* ,

SPE 19689

Mobility Control Using C02 FormsS.H.Yang and R.L.Reed, Exxon ProductionResearch Co.

SPE Members r

Cop@ght 1SS9,Sdety of PetroleumEnginaar8,Inc.

This paperwaapreparedfor preaentatimal theS4thAnnualTeohnicslConferenceand Exhlbltlonof the Societyof PetroleumEngineer. hatdIn SanAntonio,TX,OctoberS-11, 1SSS.

Thk paperwas ealactedfor preeerrtatkmby an SPE ProgramCommitteefollowing reviewof Inbrmatbn containedIn an abstractsubmhtadbas praaantad,have not been reviewedby the Sooletyof PetroleumEnglnaeroand are subject to cwractlon by the ●uthor(s).The materiel,as ##%#!’j%%%$U#--anypcdtbn of the Societyor PetroleumEngineers,118officers,or members.PWr8 presentedat SPEmeafinfy ●re aubjeotto publkatkm reviewby EdilorialCornmlftaaeof thvsof PatmtaumEnginaeraPamWion tocopyb reatrkfadtoanabmraofofnotmorethnn300words.Itluatratbnemaynotbecopied.The~:x-_mal=nWepkuoue ack~of where and by whomthe paper lo praeented.Write Pubtkatkne Menagar,SPE, P.O. Sox SSSSSS,Rkhardaon, TX ?WW-SSSS. ,

to increase with permeabilitylq andABSTRACT

~elativemobilities to decrease with permeabilityl . Muchdata on foam rheology are avai1 1

~:~1~~~{ reduction caused by C02 foams that are 1iterature. “ShearWinning” trends~$-~s,‘~sh%

or “unstable” in the bulk phase was!! 1!

thic n g“ trends7* , and no effeet of f1owstudied in Berea sandstoneand San Andres carbonate rate * have al1 been observed.outcrop cores at 100*F and 2000 psi. Dependingonhydrophi1icity, some surfactants 1ed to foams Foam flow in porous media is controlledby bubblehaving a favorable dependenceon permeabilityand snap-off,coalescence,movement, and trapping, Itoi1 saturation whereas another did not. Foam has been observedthat, if flltnsare unstable,foammoblllty was found “shear thinning” at highBu~~ propagates in porous edia by breaking andrates and “shear thickening”at low rates.coalescence was investigated in relation to

reformingof thin films20-$2. In micromodels,foampropagates by bubbles and thin films flowing

snap-off,transportand trapping. bubble trains), if films are more~f~~~~~f,~~;e”iornepore-level events of foam flow

INTRODUCTION have b en investigated In detail. Hirasakl andLawson2% studied by~le movement in smooth

Dense phase C02, nitrogen, and light hydrocarbons capillaries. Gauglitz measured snap-off timeare used to develop miscibility with oil in constricted capillaries. Radke and RansohoffA!enhanced oil recovery processes. Such processes found foams were generated in glass bead ackscan be efficientwhen oil is contactedby solvent, 1’but often sw;f~c:;;iciencyis poorad~ to gravity

primarilyby snap-offand lamellad~vlslon. Be ow acritical velocity, foam was generated by a

override,heterogeneity. Bond f~%er~!brook~ an~s~%$

secondarymechanismcalled “leave-behind”,

suggested the use of foam to improve reservoir In this paper, results are presented based onsweep for gas displacement processes. NumerousInvestigatorshave directed considerableeffort to

studies of the effects of oil, permeability,andflow rate on mobility of foams propagatingthrough

studiesof foams for both steam and misciblefloods sandstoneand carbonaterocks,mostly using two C02and to investigate fundamentalsof foam flow in foams that exhibited different stabilitiesin theporous media, bulk phase, Bubble coalescence is tnvestlgated,

Extensivesur a tant screeninghas been carriedoutr~

and bubble snap-off, movement, and trapping arereviewed. Pore-level events are used 1) to

for C02 foams - . The deleteriouseffectsof oil on interpret effects of permeability and flow ratefoam have been obsere by many:5-7 sometimes oil

14’observed In core floods, and 2) to relate

recovery is impaired* ; oil may destabll e foamlbby spreading at bubble/film Int rfaces ; and

surfactanthydrophilicityto foam stability in the

tbulk phase and foam mobility in rock.

partitioningof su[factant into oil 1 and seudo-emulsion f~lmss!l 1may affect foam sta ility, EXPERIMENTALDETAILSSelecttve plugging of high permeability channelshas o en been cited as a favorable effect of

{\CO foams were studied In Berea sandstoneand San

foam7~ . Resistance factors of foams were found !~:,;~ carbonate outcrop at 100”a\land 2000 psi.otherwise specified, cores had

Referencesand 111ustrationsat e~!dof paper, dimensionsof I“x1”x12”,and they were coated with

---m

2 NOBILITYCONTROLUSING C07 FOANS SPE 1-

epoxy and sealed In core holders by babbltt.Pressure differentialswere measured across fivesections of a core, as shown in Figure 1. Acapillary of 3nsn-innerdlametar was Installed atthe core exit that, in certain cases, was packedwith a string of 3nsnglass beads.

Most in situ foam generation experiments werecarried out in waterfloodedcores using dual-bankinjection:i.e., 3 to 5 PV of surfactantsolutionfollowedby 2 PV of C02. Decanewas the oil phase.The standard brfne contained 5.6 wt% sodiumchloride and 1,4 wt% calcium chloride (7% totaldissolved solids). Waterflooding and surfactantpreinjectionwere carried out at 3 ft/day. No ;~lwas, produced during surfactant injection.injection was carried out at 1 ft/day witIexceptions occurring, as will be noted, whenstudying effects of flow rate and permeability.Effectivenessof a foam was determinedby how muchthe mobility of C02 was reduced over that of waterat the end of a waterflood. The comparativemobillty is defined as follows:

Comparativemobility= (Qf/Apf)/(Qw/APw) (1)

where,APW and Qw are the pressure drop and flowrate at the end of waterflooding,and APf and Qfare the pressure drop and flow rate during foampropagation. The comparative mobility normallyreached a steady value after roughly 1 PV of C02injection. Every comparativemoblllty reported inthis aper was measured using a freshly prepared

!water looded core.

Foam stabllltywas tested In a visual cell at 100”Fand 2000 psi. The cell was filled with equalvolumes of C02 and surfactant solution, thenrotated at 25 rpm for 5 minutes. The lifetimewasmeasuredwhen substantiallyall foam had collapsed.

Most data were obtained using two surfactants:C16-diphenylether disulfonate (C16-DPEDS) andCg-ethoxylated (1.5EO) sulfonate. Studies alsoincluded C 0-DPEDS

#and CIO-ethoxylated (3EO)

benzene SU1 onate. C 0-(-1

and C16-DPEDS surfactantswere Dowfax 3B2 an Dowfax XDS 8390 from DowChemical, C9-ethoxylated sulfonate was FoamerNES-25 from Diamond Shamrock, and C O-ethoxylated

\(3EO) benzene sulfonate was Triton-X00 from Rohmand Haas. The surfactantconcentrationwas 0,1 wt%In all tests. Surfactantretentionwg:ddeterminedafter surfactant preinjection, usuallyinjectionof 3 PV of surfactantsolutlonwas enoughto enable produced surfactant concentration toapproach injectionconcentration.

MECHANISMSOF FOAM FLOW IN POROUSMEDIA

Bubble generation,coalescence,trappingment have been observed In porous media~s!8f2!:Kas shown In Figure 2a. In this section, the fou;pore-levelevents are examined, Bubble coalescenceIs Investigated first, followed by reviews ofbubble generation,movement,and trapping,

Bubble CoalescenceIn a Single Pore

When two bubbles come close to each other under anexternaldriving force,the Increasinghydrodynamicresistanceat

9narrowest gap results in a’flat

film, as shown n Figure 2b, Molecularforces startto play a role as the film thins, The long-range

.van der Uaals attractionbetween two bubbles tendsto destabilize the film while electrostaticrepulsion between adsorbed surfactantson bubble/film interfacestends to stabilizethe film, Bothinterfaclaltension gradient and surface viscosityresist thlnnlng. Modeling of such a film thlnnlngsystem,along with all the assumptions,Is detailedin the Appendix. The relationshipbetweendrainagetime and film thicknessis given by

‘“Elljii+J2Y:wdxx.

