interfacial rheology in reservoir

www.elsevier.com/locate/jpetscieng

Journal of Petroleum Science and Engineering 39 (2003) 137–158

The role of interfacial rheology in reservoir mixed wettability

E.M. Freer, T. Svitova, C.J. Radke*

Chemical Engineering Department, University of California at Berkeley, Berkeley, CA 94720-1462, USA

Received 18 March 2002; accepted 29 September 2002

Abstract

Since the early 1950s, industrial researchers have recognized that asphaltenic crude oil/water interfaces form so-called ‘‘rigid

skins’’. This work emphasizes the role that such oil/water interfacial microstructures play in establishing the mixed-wet state of

reservoirs. We utilize a new oscillating-drop dynamic tensiometer that sinusoidally and infinitesimally expands and contracts a

crude-oil droplet immersed in brine at a fixed frequency and measures the resulting dynamic interfacial stress from image

analysis and axisymmetric drop-shape analysis. Linear viscoelastic theory permits evaluation of the dilatational interfacial

elastic storage and viscous loss moduli. We find that for two crude oils, designated as Crude AS and Crude AH, immersed in

synthetic sea water, the interface behaves primarily elastically and that the more asphaltenic the oil the stronger is the interfacial

elasticity. Moreover, interfacial elasticity grows slowly in time over days and is clearly manifest even when ‘‘rigid skins’’ are

not visible to the eye. Apparently, macroscopic, networked asphaltenic structures slowly evolve in time at the interface.

Advancing and receding contact angles are also measured on smooth mica surfaces for the same crude oil/brine systems. We

find that water advancing and receding contact angles when measured within hours are about equal (i.e., there is little

hysteresis). However, aging of the drop over days dramatically alters the subsequent advancing and receding contact angles.

Water receding angles grow somewhat in time, but the corresponding advancing angles increase over days towards 180j or

towards complete pinning. Interestingly, the advancing contact angles for both crude oils do not depend on whether the drop is

aged in the brine or in contact with the mica surface. Also, the measured, receding contact angles for both crude oils are much

higher than those commonly assumed in the literature. Fascinatingly, aging kinetics of the contact angles correlates directly with

the aging of interfacial elasticities and interfacial tensions. Based on in situ AFM studies of the asphaltene-coated mica surfaces,

we explain why this happens. Upon rupture of the protective water film and adhesion of the oil droplet to the mica substrate, the

surface underneath the oil droplet is pockmarked with water-wet patches in a Dalmatian microwetting pattern. To our

knowledge the crucial role of oil/water interface aging in controlling wettability changes has not previously been recognized.

Finally, by sketching various primary drainage and imbibition pore-level events, we emphasize the importance of the observed

changes in contact angles towards the evolution of mixed-wet oil reservoirs.

D 2003 Elsevier Science B.V. All rights reserved.

Keywords: Crude oil/brine interfaces; Dilatational surface rheology; Advancing and receding contact angles; Mica surface; Asphaltene deposits;

Atomic force microscopy; Mixed wettability

0920-4105/03/$ - see front matter D 2003 Elsevier Science B.V. All right

doi:10.1016/S0920-4105(03)00045-7

* Corresponding author. Tel.: +1-510-642-5204; fax: +1-510-

642-4778.

E-mail address: [email protected] (C.J. Radke).

1. Introduction

In 1973, Salathiel (1973) demonstrated that water-

flooding of crude oils from reservoir cores reached

s reserved.

E.M. Freer et al. / Journal of Petroleum Science and Engineering 39 (2003) 137–158138

very low oil saturations, but after many pore volumes

of water throughput. For the proposed recovery mech-

anism, Salathiel (1973) pictured interconnected oil

seeping along pore walls dragged by water flow. He

termed the wettability of the core as mixed, whereby

portions of the reservoir rock are oil wet and others

water wet, but each is continuous in the pore space.

Although low water saturations exacerbated mixed

wettability, asphaltenic oils were a prerequisite.

Waterflooding of clean or de-asphalted crude oils

yielded water-wet cores with normal high residual

oil saturations. Since most crude oils contain asphal-

tene components, understanding the mixed-wet reser-

voir state is paramount. Accordingly, much effort has

been directed towards elucidating both the chemical

and physical origins of mixed wettability, particularly

the work of Melrose (1982) and Morrow et al.

(Buckley et al., 1989; Jia et al., 1991; Ma et al.,

1996; Yildiz et al., 1999; Zhou et al., 2000) and

Buckley (1993, 2001; Buckley and Liu, 1998).

Based on this body of knowledge, Kovscek et al.

(1993) outlined a pore-level scenario of how mixed

wettability might evolve in a nascent reservoir. These

authors added two important features to the original

insights of Salathiel: pore corners and rupture of

protective water films. Kovscek et al. (1993) argued

that upon initial invasion of oil into a water-filled

pore, thin water films separate the oil from the pore

walls. The stability of the water cushions arises from

repulsive forces in the thin films called disjoining

pressures. The water films remain stable as long as the

capillary pressure in the porous medium does not

Fig. 1. Deposition of asphaltene film on mineral surface (b) after ruptu

exaggerated in size.

exceed a maximum value, Pcmax (Basu and Sharma,

1996; Kovscek et al., 1993). A great deal of effort has

now been directed to water-film stability, especially

using the so-called ‘‘adhesion’’ test (Buckley et al.,

1997; Liu and Buckley, 1996, 1999; Milter, 1996;

Morrow, 1990), although there has been at least one

attempt to measure directly the maximum capillary

pressure or equivalently the rupture disjoining pres-

sure directly (Basu and Sharma, 1996).

As oil migrates into a reservoir, the capillary

pressure eventually rises to Pcmax, and the protective

water films rupture. In this case, the oil is defined to

be ‘‘adhered’’ to the surface. According to the picture

of Kovscek et al. (1993) the walls of the pores where

the thin films break become oil wet, whereas the

corners of the pores are water filled and remain water

wet. Mixed wettability, as defined by Salathiel (1973),

evolves in this manner. The pore-level scenario of

Kovscek et al. (1993) correctly predicts realistic

capillary-pressure curves in mixed-wet rock using a

bundle of star-shaped capillaries. More recently, the

underlying framework of Kovscek et al. (1993) is

adopted in a number of detailed network simulators to

predict very successfully two- and three-phase capil-

lary pressures and relative permeabilities and electri-

cal resistivity indices (Blunt, 1998, 2001; Man and

Jing, 1999, 2000; Oren et al., 1998).

Unfortunately, there are several deficiencies in the

original picture of Kovscek et al. (1993). First, these

authors did not consider carefully how the pore walls

become oil wet upon rupture of the protective water

films. Fig. 1, taken from the study of Kaminsky and

re of the protective water film in (a). Trapped water pockets are

E.M. Freer et al. / Journal of Petroleum Science and Engineering 39 (2003) 137–158 139

Radke (1997), focuses attention on this issue. Fig. 1a

accentuates the region near the pore wall early in the

drainage process when the thin water layer is present.

