AUTHOR

Alton Brown � 1603 WaterviewDrive, Richardson, Texas, 75080;altonabrown@yahoo.com

Alton Brown worked as a research geologistat ARCO’s Plano, Texas, Research Centerfrom 1980 until ARCO’s merger with BP.Since then, he has been an independentconsultant. His research interests includepetroleum migration, carbonate sedimentologyand diagenesis, basin analysis, and gasgeochemistry.

ACKNOWLEDGEMENTS

I thank Russell Davies for constructivecomments early in manuscript preparationand for later reviews and suggestions. I alsothank AAPG reviewers Quentin Fisher andJim Handschy for additional comments andsuggestions.

Capillary effects onfault-fill sealingAlton Brown

ABSTRACT

Capillary-pressure models and concepts were used to evaluate the

effects of excess pressure, capillary hysteresis, and relative perme-

ability on fault-fill sealing. Overpressured fault fill (fault water pres-

sure higher than reservoir water pressure) always increases the height

of the sealed petroleum column. The sealing interface moves into

the overpressured fault fill where water flows from the fault into

the reservoir. Underpressured fault fill decreases petroleum column

height only where cross-fault water flow is absent. If water flows

across the fault, column height is unaffected. Water cannot flow

across faults where the reservoir is at irreducible water saturation.

Relative permeability smoothes the transition from membrane

sealing to leakage, and thus, hydraulic-resistance sealing is possible

after membrane-seal failure. The height of membrane sealing by

homogeneous, water-wet fault fill exceeds the height of hydraulic-

resistance sealing at geological leakage rates. Hydraulic-resistance

sealing becomes more significant when charge and leakage are both

high, when trap life is short, and during production.

Trap leakage rate through a water-wet, fault-fill pore network

cannot exceed trap charge rate during initial trap charging. If charg-

ing slows, leakage exceeds charge until a new equilibrium column

height develops. If charge stops, the seal continues to leak until the

petroleum column height is reduced substantially below its original

height. Membrane sealing is reestablished at low capillary pressure.

Theoretically, restored seal capacity is close to the original capacity.

Cross-fault pressure and petroleum column height cannot be

converted to seal capacities because charge history and seal type in-

fluence sealing. Cross-fault pressure data should be analyzed in light

of the charge and pressure history so the different controls on fault-

fill sealing can be assessed.

INTRODUCTION

Fault-sealing behavior controls distribution and production charac-

teristics of fault traps. Two fault-fill–sealing mechanisms have been

Copyright #2003. The American Association of Petroleum Geologists. All rights reserved.

Manuscript received November 16, 2001; provisional acceptance April 16, 2002; revised manuscriptreceived July 15, 2002; final acceptance August 1, 2002.

DOI:10.1306/08010201127

AAPG Bulletin, v. 87, no. 3 (March 2003), pp. 381–395 381

proposed: membrane and hydraulic-resistance seal-

ing (Heum, 1996). The relative importance of the two

mechanisms remains controversial (Sales, 1993; Heum,

1996; Fulljames et al., 1997). The influence of cross-

fault water-pressure differences on fault-fill sealing is

also controversial (Myers, 1968; Heum, 1996; Bjorkum

et al., 1998).

The purpose of this article is to analyze the in-

fluence of capillary-pressure and relative permeability

variations on fault-fill sealing. Capillary-pressure varia-

tions within the fault fill control membrane sealing in

the presence of cross-fault water-pressure differences. Ef-

fective permeability changes with capillary pressure; thus,

the relative importance of membrane and hydraulic-

resistance sealing in homogeneous, water-wet faults can

be modeled as a function of capillary pressure. Hystere-

sis effects on fault-seal leakage are also evaluated.

The sealing concepts presented in this article are

based on homogeneous fault-fill properties. Real fault

fill is heterogeneous (Knipe et al., 1998). Homogene-

ity is assumed so that the article can focus on mecha-

nisms and rates, not heterogeneity characterization. The

sealing concepts developed here can be applied to well-

characterized heterogeneous fault fill in much the same

way that capillary pressure controls on saturation and

relative permeability developed for homogeneous res-

ervoirs can be applied to real, heterogeneous reservoirs.