[+[:14’ ~al - (mR2/F) 1296R8

a2 = (irR2/F)D

a3 = (6 PwR2/~) k

where 10 and 1~ are the modified Bessel functionsof the first kind of orders O and 1, ~ Is thoviscosity of the aqueous phase, R and h are theradius and thicknessof the film, F Is the externaldrivln force, v is the apparentsurfaceviscosity,

!B is t e constant for the long-rangevan der Uaalsattraction,and D and k are constantsfor electro-static repulslon. X, al a , and a3 are d4mension-

!less numbers, and XO and t representX values attimes O and t, respectively. Bubble coalescenceisassumed to occur when the film thickness reacheszero, as shown in Figure 3.

The film drainagemodel describedhere assumesthatinterracialtension gradient and surface v~scositycan be lumped together in terms of an apparentsurfaceviscosity. The model may be appliedto allwater external foams If the bubble-phaseviscosityis much smaller than the water viscosity, Atrfoams, nitrogenfoams, light hydrocarbonfoams, andCO foams are in th~s category.!

Condensationbe ween bubble and film phases must be Includedinthe model for steam foams, The model does notapply to films separating 011 and water, becausethe bubble viscosity is assumed to be much smallerthan the film viscosity, When bubble- and fllm-phase viscositiesare comparable,the Navler-Stokesequations for these phases must be solved simul-taneously(see Appendix).

Since effects of external driving force, ap arent1’surfaceviscosity,and pore size are most re evant

to interpretationof coreflooddata, only these arediscussed here, As drlvlng pressure Increases,bubble coalescence time decreases, as shown InFigure 3. As apparent surface viscosity Increases,bubble coalescence time Increases, as shown InFigure 4, In fact, correlationsbetweencoalescencetime and directly me u d surface shear viscosityhave been reported!#,~~,As~ume the ratio ofpore-body radius, rb, to film-mentscus (Plateauborder in Figure 2b) radius, rn, to be 3 for all

* .

1ama WAN H. YANG ANO RONALD L. REED 3“.- -------- -. -----. . . . . . -. ”... . . . . . . . . .

pores, then bubble coalescence time increases aspore size Increases,as shown In Figure5.

Bubble Generationin a Single Pore

Snap-off, leave-behind,bubble division, and othermechanismshave been observedfor bubble generation

&l~!~~~~~f&s’ ~nd ‘nap-off is ~e dominantadke and Ransohoff2 fou~d thatfo~mwas gener&ed in a glass bead pack by sndp-offand bubble division; however) below a criticalvelocity foam was generated by a secondarymechan~smof leave-behind.

Directmeasurementof bubble snap-offtime in poresof reservoir rock would be difficult because mostpores are multiply interconnectedwith irregularpore surface geometry. Gauglitz24 measured thesnap-off times of air bubbles in surfactantsolutions in ideal constricted cylindrical andsquare capillaries. His results in Figure 23 ofChapter 2 and in Figure 14 of Chapter 3 aresummarizedbelow. The snap-off tfmes are similarIn both geometries only when the tube capillarynumber (~ U~o) is between 10-5 and 10-4:

where AP/L is the pressuredrop per unit length ofa smooth pore, nl Is the number of bubblesper unitle#ltdL Is the length of llquld slugs, and f5,

l$;gi~{t;:~:;n~:~e;~ial tensiongradient, ‘ bubble, andpore constrictiongeometry,respectively. Assumingr~rb is constant, Equation (4) indicates thatpressuregradient increasesas pore size decreases.

Bubble Trapping

Helm et al.7 found that the presence of surfactantsignificantly increased the amount of trappnitrogen in both sandpacks and cores. 14ast~~observed that, as a micromodelwas filled with afoam, some channels were blocked and flow toplace through only a part of the system. liahid~~found that the trappedgas saturationwas 4% In theabsence of foam but 30% in the presence of foam.In our opiniontracer method’7~& “~fi~~as~n~~~~~d ~~~~immobile in pores and bubbles undergoingconstantbreaking and reforming. The time scale of tracerexperiments could not distinguish “trapping” ofm(nutes from that of hours.

[13 ~wRT Foam flow in Pyuus Mediat5 z 5X104 —

u(3)

Bubble dynamics and capillaritycontrol foam flw-in rock. Uhen the bubble phase is injected Into

where u is the interracialtension between bubbleporous rock, bubbles are first formed in the

and film phases,Ub is the bubble-frontalvelocity,largest pores and advance forward. As the local

and RT is the radtus or half width of the captllarypressurebuilds up, bubbles are also formed In the

bod . Uhen the tube capillarynumber is larger than10-~, the snap-offtimes are differentfor the two

next largest pores. Meanwhilethese bubblesmaybetrapped or undergo coalescence and regeneration,

types of capillaries. The snap-off time decreasesdependingon the local pressureand fllmstahillty.

sharply in cylindrical capillaries,where it isAs more bubbles and thin films are generated,

inversely proportional to the square of tubepressure differential across the core Increases.

capillary number. The decreasing trend is moreThe process goes on until a steady state Isreached. Limited by large capillary entry

moderat!?in square capillaries. No dependence ofsnap-off time on surfactant was found in either

pressure,bubbles do not form in very small pores.

type capillary.The locationswhere pore-levelevents occur changeintermittentlyand rando y throughout the poroussystem. Falls et al.?!J

Gauglltz’ experiments were carried out at lowused the method of

pressure for air-surfactant-solutionsystems; thepopulationbalance to accountfor fractionsof both

c~,pillariesused were 500 microns in size with an moving and insnobilebubbles In a foam flow; the

aspect ratio of 3, Coreflooding conditions ofphenomenon of snap-off was included in the

400-md permeability and l-ft/d flow velocitysimulation, Friedmann et al.3° further included

translate to an average pore-body radius of Oz

coalescence,

microns and a tube capillary number of 0,7x10- .It is not clear whetlla~sth;ndorrrelations are

The coalescence time relative to snap-off time

applicable to co5

corefloodlng determines the level of mobility reduction. When

conditions. Nonethe ess, they provide an order ofthe coalescencetime is too long, bubbles and thin

magnitudeestimationof snap-offtime.films flow together as bubble trains, resulting inextremely ;}igh pressure gradients. Such foams

Bubble Movement in a ConstrictedPorewould plug a reservoirunder a pressuregradientof1 psi/ft. When the coalescencetime is short,~~t

Hirasakl and Law$on23 derived the apparentstill longer than the snap-off time,

vtscosity for a tratn of b bles moving in smoothpropagation may occur through breaking an%

f? further Included the ‘eforming‘f thin ‘ilms” ‘s ‘he cOalescence‘lmecapillaries. Falls et al. increases,both mechanisms may contributeto foameffect of pore constrictions. Their results arerearrangedbelow.

propagation.

CO FOAMS IN BULK ANO IN ROCK

f“n1[%l[2*2’[+12’3[ ++tl+ ~Foam StabilityTest ~n High-PressureVisual Cell

C02 foams were first generatedIn the bulk phase In

8#wLsUb 8 [–1s~wub2/31

a rotating high-pressure visual cell, The

f5 f, + fglifetimes of CIO-

‘3 o (4)and C 6-DPEDS foams were

ar b/relatively short compared w th those of NES and

Triton foams, as shown in Table 1. In this paper,“stable”foams refers to those having llfetimesof

---

i IK)BILITYCONTROI

hours in the bulk phase, whereas “unstable”foamsrefers to those having lifetimesof rlnutes In thebulk phase. The “unstable”C 6-DPEDS and “stable”

iNES foams were chosen for mos of the foam studiesin cores.

Comparative Mobility and Oil Recovery of a CO>1ood

C02 floodingwas carriedout in a waterflooded 2-ftBerea core, and the pressuredrop was measuredoverthe middle section of the core.-’Comparative C02mobility leveled off at 10 after C02 breakthrough,and oil recovery was about 80% Sor (residualoilsaturation).

“Unstable”Foam in Sandstone

The “unstable”C16-DPEDS foam was generated in a400-md Berea core by dual-bank injection asdescribed in “ExperimentalDetai1s“. The compar-ative foam mobility reached 10 at 0.5 PV of C02injection and eventually leveled off at 0.15, asshown in Figure6. Comparativenobilities,measuredat all locations of the core, v:e similar exceptat the core inlet. The mob$:~+” ~f C02 was reduced70-fold in.the presence of @lJ; foam. The watersaturationwas 15% at 2 PV of C02”injectioninstead

!/. ‘Ed:?’ 4:::of 35% as in the case of Cindicationof foam generationat 1.2 PV of Cf) injectionwas similarto that of aC02 flood. tA s ut-in test was performedto inves-tigate regenerationof this “unstable”foam. Fol-lowing a 3-hour shut-in, the foam was fully devel-oped (steadyAP) after 0.4 PV of C02 injection.

