +Ky l sl]. Analogous to (7). equation of the second tracercontinuity in systems of blocks andcr cks s a s follows:

Here Dl' is the coefficient of diffusion for the second tracer.

Analogous to 8), equation of continuity for the secondtracer in blocks system has the following type:

{ ( l - x ) y 2 ( - s2 ~2 )) div (y2w2)=t

System of equations 3). (6), (7). (8), (9) and (10)describes flow of two tracers in fractured-porous media.Unknowns in this system of seven equationsare variables p,W1, W2. cl , c2, yl and y2

Analvsis of d~ men s~on g.

Pass to the dimen sionless variables:

After placing of (4) and 5) into (7) - (10) one can obtain:

div W = 0 (11)

In large scale approximation diffusionin (12), (14) isnegligible comparing with the convective tracer transfer,DI LW o


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TWO TRACER TEST METHOD FOR QUATIFICATION OF RESIDUAL OIL INFR CTURED POROUS MEDIA

SPE 025201

The problem of injection of two ar ti f~ ia lracers leads tothe following initial andboundary conditions:

The problems when the natural tracersare presented inthe reservoir initially, or combination of these two cases,mathematicallyare equivalentto (21). 22).

System (17) (20) contain the following six dimensionlessparameters: p F, a , l, s21 where a = ((1 F) / I D o

1 W L. They are independent Thereforethese parameten

can be determined from the measurements of tracersconcentrations on thecore exi t

Pescriution of the two mce rs flow

Structure of two tracers flow zone is shown on theFigure 5. The front of the first tracer propagates through thefissured syste ms with the velocity F/P. The conditions beforeit in zone1 are nitial. Along this front concentrationin blocksis zero, con centration in fissures decreases from unit a t thebeginning of injection to zero at z- . From (33) we obtainthe formulae for crack concen tration variation on the front:

c; (z)= exp - a z / p (23)

In zones I and 111 moves mixtures, in zonesN.moves w ater with first tracer concentration injected. The backfront of this zone moves through the blocks system withvelocity (1-F) / 1 - P). Along this front trajectory

concentration in fissures is equal to the injected one.concentration in mat rix increases fromz ro at the beginn ing ofinjectionto unit at the

z - . Formulae for variation of con centration on the front.that moves through the blocks system,can be obtained from(36):

Profiles of the first tracer concentrationsare shown onthe Fig 5 by continuous lines. It is shown that c, drops onthe fissures front and9 rops on the b locks front.

The velocity of the second tracer front which moves viathe system of fractures is F/P V1, where V1= 1 K sl/(l

sl). Concentration y2 on this front iszero, concentration yl+before this front is zeroas well. Concentration y ibehind thisfront is

Concentration of the second tracer on the displacementfront in cracks decreases from unit at the be ginning of injection

Behind the front which moves over the matrix withvelocity (I-F) / (1 P) V oncentrationsof the secon d tracerin fractures and in block s are equal to unit, concentration incracks before this front yl+ is equal to unitas well.Concentration of the second tracer beforethis front in blocksis

The second tracer velocity is low comparing with thefirst one because of the dissolving of the second one in the oilphase. Profiles of the second tracer concentratio ns yl, y2 andfronts velocities are shown on the Fig 5 by the dotted lines.

Determination of the Fractional Flow Function from the Dataof Laboratow Disdacement

On the Figure 1 is shown the movement of the oil spotin the single block during the displacemen t of oil by solventfrom fractured-porous media. In the laboratory study [l l ]have been done the periodical photographing of the

displacement picture in one of blocks. Position of the centreof the oil spot canbe distinguished in every m oment

We have determined above W2= (1 F) W as a velocityof flow in the system of blocks. So the velocity of flow in asingle block is W2 (1 A)/l. The velocity of the centre of theoil spo t can be ex pressed via the velocity of flow through thematrix system

This formulae allows us to calculate the value of thefraction al flow func tion in case of displacement of fluid s withthe e qual viscosity.