BASIC CAPILLARY-PRESSURE CONCEPTS

Petroleum sealing is controlled by the interaction of

petroleum with water in the pore system. It is therefore

difficult to discuss matrix-sealing properties of the fault

fill without also discussing the capillary properties of

the system. The capillary pressure (Pc) is the difference

between the petroleum pressure (Pp) and water pressure

(Pw) at the same position. Natural capillary pressure

commonly develops from buoyancy of a static petro-

leum column in water (Figure 1). The elevation where

capillary pressure is zero is called the free-water level.

The petroleum and water pressures relative to the free-

water level are calculated from the height (H ) above the

free-water level multiplied by the difference of petro-

leum and water fluid densities (Up and Uw, respectively)

and the hydrostatic gradient (g).

Pc ¼ Pp � Pw ¼ rpgH � rwgH ¼ �rgH ð1Þ

Pore systems can be characterized by total porosity

and injection capillary-pressure curves. The injection (or

drainage) capillary-pressure curve is a plot of fluid satu-

ration (horizontal axis) as a function of capillary pressure

(vertical axis) as the wetting fluid drains from the rock

(Jennings, 1987). This mimics filling accumulations.

Injection curves have three important characteristics:

382 Capillary Effects on Fault-Fill Sealing

01

Pe

PdPlateau

W-Rhysteresisloops

Pt

Si

Smax

FWL

Water + oil production;transition zone

Water-free production

Water production;spotty stain

Water production

PWC

Fractional Hg saturation

Log

(Cap

illar

y Pr

essu

re)

Figure 1. Capillary-pressurecurves. Equilibrium mercuryinjection curve is shown by theheavy solid line. Withdrawal-reinjection (W-R) hysteresisloops (mercury withdrawalfollowed by reinjection) areshown by dashed lines witharrows showing the direction ofsaturation change. Equilibriuminjection does not developirreducible saturation, and Smax

is the maximum mercury satura-tion attained at the maximumapplied capillary pressure.Air-brine tests (thin solid line)develop an irreducible watersaturation (S i). Productivezones are shown on the right.Zone thickness is distorted bylogarithmic capillary-pressurescale. Symbols are identifiedin Table 1.

the threshold pressure, the pressure at which water

saturation becomes irreducible, and curve shape factor

(Figure 1). The threshold pressure, P t, is the pressure at

which a continuous thread of nonwetting fluid extends

across the sample and petroleum permeability is great-

er than zero at higher capillary pressure. Threshold pres-

sure through an infinite medium is interpreted at the

inflection between the concave downward and concave

upward curvature in the lower part of the injection pla-

teau measured on small samples (Katz and Thompson,

1987). In practice, threshold pressure is approximated

by the displacement pressure (Pd), the extrapolation of

the plateau to 100% wetting-phase saturation (Jennings,

1987; Figure 1). At irreducible saturation (S i), wetting-

fluid permeability is zero; thus, fluid saturations remain

constant with increasing capillary pressure. Pressure at

initiation of irreducible saturation is approximated by

the pressure just above the plateau. The shape factor (l)

describes the slope of the plateau and abruptness of

change from plateau to irreducible water saturation.

Saturation as capillary pressure decreases is de-

scribed by the withdrawal curve (Figure 1). Withdrawal

mimics natural leakage from a petroleum accumulation.

Withdrawal curves are characterized by residual petro-

leum saturation at zero capillary pressure and petro-

leum saturation higher than that of the injection curve.

High saturation is caused by snap-off and isolation of

petroleum in large pores with small throats (Wardlaw

and Taylor, 1976).

Capillary-pressure curves are commonly measured

with the mercury vacuum system. This has the advan-

tage of rapid analysis and high reproducibility. Mercury-

injection, capillary-pressure tests have two major disad-

vantages. First, mercury vacuum capillary pressures have

to be converted to reservoir capillary pressure. The res-

ervoir surface tension and wettability necessary for con-

version are poorly known in most reservoir and explora-

tion settings (Schowalter, 1979; O’Connor, 2000).

Second, mercury vacuum tests do not provide a good

estimate of irreducible saturation or pressure at which

irreducible saturation develops, because mercury does

not displace a fluid as capillary pressure increases (Mor-

row, 1971; Wardlaw and Taylor, 1976).

FAULT-FILL SEALING

Upward-increasing capillary pressure divides potential

seal behavior of water-wet, homogeneous, fault fill into

three zones: membrane sealing, hydraulic-resistance seal-

ing, and seal failure (Figure 2). Membrane sealing occurs

when petroleum has insufficient capillary pressure to

invade the seal. This zone occurs in all water-wet rocks.