“Stable”Foam in Sandstone

A common practic~ in the industry is to selectfoams stable in the bulk phase for misciblemobility contrcl. The “stable” NES-25 foam wasstudied in a 450-md Berea core. Its comparativemobilityreached a level similarto the DPEDS foam,as shown in Figure 6. However, the foam differedfrom the DPEDS foam in two respects: 1) thecomparativemobility,during C02 injection,startedto decrease earlier and 2) the oil recovery wasonly 65% Ser. The early decline of mobility waspartly due to its more stablenature and partlydueto effects of oil, which will be discussedlater.

Film Breaking and Reforming in Packed Capillary@

No foam structurewas observed in a straightglasscapillary (installedat the core outlet) in bothDPEDS and NES cases, even though the latter is morestable than the former in the bulk phase.Evidently, bubbles coalesced immediately at thecore exit. Continuous breaking and reforming ofthin films was observedwhen a string of beads waspacked in the capillary,providingconstrictionsinthe pack that surved as snap-off sites for bubblegeneration. For extremelystable foams, polyhedralfoam str ctures have been observed in a straight

$capillary2,

EFFECTSOF OIL

Destabilizationby Oil

The obilitiesofDPEDS foam shown in Figure 6were!plot ed against the average oil saturation during

..=-.’

USINGC02 FOANS S~\E1~

foam eneration, as shown in Figure 7. The foam?was a most non-existentat oil saturationslarger

than 20%, but effective at oil saturations lessthan 5%. Further testing was performed toinvestigatestabilityof C02 foam in the presenceof decane. DPEDS foam was first developed In anoil-free core by dual-bank injection.The pressuredifferentialacross the core decreasedfrom 0.6 psito 0.5 psi after 3% decane was added to the COstream, and further decreased to 0.3 psi after 4of decane was added, as shown in Figure 8. Thisdestabilizing effect of decane was furtherevidencedin foam stabilitytests. The lifetimeofDPEDS foam decreased from 2.5 minutes to 1 minutewhen 50% decane was added to the C02 phase, asshown in Table 1. Deleterious

ifects of oil on

foams have often been obse ved5- .[ . Njko~\l :~re;~!f~may cause foams to fail 0

observed pseudoemulsion films b tween bubble andoil phases. IManlowe and Radke found that airfoams were destablized by dodecane because ofpseudoemulsion-filmdestabilization. In our case,the presence of decane in the CO

!phase

destabilizedDPEDS foam. Decane was firs -contactmisciblewith C02 under floodingconditions.

Oil Emulsions

Both DPEDS and NES-25 surfactantsare highly watersoluble, therefore no partitioning of sdrfactantinto the oil phase was detected under theconditions studied. However, in bulk, the NES-2Ssolution formed ViSCOUS and long-lived oilemulsionswith decane while the DPEDS solutiondidnot. Viscous emulsionfprobablycaused the poor 011recovery mentioned before. Similarly, poor oilrecoveryhas been reported in tonne tion with foamsbased on ethoxylated sulfates

“ ‘JhOx{-’#:sulfonates, and alpha-olefin sulfonates.also interestingthat for NES-25, foam lifetime inthe bulk phase increased from 4 hours to 6 hourswhen 50% decane was added to the C02 phase. Theroles of oils and the

itinteractionswith foam are

complicated. Kuhlman pointed out that foam isdestabilize when oil spreads, but can still bestable if oil-water emulsions do not collapse tooquickly, However, the poor oil recoveriesdiscussed above were probably caused by oil-wateremulsions.

EFFECTSOF PERMEABILITY

Permeabilityand Pore size

The effect of permeability on DPEDS foam wasstudied in both sandstone and carbonate cores.Comparativefoam mobility decreasedfrom 2 to 0.15as the permeabilityof sandstoneincreasedfrom 150md to 400 md. Comparativefoam mobility decreasedfrom 3 to 0.8 as the permeability of carbonateincreasedfrom 40 md to 140md. As shown in Figure9, these decreasing trends were similar but notidentical.

Pore-size distributions, measured by mercuryinjection,of 150-md and 400-md Berea cores and the140-md carbonate core are shown in Figure 10.“Average” pore throat sizes (modes of thedistributions)were 20, 9, and 15 microns for thethree cores, respectively. The 150-md Berea coreand 140-md carbonate core had similar permeabil-ities but the latter had a much wider pore size

606

●✎

SPE 19689 SWAN H. YANG AND RONALD’L. REED 5

di-stribution.The pore-size distribution of the the DPEDS case. However, fluid diversion is40-md carbonate core was not measured because the deternfinedby effects of oil and flow rate as wellcore used in the flooding experimentwas the only as those of permeability.one available and was highly heterogeneouswith

,,

irregularanhydriteembedment. Flow Mechanisms: We considertwo cases to diagnose~ oam flow using either DPEDS or NES

In Figure 11, it can be seen that the comparative surfactant. On the one hand, suppose bubblefoam mobilitydecreasesas the pore size increases, coalescencetime is relativelyshort so thin filmsregardless of whether the core is sandstone or cannot travel throughpore throatswithout rupture.carbonate. This is consistentwith the theoretical The foam propagation is mainly by breaking andresult illustratedin Figure 5. reformingof thin films. Thin films can be thought

of as “gates” to C02 flow. The longer they live,Permeabilityand SurfactantStructure the more resistance to flow. Since coalescence

time decreases as pore size decreases (Figure 5),The effect of permeabilitywas also studied for it is expectedthat foam mobility is higher in lessNES-25 foam. Comparativenobilitieswere 0.15 and permeable zones. On the other hand, suppose0.3 in 450-md and 120-md Berea cores, as shown in bubble coalescencetime is”extremelylong. In thisFigure 12. Both DPEDS and NES foams followed the event, bubbleswill tend to flow withoutrupture indecreasingtrend, but the formerwas more effective “trains”causingextremelyhigh pressuregradients;in reducing C02 mobility in high permeability or ceasing to flow altogether if there is acores. pressure gradient limitation, as there is in

reservoirs. In this event, based on Equation (4)So far, pressuredata of foam experimentshave been as discussed in “Bubble Train Movement in apresented in terms of comparativemobility for the Constricted Pore”, foam mobility increases withconveniencethat the water mobility at Sor is 1 on permeability.a comparative mobility plot. However, in somecircumstancesthis convention can be misleading. The permeabilitydependenceof DPEDS foam suggestsWhen foam data are expressed in terms of mobility, that its propagationis mainly due to breaking andthe mobility of DPEDS foam decreased with reforming. The permeabilitydependenceofNES foampermeability whereas that of NES foam S1ightly suggeststhat its p,apagationis likely to involveincreas;:swith permeability, as shown in Figure not only breaking and reformingof films but also13a. oil recovery using NES foam was some movement of bubble trains. However, thesubstantialityless than that obtained using DPEDS degree of the bubble train movementmust have beenfoam. Since NES forms oil-water emulsions in limited because of the moderate pressure gradientsbulk-phasetests and DPEDS does not, these results observed in coreflooding. The coalescencetime is

suggest that the difference in permeability estimated to be 14 seconds in a 400-md core at 1dependenceis partially a consequenceof emulsions ft/day (see ‘Estimationof Snap-offand Coalescencegeneratedin situ by NES. Times). This relatively short coalescence time

also supports minor bubble train movement for NESMore experiments were carried out to investigate foam.the impact of oil-water emulsions. Generation ofNES foam was initiated in both 450-md and 120-md All experiments were conducted at constant rate.cores at an o~,lsaturationof about 10% (after C02 CC)2injection during foam generation was carriedflooding) instsad of 35% (after waterflooding)in out at either 1 ftjday or 0.5 ft/day to keeporder to minimize possible emulsion formation pressure gradient roughly constant, as shown induring surfactantinjection. In 450-md cores, foam Table 2. In retrospect, experimentsdesigned tonobilities were similar in bath the 10% and 35% study effects of permeability should have beencases. In 120-md cores, the foam mobility was conducted at constant pressure gradient so as tolower for the 35% case, as shown in Figure 13a; more nearly represent the effect of foam on localprobablyboth foam and oil-emulsioncontributedto diversion of C02 from a region of higherthe low mobilitywhen foam generationwas initiated permeabilityto one of lower permeability.after waterflooding, The mobility of NES-25 foam,generated after C02 flooding, still increased The first two entries in Table 2 show mobility isslightly with permeability,though probably very insensitiveto flow rate from 0.5 to 1.0 ft/daylittle oil-water emulsionwas present. Note that, (see Fig. 14, as well). For all except the lasteven though surfactant injectionwas.initiated at two entries (where NES foams were thought compli-35% or 10% oil saturation, foam nobilities were cated by oil-water emulsions), VP = 2,4 k 0.8measured at Sorm in both cases, i.e., 15% and 9%, psi/ft ((vP) v t std. dev.).