In this schematic, various proposed asphaltenic spe-

cies are pictured in the oil phase (Agrawala and

Yarranton, 2001; Murgich et al., 1999; Stausz et al.,

2002). Agreement on exactly what these species are

and how they complex in the bulk oil phase remains

elusive. Even more complicated is how the asphaltene

components configure at the oil/brine interface. Since

the early work of Bartell and Neiderhauser (1949) and

others (Kimbler et al., 1966; Reisberg and Doscher,

1956; Strassner, 1968), interfacial films have been

noted at the asphaltenic crude oil/water interface, such

that upon retraction of an oil droplet in water, wrinkled

skins are visible. Simple reversible adsorption at the

oil/water interface of the smaller and more polar of the

asphaltenic components is an unlikely explanation.

More likely, the interfacial region consists of an

irreversibly congealed, macroscopic film instead of a

reversibly adsorbed monolayer of amphipathic surfac-

tant molecules. Indeed, Neustadter et al. (1979) and

Mohammed et al. (1993) demonstrate that crude oil/

water interfaces, especially those from asphaltenic oils,

exhibit substantial elastic mechanical strength. Among

others, this is one reason why crude oil/water emul-

sions can be difficult to break (McLean and Kilpa-

trick, 1997a,b; Strassner, 1968).

Fig. 1a diagrams the smaller, more polar compo-

nents from the oil phase adsorbed onto the rock

surface. Kaminsky and Radke (1997) argue that

components in the oil phase with even a miniscule

amount of water solubility can readily diffuse through

the water layer to adsorb at the solid surface on

laboratory time scales. Thus, water cushions between

the oil and the rock do not protect against solute

adsorption from the water phase. Since rock surface

adsorption of water-solubilized polar-oil species is

permitted on all surfaces of a pore, any subsequent

wettability alteration must occur homogeneously.

Accordingly, the type of heterogeneous mixed wett-

ability envisioned by Salathiel is precluded.

Altenatively, Fig. 1b illustrates the wettability–

alteration process after water-film rupture. The asphal-

tenic interfacial film, initially confined to the oil/water

interface, now deposits directly onto the rock surface

(Reisberg and Doscher, 1956). It is this asphaltenic

deposit or coating that apparently leads to the alter-

ation of wettability where the thin water films rupture

and no where else along the pore wall (Kaminsky and

Radke, 1997; Salathiel, 1973). During the deposition

process, some water is inevitably trapped in the

asphaltene coating yielding a dalmation pattern of

water patches on the solid surface (Kaminsky et al.,

1994). During aging, some of this trapped water may

migrate from the surface deposit (Liu and Buckley,

1996).

It follows from Fig. 1b that the coherent asphal-

tene-rich film born at the crude oil/water interface

controls, in large part, the resulting oil-wetting behav-

ior of the subsequently asphaltene-coated solid sur-

face. In this paper, we investigate the mechanical and,

in particular, the aging behavior of the crude oil/water

interface and its impact on wettability alteration of the

rock surface.

A second and major deficiency of the Kovscek et

al. (1993) theory of mixed wettability is the imposi-

tion of a zero water receding contact angle of the

three-phase contact line after film rupture in Fig. 1b

and complete pinning of the advancing oil/water

interface on the solid surface (i.e., a water advancing

contact angle of 180j). In actuality, after breakage of

water films, a range of receding and advancing con-

tact angles is expected for various crude oils in

different mineral-content and permeability reservoirs,

rather than one asymptotic case. Commonly, water

receding angles are small, usually less than 30j (Ma et

al., 1996; Yang et al., 2002). However, we show later

that, when appropriately measured with aged interfa-

ces, water receding angles for adhered oil range well

beyond 30j.Values of advancing (hA) and receding (hR) contact

angles dramatically control drainage and imbibition

pore-level events, thereby dictating oil-recovery

behavior. This point is amplified in the detailed

discussion in Appendix A where various primary

drainage and imbibition pore-level events are catego-

rized, depending on the values of hA and hR after oil

adhesion. Fascinatingly, different events occur beyond

those enunciated by Kovscek et al. (1993) and Ma et

al. (1996), depending on the receding and advancing

contact angles that the oil/water interface makes with

the pore surface and on the morphology of the pore

cross section. Hence, understanding mixed wettability

of oil reservoirs demands investigation of what con-

trols advancing and receding contact angles for

Table 1

Properties of crude oils

Property Crude AS Crude AH

API gravity 22.2 24.1

Sulfur (wt.%) 0.52 0.75

Nitrogen (ppm) 4306 4806

Acid number (mg KOH/g) 1.75 1.25

Kinematic viscosity at 40 jC (cSt) 37.3 38

Saturates (wt.%) 49.7 37.5

Aromatics (wt.%) 23.7 34.3

Resins (wt.%) 24 24.3

Asphaltenes, n-C7 insoluble (wt.%) 2.6 3.9


asphaltenic crude oils after adhesion of the oil to the

solid surface. This is a second goal of the present

work. Thus, as opposed to others, we exclusively

study contact angles after oil adhesion. We do not

focus primarily on water-film rupture and adhesion

physics. Both crude oils in this study exhibit adher-

ence.

We attempt, as far as possible, measurements of

water advancing and receding angles reflective of

reservoir processes. Mica is chosen as the solid sur-

face because it is an alumino-silicate mineral and

because it is smooth permitting optical visualization

of the contact angles (Liu and Buckley, 1999; Yang et

al., 1999). The brine is simulated sea water (SSW)

containing both calcium and magnesium hardness.

Images from in situ atomic force microscopy (AFM)

permit study of the deposited asphaltene coatings and

their changes during aging. Due to the strong role that

oil/water interfacial skins are expected to play in

wettability alteration, we also measure dynamic inter-

facial tensions and, for the first time, the dilatational

elastic and viscous moduli of the crude oil/water

interface.

Formation of rigid skins at the oil/water interface

with significant mechanical strength demands inter-

connection of and growth into large-scale network

structures. Such structures are expected to evolve

slowly. Therefore, in this study, we also focus on

aging of both the oil/water interface and the asphal-

tene-coated solid surface.

2. Experiment

2.1. Materials

Two different crude oils, designated as Crude AS

and Crude AH, are used in the experiments. Their

physical properties are listed in Table 1, as determined

by ChevronTexaco Exploration Production. Resin

contents of both crude oils are about the same, but

Crude AH contains significantly more asphaltenes in

comparison to Crude AS. Remaining properties vary

somewhat between the two oils.

Simulated-sea-water (SSW) brine solutions are

made with distilled water further purified using a

Milli-Q filtration unit (greater than 18.2 MV cm re-

sistivity). A liter of synthetic brine contains 24.0047 g

of NaCl, 1.4673 g of both CaCl2 (2H2O) and MgCl2(6H2O), 3.9163 g of Na2SO4, and 0.0382 g of

NaHCO3 (Liu and Buckley, 1996). All salts are from

J.T. Baker Chemical (Phillipsburg, NY) and are of

analytic grade. They are used as received. The pH of

the prepared synthetic brine is 8.0F 0.1. All brine

solutions are pre-contacted with the oil in a 6:1 volume

ratio for at least 8 h to permit equilibration of the brine

with the crude oils. The pH of the oil-equilibrated SSW

brine remains close to 8. In all experiments described

below, the SSW brine is always pre-equilibrated with

the crude oil under study.