Higher in the petroleum column, capillary pressure is

sufficient to invade the fault fill; thus, petroleum leaks.

Low in the zone of leakage, effective permeability is in-

sufficient for geologically significant leakage; thus, the

fault seals by hydraulic resistance (Heum, 1996). Effec-

tive fault-fill permeability and cross-fault pressure gradient

Brown 383

Table 1. Symbols Used in Equations and Figures*

Symbol Meaning

FWL free-water level, the elevation where

capillary pressure is zero

H height above free-water level

h height of truncated pyramidal trap geometry

used for calculating trap leakage

H si height above FWL where irreducible

saturation develops in reservoir

H t height above FWL where capillary pressure

equals threshold pressure

k a absolute permeability

k ro relative permeability to petroleum

k w water relative permeability

L length of edge of truncated pyramidal trap geometry

PWC petroleum-water contact (either oil or gas)

P c capillary pressure

Pd displacement pressure

P e entry capillary pressure

Pp petroleum pressure

P t threshold pressure

P tf threshold pressure in fault fill

P tr threshold pressure in reservoir

Pw water pressure

S i irreducible water saturation

Smax maximum mercury saturation during

mercury-injection, capillary-pressure test

Sw water saturation

DP excess pressure at sealing interface

DP t total excess pressure (water pressure at aquifer

side of fault-fill minus water pressure

in reservoir at same elevation)

DUg capillary-pressure gradient, water density minus

petroleum density (DU) times

local hydrostatic gradient (g)

l capillary-pressure curve shape factor

Up in-situ petroleum density

Uw in-situ water density

*Symbols used only in the Appendix are not listed.

increase upward; thus, leakage increases upward until it

becomes geologically significant. This is the zone of fault-

fill seal failure. Seal-failure threshold is controlled by the

charge rate, timescale of interest, and area of leakage.

Exceptionally high petroleum columns are needed to

cause failure of low-permeability, fault-fill seals. The

absence of this highest zone allows faults to seal.

Relative permeability smoothes the transition from

membrane sealing through hydraulic-resistance seal-

ing to seal failure. If permeability abruptly increased

to the absolute permeability once the threshold pres-

sure was exceeded, then it would be possible for some

rocks to form a membrane seal but not a hydraulic-

resistance seal. With relative permeability effects, pe-

troleum columns exceeding membrane-seal capacity

will always have a zone of hydraulic-resistance seal-

ing if fault fill is homogeneous. Likewise, all water-

wet hydraulic-resistance seals have an underlying

zone of membrane sealing.

Membrane Sealing

Membrane Sealing under Hydrostatic Conditions

Membrane sealing is sealing by surface tension between

water and petroleum (Watts, 1987). Petroleum perme-

ability is zero when capillary pressure is less than the

384 Capillary Effects on Fault-Fill Sealing

Fau

lt fil

l

Res

ervo

ir

Pc = 0 (FWL)

Mem

bran

ese

alH

ydra

ulic

-re

sist

ance

sea

lN

ot a

seal

Geologicallysignificantleakage

Pc

= ∆

ρgH

H, P

c

Pc = Ptf

Pc = Ptr (PWC)

(B)

C

Slowleakage

OWC

Si

Fault fill

Res

ervo

ir

Top Seal

Ptf

FWL

)

Fault fill ReservoirAquifer

Pw

Pp

Pc

Distance

pres

sure

Pw+Pt(C)

Membrane sealFWL

Not a seal

seal

Hydraulic-resistance

(AFigure 2. Fault-seal mecha-nism zonation caused bycapillary-pressure variationunder hydrostatic conditions.(A) Block diagram showingreservoir and fault-fill seal zo-nation. Free-water level (FWL)is elevation with zero capillarypressure. Petroleum-watercontact (PWC) occurs wherecapillary pressure equals reser-voir threshold pressure (P tr). S i

is the base of the irreduciblewater zone in the reservoir. Theboundary between membraneand hydraulic-resistance sealingis elevation where capillarypressure equals the fault-fillthreshold pressure (P tf). (B)Section along fault fill andadjacent reservoir showing dis-tribution of petroleum (hori-zontal line pattern) in reservoir(right column) and fault fill (leftcolumn) as a function of height(H ). Hydraulic-resistance seal-ing fails where cross-fault leak-age becomes geologicallysignificant. (C) Pressure crosssection of reservoir-fault fill-aquifer at level ‘‘C’’ labeled inB. Fault-fill seals because capil-lary pressure is less than fault-fill threshold pressure at thereservoir interface. Thresholdpressure in aquifer is assumedto be small, thus, the aquifer isnot shown in A and B. Symbolsare identified in Table 1.

displacement pressure, and the rock acts as a perfect seal.