%Further, for the

respectively. second throug fifth entr”;esthat define the uppercurve in Fig, 13a, VP = l,8t0,2 psi/ft,

Expressionof floodingdata in terms of mobility isuseful to assess fluid diversion and mechanismsof Literatureon PermeabilityDependencefoam displacement,

Bernard and Holm7 first suggested that highFluid Distribution: Assume that both 450-md and permeabilitychannels could be selectivelyplug edO-red layers in an over-simplified model are by a foam, !In their study, the permeabilityo a

oil-free and saturated with a surfactant solution “loose”sandpackwas reduced from 125 darcy to 3 mdprior to C02 injection, The ratio of C02 while the permeabilityof a “tight” sandpack wasnobilities between the high and low permeability reduced from 4 darcy to 7 md. These 40,000-foldlayers is 3:1 in the absence of surfactant, This and 600-fold mobility reductionssuggest }~s~e~~ratio becomes 1:2 in the resenceof DPEDS foam and

/sandpacks were plugged by the foam, !!

1:1 in the presence o NES foam. Hence, the simulatedthe behaviorof an “imaqinary”foam in astratifiedreservoir. Only if the mobilityof foam

..—

6 MOBILITYCONTROLUSItiGC02 FOAMS

.

SPE 196S9 9

stratifiedreservoir. Only if the mobilityofc~~decreased as permeability Increasedadditionaloil be recoveredin a timely fashion.

Gall14 studied alkylaryl’sulfonate/steamfoam inbeadpackswith permeabilities varyingfrom 3 to 100darcy. The resistancefactor of the foam increasedlinearly with the permeability. Informationwasnot available in Gall’s paper to calculate foamnobilities. If resistance factor divided bypermeabilityis taken as the foam mobility, then,as shown in Fig. 13b, the foam mobility stayedalmost independent of permeability. The flowcapacitiesof low and high permeabilityzones arealmost equal, but not reversed as suggestedby theauthor. Khatib et al.32 studied alpha-olefin-sulfonate and alkylaryl-sulfonate foams in asandpack and found the foam mobility increasingsignificantlyas the permeabilityincreasedfrom 70darcy to 10,000 darcy, as shown in Figure 13c. Thelatter case is an example of an extremely stablefoam where bubbles and thin films may flow togetheras bubble trains.

Most effects of permeability reported in theliterature were observed using sandpacks withpermeabilities ranging from 3 to 10,000 darcy,unrealistically high permeabilities for mostreservoirs. Lee and Heller15 stu+ied thepermeability effect in sandstone cores. Therelative nobilities decreased from 0.? CP-l to0.005 CP-l as the permeabilityincreasedfrom 14.8md to 305 md. These data translate to foamnobilitiesof 2.9 md/cp and 1.5 md/cp for the twocores. However, since a different surfactantwasused in each core, it is difficult to draw anyconclusions.

EFFECTSOF FLOW RATE

In our experiments, the compar~’,ivemobility ofDPEI)Sfoam in 400-md Berea cores increased from0.15 to 1.0 as the flow velocity increasedfrom 1ft/day to 9 ft/day, following a “shear thinning”trend as shown in Figure 14. The foam mobilitydidnot change much as the flow velocitydecreasedfrom1 ft/day to 0.5 ft/day. However, the comparativefoam mobility increased from 0.15 to 0.5 as therate further decreased from 0.5 ft/day to 0.1ft/day, following a “shear thickening”trend. Thehigh foam mobility at a high velocity (> 1 ft/day)seems desirable. This foam should not cause alarge pressure gradient around the wellbore toimpair the overall injectivity, while it iseffectiveat low rates (0,1-1 ft/day)deeper in thereservoir,

Both “shear thinning”and “shear thickening”trendscan be interpretedin terms of the relativeeffectsof flow rate on bubble snap-off and coalescence,The driving pressure for bubble coalescenceincreases as the flow rate increases, Figure 3shows that bubble coalescencetime decreases withincreasing driving force. Therefore, thin films~~;~ shorter resulting in less resistanceto C02

. As mentioned before, the snap-off time isnegligiblecompared with the coalescencetime foran effective foam, The fact that snap-off isprobablymore efficientat high rates cannot offsetthe effect of rate on bubble coalescence, This is

L

consistentwith the “shearthinning”trend,

I#henthe rate decreases in the transition zone,snap-offbecomesless effective. At the same time,bubble coalescence occurs slower. The effect oflow rate on snap-off offsets that on coalescence,so foam mobility seems constant. As the ratefurther decreases, the effect of low rate onsnap-off is greater than that on coalescence.Probably snap-off completely stops, and bubblegenerationmay rely on some secondarymechanisms.This results in fewer thin films to resistC02 flowannndis consistent with the “shear thickening

.

Literatureon Foam Rheology

Extensiveliteratureexists on foam rheology. Onearea of study involvedshearingof a pre-generatedfoam in a viscometeror capillary. The other areainvolvedfoam flowing in porous media. It appearsthat flow of foams in the bu

1! 5base always

followed “shearthinning”behavior ~3 .

Literaturedata on rheology of foam flow in porousmedia appear controversial. Some authors observed“shear thinning” trends, some observed “shearthickening”trends, and others observed no effect.These studies involved various surfactant struc-tures, porous media, and flow rates. Seven exem-ples are given in Table 3. Our finding of bothshearing trends and a transitionregion seems toprovide a reasonableexplanationfor these diverseobservations. As implied by dat~ in Table 3, therange of flow rate for each shearingregimedependsstronglyon the surfactantstructureand concentra-tion, pore size and geometry, pore size distri-bution, and other variables of a foam system suchas salinity,and bubble composition. The seeminglycontradictorydata probably resulted from the factthat the range of flow velocities studied wasinsufficientlylarge.

SURFACTANTHYDROPHILICITYAND FOAM STABILITY

Hydrophilicityof the surfactantsstudieddecrea din the order ofC

k?-, C16-DPEDS,NES, and Titron$!

Surfactanthydrop licitycorrelatedwith lifetime;of foams in the bulk phase, comparativemobility,and surfactantretention,as shown in Table 4. Asexpected,surfactantretentionincreasedas surfac-tant hydrophilicitydecreased. In general, foam1ifetime increased as surfactant hydrophilicitydecreased. The film drainage model suggests thatfoam stabi1ity or bubble coalescencetime stronglydepends on surface viscosity and interracialtension gradient of a film system, as shown in.Figure 4, It is believed that both foam stabilityand dynamic surface properties are related to~;~~hilicity of a surfactant. For a homologous

of surfactants, the relation betweenhydrophilicity and coalescencetime may originatefrom lower surface concentrations for the morehydrophilic species; possibly implying lowersurface viscositiesand surface tension gradients,leadingto unstable foams.

I ~oAL~scENcETIM~sORDER OF MAGNITUDE ESTIMATION OF SNAP-OFF AND

There are two interestingfacts in Table 4,!

(1)C 0-DPEDS foam provideda most no resistanceto C02flow in a 400-md corfi,while C]6=DPEDS foam waseffective, The similar lifetimesof the two foamsdid not suggest such drasticallydifferentbehavior

.

SPE 19689 SHAN H. YANG AND RONALD L. REED 7-. --- .-. ------ .. .. . ..

“In rock. (2) C16-DPEDSfoam was much less stablein the bulk phase than NES and Triton foams, butall three foams resulted in similarly low nobil-ities in 400-md Berea cores. In this section,snap-off and coalescencetimes in a 400-md Bereacore are roughly estimated for the three foams inorder to understandthese results.

