Surfactant-Based Mobility Control - American Chemical Society

Chapter 12

Foam Formation in Porous Media A Microscopic Visual Study 1

Downloaded by TUFTS UNIV on November 24, 2015 | http://pubs.acs.org Publication Date: July 20, 1988 | doi: 10.1021/bk-1988-0373.ch012

Arthur I. Shirley

Research and Technical Services, ARCO Oil and Gas Company, 2300 West Piano Parkway, Piano, TX 75075 A microscopic examination of foam flow in model porous media is presented. Experiments were conducted examining foam formation and displacement efficiency in glass micromodels with widely different pore properties. The micromodels were designed: (1) by petrographic image analysis to generate complex pore geometries, and (2) by drafting in order to obtain more homogeneous pore geometries. A study of the effect of pore geometry on foam formation mechanisms shows that "snap-off" bubble formation is dominant in highly heterogeneous pore systems. The morphology of the foams formed by the two mechanisms are quite different. A comparison of two foam injection schemes, simultaneous gas/surfactant solution injection (SI) and alternate gas/surfactant solution injection (GDS), shows that the SI scheme is more efficient at controlling gas mobility on a micro-scale during a foam flood.

High gas mobility and low sweep e f f i c i e n c y are t y p i c a l problems encountered i n o i l recovery processes using gas i n j e c t i o n . Improving gas mobility to increase reservoir sweep can add s i g n i f i c a n t l y to recoverable reserves and impact the economics of these t e r t i a r y recovery procèsses^. One technique that has received much attention as a mobility control aid i s foam flooding. In t h i s process the injected gas i s dispersed i n a l i q u i d containing a surface-active agent, forming a foam. The foam i s composed of a stable configuration of microscopic bubbles that behave as a very viscous material when the foam i s made to flow i n a porous medium. This high apparent v i s c o s i t y Current address: Group Technical Center, The BOC Group, Inc., 100 Mountain Avenue, Murray Hill, New Providence, NJ 07974 0097-6156/88/0373-0234$07.00/0 ° 1988 American Chemical Society In Surfactant-Based Mobility Control; Smith, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.

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Foam Formation in Porous Media

i s responsible for the often sizeable reduction i n gas mobility given by foams, which may have mobilities of less than 1/10000 of the gas mobility2. Foams can improve areal sweep and also l i m i t gravity override by gases^»^.


A high-pressure micromodel system has been constructed to v i s u a l l y investigate foam formation and flow behavior. This system uses glass plates, or micromodels, with the pattern of a pore network etched into them, to serve as a transparent porous medium. These micromodels can be suspended i n a confining f l u i d i n a pressure vessel, allowing them to be operated at high pressure and temperature. Because of t h i s pressure c a p a b i l i t y , reservoir f l u i d s can be used i n the micromodel, and any effects of phase behavior or pressure- and temperature-dependent properties on foam flow can be examined. Micromodels have been used i n previous studies of foam i n porous media to observe bubble formation and size d i s t r i b u t i o n as well as the effect of i n j e c t i o n scheme or flow heterogeneities (13-17). These experiments were conducted at low pressure and temperature. For studying foams with dense hydrocarbon gases, and f o r examining the effect of l i v e o i l s or m i s c i b i l i t y , the high-pressure and temperature system i s necessary. Both low- and high-pressure and temperature micromodel systems have been used i n studying other recovery techniques such as waterflooding^, immiscible-gas flooding**, low-inter facial-tension flooding^, micellar flooding**"^ and f i r s t - c o n t a c t and multicontact miscible floodinglO"™ j case they have provided valuable pictures of f l u i d - f l u i d interactions on the microscopic scale. β

n e

a

c

n

The high-pressure and temperature micromodel system has been used i n this study to investigate the formation, flow behavior and s t a b i l i t y of foams. Micromodel etching patterns were made from binary images of rock thin sections and from other designs for a comparison of pore e f f e c t s . These experiments show how simultaneous i n j e c t i o n of gas and surfactant solution can give better sweep e f f i c i e n c y on a micro-scale i n comparison to slug injection. Micromodel and High-Pressure System Design Pressure Vessel and Flow System Design. The operation of glass micromodels at high i n t e r n a l pressure requires a confining or external pressure to prevent glass f a i l u r e . Micromodels have survived internal-external pressure differences of over 700 PSI, but prolonged exposure leads to fatigue and rupture. The choice of confining medium i s limited by the additional requirements of o p t i c a l t r a n s m i t t a b i l i t y and r e f r a c t i v i t y needed for viewing the micromodel from some distance away. The t y p i c a l solutionis "!?- i s to place the micromodel In some kind of prèssurizable v i s u a l c e l l and provide confining pressure with an o p t i c a l l y compatible and transparent f l u i d . -

In Surfactant-Based Mobility Control; Smith, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1988.

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SURFACTANT-BASED MOBILITY CONTROL


