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by: Ron Huel


Ron Huel
GPA 3.77

S. Kam

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S. Kam
Class Notes
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This 20 page Class Notes was uploaded by Ron Huel on Tuesday October 13, 2015. The Class Notes belongs to PETE 2031 at Louisiana State University taught by S. Kam in Fall. Since its upload, it has received 51 views. For similar materials see /class/222992/pete-2031-louisiana-state-university in Petroleum Engineering at Louisiana State University.

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Date Created: 10/13/15
Capillary pressure amp Interfacial tension SurfaceInterfacial tension SurfaceInterfacial tension Unequal molecular attractions of fluid particles at the surfaceinterface contractile force at the interface Interface implies the existence of immiscible phases lFT 039 a forcelength dynelcm forces acting along the boundary Surfacelnterfacial tension Measurement Energy or work proportional to the area created 039 proportionality constant gt Sliding membrane Work done Fdx 2Ladx 0AA AE Wettability I Contact Angle Wettability is a tendency for one fluid to spread on or adhere to a solid surface in the presence of other immiscible fluids ln petroleum reservoir either water or oil is wetting phase gas is always nonwetting phase Contact angle 9 is one way to measure the wettability of solid 9 lt90 is preferentially waterwet solid Young Dupre equation Um 0 CW 0056 Wettability I Contact Angle Examples of wettability effect Mercury Capillary Pressure In the presence of immiscible phases under capillarity there is a pressure difference capillary pressure across the interface Capillary pressure P0 2rtuhe acos627239r Apgh rnibe in 7 PW mnibe Capillary Pressure Laplace Equation Equilibrium pressure difference across the curved interface between two immiscible fluids capillary pressure P PW PW o ii 1 r2 r1 and r2 principal radii I quot Laplace Equation quot r1 Example Spherical liquid drop Pc 26 r Flat interface Pc 0 Capillary rise Pc 2039 cose I rtube Soap bubble Pc 46 r Laplace Equation Example of Capillary tube in the absence of gravity effect v I I I lwater A aIr water I I 0 quot rlube rim V1 r2 rmt rmbe Capillary Pressure Laplace Equation r1 x rZ can be smaller than zero E 0 does not necessarily mean that r1 0 and r2 0 Capillary Pressure Examples Calculate the pressure in the gas bubble given 1 2 Wm 5110 an 7zdynecm Pm Zarm xalunan 1 0LL z 72 32 m 144 Xw dyne m 391 392 IX 10 cm PB Zatml 44x1u dynem2m 39 r3 4am lEIlKleEI dynecm glven rm 01041 6 20quot quot5 My m39 P m 100 psm Solution 15 a1 1 lame 391 392 2x72dyn2cmxca520 7 2 I 135x10 dynEcm 01x10 cm ae 10Epnal zsnuidyngm 14 7px 295 m lulzzxm dynem p Capillary Pressure swimmer p lEIUUm Wduxmmm39 P 47 Mar x 39 MM39AL 1m Wiral is lire liquid pressure quot3215quot Capillary Pressure xamples Calculale lire height ul capillary rise sham i3EI39 yum pr 3 2x724 ecmxcns3039mmcm mm rs b42747 4 lgmwzomy Capillarv Pressure Rock e U CAPILLARY PRESSURE c056 P PW PW where PmV pICSSUl39E tn the nonwetting uid P n essure 1n the wetting uid 13 Pa 13W 0 IFT between the uids 139 a adium of miniature of the interface 7 1 7392 Principle Radii O39Curv fure 7 ve in i 7v 39 inter 8 4011mm angle i9 8 PAS ca also be regarded as measure of the curvature be P n tween two fluid phases in a porous medium For oil reservoirs there can be three types of PC P PW between gas and water g pg and they are interdependent ie if any two Ps are known the third can be computed gro chm Capillary Pressure Capillary Entry Pressure Threshold value of pressure difference for nonwetting phase to enter a capillary tube or pore throat capillary entry pressurequot Maximum capillary pressure occurs at minimum pore radius distance Capillary Pressure cf Trapping of Oil Droplet Decrease in residual oil saturation is the key to EOR process Displacing oil droplet at pore constriction requires enormous pressure gradient The interfaces under dynamic condition are different from those in equilibrium Water distance Capillary Pressure c f Snapoff Snapoff occurs when pc falls below a certain threshold value ie pee2 in the case of circular pore geometry This means the condition for snapoff is r gt 2rt in circular geometry pc lt Poe2 r gt 2r Capillary Pressure Exam ples Calculate the minimum oil pressure for the oil phase to invade the pore throat filled with stationary water phase Injection ofoil 01W 9 0i gzvenrym 7 Water h aw 72dynecm PMquot 1000psza 2039 7 2gtlt 72dyne m r 01x10 4m 501142107 P 144gtlt107cyne cm2 Sandman fur emermg next pure P 2P RZEiPWZPJ EZPHPJ I 21000ps1a 144x107dyne Arm 1 1209ps1a 10133 gtlt10 dyne my Capillary Pressure Exam ples Derive the condition for snapoff to occur in the cylindrical geometry given below neglect gravity effect gas Igt