The “average” radius of pore throat in a 400-mdBerea core was 10 microns, as shown in Figure 10.The radius of pore body was assumed to be 50microns at an aspect ratio of 5. Therefore, a50-micronpore body was used in the estimationofsnap-offand coalescencetimes in a 400-md core.

Equation (2) is used to estimate coalescencetimein 50 micron pores. Electrostatic repulsionprobably is not significant for systems using 7%TDS brine, so the constants D and k are set tozero. Assume that two bubbles are pressed under aconstant external force so rb/rm = 3. All otherparametersneeded for the calculationare listed inTable 5. The order of magnitude for apparentsurface viscosities is estimated to be 10 cp”cmbecause 1) the surfaceshear viscosityvari$~ from1 to 18 cp”cm for air/laurylsulfatesystems , and2) the apparent surface vi cosity was 40 cp’cm for

%. Itwasfound that ifnitrogen/glycerol systems3the apparent surface viscositieswere selected tobe 1, 2, and 100 cp”cm for C o-, C16-DPEDSand NES

kfoams, respectively,then t e calculated coales-cence times for single films are about 10-30% ofthe measured bulk-foam lifetimes for each system,as shown in Table 5. Although the relationbetweensingle-filmand bulk-foamlifetimesis complex,thechoicesfor apparentsurfaceviscosityare at leastconsistentwith observed bulk-foamlifetimes. Thecoalescence times in a 50-micron pore were thencalculatedto be 2, 3, and 14 secondsfor the C1O-,C16-DPEDSand NES foams. Using Equation (3), thesnap-offtime was calculatedto be 1.4 seconds forall three foams.

Even though calculated snap-off and coalescencetimes are only order of magnitudeestimations,theyprovide some insightson mechanisms. The snap-offand coalescence times are about the same forC1O-DPEDS foam. This is consistent with nomobilityreduction,as observed The snap-offandcoalescence times are 1.4 and 3 seconds forCl -DPEDS foam.!

This suggestsrapid film breakingan reforming is the operative mobility reductionmechanism in a 400-md core, even though C16-DPEDSfoam is “unstable”in the bulk phase,

Snap-off and coalescence times are 1.4 and 14secondsfor NES foam. Both C ~-OPEDSand NES foams

Iresulted in 50-70 fold mobi lty reduction thoughthin films in the NES case lived longer. It ispossible that 1) both fast and slow breaking/reforming of thin films were effective to reduceC02 flow, and 2) the fractionsof immobilebubblesmight be quite different for these cases, Thissubstantiatesthe difficulty q hoosingparameters

48for a mechanistic simulator2*3 , As pointed outearlier, a routine tracer experiment probatlycannot distinguish immobile bubbles from bubblesundergoingbreakingand reforming,

FOAMS UNDER RESERVOIRCONDITIONS

All flooding experiments reported here involvedpure decane in untreated Berea sandstone and San

,...--

1---

Andres outcrop carbonate cores and hence wereconducted under preferentially water-wet con-ditions. This was c eked using the USBM wetta-

btbility index method . The favorable resultspresented in this paper may, in large measure,l~consequent to these special circumstances.under reservoir conditions, the rock/crude/brin&system leads to so-called mixed-wettability,resultswill be less favorable.

A tenable foam process must, under reservoircon-ditions entail the following:

Moderatemobility reductionunder reservoirpressure gradients and low surfactantretention;

A dependence of mobility on permeabilitymore favorable than that derived fromordinary WAG (water alternatingwith gasinjection);

A dependence on oil saturation so thatfoams form and reduce mobility in regionswell swept by solvent but do not interferewith oil production (through formation ofintractable emulsions, for example) frompoorly swept regions. .

Although systems studied here are ideal, theresults may provide a reference useful as astandardof effectivenessfor screeningsurfactantsfor reservoirapplications.

CONCLUSIONS

Experimentson C02-foam enhanced mobility controlwere carried out in water-wet systemsat 100”F and2000 psi under conditions of first-contactmiscibility. Further, a film drainage model wasdeveloped that was similar to others in theliteratu~or~~~ in:~:des both long-range van derWaals electrostatic repulsion.Experimental results and model predictions werecombinedto interpretmechanismsoperativefor foamdisplacement processes as functions of permea-bility, oil satura:~i~ f~fl rate, and surfactanthydrophilicity. resulted in thefollowing:

1, It is favorablethat a foam is destabilizedbyoil at waterflood residualoil saturationbutis effective in reducing C02 mobility ;:miscible- flood residual oil saturation.is unfavorable if the recovery of waterfloodresid~:aloil in unswept zones is impaired byoil-water emulsions or by interactions offilms and emulsions,

2. For promising foams, mobility should notincreaseas permeabilityincreases,

3. The effect of permeabilityon foam mobilitydepends on surfactanthydrophilicityand foamstability, The trend is that more stablefoams give less favorableor even unfavorablepermeabilityeffects.

4. For flow of one foam in porous rock, foammobility followed a “shear thinning”trend athigh rates but a “shear thickening”trend atlow rates,

●

,P

8 / NOBILITYCONTROLUSING C07 FOANS SPE 1964

-4

)6.

7.

8.

9.

10,

11.

A film drainage model was developed. Bubblecoalescence time decreases as driving pres-sure, pore size, and molecular attractionincrease, but increases as apparent surfaceviscosity and electrostatic repulsion in-crease.

The mobility of “unstable” DPEDS foamdecreased as the average pore size of a coreincreased. This suggests that, the foamtransport was governed by film breaking andreforming. According to the film drainagemodel, thin film lifetimes are longer inlarger pores, thus providing more resistanceto C02 flow there.

The mobilityof “stable”NES foam increasedasthe permeability increased. Thi$ suggeststhat, the foam transportwas not only throughfilm breaking and reforming,but also throughsome bubble train movement However,moderatepressure gradients and estimated coalescencetimes suggest the degree of bubble trainmovement was very limited for the NE~ foam.Oil-water emulsions may have made the effectof permeabilityeven less favorable.

The “shear thinning” and “shear thickening”trends can be interpreted in terms of theeffects of rate on bubble snap-off andcoalescence. At high rates, the snap-offtimeis negligible, while the coalescence timedecreases as rate increases. At low rates,snap-off is less effective,and the effect ofrate on snap-off is greater than that oncoalescence.

Foam mobility in rock and foam stability inthe bulk phase correlated with surfactanthydrophi1icity. It is conjectured thatsurface viscosity and interracial tensiongradientdecrease as surfactanthydrophilicityincreases,

A foam “unstable”in the bulk phase may stillbe effectivein reducingC02 mobility in rock,dependingon the relativemagnitudesof bubblecoalescencetime and snap-offtime,

Two foams exhibitingdifferent stabilitiesinthe bulk phase may result in the same mobilityreduction to C02 flow in rock under certainconditions. Fast film breakina and reforminamay be as effective as slow-film-breakingandreforming, Besides,the fractionsof immobilebubblesmay be differentin the two cases.

NOMENCLATURE

B Constant for the long-range vanattraction,erg cm

D Constantfor the electrostaticrepu’dyne cm-2

F Externaldriving force,dyne

i Total driving force,dyne

der Waals

sion term,

‘g !i’qi!ly’ess‘unction‘f ‘eometry ‘n

fl

fs

h

k

Ls

nl

Apf

Apw

Qf

QW

R

RT

r

rb

rm

t

ts

Ub

Vr

Vsx

Xo,Vz

I z

al,

o

M

M

Pw

mj

f)

Dimensionless f ction of fractional filmlength of bubble!!

Dimensio ess function of interracialtensiongradient?~

Film thickness,cm

Inverseof the Debye length,cm-l

Length of liquid slugs23,cm

Number ofletlgthzs,cm-equivalentlamellae per unit

Pressuredrop during foam flow, dyne cm-2

Pressure.drop at the end of a waterflood,dyne cm-z

Flow rate of foam flood, cm3 see-l

Flow rate of waterflood,cm3 see-l

Film radius, cm

Radius or half width of cylindrical’capillarybody, cm

or square

r-directionin cylindricalcoordinates

Radius of pore body, cm

Radius of meniscus (Plateauborder) outside a Ifilm, cm

Film drainage time, sec

Bubble snap-offtime, sec

Bubble frontal velocity,cmsec-l

Velocity in r-direction,cmsec-l

Surface velocityat film interfaces,cm see-l

Dimensionlessnumber relatedto film thicknessin Eq. (2)

Xt X values at times O and t

Velocity in z-direction,cmsec-l

z-directionin cylindricalcoordinates

a2, a3 Constantsin Eq, (2)

Interracial ten ion between bubble and filmtphases, dyne cm-

Dilationalsurfaceviscosity,poise cm

Shear surfaceviscosity,poise cm

Viscosityof aqueousphase, poise

;~;;re;t d~~~~nalowface viscosity,repre-interfacial tension

gradient,poise cm

Apparent surfaceviscosity,poise cm

:DFlQ~RQ QMAN M. VaNC ANn RONAln1. REED e,, - .-”w- “,., ,,. . . . .. ”.- . - -. ----- .