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SPE 025201 P.G BEDRIKOVETSKY J.S RCHER 5

In laboratory study ll] model of the fractured-porousreservo ir consist of10 blocks along the length (in the k t i o nof displacement) and of 4 block s along the width. Block sizeis 1 = O.lm. Effective permeabili ty of the fractured -porou smedia is 1755 mD. s elf permeability of blocks is 32mD.Dimensionless opening of fracturesis = 0.14. Totalvelocity of flow W i nthe series of experiments was changed inthe interval W= (1.6 2.1)* 10.~ ls.

Variation of the F value from thethree experiments datawas changed in the interval 0.96 0.99. Such l a m value ofthe fracti&al flow function canbe explainedas a &lt of bigopening of fracturesin the model of artificial fractured-porous-reservoir.

In order to estimate the 'convective' size of block wediscuss the problem of flow of a liquid with tracer (neutraladmixture) through the porous media with the law perm eableinclusion. Thi s is an internal problem for the theory ofmiscible displacement in fractund-p orous media6) (10).

We consider thr dimensional flow of incompressible

liquid in porous media with permeability kl which containprolate ellipsoid of rotation with perm eabilityk2 1121. Theinitial conditions for the tracer concentrationare as follows:presence of tracer inside the inclusion c= 1 and ab sence oftr cer outside the inclusion c= 0.

The solution of the problem for pressure (Laplaceequation with conditions of constant flow on infinityX +- and w ith conditions of continuity of pressure and of theflux on the inclusion boundary) [12] shows that st m m linesinside the axisymmetric body are straight lines. Streamstraight linesare parallelto the vector of the external flow. So

the boundary of the 'oil spot' will move inside the inclusionalong the parallel lines. It allows us to determine theconvective size of the block 1 [13].

The m ass flux of tracer throughth boundary of inclusion is

and canbe calcula ted from the explicit solution of the problem.Th e same flux from the phenomenological model (6) (10) is

From conditions of the equality of these fluxes we obtainexpression for the size 1

Discu ss ellipsoids with the d ifferent ratios of axisX

With the + o ellipsoid is approachingto the axis offlow, and lw + -. With the + llipsoid is approachingto the circle which is located within the plane perpendicular tothe axis of flow, 1, o. For the spherex = 1 we obtain 1= R

So the convective size of blqcklw as he same orderas

a geo metrical block siz e 1.The interesting conclusion from the formulae for the

convective size of block is that the value of 1 is independent

on the permeability ratio6 = k c l and on the velocity of flowW.

The internal problem for the determination of the'diffusive' size of block lD is the pro blem of diffusion into thesphere from the surrounded media without the co nvective flux.Analytical solution of this problem 1141 shows thatth averagetime of diffusion into sphere isR~/D So the 'diffusive' sizeof block lD has the same ord er as the geom etrical one.

The laboratory displacementof gases infracturedporousmed ia was performed [15] under the conditions as follows: kl

On the Figure 7 are shown recovery curvesq (7) fromthe laboratory displacement (continuous lines) and from themodelling dotted ines) with three different flow velocities.

We have determined coefficients fi*,i = 1 ,2 rom theformulae for relative phase permeabilities (2) from therequirement of the agreement between theoretical andexperimental results. For the three magnitudes of the velocityW we obtain fl = 1.92, 2.88, 4.0 and f2= 0.74, 82, 0.90respectively.

The more is the displacement velocity the less is theaverage time for tracer mass transfer between blocks andfractures, the low is the displacement coefficie nt

Values of the displacem ent coefficientq = q (1) at thedisplacement with the velocities W which was changed in awide scale re shown on the Figure 8. Comparing with thementioned above experiments the velocities hereare morehigher, the rest of conditionsare the same [16]. With thevariation of W in the interval m/s coefficients fi*change in intervals fi*= 2.6 4.8 and f2*= 0.36 0.77.