Pure muscovite mica from Ted Pella (Redding,

CA) serves as the solid substrate. For each experi-

ment, it is freshly cleaved from the supplied sample

using scotch tape and cut into 10� 20 mm rectangular

slides. The mica slides are then equilibrated with the

aqueous phase (that has been previously equilibrated

with oil) for at least 3 h before any contact-angle or

atomic-force-microscopy (AFM) studies. All experi-

ments are performed at ambient temperature.

2.2. Interfacial tension

To determine the dynamic interfacial tension of

the crude oil/water interface we use pendant-drop

tensiometry, with the less dense oil drop formed

upwards at the tip of a U-bent stainless-steel needle

(3.2 mm in diameter) immersed in the aqueous

brine. The homebuilt apparatus combines both the

interfacial tension and interfacial rheology measure-

ments, as illustrated in Fig. 2. The imaging system

includes a video camera manufactured by Rame-

Hart, a Cole-Parmer fiber-optic illuminator, and two

polarizers. The polarizers eliminate stray light

reflections and also permit fine tuning of the light

Fig. 2. Oscillatory pendant-drop tensiometer.


intensity. Positions of the camera, sample holder,

and drop-dispensing capillary are adjustable in three

directions by means of multi-movement Oriel

Instruments translation stages. Likewise, fine posi-

tioning of the optical glass cell (HellmaR Model

700.00) is obtained using an Oriel Instruments

vertical and horizontal translation stage. The optical

cell is filled with 30 ml of brine and covered with

a 5-ml layer of the crude oil under study to

maintain saturation of the water phase with any

soluble oil components. The cell is sealed with a

TeflonR lid to prevent water evaporation and com-

positional changes of the oil phase. The entire

apparatus is mounted on a pressurized vibration

isolation table from Newport (Model VW-3046-

OPT-2).

After forming a fresh oil drop at the needle tip, the

dynamic tension is followed in time using axisym-

metric drop-shape analysis (Rusanov and Prokhorov,

1996). Image acquisition and regression of the inter-

facial tension is performed with commercially avail-

able Dropimagen software by fitting the Laplace

equation to the drop shape. Dropimagen software

also controls an automatic pipetting system (manufac-

tured by Rame-Hart) that maintains constant drop

volume for the very long time periods (3 days) over

which dynamic tensions are measured. Typical pre-

cision in tension is F 1%.

2.3. Interfacial rheology

Simple visual observation of rigid skins when

brine-immersed crude oil droplets are retracted pro-

vides no quantitative information on their strength.

Hence, we measure the surface dilatational storage

modulus, EV, and the surface dilatational loss modulus,

EW by subjecting the oil/water interface to an infin-

itesimal periodic expansion and contraction. The sur-

face dilatational modulus is defined as

E ¼ drdlnA

¼ EVþ iEW ð1Þ

where A is the oil-drop interfacial area and r is the oil/

water interfacial stress. Since the drop area periodi-

cally oscillates, the dilatational modulus exhibits two

contributions: an elastic part accounting for the recov-

erable energy stored in the interface (storage modulus,

EV) and the dissipative part accounting for energy lost

through relaxation processes (loss modulus, EW). Theinterfacial storage and loss moduli correspond to the

real and imaginary components of the dilatational

modulus (Edwards et al., 1991).


In this work, we apply a periodic strain by differ-

entially oscillating the drop area, and we measure the

periodic stress response using pendant-drop tensiom-

etry and axisymmetric drop-shape analysis. Since the

drop oscillates, the resulting transient Laplace shapes

measure the interfacial stress which includes both

isotropic (interfacial tension) and viscous contribu-

tions (Edwards et al., 1991). For sinusoidal variations

in drop surface area at a given oscillation frequency,

EVand EW are independently determined from the fol-

lowing relations (Tschoegl, 1989):

EV¼ DrAo

DAcosu ð2Þ

and

EW¼ DrAo

DAsinu ð3Þ

where Dr is the amplitude of periodic interfacial-

stress variation, Ao is the unperturbed interfacial area

of the drop, DA is the amplitude of periodic interfacial

area variation, and u is the phase angle between the

periodic stress and strain curves. Results for a typical

drop-oscillation experiment are shown in Fig. 3 for

Crude AH at an oscillation frequency of x/2p = 0.025

Hz. Experimental data for the measured surface area

and interfacial stress are shown as circles and trian-

gles, respectively. To determine the surface storage

and loss moduli from Eqs. (2) and (3) above, the

Fig. 3. Stress response (interfacial stress) to oscillatory strain

(surface area) for Crude AH in SSW at x/2p = 0.025 Hz.

surface area and interfacial stress are fit to the follow-

ing functions

A ¼ Ao þ DAsinxt ð4Þ

and

r ¼ ro þ Drsinðxt þ uÞ ð5Þ

where the unknown parameters ro, Dr, Ao, DA, and uare regressed using a least squares method. Fits of

Eqs. (4) and (5) are shown in Fig. 3 as solid and

dashed lines, respectively. Once the fitting procedure

is complete, the surface storage and loss moduli

follow from Eqs. (2) and (3). Miller et al. (1996)

provide a comprehensive review of oscillatory pend-

ant-drop tensiometry.

Modification of the pendant-drop tensiometer in

Fig. 2 enables sinusoidal variations in the drop surface

area. Oscillation hardware consists of a 50-ml Ham-

ilton gas-tight syringe (Model 1050) mechanically

coupled to a linear piezoelectric actuator manufac-

tured by Physik Instrumente (Model P-840.3). Actua-

tor motion is forced using a Hewlett-Packard function

generator (Model 3325A) that is computer controlled

with National Instruments LabView software. The

piezoelectric actuator is capable of subnanometer

resolution ensuring the smoothest possible drop-vol-

ume oscillation.

Similar to the dynamic-tension measurements

above, surface rheological behavior is followed over

long time frames. To avoid continually oscillating the

drops for such long times, fresh drops are formed for

each experiment and aged for the desired amount of

time prior to imposing periodic oscillation. Eqs. (2)

and (3) demand small strains so that the interface lies

in the linear viscoelastic regime. We set DA/Ao at

2.5%, since above a relative strain of about 4.0%,

nonlinear effects are seen. Below this value, we find

that the surface dilatational moduli are independent of

strain. In order to maintain a Laplacian shape for the

oscillating drop, we restrict attention to drops that are

not highly viscous (Wong et al., 1998).