ACKNOWLEDGEMENT

Ue thank J, E. Scott and il.A. Dahl for carryingout most of the experiments reported here, andD. C. Dankworth for measuring the C02/surfactantsolution Interracialtensions.

REFERENCES

1. Bond, D.C., and Holbro~k~O.C., “Gas Drive OilRege~ry Process,” . . Patent 2,866,507

.

2. Fried, A.N., “The Foam Drive Process forIncreasingThe Recovery of Oil,” U.S. Bureauof Mines, Rep. Inv. 5866 (1961).

3. Bernard, G.G., Helm, L.W., and Harvey, C.P.,“Use of Surfactant to Reduce CO Mobility in

1Oil Displacement,” Sot. Pet. ng. J., 281(August1980).

4. Casteel, J.F., and Djabbarah, N.F., “SweepImprovementin Carbon Diox~de Flooding UsingFoaming Agents,” SPE 14392, presented at the60th Annual Technical Conferenceof SPE, LasVegas, Nevada, 1985.

5. Borchardt,J.K., Bright, D.B., Dickson, M.K.,and Wellington, S.L., “Surfactants for C02Foam Flooding,” SPE 14394, presented at the60th Annual Technical Conferenceof SPE, LasVegas, NV, 1985.

6. Raza, S.H., “Foam in Porous Nedla: Charac-teristics and Potential Applications,” Sot.Pet. Eng. J., 328 (December1970).

7. (a) Bernard,G.G., and Helm, L.U., “Effect ofFoam on Permeabilityof Porous Media to Gas,”Sot. Pet. Eng. J., 267 (September,1964). (b)Bernard, G.G., Helm, L.W., and Jacob, W.L.,“Effectof Foam on Trapped Gas Saturationandon Permeability of Porous Media to Water,”Sot. Pet. Eng. J., 295 (December,1965).

8. Manlowe, D.J. and Radke, C.J., “A Pore-LevelInvestigation of Foam/Oil Interactions inPorous Media,” SPE 18069, presented at the63rd Annual Technical Conference of SPE,Houston,Tx., 1988.

9. Irani, C.A. and Solomon, C,,Jr, “Slim-TubeInvestlgatlonof CO Foams,” SPE/DOE 1496?,

7presentedat the SPE DOE EOR Symposium,Tulsa,OK, 1986,

10, Khulman, M.I,, “Visualizing the Effect ofLight Oil on CO

hFoams,” SPE/DOE 17356,

presentedat the S /DOE EOR Sympostum,Tulsa,OK, 1988,

11. Wellington,S.L., Relsberg,J,, Lutz, E.F, andBright, D,B,, “PolyalkoxySulfonate, C02 andBrine Drive Process for Oil Recovery,” U.S.Patent4,502,538,1985.

12. Nikolov, A.D., Wasan, DOT., Huang, D,W,, andEdwards, D.A., “The Effect of Oil on FoamStability:Mechanismsand Implicationsfor OilDisplacement by Foam In Porous media,”

13.

14.

15.

16.

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26.

presented at the 61st Annual Technical Con-ference ofSPE, New Orleans, LA, 1986.

Fussell, L.T., “Sweep Improvement ScopingStudies,” SPE 13168, presented at the 59th~nu~~8pchnical Conference of SPE, Houston,

9 . t

Gall, J.W., “Steam Diversionby Surfactants,”SPE 14390, presented at the 60th Annualfi;~nical Conference of SPE, Las Vegas, NV,

.

Lee, H.O. and Heller, J.P,, “Laboratory’measurements of C02-Foam Mobility,” SPE/DOE17363, presentedat the SPE/DOEEOR Symposium,Tulsa, OK, 1988,

Heller, J.P., Lien, C.L. and Kuntamukkula,M.S., “Foam-Like Dispersions for MobilityControl in C02 Floods,” SPE 11233, presentedat the 57th Annual Technical Conference ofSPE, New Orleans, LA, 1982.

Falls, A.H., Musters, J.J., and Ratulowski,J “The Apparent Viscosity of Foams InH~&ogeneous Beadpacks,” SPE Res, Eng., 155(May 1989).

Huh, O.G., “Flow of Gas and Foaming SolutionThrough Consolidated Porous Media,” Ph.D.Thesis, Univ. of SouthernCalifornia,1986.

Huh, D.G., Cochrane,T.D,, and Kovarlk, F.S.,“The Effect of Microscopic HeterogeneityonC02/Foam Mobility: A Mechanistic Study,”SPE/DOE 17359, presented at the SPE/DOE EORSymposium,Tulsa, OK, 1988.

Helm, L.W., “The Mechanism of Gas and LiquidFlow Through Porous Media in the Presence ofFoam,” Sot. Pet. Eng, J., 353 (December,1968).

Mast, R. F., “MicroscopicBehaviorof Foam inPorous Media,” SPE 3997, presentedat the 47thAnnual TechnicalConference? SPE, SanAntonio,TX, 1972.

Owete, 0.S, and Brigham,W,E., “Flow Behaviorof Foam: A Porous MicromodelStudy,!’SPE Res.Eng., 315 (August1987).

Hirasaki, G. J., and Lawson, J. B.,“Mechanisms of Foam Flow in Porous Media-Apparent Viscosityin SmoothCapillaries,”SPE12129, presentedat the 58th Annual TechnicalConferenceof SPE, San Fransclsco,CA, 1983,

Gauglitz, P.A., “Instabilityof Liquid Filmsin Constricted Capillaries: A Pore LevelDescri tio~h~f Foam Generation in PorousMedia,1! Thesis, Univ. of CalIf.Berkeley, 1986,

Radke, C.J. and Ransohoff, T.C., “Mechanismsof Foam Generation in Glass Bead Packs,” SPE15441, presented at the 61st Annual TechnicalConferenceof SPE, New Orleans,LA, 1986.

Nahid, B.H,, “Non-Darcy Flow of Gas throughPorous Med{a in the Presenceof SurfaceActive

10 NOBILITYCONTROLUSING C02 FOANS SPE 1968S

27.

28.

29.

30.

31.

32.

33.

34.

35,

36.

37,

38,

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40,

Agents,” Ph.D. Thesis, Univ. of SouthernCalifornia,1971.

~harma, M. K., Shah, D. 0., and Brigham, U.“Effect of Mixed-Chain-LengthSurfactants

o;’ Fluid Displacement in Porous Media byIn-situ Foaming Process,” SPE Res. Eng. 253(May, 1986).

Shah, D.O., Djabbarah,N.F., and Wasan, D.T.,“A Correlationof Foam Stabilitywith SurfaceShear Viscosityand Area Per Molecule in MixedSurfactant Systems,” Colloid & Polymer Sci.256, 1002 (1978).

Falls, A.H., Gauglitz, P.A., Hirasaki, G.J.,Miller, D.D., Patzek, T,W., and Ratulowski,J “Developmentof a MechanisticFoam Simu-l;~or: The Population Balance and Generationby Snap-Off,”SPE/DOE 14961, presentedat theSPE/DOE EOR Symposium,Tulsa,OK, 1986.

Friedmann,F., Chen, U.H., and Gauglitz,P.A,,“Experimentaland Simulation Study of High-Temperature Foam Displacement in PorousMedia,” SPE/DOE 17357, presented at theSPE/DOE EOR Symposium,Tulsa,OK, 1988.

Wellington, S.L. and Vinegar, H,J,, “CTStudies of Surfactant Induced C02 Mobi1ityControl,” SPE 14393, presented at the 60th$nu;:8~chnical Conferenceof SPE, Las Vegas,

* .