Determination of fractured-porous mediaproaer t i~

Data of c oncentrations measurements on the reservoirexist allows us to determine hydrodynamic properties of

fractured-porous mediaP , d nd residual oil saturationsinblocks andin crac ks si.

Concentration of the first tracer, which is measured onthe exist of reserv oir c (1,z Figure 6) is

c (1.7) = c 1 (1, ~ ) F + c z1 , ~ )1 - F ) (24)


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From (12) (23) one can obtain, that average porosity offractured-porous media is

It allow s usto transfer from the real time to the dime nsionlesstime z be measured in pore volumes.

Times of cracks and blocks fronts coming to thereservoir exit3 an be identitied from the tracer app earance inproduced liquid and from the reaching by exit concentrationthe value of th e injected one:

It allows us to determine fractional flow function F andporosity of the fractured systemP:

Analogous formulae are performing for coming times of thesecond racer front3 :

From (26). (28) we obtain

It allows us to obtain oil saturations in cracks sl andin blocks

Sz

si = (Vi l)/(Vi + K - 1) (29)Coe fficient of intensivity of blocks-cracks mass transfer

a can be obtained from the data ofthe irst tracer concentrationat the momentzl. From (23). (24) we obtain

c (1, zl) = exp - a zl/P) (30)

It permits us to calculatea value, a = p In c (1. rl)/z l.

Analogous fo r the second tracer, a = P V1 In y (1.

=1

Values of constants F, p sl, s2, a, a which weredetermined by (27). (29). (30) re the initial data for iterativealgorithm, that minimises average quadratic variation of theconcenmiion measurements:

For solution of this problem canbe used any method ofthe quadratic optimization (gradient descent method or linear

Let us know propexties of the fractured-porousmedia F,and a from the first tracer data c (1. r). Oil saturation in

fractures and in blocks can be found from the second tracerdata duringthe period of produ ction of the 'mixture zone'.

Consider two moments z and z' when concentrations oftracers on the exit of the reservoir are equal: c (1, z)= y (1.

'). The linear substitutions of (y,z and (y', z') into the

independent variablesx, z) lead to the same initial-boundary

problem. So y (x= 1, z) = y'(x =1, r . V1, V2, a ' ) an d z(X= 1, z) = Z (1, z', V1, V2, a'). These equations allow usto determine the ratio V2/Vl. Consideration of the second

couple of moments when concentrations c andy are equalpermits us to determine values of V1. V2 anda .

Results of calculation of concen trations of two tracers onthe exit of the reservoir re shown on the Figure 10.

F i s t tracer cannot be dissolved in oil, distributionconstant for the second tracer k= 0.5. Prope rties of the floware as follows: kl = 5 D kz = 5mD. A = 0.5 mm = 5m. F =

0.83, = 0.05 anda = 3.4. We have calculated concentrationof the first tracer in the produced fluid (curveI), concentrationof the second tracer on the exit of the reservoir for sl= 0.1and for values of oil saturationin blocks z = 0.2.0.4 and 0.6(curves2.3 and 4 respectively).

Momen ts of the tracer breakthrough in four mentionedabove cases are z1 = 0.06, 0.068, 0.08 and 0.1 1 of p.v.

injection. Moments of the total displa ceme ntre % = 5.7 and6.0.

Results of calculations show that the effect of theresidual oil on the d elay in the seco nd tracer movementis quitesignificant (taking into account high resistivity of the tracerchromatography). It allows us to conclud e that results of theproposediw6Gc er s method of identification of residual oil infractured-porous media are stable relatively to the smallperturbations of the inp ut data.