2.4. Contact angles

A second homebuilt apparatus is used to measure

the advancing and receding contact angles, as illus-

trated in Fig. 4. This apparatus is also mounted on a

Fig. 4. Contact-angle apparatus.


pressurized vibration isolation table from Newport

(Model VH-3036-OPT), and the video-system

includes a Pulnix video camera, a Cole-Parmer

fiber-optic light source, and two polarizers (see

description of the tensiometer above). The positions

of the camera, sample holder, and drop dispenser

(Gilmont micro syringe with a U-bent stainless steel

needle of 0.5 mm diameter) are adjustable in three

directions by means of multi-movement optical

stages. The position of the 100-ml optical glass cell,

filled with the aqueous phase, is also adjustable by

movement of a support plate attached to an optical

support column. A 90j-bent glass rod serves as the

solid-substrate holder. Mica slides are attached to the

flattened end of the bent glass rod by melted Paraffin,

and the rod is then adjusted to fix the mica slide in the

horizontal plane. A drop of oil, usually 1–3 mm3 in

volume, is formed underneath the water-immersed

mica slide and then is slowly brought into a contact

with the solid substrate by the syringe needle. Drop

images are captured by an IMAQ frame-grabber and

interpreted by an in-house software program (virtual

instrument, VI) written in LabView (National Instru-

ments). The VI determines drop edge coordinates,

drop height, diameter of the drop-solid contact, and

left, right, and average contact angles with a max-

imum speed of eight measurements per second. 2nd

order polynomial fitting of 25–50 points nearest to

the drop edges are used to calculate the contact angles.

To check for consistency, a commercial sub-VI pro-

vided by National Instruments is also used for contact-

angle determination. Agreement between the two

angle determinations is always within F 2j. For some

systems, we compare contact-angle measurements

made using our homebuilt setup with those from a

Kruss DSA-10 apparatus. Good agreement is found

for angles less than 90j (F 0.5j) and reasonable

agreement for angles greater than 90j (F 3j). All

contact angles in this work are measured through the

water phase.

Two types of contact angles are measured. While

on the syringe capillary, the oil droplet is brought into

contact with the mica surface and then slowly

increased in volume until the contact line moves

outward. This gives the water receded contact angle.

After this, the oil droplet is decreased in volume until

the contact line now moves inward. This exercise

yields the water advanced contact angle. Extreme care

must be taken to change the oil-drop volume very

slowly to avoid influence of viscous forces on the

contact angle. We use flow rates in the syringe of less

than 0.2 mm3/min. Advanced and receded angles are

studied as function of aging both of the oil/water

interface and of the oil droplet adhered to the solid. In

addition, we report some measurements of relaxing

water advanced contact angles. Here, after initial oil-

Fig. 5. Dynamic interfacial tension of Crude AH and AS.


drop attachment and expansion on the mica surface,

the drop is left to age for a specified period. Oil is then

withdrawn through the syringe needle until an oil

neck forms and ruptures. The resulting remnant drop

is allowed to self relax as a function of time. We

designate this contact angle as a secondary-relaxed

advancing angle.

2.5. Atomic force microscopy

Morphology of the surface of clean and asphaltene-

coated mica substrates is studied using AFM. For in

situ AFM imaging, a Digital Instruments (DI) Mutli-

Mode SPM Nanoscope II is used in the tapping mode.

This mode is convenient for adsorption-layer studies,

giving stable and reproducible images (Svitova et al.,

2001). Probes are oxide-sharpened silicon-nitride can-

tilevers (Model NP-S) with nominal spring constants

of 0.3 N/m. All studies are performed in the aqueous

medium at ambient temperature using the fluid cell

supplied by DI. Besides common flattening along

scan lines, no other image filtering is performed. Scan

rate is usually 1–1.5 Hz, and the driving frequency is

in the range of 30–130 kHz.

The mica slides, prepared as above, are immersed

into the oil-saturated aqueous brine for equilibration

with the solid surface. A large (0.5 ml) oil drop is

carefully attached to a pre-marked area on the brine-

immersed mica surface, aged on the surface for a

desired period of time, and then slowly retracted (at

less than 1 mm3/min) until the oil column breaks from

the capillary tip leaving a remnant oil patch on the

mica surface. With the mica slide still immersed in the

aqueous brine, excess oil is removed from the asphal-

tene surface deposit by ultrasonication under constant

refreshing of the aqueous phase with distilled/deion-

ized water. During mica sample preparation for sub-

sequent AFM, we take special precautions not to

move the mica slide through the water/air interface,

thus avoiding deposition of a thin oil film that may

have previously spread on the water surface. We

choose not to wash the remnant oil left on the mica

surface with any solvents (Buckley et al., 1997; Lord

and Buckley, 2002; Xie and Morrow, 1998; Yang et

al., 1999), as this process likely alters the morphology

of the asphaltenic coating. AFM images are taken

inside and close to the border of oil-drop/mica contact

area. We assert that this sample-preparation method

provides an adequate picture of a natural oil-retraction

event.

3. Results and discussion

3.1. Interfacial tensions

Fig. 5 reports the dynamic interfacial tensions, c(t),on a semi-logarithmic scale for the two crude oils

immersed in the oil-equilibrated SSW. A significant

difference in the tension lowering is evident with

Crude AS providing more tension reduction than

Crude AH. Another important feature of Fig. 5 is

the significant aging of the two oil/water interfaces.

Crude AS apparently achieves a nominally steady

tension value after about 3–4 h, whereas the Crude

AH tension continues to fall for up to 3 days, at which

time a finite slope remains but the experiment was

terminated. When the oil-equilibrated brine in Fig. 5 is

replaced by fresh brine not contacted by oil, no rise in

tension is evidenced. Hence, the material causing

tension reduction in Fig. 5 does not desorb into the

aqueous phase. Surface-active species in Fig. 5 are

irreversibly attached to the oil/water interface, at least

with respect to exchange with the water phase. The

long time scales for tension lowering in Fig. 5 are

reminiscent of those of large molecular weight mol-


ecules that require long relaxation times for adsorption

and reconfiguration at interfaces (Beverung et al.,

1998; Munoz et al., 2000). Apparently, asphaltenes

and resins in the oil phase produce network surface

structures that slowly evolve at the oil/water interface.

If the oil droplet in Fig. 5 is retracted only slightly

for Crude AH, a rigid skin is clearly visible. However,

for the same retraction experiment, Crude AS does not

produce a visible film until the oil is almost completely

retracted into the capillary. This difference and the

difference in time scales for relaxation of the tension

for the two crude oils in Fig. 5 are surely due to the

larger asphaltene concentration for Crude AH (see

Table 1). The ability of Crude oil AS to lower tension

somewhat more effectively may be due to the relatively

large ratio of resin to asphaltene concentration. The

molecular mechanisms by which tension is lowered

when macroscopic skins form are not understood.

Indeed, tensions reported in Fig. 5 at the very long

times may not arise from molecular-scale phenomena,

but rather from a macroscopic elastic interphase that

obeys Laplace’s equation for drop shape.

3.2. Interfacial rheology

Fig. 6 displays the oil/water dilatational surface

moduli for the two crude oils as a function of time on

Fig. 6. Dynamic dilatational elasticity of Crude AH and AS.

a semi-logarithmic scale. Lines drawn on this figure

simply guide the eye; aging times up to 3 days are

investigated. We note that the interfacial loss modulus,

EW, is considerably smaller than the interfacial storage

modulus, EV, for each crude oil. Thus, the asphaltene

films growing at the oil/water interface are primarily

elastic in nature. Consistent with the interfacial ten-

sions shown in Fig. 5, the dilatational moduli evolve

over very long time periods indicative of interfacial

structure development. In particular, Crude AH,

which is more asphaltenic, slowly builds surface

elasticities that surpass those of Crude AS and that

continue to increase in time, just as the interfacial

tension of Crude AH continues to fall in time. Similar

to the dynamic-tension evolution of Crude AS in Fig.