The p r e s s u r e v e s s e l d e s i g n used here i s s i m i l a r t o one developed by Campbell and O r r ^ . I t c o n s i s t s of a m i d s e c t i o n h o u s i n g the micromodel, sandwiched between two p o l y c a r b o n a t e windows, w h i c h i n t u r n a r e c o v e r e d on each end by doughnut-shaped end p l a t e s ( F i g u r e 1). The whole assembly i s h e l d t o g e t h e r by a b o l t c i r c l e and s e a l e d between m i d - s e c t i o n and windows by an o - r i n g and gasket c o m b i n a t i o n . To a c h i e v e a p r e s s u r e r a t i n g o f 3000 p s i a t 150°F, the windows were machined from 3 - p l y G.E. L e x g a r d P o l y c a r b o n a t e L a m i n a t e , and the m e t a l p a r t s were made o f J-45 s t e e l from the E.M. J o r g e n s e n Co. The micromodel i s l o c a t e d i n the m i d - s e c t i o n o f the p r e s s u r e v e s s e l . I t i s s e a t e d i n a s l o t where the f e e d p o r t s e x i t the m i d - s e c t i o n and i s clamped down by r e s t r a i n i n g b a r s . The h o l e s tapped i n the micromodel a r e a l i g n e d w i t h the f e e d p o r t e x i t s , and a s e a l i s m a i n t a i n e d by 0 - r i n g s s e a t e d around t h e s e e x i t s . T h i s d e s i g n d i f f e r s from t h e Campbell-Orr p r e s s u r e v e s s e l w h i c h uses t u b i n g f i t t e d t o C-claraps t o c a r r y f l u i d s t o and from the micromodel. The d e s i g n employed here r e s t r i c t s the s i z e o f the micromodels t o a p a r t i c u l a r s e t o f s p e c i f i c a t i o n s , but does p r o v i d e a more s e c u r e way of p r e s s u r i z i n g the micromodel. The f l o w o f f l u i d s t o and from the micromodel i s a c c o m p l i s h e d by the f l o w system shown i n F i g u r e 2. Two ISCO 5000 LC pumps a r e used to meter gas and l i q u i d t o t h e micromodel a t h i g h p r e s s u r e . The pump f o r the l i q u i d a l s o p r e s s u r i z e s a t r a n s f e r v e s s e l o f g l y c e r o l t h a t g i v e s t h e overburden p r e s s u r e . When b o t h gas and l i q u i d a r e f l o w i n g i n t o the micromodel a s a m p l i n g v a l v e breaks the f l o w i n t o 15 pi s l u g s t o i n s u r e i n t i m a c y o f the f l u i d s w i t h o u t foaming. Downstream a TEMCO s t a t i c back p r e s s u r e r e g u l a t o r i s used t o m a i n t a i n system p r e s s u e w i t h v e r y s m a l l f l u c t u a t i o n s . Micromodel f l o o d s were r e c o r d e d on v i d e o t a p e f o r l a t e r a n a l y s i s . A t e l e v i s i o n camera w i t h a zoom l e n s a l l o w e d m a g n i f i c a t i o n l e v e l s from 33x t o 333x as measured on the m o n i t o r ' s s c r e e n . A F u j i n o n 35mm l e n s was used f o r l a r g e r f i e l d s o f v i e w . R e c o r d i n g was made i n time l a p s e f o r r e p l a y i n r e a l t i m e , a l l o w i n g up t o 10 days w o r t h of r e c o r d i n g on a two-hour t a p e . Micromodel D e s i g n and F a b r i c a t i o n . I n p a s t s t u d i e s u s i n g micrmodels the e t c h i n g p a t t e r n s were d r a f t e d by h a n d ^ " ^ . These p a t t e r n s were e i t h e r r e g u l a r pore networks o f i d e n t i c a l pore b o d i e s and throats** AO o r t r a c i n g s o f t h i n - s e c t i o n s H > ^ ^ . I n e i t h e r case the i n f l u e n c e of human hand and mind i s g r e a t enough t o r a i s e the q u e s t i o n o f whether o r n o t micromodel r e s u l t s a r e a f f e c t e d by the d r a f t i n g t e c h n i q u e . T h i s may be e s p e c i a l l y t r u e f o r foam f l o w i n micromodels, where bubble f o r m a t i o n , and breakup and d e f o r m a t i o n w i l l depend on pore g e o m e t r y ^ . I t may seem odd t o be so concerned about h a v i n g e x a c t l y the same pore shapes as a r e found i n n a t u r e when the micromodel i s a l r e a d y a g r e a t a p p r o x i m a t i o n ; i . e . , a t h r e e - d i m e n s i o n a l problem ( f l o w i n porous media) i s reduced t o two-dimensions, and r e l a t i v e l y smooth, c l e a n g l a s s i s s u b s t i t u t e d f o r rough, d i r t y r o c k . Pore geometry i s p a r t i c u l a r l y i m p o r t a n t , however, because the v a r i a b i l i t y i n pore dimensions w i l l determine



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SCREW

Figure 1.

Micromodel Pressure Vessel:

Exploded View


238


DIFFERENTIAL PRESSURE TRANSDUCER

SI'