water rrhma rimy SolutionFor nonwetting phase invading pores lled with wetting phase the condition for snapoff mechanism to occur is 1 g B gaPc therefore rbady 2 25mm Capillary Pressure Capillary pressure curve Macroscopic Capillary Pressure Capillary rise experiment with a large number of capillary tubes with differentwradii 3 m m a l D e k 2 39E N o l D E 57 39n SW water saturation F SW 3 z One of the most dif cult to estimate a E parameters Often rellablllty Is In a 0 question Various methods are aeggggg fquot stimate it well logs g7 3333233 o welltesting material balance i 233 e aaaaeza quation tracer surveys core analysis mm me all f mnm s e o e s w Gs 9s 38 o s 36 so as so 465 Dining WE onnate water saturation ie the water saturation the rock is born with 39 ater cannot be removed Similarly we have 30 residual oil saturation 8 so 88 36 so a s 8 933 2 s so mom mr Therefore if the reservoir has only oil 9 an watert e moveable DI Wlll be adova k PIEZo Pore Volumequotr 1SorchlBL7 w 43 39 e spend more time on estimation of Analogy bEtWeequot capillary tUbe Emil fluid saturatiOn ater Porous Medium Fluid Distribution Capillary Pressure Capillary pressure curve drainage injection of nonwetting phase into pm imbibition injection of wetting phase into pm Primary drainage injection of nonwetting phase into pm at Sw1 capillary pressure l Displacement pressure 0 5quot Sw water saturation A typical primarydrainage capillary curve Capillary Pressure Displacement Pressure Nonwetting phase invades the largest pores first Threshold value of pressure to overcome to enter pore space Nonwetting phase in large pores wetting pores in small pores Gas injection into brinefilled rock Small pore needs high capillary entry pressure Capillary Pressure Leverett J Function Different rock samples usually exhibit different capillary pressure curves In spite of different petrophysical properties porosity and permeability one may use a standard capillary pressure curve for the same rock type which is called Leverett J function V P P k Leverett J mction JSW cos 6 0 cos 6 where r is a characteristic length ofpore dimension Same rock type gt Same Leverett J function This concept works OK for idealized systems ie sandpack and beadpack less effective for the rock samples because of the different depositional environment and history Capillary Pressure Leverett J Function Example of Leverett J function using unconsolidated sands and beads g Different perm 0052000 darcy 7 o and uids brine air kerosene A O water a 1 quotQ A I V Ask P 5 WUCOS LLF 3LL 1 SW water saturation Capillary Pressure Conversion of Capillary Pressure Convert laboratorymeasured capillary pressure to field ata Most lab experiments with mercuryair system reservoir with wateroilgas system Experiments with cores taken from the field the same pore size distribution P 2o cos 6 P 2o cos mm Jab Jeszrvmr r r 0 cos 6 therefore P P 1 0 cos 6 Capillary Pressure Example 5 Question Labmeasured capillary pressure quotmmquot quot 5quot with a core sample porosity02 1 33 permeability100md using airbrine 09 45 system is given as follows Calculate 7 Leverett J function for the core sample M 9 Assume o 72 dynelcm and e0 05 11 04 20 03 40 Answer 029 60 Sw Fe Fe JSw 45 fraction psi dynelcmAZ 4 1 0 1 33 201941497 025550 5 3395 09 45 310193373 0302037 2 3 03 0 413591337 0403510 E 25 07 74 510090599 049707 3 2 00 9 020337755 0005274 E 15 05 12 327133073 0307033 3 1 04 20 137303940 1345054 05 03 40 275727391 2090103 0 029 00 413591337 4035103 0 02 04 05 05 1 1atm 147 psi 10133x10quot6 dynelcm wa ersmmioquot 1darcy9869x10quot9 cmAZ Capillary Equilibrium When two porous media with different 4 and k are in contact capillary pressure at the boundary is the same capillary equilibrium Very slow process Capillary Pressure Water injection into oil saturated layers SW Extreme case of capillary equilibrium is capillary end effect commonly observed in laboratoryscale experiment I 39U n Layer1 hi k Layer 2 lo k Question Suppose two segments of porous media in equilibrium The properties of segment 1 are given in the previous example and the properties of segment 2 are the same as those of segment 1 except for the permeability k for segment 2 500 md Given that the water saturation from the segment 1 is 40 what is the water saturation of segment 2 Assume that the two segments are so thin that there is no gravity effect sw4o l Segment 1 Capillary Pressure Example sw Jr Segment 2 Capillary Pressure Example Answer one can start with the Leverett J function in the previous example SW PM P92 psi psi 0 0 o 70 SW J fraction 1 1 025556 38 1699412 60 09 0302637 45 2012461 6 08 0403516 6 2683282 50 07 049767 74 3309381 5 06 0605274 9 4024922 3 4 05 0807033 12 5366563 5 30 04 1345054 20 8944272 03 2690108 40 1788854 20 029 4035163 60 2683282 3 o o 0 02 04 06 08 Swin segment 2 is roughly