5, the elasticity of this crude oil/water interface rises

more quickly than that of Crude AH, but then levels

off. Clearly, this difference in behavior of Crude AH

and AS reflects the larger asphaltene content of Crude

AH causing slow growth into a strong skin. For a

model heptane/xylene oil containing asphaltenes and

resins, Mohammed et al. (1993) measured the com-

pressional modulus of the oil/water interface using a

Langmuir trough. Similar to our findings, these

authors conclude that the rigidity of the oil/water

interface arises from the formation of an asphaltenic

network structure that strengthens with aging. Identi-

cal findings have recently been reported for long-time

interfacial network formation of asphaltenes adsorbed

at the oil/air interface (Bauget et al., 2001).

Note that Crude AS barely displays a visible skin

upon drop retraction, but nevertheless, does exhibit

substantial dynamic surface dilatational moduli.

Hence, reliance only on the appearance of rigid

interfacial skins may be misleading, since clearly

interfacial elasticity is evident even when skins are

not visible to the eye. Figs. 5 and 6 also suggest that

the relaxation time scales (Lucassen and van den

Temple, 1972) for the Crude AH/water interface are

much greater than those of the Crude AS/water inter-

face, a point that is elucidated further when we

compare secondary-relaxed advancing water contact

angles for Crude oils AH and AS.

The most important point from Fig. 6, and also

from Fig. 5, is the long time aging of the oil/water

interface characteristic of surface asphaltenic net-

works (McLean and Kilpatrick, 1997a,b; Mohammed

et al., 1993; Neustadter et al., 1979). As noted in

Fig. 8. Receding and advancing contact angles for Crude AS.


Section 1, we expect that when protective water films

rupture, the oil/water asphaltenic film deposits directly

onto the reservoir rock. Accordingly, it is the phys-

icochemical characteristics of the oil/water film that

initially control wettability alteration.

3.3. Oil adhesion

As part of the contact-angle studies, standard adhe-

sion tests were performed (Buckley et al., 1997; Liu

and Buckley, 1996, 1999; Milter, 1996; Morrow,

1990). In the synthetic seawater, both crude oils adhere

to mica over the pH range from 4.5 to 9.5. Crude AH

does exhibit a transition to nonadhesion near pH= 9.5,

but we are unable to examine higher pH values because

of aqueous hardness precipitation. Thus, for the natural

pH = 8 conditions in this study, neither crude oil is

protected by a stable water film. This means that upon

oil entry into a pristine reservoir, wettability alteration

to the mixed-wet state occurs at relatively high water

saturations. The receding contact angle and pore shape

now determine how mixed wettability evolves during

drainage per Fig. A1 of Appendix A.

3.4. Contact angles

Figs. 7 and 8 give the main wettability results of

this study. Here we graph advanced and receded water

Fig. 7. Receding and advancing contact angles for Crude AH.

contact angles of the two crude oils on mica as a

function of aging time on semi-logarithmic scales.

Crude AH is shown in Fig. 7 and Crude AS in Fig. 8.

Lines drawn in the figures again merely aid the eye.

Aging time in these plots represents two different

physical processes. First, the oil droplet is aged in the

oil-equilibrated SSW and then brought into contact

with the mica surface for contact-angle determination

(per the procedures described above in Section 2).

These data are represented by open symbols. Second,

the oil droplet is brought into contact with the mica

surface immersed in the oil-equilibrated SSW and left

for the aging time before contact-angle measurements.

These data are exhibited as closed symbols in the two

figures. The fascinating result is that both types of

aging give identical results for the advanced and

receded contact angles of both crude oils for aging

times up to 5 days.

Hence, the dominant aging process over this time

period is that of elastic skin development at the oil/

water interface, a rather unexpected result. Appa-

rently, upon first rupture of the aqueous layer between

the oil drop and the solid substrate, water is left on the

solid substrate making aging of the deposited asphal-

tene coating somewhat akin to the aging of a drop

immersed in bulk water. Dalmation water patches (cf.

Fig. 1b) are repeatedly observed underneath oil drop-

Fig. 9. Secondary-relaxed contact angles for Crude AH.


lets adhered to solid substrates (Buckley et al., 1997;

Ese et al., 2000; Kaminsky et al., 1994; Milter, 1996;

Yang et al., 1999) and reconfirmed later here using

AFM.

The second striking feature from Figs. 7 and 8 is

the very large growth in time of the advanced angle.

After over 100 h, both crude oils approach hA= 180j,the complete pinning case originally discussed by

Kovscek et al. (1993) and illustrated in Fig. A2e

and f of Appendix A. However, if not aged, the

advanced angle is low, less than 90j, giving totally

different pore-level drainage and imbibition events

(cf. Figs. A1 and A2). Indeed, if the advanced contact

angle after oil attachment is less than the critical pore

corner angle, water displacement of oil occurs as if the

pore is water-wet yielding high residual oil saturations

(see Fig. A2b). Thus, it is crucial, and not well

recognized, to age the system before contact angles

are assessed.

Note that hA for Crude AS ages much more

quickly than that for Crude AH. This result emerges

directly from the aging of the oil/water interface, as

predicted from the dynamic interfacial tension in Fig.

5 and, most strikingly, from the dilatational interfacial

elasticities in Fig. 6. The higher asphaltene concen-

tration in the AH oil develops stronger interfacial

structures that take longer to form. However, the

long-term advanced angles do not seem to differ that

much between the two crude oils. Each approaches

180j.Receding angles in Figs. 7 and 8 do not demon-

strate as dramatic effects upon aging. However, aging

cannot be ignored. Receding angles increase in time,

again at a rate dictated by the asphaltene content of the

crude oil. Somewhat surprising is the rather large

values of hR. As highlighted in the introduction,

receding contact angles are normally thought to be

less than 30j (Ma et al., 1996; Yang et al., 2002). In

our work, receding angles up to 50j are found for the

aged AS oil/brine system. This observation has impor-

tant implications for reservoir wettability alteration, as

now oil may directly enter pores whose critical corner

angles are less than hR, as illustrated in Figs. A1d and

A4 of Appendix A.

Perhaps one reason why the receded angles in Figs.

7 and 8 are higher than normally reported is because

of the slow contact-line displacement rates employed

in our work. By increasing this rate, we find smaller

values for hR (and higher values for hA). Thus, toobtain meaningful receding contact angles, it is impor-

tant to minimize the rate of contact-line motion, in

addition to aging sufficiently long.

We also measure secondary-relaxed advancing

water contact angles, which reflect the relaxation of

a crude-oil droplet over a previous asphaltene surface

coating. These are reported in Figs. 9 and 10 for the

AH and AS crude oils, respectively. In Fig. 9, we find

that after sufficient aging of the AH-crude-oil drop on

the mica surface, the advancing angle is high (see Fig.

7) but there is no relaxation of the remnant drop.