BOTTLE


BACK PRESSURE REGULATOR

CHART

VIDEO _ CAMERA

RECORDER

0

Π

a

VIDEO RECORDER

b-e-

-Φ—U CAPILLARY SIGHT GLASS

MICROMODEL PRESSURE VESSEL

Γ±| H LjJ

MONITOR

LIGHT

RLTER

FLOW LINES CABLES VALVES PRESSURE TRANSDUCER ISCO PUMP

ISCO PUMP

Li

V

CHECK VALVE

Figure 2. Micromodel Flow System Schematic


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the h e t e r o g e n e i t y o f the porous medium, and t h i s q u a l i t y i s a c r u c i a l p a r t of many p h y s i c a l p r o c e s s e s i n f l o w i n porous media^. H a n d - d r a f t e d p a t t e r n s cannot d u p l i c a t e the c o m p l e x i t y of n a t u r a l pore systems, so i t i s d e s i r a b l e t o copy the n a t u r a l pore networks e x a c t l y . To a c c o m p l i s h t h i s a pétrographie image a n a l y s i s ( P I A ) t e c h n i q u e f o r g e n e r a t i n g micromodel p a t t e r n s was developed by M. Parma and W.J. Ebanks-^ t h a t can t a k e c o l o r images of t h i n - s e c t i o n s and c o n v e r t them t o d i g i t a l maps f o r making b l a c k - a n d - w h i t e e t c h i n g p a t t e r n s . I t uses f a l s e - c o l o r p r o c e s s i n g t o s e p a r a t e the c o l o r s i n a t h i n - s e c t i o n i n t o d i f f e r e n t grey l e v e l s , w h i c h can be segmented by computer i n t o v a r i o u s components o f the t h i n s e c t i o n . S i n c e the epoxy f i l l i n g the pore spaces i s b r i g h t b l u e , i n c o n t r a s t t o the d u l l shades of the r o c k m a t r i x , p o r o s i t y and n o n - p o r o s i t y can be easily distinguished. The r e s u l t i n g computer-processed image, as viewed on a v i d e o m o n i t o r , i s a m i x t u r e o f green ( f o r p o r o s i t y ) and b l a c k ( f o r n o n - p o r o s i t y ) p i x e l s . The green p i x e l s can be counted and d i v i d e d by the t o t a l p i x e l number t o g i v e the p o r o s i t y o f the s e c t i o n under view. The v i d e o b i n a r y image can t h e n be f e d t o a f l a t - s c r e e n TV f o r photographing. Because the t h i n s e c t i o n has t o be h i g h l y m a g n i f i e d ( ^ 1 0 0 x ) t o make the pores show up c l e a r l y a s i n g l e v i e w i s i n s u f f i c i e n t f o r making a p a t t e r n . To get a l a r g e enough a r e a f o r a p a t t e r n , the f i e l d of v i e w i s moved over s l i g h t l y i n one d i r e c t i o n ( t o where i t i s s t i l l p a r t i a l l y o v e r l a p p i n g the p r e v i o u s v i e w ) , and a n o t h e r b i n a r y image i s g e n e r a t e d . T h i s procedure i s c o n t i n u e d u n t i l the photographs o f the o v e r l a p p i n g views can be p l a c e d t o g e t h e r t o form a montage, u s u a l l y f i v e photos l o n g by two photos wide. The montage i s t h e n reduced (=10x) onto h i g h - c o n t r a s t b l a c k - a n d - w h i t e photo paper o r onto t r a n s p a r e n c i e s t o get the f i n a l e t c h i n g p a t t e r n . I n t h i s way the s c a l i n g o f the t r u e pore network t o t h a t on the e t c h i n g p a t t e r n can be c o n t r o l l e d p r e c i s e l y a l t h o u g h an e x a c t 1:1 s c a l i n g would r e q u i r e an i m p o s s i b l y l a r g e montage. U s i n g t h i s t e c h n i q u e e t c h i n g p a t t e r n s f o r d i f f e r e n t r o c k t y p e s have been g e n e r a t e d . One of t h e s e r o c k s i s a r e s e r v o i r sandstone ( F i g u r e 3) showing a f a i r l y r e g u l a r g r a i n s i z e ( b l a c k a r e a s ) and h i g h l y i n t e r c o n n e c t e d pore b o d i e s ( w h i t a r e a s ) . P o r o s i t y f o r t h i s sample was c a l c u l a t e d t o be 30% w i t h v e r y few dead-end pores and the t o t a l m a g n i f i c a t i o n or s c a l e from t h i n - s e c t i o n t o e t c h i n g p a t t e r n ( a reduced v e r s i o n of F i g u r e 3) was 10.9x. A second e t c h i n g p a t t e r n was i n c l u d e d i n t h i s work t o a l l o w f o r a comparison between the imaged-analyzed and h a n d - d r a f t e d p a t t e r n s . The d e s i g n i s an a r c h i t e c t u r a l t r a n s f e r c a l l e d " P a t i o Stone" t h a t i s made by Para-Tone, I n c . I t i s used t o i n d i c a t e masonry o r stone f l o o r s on b l u e p r i n t s , but has been p r e v i o u s l y used as an e t c h i n g p a t t e r n because of i t s s i m i l a r i t y t o a pore network ( F i g u r e 4 ) . As can be seen from the f i g u r e , t h i s p a t t e r n g i v e s v e r y r e g u l a r , l a r g e pores when e t c h e d , w i t h a pore body/pore t h r o a t a s p e c t r a t i o o f c l o s e t o u n i t y . I t would be expected t h a t t h i s l a c k o f h e t e r o g e n e i t y might




240

Figure 3.

Reservoir Sandstone Binary Image

Figure A.

"Patio Stone

11

Binary Image


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have a profound e f f e c t on d i s p l a c e m e n t s t a b i l i t y , phase m i x i n g and t r a p p e d phase s a t u r a t i o n s . The e t c h i n g p a t t e r n s i n F i g u r e s 3 and 4 were reduced by r o u g h l y the same amount o f f o r the a c t u a l e t c h i n g f i l m s . T a b l e I g i v e s t h e e s t i m a t e d range o f pore s i z e s , s c a l e , and p o r o s i t y f o r t h e s e e t c h i n g p a t t e r n s , a l o n g w i t h the pore volume o f the e t c h e d micromodels. 1

TABLE I . P e r m e a b i l i t i e s , Pore S i z e Ranges, S c a l e , Pore Volume and P o r o s i t y o f Micromodels


M-M

k - t , Darcy-yun-

Sandstone Patio Stone

385 473

1

Pore S i z e s , yam S c a l e 50-200 400-1300

3

10.9 N/A

1

k - t = QuL/WAP

2

S c a l e = Avg. Pore S i z e o f Micromodel Avg. Pore S i z e o f T h i n S e c t i o n

3

From R e f . 10

L = 2.75", W =

z

P.V.,

cc P o r o s i t y % 0.18 0.39

30 —

1.75"

Subsequent t o the c o m p l e t i o n o f the image a n a l y s i s work f o r g e n e r a t i n g e t c h i n g p a t t e r n s , a paper by T r y g s t a d , e t a l . 19 appeared i n the l i t e r a t u r e w h i c h d e s c r i b e s e s s e n t i a l l y the same p r o c e s s . The e t c h i n g p a t t e r n s of T r y g s t a d , e t a l . have s c a l e f a c t o r s from l O x t o 25x, and m i c r o s c o p i c e x a m i n a t i o n o f t h e i r micromodels r e v e a l s t h a t t h e e t c h e d pores and the t h i n - s e c t i o n pores have an almost e x a c t g e o m e t r i c s i m i l i t u d e i n terms of a s p e c t r a t i o and pore shapes. Displacement experiments i n t h e i r micromodels c o n f i r m the a n t i c i p a t e d f l o w e f f e c t s o f the r e a l r o c k h e t e r o g e n e i t i e s , and show t h a t t h e s e models a l l o w f o r a more a c c u r a t e comparison between p o r e - l e v e l f l o w b e h a i o r i n micromodels and c o r e - f l o o d r e s u l t s . The e t c h i n g o f the micromodels used i n t h i s s t u d y was performed by M. Graham o f Adobe Labs Co. u s i n g a t e c h n i q u e developed by B.T. Campbe

uio 2

and I . C h a t z i s ^ . Micromodel Foam F l o o d s T a b l e I I l i s t s the micromodel experiments performed i n t h i s s t u d y . Only two micromodels, t h e R e s e r v o i r Sandstone (RS) and t h e " P a t i o Stone" ( P S ) , were used. I n t h e s e experiments the performance o f d i f f e r e n t i n j e c t i o n schemes and the e f f e c t s o f s u r f a c t a n t on gas d i s p l a c e m e n t o f water were i n v e s t i g a t e d . Each experiment would b e g i n w i t h the micromodel f i l l e d w i t h e i t h e r water o r s u r f a c t a n t s o l u t i o n . I f o n l y gas were t o be i n j e c t e d , t h e gas pump would be s e t t o meter a t the a p p r o p r i a t e r a t e and t h e n the



242

flow l i n e s to the pressure vessel would be purged u n t i l the gas reached the i n l e t to the pressure vessel. At t h i s point the purap would be stopped, the value c o n t r o l l i n g flow to the micromodel set open, and the system would s e t t l e to the preset back pressure. At t h i s point i n j e c t i o n would begin, and the pressure and video recording would s t a r t .