Khatib, 2.1., Hirasaki,G.J,, and Falls,A.H.,“Effect of Capillary Pressure on Coalescenceand Phase Nobilities in Foams Flowing ThroughPorous Media,” SPE 15442, presented at the61st Annual Technical Conferenceof SPE, NewOrleans, LA, 1986,

Raza, S.H., and Marsden,S.S., “The StreamingPotentialand the Rheologyof Foam,” Sot, Pet.Eng, J., 359 (December1967).

Puerto,M.C., privatecommunication,1986.

Barber,A.D. and Hartland,S., “The Effect ofSurface Viscosityon the AxisymmetricDrainageof Planar Liquid Films,” Can. J. Chem..Eng,,54, 279 (1976),

;o~aldson, E,C,, Thomas, R.D,, and Lorenz,. “Nettability Determination and Its

Eff~~ton RecoveryEfficiency,”Sot, Pet. Eng.J,, 13 (March 1969),

Reynolds,0,, “On the Theory of Lubrication,”Phil, Trans, R, Sot, London, Ser. A, 177, 157(1886).

—

Ivanov, I.B. “Effect of Surface Mobility onthe Dynamic Behavior of Thin Liquid Films,”Pur~ 3Appl. Chem,,52, 1241, (1980),

Chen, J,D., “Effects of London-vander Waalsand Electric Double Layer Forces on theThinning of a Dimpled Film between a SmallDrop or Bubble and a HorizontalSolid Plane,”J. Coil, Int. Sci., 98, 329 (1984),

InterracialEffects in Low Tension Flooding’,AIChE Symp.,78, 113 (1982).

41. Lass, H. Vector and Tensor Anal sis, ticGraw-Hill Book=nynew=, *

42. Hahn, P.S., Chen, J.D., Slatte+y, J.C.,“Effectsof London-vander Maals Forceson theThinning and Rupture of a Dimpled Liquid Filmas a Small Drop or Bubble Approachesa Fluid-Fluid Interface,” AIChE J., 31, 2026 (1985).

43, Scheludko,A., Platikanov,D,, and Manev, E.,“DisjoiningPressure in Thin Liquid Films andthe Electro-tiagnetic Retardation Effectof theMolecule Dispersion Interactions,” Discuss.FaradaySot., 40, 253 (1965).

44. Pashley, R.M. and Israelachvili, J.N., “AComparison of Surface Forces and InterracialProperties of Mica in Purified SurfactantSolutions,” Coil. and Surt.,~, 169 (1981).

45. Sheludko, A., “Thin Liquid Films,” Adv. Coil.Int. Sci., ~, 391 (1967).

~PPENDIX - FILM DRAINAGENOOEL

Reynolds37 first studied the drainage rate of athin film by assuming that film interfaceswereflat and rigid (i,e,, infinitely large surfaceviscosity). Since then many modifications havebeen made to the system. Some included only theeffect of

J&rfacial tension gradient and surface

Viscosity $ Some includedonly the disjoinipressures of ~ondon va der Naals attractif “an,owe and ~adk$ #electrostaticrepulsion9.the latter approach to model drainage of aqueousfilms betweenbubble and oil phases.

Barber and Hartland35assumed that surface tensiongradients COU1d be represented as an additionaldilational surface viscosity and derived a s$:~analytical soluti n for film drainage

\Flumerfelt et al,4 added the short-range Londo~van der Waals disjoining pressure to 8arber andHartland’smodel to calculatethe apparents;[~viscosity for oil/surfactant-solutionHowever, the model was not valid for such system;because it assumed the bubble-phaseviscosity wasmuch smaller than the film-phase viscosity. Inthis paper, Barber and Hartland’smodel is modifiedto include both the long-rangevan der Waals forceand electrostaticrepulsion.

The Navier-Stokesequationsare formulatedonly forthe film phase because for CO fnams the bubble

iviscosity is much s~allerthan he film viscosity.The flow in a thin film obeys simplifiedNavier-Stokes Equations(5a) and (5b) below since the filmthickness,h, is much smallerthan the film radius,R, The equationof continuityis expressedin (Se),

4!?.082

(5a)

(5b)

Flummerfelt,R. W,, Oppenheim,J, P,, and Son,J. R., “Magnitude and Role of Dynamic

61Z

J .,

SPE 19689 SHAN H. YANG ANf) RflNAln 1. RCFn 11

8V18 Wp-Og+-—r ar (5C)

where Vr(r,z) and V are the velocitycomponentsin$the r and z dlrec ions, respcttively,P is the

dynamic pressure, and pw is the viscosity of thefilm phase. The driving force for thinning isassumedto be independentof time, and V is simply

#expressedin terms of the thinningrate elow.

-.dh‘z z=h dt

(6)

Boundary conditions (7a) and (7b) result fromradial symmetry, Boundary condition (7c) assumesthat surface velocity reaches a maximum at r=R,Boundary condition (7d) assumes that dynamicpressure is negligibleoutside the film. Boundary

~ condition (7e) balances the bulk stress withsurface stress at film interfaces.They are givenas follows:

(7a)

Vs=tl atr=O (7b) I

8VSF =0 atr=R (7C)

P(r) -O atraR (7d)

where Vs (i.e., Vr(r,o)) is the surface velocity,

“fand pd are the shear and dilational surface

v scosities,u is the interracialtension betweenthe bubble and film phases, and aU/ar is theinterracialtensiongradientat film interfaces.

As the liquid phase flows out of a film duringthinning, it also carries the surfactantsadsorbedon film interfacesoutwards,resultingin an inter-racial tension gradient, The interracialtensiongradient generates a reverse flux to restore thedisturbed surface back to the equilibrium condi-tion, Meanwhile, the adsorbedsurfactantlayer atfilm interfaces undergoes dilational and sheardeformationduring thinning. Both surfacestressescounterbalancethe tangentialbulk stressgenerateddue to film thinning, A rigoroustreatmentof suchsurface tension gradients involves surfactantadsorption and diffusion at film interf es and

!%demands extensive numerical computationfollowed Barber and Hartland’s simplificati’on~represent the effect of interracial tensiongradient as an apparent dilational viscosity, qd,The interfacial tension gradient is then 1umpedwith the surface shear and dilationalviscosities,Equation (7e) becomes:

avr

[

a2vsm —m

? —+

~ 8VS Vs

az ~p2 ‘—-~r or 1(8)

where ~ is the apparent surface viscosity, and~ = M + pd + q . The apparent surface viscosity

1relates to the endency of a fluid interface tostay at equilibriumor to be restored to equilib-rium after disturbance,

The total driving force, i, is the sum ofthe external driving driving force, F, and twoterms contributedby molecularinteractions,

~=~+B_ -Oe-kh (9)rR2 =R2 h4

Ihe externaldrivinq force initiatesfilm thinndng,In fact, the filr radius depends on the externaldriving ‘orce as follows.

F—-(L+ 1.a rm 1

1

(10)~R2

1 rb(~) -rm(~- 1)

where e is 45 degrees and rm equals (rb - R), asshown in Figure 2b, The bubble radius is madi+equal to the pore radius beca~se the film is

!enerallythin. The derivationo Equation 10) is

fased on the Meusnier theorem 1. AThe rivinpressure is minimum at t of90” and maximum at + o!0’. The average driving pressure is simply takenat 45*. The external drivin pressure has been

!taken to be 2u/r in most MO els de loped for ●

t Jtfilm and twobubb es in an open space .