Rather, once the drop is isolated by needle removal,

its configuration remains unchanged. Apparently, the

strong elastic skin of Crude AH freezes the drop not

permitting relaxation on the time scales investigated.

Conversely, the AS crude oil in Fig. 10 does relax.

Indeed, Fig. 10 reveals that the secondary-relaxed AS

contact angle falls below 90j over the experimental

time scale if the drop is aged on the mica surface for

less than about 3 h. The results in Figs. 9 and 10 are in

accord with the interfacial rheology experiments in

Fig. 6 that reveal long elastic relaxation times for

Crude AH compared to Crude AS.

The importance of secondary-relaxed advancing

contact angles lies in the behavior of rivulets that

can form on pore walls during forced imbibition, as

Fig. 10. Secondary-relaxed contact angles for Crude AS.


described in Fig. A2f. For secondary-relaxed ad-

vanced contact angles greater than 90j, rivulets are

unconditionally stable and can slowly produce oil as

Fig. 11. AFM of asphaltene/oil deposits o

described by Salathiel (1973). In the converse case,

where the secondary-relaxed advanced contact angles

are less than 90j, the rivulets now become unstable

and breakup in the axial direction leaving trapped oil

droplets along the asphaltene-coated pore walls.

3.5. Atomic force microscopy

Figs. 11 and 12 show, respectively, AMF images of

what is left on the SSW-immersed mica surface after

contact with Crude AS and Crude AH oil droplets,

aging for 3 days, and subsequent ultrasonic washing,

as described in the experimental section. In Fig. 11 for

Crude AS, we observe the asphaltene deposit near the

drop edge. Thus, the smooth upper right portion of

this picture shows the mica surface beyond drop

contact. Here the mica remains water wet. Only

directly beneath the drop is there any asphaltenic

material that changes surface wettability. In the lower

left part of Fig. 11, we see the asphaltenic oily deposit.

It is composed of oil microdroplets protruding from

bare mica regions that originally correspond to trap-

ped water droplets, as pictured in Fig. 1B. This leads

n mica: Crude AS aged for 3 days.

Fig. 12. AFM of asphaltene/oil deposits on mica: Crude AH aged for 3 days.

Fig. 13. AFM of asphaltene/oil deposits on mica: Crude AS aged for 3 weeks.



to the so-called dalmation wetting patterns previously

reported by Kaminsky et al. (1994) and others (Buck-

ley et al., 1997; Buckley, 2001; Ese et al., 2000; Yang

et al., 1999).

Note that for Crude AH in Fig. 12, the oil micro-

droplets are somewhat larger, but rather sparsely

distributed compared to Crude AS after 3 days of

contact. Apparently, the stronger rigid oil/water films

for Crude AH initially trap more water adjacent to the

mica surface. Microscopic water/oil contact angles for

the surface droplets, as estimated from AFM image

analysis, are f 150j for Crude AS and f 155–

160j for Crude AH. These values are in reasonable

agreement with the macroscopic, water advancing

angles (cf. Figs. 7 and 8) of these oil drops on mica.

There is not a large difference between Crude AS and

Crude AH microdroplets after 3 days of contact with

mica.

Next, Figs. 13 and 14 display AFM images of

Crude AS and Crude AH oil remnants deposited on

the mica surface after 3 weeks of aging in SSW brine.

For Crude AS in Fig. 13, the microdroplets appear

Fig. 14. AFM of asphaltene/oil deposits on

quite similar to those after aging for 3 days in Fig. 11.

However, there are fewer trapped-water domains

indicating water escape during prolonged aging at

the mica surface. More dramatic aging behavior is

observed for Crude AH in Fig. 14. Here there is a

much larger amount of asphaltenic deposit with con-

siderably smaller microdroplets that merge into each

other. This coating has a distinctive scaly appearance,

especially when compared to that for Crude AH

reported in Fig. 12. A possible reason is that when

the aged oil/water film above the trapped water

pockets collapses, a much finer textured coating is

deposited on the mica surface.

Figs. 11–14 confirm many of the ideas presented

in the mixed-wettability picture outlined in the

introduction. Wettability alteration arises mainly

from an asphaltene coating deposited on the rock

surface where intervening water films rupture.

Hence, the process is one of deposition of the oil/

water asphaltenic film. Aging at the oil/water inter-

face and aging at the rock surface are both impor-

tant.

mica: Crude AH aged for 3 weeks.


4. Conclusions

Advancing and receding contact angles that

emerge after the rupture of protective water films

between invading crude oil and reservoir rock are

paramount to the evolution of the mixed-wet reservoir

state. Configurations of the oil/water interface in

cornered pores depend strongly on the pore cross-

section shape and on the advancing and receding

contact angles. A rich variety of behaviors may arise

during drainage and imbibition processes including

mixed-wet pores where the pore walls are oil-wet and

the pore corners water wet, complete oil-wet pores,

and lens, rivulet and oil-globule formation depending

on the relative magnitudes of the advancing and

receding contact angles and the critical pore-corner

angle.

When crude oil first invades into a pristine reser-

voir, asphaltenic material accumulates at the oil/water

interface. Depending on how asphaltenic the oil is,

rigid skins develop at the oil/water boundary. For the

first time, we measure the dilatational strength of

these skins using a periodically-oscillating pendant

oil drop. For the two oils studied, Crude AH slowly

evolves a strong elastic oil/water film. Crude AS, with

lower asphaltene content, shows a more quickly

developing dilatational storage elasticity. However,

leveling off of the dilatational storage elasticity after

this initial increase indicates weak network formation.

Advancing and receding contact angles after adher-

ence of these two crude oils to mica exhibit dramatic

aging behavior with both angles increasing in time

over days. Fascinatingly, we find that aged oil/water

interfaces exhibit water receding angles that are much

larger than the commonly expected value of 30j.Contact-angle maturation parallels that seen in the

elasticities of the oil/water interface and indicates that

the age of the oil/water interface when protective

water films rupture is a critical parameter in the

development of mixed wettability.

Atomic force microscopy of the asphaltene coat-

ing confirms a deposition process whereby asphal-

tenic material originally at oil/water interface coats

directly onto the solid surface once the water film

ruptures. The subsequent advancing and receding

contact angles of the asphaltene-coated solid surface

then control pore-level drainage and imbibition

events. Aging of the asphaltene deposit on the

solid surface expels trapped water giving a more

coherent and finer textured coating depending on

the asphaltene content of the crude oil. Thus, aging

of the oil/water interface and the asphaltene-coated

surface are both important in the evolution of

mixed wettability.

Only two crude oils were studied in this work with

only one solid surface (mica) and one brine compo-

sition (synthetic sea water at a natural pH of 8) and at

ambient temperature. Examination of a wider range of

oils, solids, aqueous-solution compositions, and tem-

peratures is necessary before the aging behaviors

observed here at both the oil/water and solid interfaces

can be generalized.