For simultaneous gas and l i q u i d i n j e c t i o n , the procedure was altered to purge the flow l i n e s with both f l u i d s . A mixing chamber upstream of the purge outlet allows for a gentle blending of the f l u i d s . Once the pressure was s t a b i l i z e d i n j e c t i o n of the preraixed f l u i d would begin. To quantify micromodel flow c h a r a c t e r i s t i c s , the mobility-thickness, M-t, and the permeability-thickness, k-t, can be calculated. These quantities are used here instead of mobility and permeability because the flow i s only two-dimensional. Mobility-thickness i s defined as M-t = QL W ΔΡ

(1)

where Q i s the flow rate, and L and W are the length and width of the micromodel, respectively. For example, the SAG foam flood gave M-t=10.7 darcy-um/cp, while the straight surfactant solution flood gave M-t=55.0 darcy-um/cp. When the flow i s single phase at 100% saturation, then k-t can be calculated from k-t

=

Q JLAL

WAV

(2)

where u i s the flowing phase v i s c o s i t y . Using the surfactant solution v i s c o s i t y of 8.6 cp as measured with a Brookfield viscometer, this gives ^ ί = 4 7 3 darcy-um for the PS micromodel. Similar calculations give k-t=385 darcy-ura for the RS micromodel (Table I ) . A.

"Patio Stone" (PS) Micromodel

Of the many experiments run i n the PS micromodel, only Test 11-19A i s described here (see Table I I ) . I t was a gas-drive of surfactant solution (GDS), i n which the pressure drop across the micromodel was measured and analyzed i n terms of the flow behavior recorded simultaneously on videotape. I t was also of interest to examine bubble formation and breakup processes i n the PS model, where the large and f a i r l y regular pores might give a different behavior than the smaller, more variable pores of the RS model. The surfactant used i n the PS model was an anionic-nonionic blend i n a 10 wt.% (weight percent active) solution, and nitrogen was the gas used i n the GDS test. Conditions were 1000 p s i back pressure and ambient temperature. Bubble formation i n the GDS process was found to occur by two separate mechanisms. The f i r s t mechanism has been i d e n t i f i e d


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TABLE I I . Experimental Conditions, Flow Rates and Fluids For Micromodel Experiments

Test // Micromodel

P,psi T,°F

11-19A 11-21A 1-13A 1-14A 1-16A 1-24A 1-27A 1-27B 2-3A 2-3B 2-3C 2-5A 4-1.1A 4-11B 4-14A 4-14B 4-15A 4-15B 4-16A

1000 1000 1000 1200 2000 1000 500 2000 2000 2000 2000 2000 1000 1000 1000 1000 1000 1000 1000

PS PS RS RS RS RS RS RS RS RS RS RS RS RS RS RS RS RS RS

75 75 75 75 75 75 75 75 120 120 120 120 120 120 120 120 120 120 120

I n j . Scheme GDS S S S S, GDS GDS GDS GDS GDW GDW SI, 3:1 ST, 3:1 GDW GDW GDS GDS GDS GDS GDW

Q,cc/HR 0.3 0.3 0.3 0.3 4.0 0.23 0.23 0.23 0.23 0.23 0.23 0.23 0.3 0.3 0.3 0.3 0.3 0.3 0.3

Gas

Liquid

A A B B B B B B C C C

c c c c c c c c

A A B B B B B B C C D D C C E E E E C

KEY PS RS S GDS GDW SI, 3:1

= = = = •

Patiostone Micromodel Sandstone Micromodel Surfactant Injection Only Gas Drive of Surfactant Solution Gas Drive of Water Simultaneous Injection, Gas:Liquid Ratio = 3:1

Gases A - N Β = CH4 2

C • Reservoir Injection Gas (Mostly C^) Liquids A Β C D Ε

- 30% Liquinox i n H2O = 0.5% A l i p a l C0-128 i n 15% NaCl Brine = Reservoir Brine 0.1% A0S-1618 In Reservoir Brine - 0.5% A l i p a l CD-128 In Reservoir Brine

55


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SURFACTANT-BASED MOBILITY CONTROL 15

17

previously as " s n a p - o f f " * , i n which a gas finger invading a l i q u i d - f i l l e d pore body w i l l snap o f f smaller bubbles by forming lamellae at the pore throat (Figure 5a, b). At f i r s t the bubbles tend to be the same diameter as the throat, but as the l i q u i d i s depleted the bubbles become larger u n t i l lamellae formation f i n a l l y stops. Snap-off i s governed by a set of equations r e l a t i n g pore dimensions (such as aspect r a t i o ) to pressure drop and surface t e n s i o n , which for gas-liquid systems t y p i c a l l y requires a large pore body/pore throat aspect r a t i o vv3). Because the pore dimensions were f a i r l y uniform ( i . e . constant pore radius) for the PS model, snap-off was rarely observed.


2 1

The second bubble formation mechanism i s shown i n frames c and d of Figure 5. I t occurred only i n those areas where one pore crossed another. I f a long gas finger were moving i n one pore, and another gas bubble were to be forced into the i n t e r s e c t i o n of the two pores by a p r e v a i l i n g pressure gradient, the long finger would break towards i t s t a i l i n g end into a long piece and short piece. The gas bubble i n the i n t e r s e c t i n g pore could then s l i p between the long and short pieces, leaving three bubbles where only two had existed before. This process would continue at different intersections u n t i l the long finger had been broken into several smaller ones. The majority of the bubbles i n the GDS experiment were formed i n this manner. Bubbles formed by t h i s second mechanism are several times larger than the pore radius, whereas bubbles formed by snap-off tend to be the same size as the pore throat radius. As the gas would finger through the surfactant solution during the GDS sequence, the pressure drop across the micromodel fluctuated as a slugs of gas and l i q u i d moved through the major flow channels. This i s because the t o t a l pressure drop across the model i s the sum of the pressure drops across the i n d i v i d u a l lamellae moving i n the main flow path. By synchronizing the pressure recording on a s t r i p chart with the video tape, i t was found that the peaks i n the pressure difference fluctuations occurred when no gas movement was v i s i b l e . The pressure difference would decrease when a gas finger would enter a major flow channel, and the gas finger would rapidly move through the channel. As the flood proceeded, the size of the l i q u i d slugs separating the gas fingers decreased u n t i l l i q u i d production ceased, at which point an uninterrupted gas path existed through the micromodel (breakthrough). Simultaneously, the pressure drop decreased from 1.8 to 0.5 p s i . A plot of the volume of l i q u i d between gas fingers (as measured by the distance between pressure peaks) against the logarithm of the gas throughput appears to give a l i n e a r r e l a t i o n s h i p (Figure 6). This behavior i s consistent with the observation that as the gas saturation increases, there i s less l i q u i d i n the micromodel to be produced; thus, the size of the lquid slugs separating the gas fingers decreases. The logarithmic r e l a t i o n s h i p i s not as e a s i l y explained, however. As the l i q u i d saturation decreases the pressure drop must increase to force l i q u i d i n other regions of the model to flow. Thus, the pressure loss gets larger as the flood progresses u n t i l breakthrough, when i t must decrease since there i s no longer any resistance by l i q u i d to gas flow. Unless l i q u i d i s


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Figure 5.