between 029 and 03 water saturation Advanced Topics Capillary Pressure Characteristic shape of Pc curves Lower permeability Particle size Slope provides information pore size distribution Largest pore size Pore Throat Profiles Capillary Pressure Curves Folymodal V 39 59339 Pore System Thresho d Entry Pressure Mercury Invades Capillary Pressure m snipeg mm and 5 R35 Mercury saturation of Pore Volume After Coalson Hartman and Thomas 1990 Capillary Pressure What does PESW Curve tell us PCSW curve gives information pertaining to fluid distributions saturations wettability and the connectedness of flow paths within a porous medium PcSW curves also represent an experimental correlation of the pressure difference between the two phases at equilibrium in a porous medium The shape of the curve is a function of the rock type with finegrained rocks having higher capillary pressure at a particular saturation Any point on PC curve represents an equilibrium condition Therefore when we obtain a capillary pressure curve for a reservoir it conveys a message that it contains the amounts of water and oil as required to attain an equilibrium between the gravitational and capillary forces Capillary Pressure Hysteresis in capillary pressure Hysteresis in capillary pressure curve caused by pure level phenomenon invasion of smaller pores capillary pressure Capillary Pressure Hysteresis in capillary pressure FA PC not enough to push oil into even largest pore throats 3 Minerals FE Increased l5c forces oil in but D Wetling Fluid dropping PC to PA imbibition does not expel all oil or result in s 0 Nonewetling A PC Raise PE to PC and then reduce it 539 below Pk We end up with a higher 5 This PE hysteresis is caused by imbi tion and drainage process and saturation history l i lmhibitiori l l l1 4 ll Hysteresis depends on the direction of saturation change ie drainage or imbibition Capillary Pressure More on Capillary Pressure Hysteresis Hysteresis depends on the shape of fluid interfaces and the degree of 39 along the direction of saturation change Direction of saturation changeDdepends on contact angle Thus Pc is also a function of the difference between the advancing and receding contact angles During drainage receding contact angle displacement first takes place in the large pores and then in the smaller pores Consequently some nonwetting fluid remains trapped in smaller purest This behavior of capillary retention in smaller pores illustrates why the capillary pressure corresponds to a higher saturation on the drainage curve In imbibition advancing contact angle fluid in smaller pores gets displaced first Hence the lower capillary pressure for the corresaonding saturation in an imbibition process The drainage F c curve exists over a larger range of saturation than does P curve for an imbibition process For this reason of PCS curve hysteresis the P55W curve is not used to estimate the residual oil saturation in an imbibition process Capillary Pressure Capillarity vs Recovery Factor Water will displace all oil in the pore doublet provided viscous forces equal capillary forces but this is highly unlikely in reservoir conditlons Under normal flow conditions viscous quotquot quotmm 4 forces are smaller than capillary forces Here PC is much higher in the smaller capillary which is also say waterwet Hence the water will move more rapidly W V through the narrow capillary thus displacing 39ts oil content rst When that m happens ie when the water reaches the wme downstream point where the capillaria rejoin Pc now ecreases as t e radius increases but a signi cant amount of oil is already entrapped in the larger capillary Less trapping would have occurred had the relative velocity in the smaller capillary would have been lower swam Capillary Pressure Capillarity vs Recovery Factor odel 39 quot 39 L quot39 Lquot 39 39 39 lled with the oil and the pore surface is waterwet and is coated with a thin film of water Obviously PC will be lower at the pore than at the throat and will be dictated by aspect ratio of pore diameter to the throat As the displacing water flows some oil will be displaced out o t e system but when the Pc ecomes very high say at the throats snapoff of the oil will occur This will result in oil entrapment in the form of globules within the pore body It is speculated that in reservoirs 50 of the entrapped oil may be due to the porethroat snapoff mechanism Capillary Pressure Wldely used k1 and p0 eqautions u ml WK OIL luv Sum H S 9 mm K Lm 45 5 w Mum M mm mm m mm 7 ml ml e mmeammi m mum 113 mmmlinn s mm an mummy m m wmml wequot r New wwa wsmn n premm nrgamn We mm ml r an H x L m an 11 m l H u Wm y W mum pmum M mum hun mum mmmimi exponents nu rclamc permcnmllly cums ms npulm ptcssum ofwmmrmlsysw Mme Emums m duemunad by leastrmuarzs memud am am


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