Nomenclature

A surface area, m2

Ao unperturbed surface area, m2

C mean curvature of oil/water interface, m� 1

E dilatational modulus, N/m

EV storage modulus, N/m

EW loss modulus, N/m

g(h) = p� 3h + 6cosh sin(p/3� h)i imaginary number

Pc capillary pressure, Pa

Pcmax disjoining pressure of thick wetting-film

collapse, Pa

Po oil-phase pressure, Pa

Pw water-phase pressure, Pa

R radius of largest inscribed circle in pore

cross-section, m

t time, s

x distance from pore corner to arc meniscus, m

a half corner angle

u phase angle between periodic stress and

strain

c interfacial tension, N/m

r interfacial stress, N/m

ro unperturbed interfacial stress (i.e., interfacial

tension), N/m

hA advancing contact angle

hC critical contact angle

hL limiting contact angle

hR receding contact angle

DA amplitude of periodic drop area change, m2

Dr amplitude of periodic interfacial stress

change, N/m

x oscillation frequency, s� 1


Acknowledgements

This work was supported by the U.S. Department

of Energy under Contract No. DC03-76SF00098 to

the Lawrence Berkeley Laboratory of the University

of California. We thank Drs. E. deZabala, J. Creek,

and S. Subramanian of the ChevronTexaco Explora-

tion Production for supplying the crude oil samples.

Appendix A. Role of advancing and receding

contact angles in pore-level events

To illustrate the importance of water advancing and

receding angles on the development of mixed wett-

ability in reservoir rock, consider an equilateral trian-

Fig. A1. Primary drainage in an equilateral triangular pore. Shading represe

shown as thick solid lines.

gular pore cross-section with smooth walls, as

illustrated in Fig. A1. Such a pore shape is highly

idealized, but is sufficient to document the roles that hAand hR play in oil-recovery behavior (Ma et al., 1996).

Initially, the pore is filled completely with water, and

the solid walls consist of oxide minerals that are

naturally water wet to a non-asphaltenic, clean oil. As

oil migrates into the reservoir during primary drainage,

the capillary pressure, Pc, rises. Since the concepts of

wetting and nonwetting phases become ambiguous in

what follows, we define the capillary pressure as the

difference between the oil and water-phase pressures

Pc ¼ Po � Pw ¼ cC ðA1Þwhere P is pressure with the subscripts o and w

denoting the oil and water phases. c is the interfacial

nts the oil phase and asphaltene deposition on the mineral surface is


tension between the oil and water, and C is the mean

curvature of the oil/water interface in the pore.

Oil first enters the larger pores when the capillary

pressure exceeds the entry curvature value corre-

sponding to a zero water receding contact angle

(Ransohoff et al., 1987), and drainage commences at

C ¼ 1:77=R ðA2Þwhere R is the inscribed-circle radius of the pore. This

oil configuration consists of circlular arcs in the

projected prospective of Fig. A1. Throughout, pos-

itive capillary pressures (i.e., Po>Pw) correspond to

oil/water interfaces that are convex to the oil phase.

Following classical Deryagin–Frumkin theory (Der-

gaguin, 1955; Hirasaki, 1991), a zero contact angle is

equivalent to having a thin water film sandwiched

between the crude oil and the pore wall and stabilized

by repulsive disjoining forces. This situation is por-

trayed in Fig. A1 by thin black lines along the solid

walls. As oil accumulates in the reservoir, the capil-

lary pressure rises, water recedes at zero contact angle

toward the pore corners, and eventually the thin

protective water films rupture depositing asphaltenic

material, originally formed at the oil/water interface,

directly onto the solid walls (Kaminsky and Radke,

1997; Kaminsky et al., 1994; Kovscek et al., 1993).

Fig. A1b portrays this series of events. The solid walls

in Fig. A1b are shown as dark heavy lines depicting

adherence of the oil to the pore surfaces through an

asphaltene coating. Because the thin protective water

films are now broken, finite receding contact angles

emerge in the water-drainage problem.

Thin water films rupture at a positive capillary

pressure commonly designated as Pcmax (Basu and

Sharma, 1996; Kovscek et al., 1993). Smaller pores

whose entry capillary pressures lie above Pcmax are

invaded and drain slightly differently than those in

Fig. A1b. Protective water films never form, and

asphaltene material deposits onto the pore walls upon

initial oil invasion into the pore. The entry capillary

curvature no longer follows Eq. (A2) but corresponds

to that of the water receding angle for the asphaltene-

coated surface (Ransohoff et al., 1987)

C ¼ �gðhRÞ=Rh3

ffiffiffi3

pcoshRF

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi27cos2hR þ 3

ffiffiffi3

pgðhRÞ

q i

for a ¼ p=6 ðA3Þ

where g(hR) = p� 3hR + 6coshRsin(p/3� hR) and a is

the half corner angle (i.e., a= 30j for equilateral

triangular pores). (Note in this appendix we use angles

in radians when they appear in formulae and in

degrees otherwise). The entry configuration and sub-

sequent further water drainage is pictured in Fig. A1c.

Configurations in this diagram are identical to those

occuring later in Fig. A1b after Pcmax is exceeded and

the water films break. Thus, after water-film rupture,

Figs. A1b,c are identical.

Every pore corner has a characteristic critical angle

given by hC = 90j� a (Concus and Finn, 1974; Ma et

al., 1996; Wong et al., 1992). If the water receding

angle after water-film rupture is less than the critical

angle, the oil/water interfaces advance into the pore

corners at hR( < hC) depositing an asphaltene coating

underneath until the connate water configuration is

established. This scenario is pictured in Fig. A1b,c.

Conversely, if the water receding is greater than the

pore-corner critical angle, then crude oil completely

fills the pore, coating the pore walls everywhere with

asphaltenes, including in the pore corners. Fig. A1d

illustrates this situation. Fascinatingly, in this case, the

pore may be considered as oil-wet even though the

receding water contact angle is less than 90j.As noted in the introduction, it is often thought that

water receding angles are small, usually less than 30j(Ma et al., 1996; Yang et al., 2002). Thus, common

perception is that complete oil filling in Fig. A1d does

not happen (unless, of course, hR>90j). Accordingly,Figs. A1b,c represent the expected behavior. How-

ever, our contact-angle measurements in Fig. 8 dem-

onstrate that water receding angles can be significantly

greater 30j and can realistically exceed the critical

pore-corner angle, hC. Hence, it is possible for the

configuration in Fig. A1d to emerge. Such a case is

characterized by heterogeneous wettability with some

pores completely oil filled and others that are small and

completely water filled. This type of mixed wettability

is contrasted to that in Figs. A1b,c where the wett-

ability is different within the same pore. Our discus-

sion of primary drainage thus emphasizes the need for

understanding hR once water films break and the crude

oil adheres to the rock surfaces.

We turn our attention now to the primary imbibition

process where the role of the water-advancing angle is

emphasized. A number of subcases arise depending on

the magnitude of hA and on whether the connate-water


saturation corresponds to configurations in Figs. A1a–

d. We discuss each of these cases in turn.