Bubble Formation During Gas-Drive a,b. Front of Finger c,d. End of Finger


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continually replenished, the mobility control by surfactant w i l l be only temporary. The magnitude of the pressure drop fluctuations (the peaks and valleys on the s t r i p chart recording of ΛΡ) increased as the average pressure drop increased during the GDS flood. Similar results have been found i n foam floods i n bead packs and core f l o o d s . Figure 7 i s a plot of height of a f l u c t u a t i o n , ^ versus the average pressure drop duing that fluctuation, A^avgThe data seem to f a l l along a l i n e having a slope around unity ( i . e . , average pressure drop change proportional to fluctuation width change) and an intercept (d • 0) of AP vg£°« intercept may be due to additional pressure losses i n the flow l i n e s outside the micromodel between the pressure transducer taps, or perhaps due to c a p i l l a r y pressure. The interpretation of Figure 7 would be that the fluctuations, which are correlated with the movement of the l i q u i d slugs i n the main flow channels, are one-half the amount of pressure loss necessary to i n i t i a t e movement of the l i q u i d slugs i n the main flow channel. This pressure loss increases as the volume of l i q u i d decreases i n the main channel, the pressure drop increases u n t i l i t reaches a l e v e l at which the c a p i l l a r y forces opposing the flow are overcome, i t then decreases u n t i l the l i q u i d exits the micromodel. This behavior i s s i g n i f i c a n t because i t indicates that the foam pressure drop i s not primarily due to viscous flow but rather c a p i l l a r y resistance, at least i n the two-dimensional model. 4

T

h

i

s


a

Reservoir Sandstone (RS) Micromodel. The RS micromodel was used i n a variety of experiments examining the effects of surfactant, foam quality, i n j e c t i o n scheme and pressure l e v e l on foam displacement e f f i c i e n c y and flow patterns. Various gases and brines or surfactant solutions were used, primarily f i e l d i n j e c t i o n gas and brine, and the surfactant AES (trade name: A l i p a l CD-128) at a concentration of 0.5 wt.%. Figure 8 shows an o v e r a l l view of the micromodel a f t e r simultaneous i n j e c t i o n (SI) of gas and surfactant solution (Frame a) and a f t e r GDS flooding with only one cycle of gas i n j e c t i o n (Frame b). The SI process was filmed during Test 2-5A while the GDS process was filmed during Test 4-15A. Foam flow i n the SI process spreads out from the major flow channel more than the GDS flood, and the average size of the bubbles i s smaller i n the SI case than i n the GDS case. The SI process appears to d i s t r i b u t e the gas i n a more uniform fashion throughout the porous medium when compared to the GDS flood. When comparing the gas-drive processes GDS and GDW the presence of surfactant i n the displaced l i q u i d has a great effect on the displacement mechanisms and flow patterns. Figure 9 shows schematically the f i n a l extent of sweep for gas-drive of brine without surfactant (Frame a) and with surfactant (Frame b). In each case the gas appears to have p r e f e r e n t i a l l y flowed through a few large channels that zig-zag across the micromodel; however, i n


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0.15 η

BREAKTHROUGH

.1

1

10

PORE VOLUMES INJECTED

Figure 6.

Volume of Liquid Between Gas Fingers During Drainage Displacement (GDS Flood) (Test 1-24A)

1.50

-ι

0.2

0.4

0.6

0.8

1.0

FLUCTUATION HEIGHT, PSI

Figure 7.

ΔΡ Fluctuations vs. Average ΔΡ (Test 1-24A)

American Chemical Society Library 1155 16th SU N.W.

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a. SIMULTANEOUS INJECTION

I

Figure 8.

I

LIQUID

b. SURFACTANT-ALT.-GAS

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F i n a l Fluid Saturations f o r Foam Displacement of Brine a. Simultaneous Injection (Test 2-5A) b. Gas-Drive of Surfactant Solution (Test 4-15A)

a. WITHOUT SURFACTANT

I

Figure 9.

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b. WITH SURFACTANT

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F i n a l F l u i d Saturations for Gas-Drive of Brine a. Without Surfactant (Test 4-1IB) b. With Surfactant (Test 4-14B)


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the g a s - d r i v e where s u r f a c t a n t was used, the gas spread out from these major c h a n n e l s more t h a n when s u r f a c t a n t was not p r e s e n t , l e a v i n g a l a r g e r swept a r e a i n the model and d e l a y i n g b r e a k t h r o u g h . T a b l e I I I shows t h i s n u m e r i c a l l y , as t h e number o f pore volumes i n j e c t e d b e f o r e b r e a k t h r o u g h i s n e a r l y t w i c e as l a r g e w i t h s u r f a c t a n t as i t i s w i t h o u t . I n t e r e s t i n g l y , p r e s s u r e drop measurements a t b r e a k t h r o u g h as g i v e n i n Table I I I show t h a t the p r e s s u r e drop f o r g a s - d r i v e i s s m a l l e r when s u r f a c t a n t i s p r e s e n t . T h i s r e s u l t i s unexpected, and w i l l be examined i n the d i s c u s s i o n s e c t i o n of t h i s paper.


TABLE I I I .

Test 4-11A 4-11B 4-14A 4-14B 4-15A 4-15B 4-16A

E f f e c t of S u r f a c t a n t on Gas-Drive P r e s s u r e Drop

Surfactant? Ν Ν Y Y Y Y Ν

AP L i q u i d , p s i 0.05 0.05 0.05 —

0.10 0.03 0.02

AP Gas-Drive Cum. Flow at B.T., psi 0.20 0.25 0.13 —

0.18 0.13 0.24

0.13 0.10 —

0.19 0.20 0.18 —

N O T E : See Table I I for experimental conditions and fluids.