One of the authors (PGB) thanks the company ShellInternationale Petroleum Mij. B.V. for sponsorship of theattendance of the SPE Conference. PGB also thanks PhDstudents li Al-Gheithy and James Wang flmperial College)for the kind help in the computing and Andrey Evtjukhin(Moscow) for help in the treatment of the laboratory data.Authors thankMIS Karen Clarke for the helpful assistance inpreparing this manuscript

t timci concentrations of the first tracer


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concentration of the second tracersaturations of the residual oilaverage porosityporositiesvelocities of flow in systems of fractures and of matrixtotal fluxself permeabilities of the porous media

relative phase permeabilitiespseudo relative permeabilities for systems of fracturesand of matrixfractional flow functionvolume fraction of the space engaged by cracksvolume fraction of the pore space engaged by crackscoefficients of diffusionaverage coefficient of diffusion on the crack-blockboundarygeometric size of blockdiffusive size of blockconvective size of blockconstant of the tracer distribution between oil and water(between condensate and gas

dimensionless linear coordinatedimensionless time expressed in pore volumes of theinje ted iquiddisplacement coefficient

coefficient of displacement ker one p x njection

moment of bnakthrough of the first tr cer

moment of breaIahrough of tht second tracer

moment of coming of the first tracer to the exit of thereservoir through the matrix systemmoment of coming of the second tracer to the reservoirexit through the blocks system

Tomich. J.F.. Dalton, R.L.. Deans, H.A. andSkellenberger, L.K.: 'Single Well Tracer Method toMeasure Residual Oil Saturation', JPT (February1973). 211; Trans. AIME 255.

Archer, J.S. and Wall, C.G.: 'Petroleum Engineering,minciples and Practice. 'Graham 6 Trotman, London,1986.

Golf-Racht, T.D.: 'Fundamentals of fracturedreservoir engineering'. Elsevier Publishing Company,Amsterdam-Oxford-New York, 1982.

Barenblatt, G.I., Zheltov, Y.P. and Kochina. I.N.:'Basic Concepts in the Theory of Seepage ofHomogeneous Liquids in Fissured Rocks', AppliedMathematics and Mechanics PMM), 1960. Vol24,No 5 852.

Sanchez-Palensia, E.: Won-homogqwus media andvibration theory', Springer Verlag, Berlin. 1980.

Panfilov, M.B.: 'Irregular Averaging of FiltrationTransfer Process in Heterogeneous Media', 2ndEuropean Confereoce on the Mathematics of OilRecovery, September 11- 14,1990, Arles, France.

Basniev. K.S.. Bedrikovetsky, P.G. and Dedinez,E.N.: 'Deteimination of the Effective Pexmeability ofFractured Porous Medium', Engineering PhysicalJournal (Injenerno-Fizichesky Jurnal). 1988, Vol 55,No 6, 940.

Bedrikovetsky. P.G.: 'Hor izontal MiscibleDisplacement in Fractured-Porous Media', FluidDynamics (Mechanics Jidkosti i Gasa), 1992, No 3,101.

Buckley. S.E. and Leverett, M.C.: 'Mechanism ofFluid Displacement in Sands', Trans. AXME, 1942,Vo1 146, 107.

Basniev, K.S. and Bedzikovetsky, P.G.: 'MiscibleDisplacement in Fractured-Porous Media (Theory andExperiments)', 6th European Conference on ImprovedOif Recovery, May 21-23, 1991, Stavanger, Norway,803.

Schneider. G.: 'Investigation of the displacement of oilby solvent (alcohol) in fractured-porous media'. PhDThesis, Moscow State Oil and Gas Academy, 1972.

Cala, M A and Greencorn, RA.: 'Velocity effects ondispersion in porous media with a singleheterogeneity', Water Resources, 1986, Vol22, No 6,912.

Bedrikovetsky, P,G. and Dedinez, E.N.: 'Miscibledisplacement of liquids with the equal viscosities fromthe inclusion of a model shape'. Fluid Dynamics(Mechanica Jidkosti i Gasa), 1992, in print.

Carslow, H.S. and Jaegcr, J.S.: 'Conduction of heatin solids'. 1959.