Fig. A2a reflects the first and simplest case where

connate-water saturation is at a capillary pressure

below that of water-film rupture (i.e., below Pcmax as

in Fig. A1a). Since the water advancing angle with

water-film cushions remains zero, the water/oil inter-

Fig. A2. Primary imbibition in an equilateral triangular pore. Shading repr

shown as thick solid lines, and pinning of the three-phase contact line is

face advances, upon spontaneous imbibition, toward

the pore inscribed circle in Fig. A2a, a configuration

that is unstable (Kovscek et al., 1993). The resulting

axial liquid thread in the pore undergoes capillary

snap-off resulting in trapped oil blobs (Chambers and

Radke, 1990; Gauglitz et al., 1987; Kovscek and

Radke, 1996; Ransohoff et al., 1987).

esents the oil phase, asphaltene deposition on the mineral surface is

represented by small open circles.

Fig. A3. Limiting contact angle for an equilateral triangular pore.


An almost identical case emerges when the initial

state is that in either Fig. A1b or Fig. A1c where the

pore walls away from the corners are coated by

asphaltene deposits yielding a finite water advancing

contact angle, hA ( < hC). Since advancing angles are

greater than (or equal to) receding angles, the oil/

water interface remains pinned, but bows until the

advancing angle is attained. Once this happens and

since the water-advancing angle is less than the

critical angle of the pore corners, the oil/water inter-

faces advance until the contact lines touch yielding yet

another unstable configuration and trapped residual

oil. Fig. A2b illustrates this sequence. The amount of

trapped residual oil is less than that for the completely

water-wet case in Fig. A2a, but marginally so.

A second imbibition behavior emerges for the

initial state in Figs. A1b,c whenever hA is greater

than hC. In this case, upon spontaneous water imbi-

bition into the pore of Fig. A1b or Fig. A1c, the

contact line remains pinned, but the contact angle

increases until hC is attained. At this point, the

capillary pressure falls to zero, and the oil/water

interface is flat. Further water imbibition now occurs

under forced conditions where Pc is negative (i. e., the

oil/water interface flexes toward the oil phase). The

three-phase contact line hinges allowing negative

curvatures, but remains pinned until hA is attained.

Now once hA is reached and provided that hA is

greater than hC but less than 90j, the contact lines

translate along the pore walls and away from the

corners until they encounter one another, as shown

in Fig. A2c. Yet again, this particular configuration is

unstable to fluctuations in the interface shape, and the

oil core breaks to form trapped oil globules. The

amount of residual oil is, however, smaller than either

of the two cases described above.

The maximum advancing contact angle at which

the translating arc menisci meet at along the pore wall

is 90j, which is the largest advancing angle for which

snap-off can occur. If hA is greater than 90j but less

than or equal to 180j� hC, another scenario emerges

that is shown in Fig. A2d. Here the arc menisci

advance toward the pore center and approach closest

away from the walls forming oil lenses within the

pore. Continued expansion of the oil/water interface

leads to lens rupture leaving small oil globules trapped

within the pore and oil rivulets on the centers of the

pore walls.

When hA exceeds 180j� hC, a more complicated

but important behavior emerges, as portrayed in Fig.

A2e. Here the corner-water contact angle increases

until it reaches a limiting value that we designate as

hL. The limiting angle corresponds to the particular

arc-meniscus curvature that just equals the water-entry

curvature into an oil-filled pore at the specified water

advancing angle hA. C in Eq. (A3) is now defined by

(Ransohoff et al., 1987) replacing the receding angle

with the advancing angle

C ¼ �gðhAÞ=Rh3

ffiffiffi3

pcoshAF

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi27cos2hA þ 3

ffiffiffi3

pgðhAÞ

q i

for a ¼ p=6 ðA4Þ

Once the arc meniscus bows to attain the curvature C

in Eq. (A4), the angle that water makes with the pore

wall defines hL. As opposed to hC, the limiting angle

is not a purely geometric quantity, but depends on

how far the water/oil interface penetrates into the pore

corners at the end of primary drainage (i.e., it depends

on the connate-water saturation). Fig. A3 graphs the

limiting contact angle as a function of the reduced

distance from the pore corner, x/R, where x is the

distance along the pore wall from the corner. Clearly,

x gauges the water content in the pore (Ma et al.,

1996). The limiting contact angle increases almost

linearly with x/R. Note that hL is considerably less

Fig. A4. Water entry into an oil-filled pore (forced primary

imbibition): hR>hC.


than the corresponding advancing contact angle and

always lies below 90j. It is larger, however, the largerthe value of hA. When the oil/water interfaces in Fig.

A2e distend away from the corner such that the

contact angle reaches hL, water enters into the center

of the pore, and oil lenses form (Kovscek et al., 1993).

Eq. (A4) gives the water entry curvature for this event.

Thus, the advancing contact angle in the center of the

pore (i.e., hA) is not the same as the pinned contact

angle in the corners (i.e., hL), but the curvatures of thetwo oil/water interfaces match.

Additional forced imbibition proceeds by the central

core of water advancing toward the pore corners with

the corner-water contact line remaining pinned but with

increasing corner angles greater than hL. Provided oil iseverywhere continuous, very low oil saturations can be

reached in this manner, but at very slow rates. The

configurations in Fig. A2e are those originally of

Kovscek et al. (1993) in their description of the origin

of mixed wettability in reservoirs. However, the picture

of Kovscek et al. (1993) employed only the case of

hR = 0 and hA= 180j (complete pinning).

Eventually, the expanding oil/water interface in the

pore center encounters that of the pore corner leading

to lens rupture. This event corresponds to the termi-

nation points of hL versus x/R lines in Fig. A3. Oil

rivulets appear on the pore walls near the corners, as

illustrated in Fig. A2f. Since the water advancing

contact angle is greater than 120j, these rivulets are

stable (i.e., rivulets with oil contact angles less than

90j are stable to axial breakup whereas those with

angles great than 90j are unstable) (Davis, 1980). The

stable rivulets slowly empty under the imposed water

pressure gradient into oil-continuous regions in sur-

rounding downstream pores.

The final imbibition event to describe reflects the

connate-water state in Fig. A1d. Here, the water

receding angle is greater than the corner critical angle,

hC. Water imbibition can only occur under forced

conditions and then only for advancing angles greater

than 180j� hC. As illustrated in Fig. A4, the process

is identical to water entry in Fig. A2e, except that oil

completely fills the pore corners. As water continues

to invade the pore, oil drains from the corners pro-

vided there is continuity with oil in other nearby

pores. Again, the process is very slow because of

the large hydrodynamic resistance for fluid flow in

corners (Ransohoff and Radke, 1988).

The picture painted above is highly oversimplified.

Pore cross-sections are taken as triangular, and the

pore walls are smooth. There is no recognition of the

distinction between pore bodies and pore throats, and

no interconnectedness is accounted for. A pore-size

distribution is implicit in the discussion but not

utilized. Although the rich drainage and imbibition

events described above serve as rules for later network

simulations, our purpose here is to emphasize the role

of the water advancing and receding angles in under-

standing waterflooding from mixed-wet reservoirs.

Rupture of water films and oil adherence to pore

walls is a critical foundation for establishing mixed

wettability, but the subsequent values of hA and hR,characteristic of oily asphaltene-coated rock surfaces,

dramatically control the course of water imbibition

and oil recovery.

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interfacial rheology in reservoir

Documents

advancing contact angles

corresponding advancing

crude oils

crude ah

role of interfacial

crude oilbrine systems

interfacial tensions

interfacial elasticity