The SI p r o c e s s i s more e f f e c t i v e a t d i s p l a c i n g a l i q u i d t h a n t h e GDS p r o c e s s , w h i c h i n t u r n i s b e t t e r t h a n the GDW p r o c e s s . The reasons f o r t h i s r a n k i n g can be u n d e r s t o o d from a m i c r o s c o p i c e x a m i n a t i o n o f the f l o w b e h a v i o r . F i g u r e s 10 and 11 demonstrate how i n t i m a t e m i x i n g o f gas and l i q u i d d u r i n g s i m u l t a n e o u s i n j e c t i o n a f f e c t s the d i s p l a c e m e n t p r o c e s s . I n F i g u r e 10a, s m a l l bubbles can be seen f l o w i n g i n t o and out of a pore body i n the c e n t e r o f t h e f i g u r e , moving from bottom t o t o p . Stagnant l a r g e bubbles f i l l the pores below and t o the l e f t and r i g h t o f t h e c e n t e r pore. The f l o w g o i n g t h r o u g h the c e n t e r pore i s v e r y wet, h a v i n g o n l y a few e n t r a i n e d b u b b l e s , because a l a r g e s l u g o f s u r f a c t a n t i s p a s s i n g t h r o u g h . The p r e s s u r e drop measured a t t h i s time was 1.65 p s i . As more gas e n t e r e d t h e micromodel d u r i n g s i m u l t a n e o u s i n j e c t i o n , t h e q u a l i t y of t h e foam i n c r e a s e d and t h e bubbles got l a r g e r ( F i g u r e 1 0 b ) , and the p r e s s u r e drop i n c r e a s e d , r e a c h i n g 2.1 p s i . As t h e p r e s s u r e drop f l u c t u a t e s and the average bubble s i z e changes d u r i n g s i m u l t a n e o u s i n j e c t i o n , the f l o w paths a l s o change. Such changes l e a v e some pores f i l l e d w i t h s t a g n a n t bubbles w h i l e foam f l o w s by i n n e i g h b o r i n g p o r e s . F i g u r e 11 shows a l a r g e r v i e w o f t h e a r e a s u r r o u n d i n g the c e n t e r pore i n F i g u r e 10 ( s e e n j u s t below the date and time i n d i c a t o r ) . A low q u a l i t y f l o w o f s m a l l bubbles can be seen i n the c h a n n e l t h a t goes d i a g o n a l l y from the bottom l e f t t o the t o p r i g h t o f t h e photograph, w h i l e connected t o t h i s c h a n n e l i s a network o f o t h e r pores f i l l e d w i t h l a r g e r s t a t i o n a r y b u b b l e s . As time went on, the bubble s i z e i n c r e a s e d , f i l l i n g t h e f l o w p a t h w i t h l a r g e b u b b l e s . These became t r a p p e d due t o t h e i r




250

Figure 10. Bubble Size and Flow Resistance (Test 2-5A) a. Low Quality Foam (ΔΡ=1.65 p s i ) b. . High Quality Foam (ΔΡ=2.10 p s i )


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size, and the r i s i n g pressure drop required to raove these bubbles also dislodged the previously stagnant bubbles. In this way the flow paths were continually changing and new flow areas were opened up during SI of gas and surfactant. This behavior i s quite different from that observed during gas-drive of surfactant solution. In the GDS foaming process the fingering gas enters the pores along the major flow path and snaps off the bubbles. Because the l i q u i d f i l l i n g these pores has been displaced and no new l i q u i d i s entering the micromodel, the foam that i s l e f t i n these pores has a very high quality and i s almost always trapped. Figure 12 i s a photograph of a highly magnified view of the area immediately surrounding a major flow channel running from upper l e f t to lower r i g h t . As i n previous photographs, the l i g h t areas are the "grains" of the glass matrix, the darker gray areas are f i l l e d with gas, and the thin black l i n e s are water-films along the pore walls or foam lamellae separating gas bubbles. This shot was taken shortly before breakthrough, and i t can be seen that the major flow channel i s almost e n t i r e l y g a s - f i l l e d with only a few lamellae breaking up the gas. The pores connected to t h i s channel are f i l l e d with a high-quality polyhedral foam that i s stationary. After breakthrough, only gas w i l l flow i n the main channel while the foam i n the neighboring pores w i l l be unmoved. The back pressure at which a gas-drive i s operated w i l l affect the e f f i c i e n c y of the displacement, as the data i n Table IV indicates. As the back pressure i s increased, the ultimate pressure drop also increases and the number of injected pore volumes before the f i n a l state (the point where e s s e n t i a l l y only gas i s produced) decreases. A piston-like displacement would require one pore volume of injected gas before a l l the l i q u i d was produced, while increasingly less e f f i c i e n c y displacements would require more volumes. TABLE IV.

Test 1-27A 1-24A 1-27B 1

Effect of Pressure on Foam Flow Pressure Drop and Breakthroughl

P, psia 500 1000 2000

Δ Ρ F i n a l State*, p s i 0.50 0.50 0.60

2

PVI F i n a l , PV 1.25 1.10 1.05

See Table II f o r experimental conditions and f l u i d s

2 " F i n a l " conditions are defined here as the point at which only gas i s produced from the micromodel, i d e n t i f i e d by a constant pressure drop. Discussion Effect of Injection Scheme on Foam Displacement. I f the main interest i n using foam i s f o r c o n t r o l l i n g gas mobility, then i t i s necessary to have a c r i t e r i o n to judge the effectiveness of a foam



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Figure 11. Enlarged View of the Pores i n Figure 10, Showing Foam Flow i n Channels with Neighboring Water-Filled Pores (Test 2-5A)

Figure 12.