The second term in Equation (9) represents thelong-rangevan der Uaals attr tion at a distance

N. The short-rangeof 400 A, and B is a constantLondon van der Uaals at action used in mostemulsion stability studiesii is effective when afilm is thinner than 100 A. Most bubbles in bulk-phase foam coalesce at a film thickness larger

1than 150 A 2. Bubbles are much smaller in reser-voir rock than those in the bulk phase. It isreasonableto believe that coalescenceoccurs at athickness larger than 100 A for foams that canpropagatethrough a r ervoir under 1 psi/ft,:~~:~;~~dB$ 2~;xl~~~~o:;g~fi~\r b~~e~~ b;~$~

smaller for dense-phaseCO~ bubble: separatedby an

~~~li”~r~~~’fopT$2 ~~~nt B ‘s assumed ‘0 be.

The third term in Equation 9 represents the\)re ulsion between surfactantmo ecules ads rbed on

! 1 Fewfi m interfaces,and k and D are constants4,values of k and D are available for systemscontainingboth electrolytesand surfactants,

The problem of film drainage is stated above, The~;ri~;:on of film drainagetime followedt~~ steps

Flumerfelt~g~k;: g~fi~nsl!?~ b~~{~~~n!drains~time and film thickms is given in Equation (2 ,It is simply assumed thatcoalescenceoccursat afilm thickness of zero.

1“ K~al~~{’s~ec[~~rupturesat a criticalthickness4of initial film thicknessho, or the correspondingdimensionlessnumber X in Equation (2), was not

fcritical for the calcu ation of bubble coalescencetime, because the initial thinn ng was fast, Aninitial film thickness of 104 or 10 micronsresulted in the same results for all of the calcu-lations in this study,

SRE 19689

Tabla 1. Lifotlmes of C02 Foams and Oil Emulstons in tho bulk Phas@

C02 50% Cwcana tn COZ Oectn@

C1O-OPEOS 1.3minutes . . 0,8 minutes

c16-Op~Os I 2.5 minutes I 1 minute I O.8 minutes

NES-25 I 4 hours I 6 hours I >3 years

Triton X-200 I 5 hours I 7 hours I > 3 years

Table 2, Injection Rates and Pressure Gradientsin Studying ffects of Permeabi 1i ty

IFoam I Core

C16-DPEOS1 400-mdBerea

I 420-md Berea

I 150-md Berea

I i40-Ied Carbonete

40-md C@OnateJ.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .NES2 450-md Berea

C02 Injection Rete Pressure FoamOurtng Foam Generation Gradient

I fpsi/ft)140bf1i ty

(ft/day) (lnlvcp)

1 3.2 10

0.5 1.7 9.6

1 1,6 22

1 1.B 18

0,5 2.0 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 3.9 0.4

0,6 2,5 6,5

NES1 450-mdBerm

120-ti Beree

1 4.2 7.8

0.s 6.6 2.5

1 - Surfactant pro-injection was tnit iatedetanoilsaturationof35x.2- Surfactantpre-inject~onwasinitiat@atanoilsaturationof10%.3 - HighlY heterogeneouscorewithtrreuulac’anhydriteembedment.

~bl e 3, Effects of F1ow Ra~e on Fo*ms

~MtK:~e Porous VelocityMedi urn Range ( ft/d ) Mobi 1 i ty Trend

1 1 , 1

Holler et al .16 No:~;ni c Surfactant/ 4,5 md 50-250 Shear Thinnl ngSendstone

1 , , ,

Falls et a\,17 Benzene Sul fonate/ 7 dareN2 i

- 2B.2BO0 Shear ThinningSandp&c

1 1 , ,

Huh18 Tol&ene Sul fonate/ 500 md 4.11 Shear Thinning. Sandstone

1 r L ,

Holler et al .16 No:~ic Surfect&nt/ 4,5 md 20.60 No EffectSandstono

1 , , ,

Lee h Hel ler15 0-01 ef in sul fonate/ 300 md 3.10C02

No EffectSandstone

1 , , 1

Be;:t’:j & Al~;l Sulfate/ 3 dbrcII

-2.70 Shear ThickeningSendpae

1 ,

Huh et al ,19 Ethoxyl Ned MicromodelSul fonete/C02 i 10~Y

k014

.,, ‘,1‘ ,“ ,1 ,, : ,

S~E 19689

Tabla 4. Wrfactant Hydroohi 1ic{ty and Fear Behavior

Surfactant Uulk Foam Surf. ffctent{on* Cg ;, {:p*Hydrophil icity Lifatfme (mB/e-rock) I

C1O-OPEOS 1,3 min. 0,12 10

C16-DPEDS 2,5 min. 0,20 0,15

NES-25 v 4 hr. 0,3 0,15decreasing

Trfton X.200 5 h?’, 0.5 0,2

*F1oodf ng data from 400-md Berea sandstont torus,

Table 5. Order of tkanftude E$tfmation. al$cence Timq

;O!O#!O ~~~~~ 7%’’TDS brf;d ‘0 vr rm=3F ow rete = 1 ft/day

Tube Captllary Number ● 0,7xI0-60=0 KOO”5 ‘p

I CIO-DPEOS I C16.DPEOS I NES-25

.

-A01s

.- .-

I (nwesured) 3,9 dyne/cm 4,6 dyne/cm -.

Iubble sf ze in bulk foam 2m 2m Wss)smured)

1P erent surface vf scosf ty1

1 cp.cm 2 Cp, cls 100 cp.cm:C osen)

Estfmated coalescence tfme of 0,4 mfn. O,B rein, 20 rein,a sfn91e fflm In bulk foam

Measured fotm 1i fet ime fn the 1,3 mfn. 2.5 mfn,bulk phase

4 hr,

Estfmtted snap-off time In 1.4 sec. 1.4 S8C, 1.4 See,SO.mfcron pore

EstfmMed coalescence ttme In Z sec. 3 sec.SO.mtcron pore

14 sec.

OSCILLATINGBACK PRESSURE

,.

INJECTIONFLUIDS

CORE“~”

II AP I API I

I ISAPPHIRETUBEPACKEDWITHGLASS BEADS

Fig,l -Core floodingapparatus

W

~

g.

Eu)’f 0.05 -zxg

z~z CGALESCENC

o- 10 20 .?0 60

TIME,SECONOS

Fig.3- Effectofdrivingpressureoncoalescencetime

‘!O’OlrnRFB= 10-20 ergcm

(

D=OF

L —. k=O

i w R2.- 0 = 4dyne/crn

rbh~ = 3g rb = Sodcronsag pw = o.76ep

z B = 10-20 ergcm6fn D=og 0.05 - k=OY

!o = 4 dyne/cm

zi

o1

0 2 8T:ME,SECON&

Fig,4- Effectofapparentsurfaceviscosityoncoalescencetime

0.10

rb/rm = 3VIz V= 10cpcmo pw = oo76cp~z B= 10-lgargcm

m’W !3=0g 0.06 k=O~ a = 4 dynelcm

F

~

o~6 10 16 20 2

TIME,SECONOS

Fig.6- Effectofporesizeon coalescencetime

616

TER

BUBBLETRAIN BUBBLE

MOVEMENT COALESCENCE

o

BtiBBLESNAP-OFF

Fig,2a - Some pore-levelevents

l-i’h \\\*---------

Fig,2b - Filmdrainagemodel

.

20 I I I I I I I

1

o

ow

&lJIJ ~C16-DpEDS

,1~’’”l’ I 1 1 1,0 0.5

J1 1.5 2 2.5 3

POREVOLUMES OF C02 INJECTED

Fig. 6- ComparativenobilitiesofC 16-DPEDS andNES-25 foams

J3%IE,, I

01 1 I 1 I 8 I 1 I 1, II 1

0 0.5\

1.5 2 2.5 3POREV: LUMES OF C02 INJECTED

Fig, 8- Effect of decane on DPEDS foam

PORE DIAMETER, MICRONS

Fig,10- PoresizedistributionsofBereasandstoneand carbonatecores

sf?E 19689

I co*10 --------------------------

o.;~,.OIL SATURATION, %

Fig. 7- Effect of oil saturation on DPEDS foamt

1C0210 -------— -------------

>

DPEDS FOAM

\

BEREA

\

CARBONATE

0.11 I Io

I200 400 600PERMEAalLITY,MD

Fig, 9- Effect of permeability on foam comparativemobility

6EREA150 MD

\

CARBONATE140 MD

BEREA400 MD

o.lo~AVERAGE PORE SIZE, MICRONS

Fig, 11- Effect of pore size on DPEDS foam

~E 19689

o.lo~oo o

PERMEABILITY, MD

\

C16-DPEDS

so = 10%prior to

‘0’”’5--200 400 6PERMEABILITY, MD

Fig, 12- Permeability effect and surfactant structure Fig. 13a - Effect of permeability on foam mobility

ALKYLARYL SULFONATE

Gas Mobility on arbitrary scale(Gsll, 1985)

‘e

8●

c

I I I 1

20 40 60 BO 1(

PERMEABILITY, DARCY

Fig. 13b - Effect of permeability (Gall,1985)

1~

ALKYLARYL SULFONATE

(Khatib, 1986)

)PERMEABILITY, DARCY

Fig, 13C - Effect of permeability (Khatib, 1986)

01 ii i 1 1 1 i 1 1 1 Io 5 10

FLOW VELOCITY, FEET/DAY

Fig, 14- Effect of flow velocity

Ma