Zakirov. S.N., Shandrigin, A.N. and Segin, T.N.:'Miscible displacement of Gases in Fractured-PorousMedia', Moscow State Oil and Gas Academy, PreprintNo 11.

Shandrigin, A.N.: 'Experimental investigation of thedisplacement of gases in fractured-porous media',Fluid Dynamics (Mechanica Jidkosti i Gasa), 1991,No 6.

Bedrikovetsky, P.G., Evtjukhinm A.V. and Shapiro,A.A.: '2D Miscible displacement in Fractund-PorousMedia (Analytical Modelling)', MediterraneanPetroleum Conference and Exposition, January 18-21.1993, Tripoli, Lybia.

S of two

We shall discuss systems (17), (18) and (19). (20)separately because they arc independent.

Linear hyperbolic system (17), (18) has two families ofcharacteristics:

PX-Fz-const (I-P)X- (1-@ =cons t

In zone I (region of the initial conditions Figure 9) areperformed initial conditions (21). X zone I1 (region of theboundary conditions) are performed boundary conditions (22).


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TW TRACER TEST h4E EIOD FOR QUATIFICATION OFRESIDUAL OIL IN SPE 25201FRACTUREDPOROUSMEDIA

On the lineX = Fz/P functio n c, (x, z) is discontinuous,function (x, y) is continuous. Therefore along this line we

obtain c2 . On the lineX = (I -F ( l - p) occurs a shockwave of c2 (x, z), function c l (x, z) is continuous, cl= 1

Let u s turn in the system (17). (18) from independentvariables x,) to variables y, z);

We shall obtain the following system:

Along the line y= 0 as was shown above c2= 0. Firstequation (32) leads ordinary differential equation withCaushy s conditions (21). The solution is as follows:

After excluding of unknown c2 (y, z) from the system (321,we obtain the following equation:

Both (33) with the condition

Determine boundary prob lem for equation (34). Functionc2 y. z) sa tisfy to the equation (34 ) as well.

The second equation (32) with taking into account (35)leads to th e ordinary differential equation with Caushy sconditions 22). The solution is as follows:

This condition both with the va lM

determines the bo undary problem fo r equation (34).These two boundary problems for second order

hyperbolic partial differential equation can be solved by themethod of Riema m function.

Here O is the Bessel function of a zero order of a f i t ind ofa complex variable:

I (s) = o (is) = ch (s sin I d I l

After the reverse turn to the coordinates (x, z) theseformulae describes concentratiom in the mixture zone(Figure9).

The problem of the second tracer flow (19) (22) issolved analogous. Introduction of new coordinates (y , z 6)

into the system (19). (20) and into the conditions21). (22)leads to the same initial-boundary probbm (33) (35) with thesame an alytica l solutio n (38), (39).

The solutionsare as follows:


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Figure 1 Motion of the oil spot centre inside a single block during thedisplacement diffusive and convective mechanisms of the masstransfer between blocks and fractures

Figure 2 escription of flow in fractured porous media in framework of

double porosity model


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TWO TRACER TEST METHOD FOR QUATIFICATION OF RESIDU L OIL IN10

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Figure 3 Fractured porous media as a porous media with the periodicalheterogeneity porosity and permeability are periodical spacefunctions with the strong variation

Figure 4 Schema of the convective mass transfer between blocks and cracks


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TWO TRACER TEST METHOD FOR QUATIFICATION OF RESIDUAL OIL INFRACTURED POROUS MEDI SPE 025201

xperimentmode ,

Figure 7 Recovery cu rves at the miscible displacement with three different velocities

Figure 8 Comparison between the modelling and laboratory displacement results for differentdisplacement veloc ities

xp rim nt


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Figure 9 Characteristic lines for linear hyperbolic system of the tracermovement n fractured porous media

Figure 10 Concentrations of two tracers on the exit of the reservoir x 1 atthe different saturations of the liquid hydrocarbon phase in matrixsensitivity of identification parameter to the input data

two tracer test method for quantification of residual oil

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