Gas Finger with High Quality Foam (Test 1-27B)


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process. For foam floods i n cores or sand packs, the pressure drop generated during foam i n j e c t i o n i s commonly the parameter used to quantify effectiveness, but for floods i n micromodels, a v i s u a l estimate of the area swept by foam i s the most natural c r i t e r i o n to choose. A. comparison of the areas swept by gas for different i n j e c t i o n schemes gives great insight into the manner i n which the foaming process redistributes and s t a b i l i z e s the gas flow, as well as being a measure of effectiveness. Of course, the two-dimensional nature of the micromodel and i t s small size make i t d i f f i c u l t to predict behavior i n three-dimensional rock. The e f f e c t of the loss of dimensionality and of model size on the micromodel results i s considered at the end of the discussion section. When comparing SI and GDS i n j e c t i o n processes i n the RS model on a microscopic l e v e l , one difference that i s immediately apparent i s i n the degree of f l u i d mixing. For the GDS process the displacement of surfactant solution by gas-drive yields only a small amount of i n t e r f a c i a l area formation at the displacement front, with l i t t l e interface generation behind the front. The SI process, on the other hand, has a continuous mixing of gas and l i q u i d due to the breaking and reforming of bubbles as they flow, and t h i s mixing occurs throughout the foam-swept area. Bubble sizes tend to be much smaller with the SI process, and the foams are much wetter than those from the GDS process. Bubble generation during GDS foam flooding occurs by the mechanisms shown i n Figure 5, p r e f e r e n t i a l l y the snap-off mechanism. Snap-off tends to be an i n e f f i c i e n t foaming mechanism^ since most bubbles are formed at the displacement front, where they are pushed ahead of the main gas body. Behind t h i s front there are fewer lamellae because the only operative bubble formation mechanism i s the breakup of gas fingers (Figure 5 c,d). During the SI foam process, however, the constant flow of surfactant solution allows both bubble formation mechanisms to operate at anytime and anywhere i n the pore space. The additional l i q u i d , at a flow rate of one-thord that of the gas, tends to make the foam wet enough that snap-off i s the predominant ^bubble formation mechanism. Bubbles appear to be generated more frequently i n the SI process. Another difference between SI and GDS foam l i e s i n the mechanism by which the foam reduces gas mobility. In each process the foam flows through the largest channels, creating flow resistance due to the foam lamellae spanning these pores. In the GDS process, the foam w i l l invade the pores connected to the main flow channels, plubbing them o f f . As the l i q u i d i s depleted from the main channel a continuous gas path i s formed, and the microscopic d i s t r i b u t i o n of gas and l i q u i d becomes permanently fixed. Mobility reduction i n the GDS process i s a result of the high trapped gas saturation which has blocked o f f some flow paths. In the SI process, foam w i l l also invade the neighboring pores around the main flow channels, but t h i s gas i s not permanently trapped. Instead, foam w i l l flow through a channel u n t i l the bubbles become so large and so numerous that the channel i s plugged (for example, the


254



t r a n s i t i o n from Figure 10a to 10b). The pressure gradient w i l l increase as a result of this blockage, dislodging bubbles that were plugging another channel. In this way, the flow w i l l move through different channels at different times, and more flow paths are opened up as a consequence (see Figure 8). The fluctuating pressure gradient that i s c h a r a c t e r i s t i c of foam flow i n cores was present i n the micromodel experiments, and a few aspects should be noted about the nature of this phenomena. The fluctuations i n the GDS foam flood (Test 11-19A) were found to correlate with the passage of l i q u i d slugs i n the main gas flow channels, and appear to be a l i n e a r function of the average pressure (Figure 7). By correlating each fluctuation with the respective l i q u i d slug size (Figure 6), i t i s found that the smallest l i q u i d slugs resulted i n the largest pressure fluctuations and average pressures. This relationship might seem counterintuitive, since i t could be expected that when the l i q u i d f r a c t i o n a l flow decreases and gas f r a c t i o n a l flow increases that the gas would be "easier" to push. However, i t should be remembered that the gas i s a discontinuous phase and that a l l the pressure losses occur i n the l i q u i d phase i n the t h i n films and lamellae. In the SI foam floods the fluctuations were much smaller than the average pressure drops, presumably because of the wetter flow, and high pressure drops could be sustained for longer times than could be done with the GDS scheme. Mobility Control as a Function of Rock Heterogeneity. Although the effect of rock heterogeneity on foam formation and propagation was not studied i n a systematic fashion i n this investigation, some observations about i t can be made from the experiments described above. To begin with, a d i s t i n c t i o n should be made between sweep e f f i c i e n c y on a macro scale (as i n core floods) and on a micro scale (as i n the present experiments). In p a r a l l e l core tests, a foam w i l l have roughly the same mobility i n a high-permeability core as i n a low-permeability c o r e , leading many to believe that foam can overcome permeability variations i n a r e a l reservoir and give a p i s t o n - l i k e displacement. On a microscopic l e v e l , however, the areal sweeps i n Figure 8 for the GDS and SI foam processes are not p i s t o n - l i k e . A sizable portion of the micromodel i s untouched by gas, being estimated from 50% i n Frame a to 70% i n Frame b. Undoubtedly the results i n Figure 8 are influenced by the small size of the model, but they are s t i l l f e l t to be indicative of the micro-sweep e f f i c i e n c i e s expected i n larger, three-dimensional porous media. Thus, even though the movement of the foam bank may appear to be p i s t o n - l i k e on a macro scale, large amounts of pore space may be bypassed. 4

The micro-sweep e f f i c i e n c y w i l l depend on the l o c a l heterogeneity of the porous medium and the foam's flow properties. The RS micromodel had a few large channels where the flow was heaviest and other regions with smaller pores that were not invaded by foam. The PS micromodel, on the other hand, had fewer pore connections, and the pores were of more uniform size; consequently, i t was almost completely swept of l i q u i d i n the GDS foam flood (Test


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11-19A). No attempt was made to quantify the heterogeneities of the two models, so no t h e o r e t i c a l interpretation of these data can be made. Further evidence of an effect of microscopic heterogeneity on foam sweep e f f i c i e n c y comes from Figure 9. During gas drive, when no surfactant i s present i n the brine, the gas traverses the model along the larger channels, breaking through at 0.12 pore volumes injected, as averaged from the data i n Table 4. When surfactant i s present, breakthrough i s delayed to 0.19 PV injected, a 52% increase i n sweep e f f i c i e n c y . By comparing Frames a and b of Figure 9, however, i t would appear that the gas has followed the same flow paths i n each case, the difference being that the gas has spread out from the main channels when surfactant i s present. This behavior indicates that the microscopic heterogeneity i s c o n t r o l l i n g foam propagation i n the micromodel, and may mean that foams cannot give a complete sweep i n r e a l porous systems. One anomalous result from the experiments summarized i n Table III i s the lower pressure drop during gas-drive of surfactant solution. An average of the tabulated data gives AP=0.15 p s i when surfactant was i n the brine versus ΔΡ 0.23 p s i when i t was not. !=

T y p i c a l l y , the gas-drive of surfactant solution require a higher Ρ than the gas-drive of brine. One possible explanation i s that the foam formation i n the "surfactant-present" gas-drives was poor, such that very l i t t l e gas was present i n a discontinuous state. The higher gas saturations i n these floods would then allow more area for gas flow, such that the pressure drop requirements were lower than when the surfactant was not present. C a p i l l a r y pressure might account for the difference, since the presence of surfactant should decrease the surface tension, resulting i n the less c a p i l l a r y pressure i n the GDS flood than i n the GDW flood. The same s i t u a t i o n would not necessarily exist i n gas-drives i n three-dimensional media, since pressure drop requirements for breakthrough are less for 3-D than for comparable 2-Ό networks^, and because c a p i l l a r i t y i s often not correctly scaled i n micromodels24.

Effect of Micromodel Size and Dimensionality on the Interpretation of the Results. It i s not known how to quantitatively adjust flooding results i n two-dimensional systems to bring them i n l i n e with results i n their three-dimensional counterparts, but i t i s possible to state how the results might d i f f e r . Loss of dimensionality can lead to lower ultimate recovery, which occurs for either of two reasons: f i r s t , because two-dimensional systems of the same coordination number have lower macroscopic connectivity and second, because loss of dimensionality often lowers the coordination number of the p o r e s ^ . Thus, a lower sweep e f f i c i e n c y by foam i n the micromodels would be expected, although lower recovery might also result for other reasons. The pore-shapes and pore size d i s t r i b u t i o n of a two-dimensional thin section d i f f e r s greatly from that of the three-dimensional



256 2 4

r o c k , thereby a l s o a f f e c t i n g the displacement. I f the t h i c k n e s s i s s u b s t a n t i a l l y s m a l l e r than the pore-width, then the t h i c k n e s s would be the c o n t r o l l i n g l e n g t h - s c a l e , w h i c h c o u l d be a problem i f t h e t h i c k n e s s i s v e r y u n i f o r m . F o r t h e micromodel experiments d e s c r i b e d h e r e , i t i s f e l t t h a t t h e foam sweep e f f i c i e n c y was l o w e r , o v e r a l l , due t o the l o s s o f d i m e n s i o n a l i t y , but t h a t the r e l a t i v e performance by S I , GDS and GDW i n j e c t i o n a r e u n a f f e c t e d by d i m e n s i o n a l i t y . I t i s not l i k e l y , e i t h e r , t h a t t h e pore t h i c k n e s s dominated any c a p i l l a r y phenomena t h a t s h o u l d i n s t e a d have depended on t h e t w o - d i m e n s i o n a l pore s i z e d i s t r i b u t i o n . I f a t y p i c a l pore t h i c k n e s s between 200 and 300mm i s taken,10 > 0 t h e n T a b l e I would seem t o i n d i c a t e t h a t t h e pore d i a m e t e r s were a t l e a s t comparable i f n o t much s m a l l e r , such t h a t the pore d i a m e t e r s would be r e s p o n s i b l e f o r any v a r i a t i o n i n c a p i l l a r y pressure.


2

The s i z e o f t h e micromodel, b o t h pore dimensions and t h e s i z e o f the e t c h e d a r e a , can a f f e c t micromodel r e s u l t s i n a number o f ways. F o r example, t h e e t c h e d pores i n the RS micromodel were d e s i g n e d t o be 10.9x l a r g e r t h a n t h e a c t u a l pores i n the t h i n s e c t i o n . One might t h e r e f o r e expect t h a t the c a p i l l a r y p r e s s u r e i n the micromodel would be about l / 1 0 t h of what i t i s i n t h e r o c k . The l a r g e r pore s i z e may a l s o i n t r o d u c e boundary and end e f f e c t s i n t o t h e d i s p l a c e m e n t s , s i n c e i t r e q u i r e s about 40 pore l e n g t h s t o remove l e n g t h e f f e c t s i n t w o - d i m e n s i o n a l s i m u l a t i o n s o f n e t w o r k s . T h i s r e q u i r e m e n t i s d e f i n i t e l y met f o r the RS model, but i s p r o b a b l y o n l y b a r e l y s a t i s f i e d , o r n o t s a t i s f i e d a t a l l , f o r the PS model. However, from F i g u r e s 9 and 10, t h e r e i s e v i d e n c e of b o t h boundary and end e f f e c t s even i n the RS micromodel: i n c o m p l e t e sweep a t t h e i n l e t m a n i f o l d of the model and r e s i d u a l l i q u i d a l o n g the s i d e s . 2 2

Conclusions The c o n c l u s i o n s reached from t h e experiments and a n a l y s e s p r e s e n t e d here a r e : ο

Foam f l o o d i n g by s i m u l t a n e o u s i n j e c t i o n ( S I ) o f gas and s u r f a c t a n t s o l u t i o n gives greater displacement e f f i c i e n c i e s than g a s - d r i v e of s u r f a c t a n t s o l u t i o n i n j e c t i o n .

ο

W i t h the g a s - d r i v e o f s u r f a c t a n t s o l u t i o n (GDS) i n j e c t i o n scheme, t h e degree of m i c r o s c o p i c h e t e r o g e n e i t y w i l l determine t h e m i c r o s c o p i c sweep e f f i c i e n c y .

ο

The dominant mechanism o f bubble f o r m a t i o n depends i n t i m a t e l y on the h e t e r o g e n e i t y of the porous media and the i n j e c t i o n scheme. R e a l i s t i c ( i . e . n a t u r a l ) pore s t r u c t u r e s w i l l g i v e a wide b u b b l e s i z e d i s t r i b u t i o n .

ο

P r e s s u r e drop f l u c t u a t i o n s were found t o c o r r e l a t e w i t h t h e passage o f gas and l i q u i d s l u g s i n the main f l o w c h a n n e l s of


12.

SHIRLEY


the micromodel. A l t h o u g h they appear random, t h e f l u c t u a t i o n s a r e found t o depend l i n e a r l y on t h e average p r e s s u r e drop.

Acknowledg ment s The a u t h o r would l i k e t o e x p r e s s h i s a p p r e c i a t i o n t o Tom Lawless f o r a s s e m b l i n g t h e f l o w system and p e r f o r m i n g t h e e x p e r i m e n t s . J.P. H e l l e r and I.M. B a h r a l a l o m p r o v i d e d v e r y h e l p f u l d i s c u s s i o n s f o r which t h e a u t h o r i s a l s o g r a t e f u l .


Literature Cited 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

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24. Dullen, F.A.L. J. Microscopy, 1986, 144, 277. Received January 5, 1988


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