Petroleum-wet rocks (such as fault fill containing mature

source rocks) have no membrane-seal potential under

hydrostatic conditions; thus, petroleum can only be

sealed by hydraulic resistance.

In water-wet rocks, the lowest capillary pressure at

which petroleum permeability rises above zero is the

threshold pressure (P t); thus, membrane-seal capacity is

equal to the capillary threshold pressure. Under hydro-

static conditions, the maximum petroleum column

height, H t, can be calculated from the threshold

pressure and the density difference using

Ht ¼ Pt=�Ug ð1Þ

The threshold pressure is controlled by the pore net-

work (Watts, 1987), saturation history (Wardlaw and

Taylor, 1976), wettability, and surface tension (Ibra-

him et al., 1970).

Excess Pressure Effects on Membrane Sealing

For purposes of faults-seal analysis, excess pressure (DP)

is defined as water pressure on the aquifer side of the

sealing interface minus water pressure in the petroleum-

bearing reservoir at the same elevation. Total excess

pressure (DP t) is the aquifer water pressure minus the

reservoir water pressure at the same elevation. ‘‘Over-

pressure’’ indicates positive excess pressure (higher water

Brown 385

Figure 3. Fault-seal mechanisms with positive fault-fill excess pressure. (A) Section along fault fill (left) and adjacent reservoir (right)showing distribution of petroleum saturation as a function of height (H ). The base of irreducible water saturation is below H = P tf/DUg,thus, sealing interface is entirely at the reservoir-seal boundary. (B) Same as A, with base of reservoir irreducible water saturation aboveH = P tf /(DUg). Sealing interface extends into the fault fill, but seal failure does not occur because DUgH < P tf + DP t. Membrane-sealfailure occurs where H = (P tf + DP t)/DUg. (C) Pressure cross sections across reservoir-fault fill-aquifer at constant elevation. Crosssection pressure behavior is referenced in A and B by the numbers at the left of each cross section. Symbols are identified in Table 1.

pressure on the aquifer side), and ‘‘underpressure’’ in-

dicates negative excess pressure (higher water pressure

on the reservoir side). Excess pressure at the sealing

interface depends on its location and the presence or

absence of cross-fault water flow. When the reservoir

water saturation equals irreducible water saturation, it

is impermeable to water. Water cannot flow across the

fault; thus, fault-fill excess pressure is uniform and equal

to the total excess pressure (pressure trend 1, Figures 3C,

5C). If the reservoir is permeable to water (water

saturation is greater than irreducible water saturation),

water flows across the fault and excess pressure varies

across the fault fill (pressure trends 2 and 3 in Figure 3C

and pressure trend 2 in Figure 5C). Excess pressure is less

than the total excess pressure except at the aquifer-fill

interface.

Capillary pressure varies with elevation (H) and

excess pressure (DP):

Pc ¼ �rgH ��P ð2Þ

A membrane seal fails when the capillary pressure

equals the fault-fill threshold pressure (Pc = P tf). From

equation 2, the maximum membrane-sealed petro-

leum column height (H t) in the presence of excess

pressure is the following:

Ht ¼ ðPtf þ�PÞ=�rg ð3Þ

Threshold pressure remains constant with variable

excess pressure, but the height equilibrated to the thresh-

old pressure varies. From equation 3, seal overpressure

enhances the petroleum column height, whereas seal un-

derpressure reduces the petroleum column height.

Fault-fill overpressure will always help seal a taller

petroleum column, as described by equation 3, with

DP = DP t. Cross-fault flow causes the sealing interface

to move into the fault fill at some elevations above the

free-water level (Table 2, Figure 3). The sealing inter-

face moves back to the fill-reservoir contact at the

elevation when the reservoir is at irreducible water sat-

uration. If reservoir’s irreducible water saturation

develops in the zone of hydraulic-resistance sealing,

the transition from membrane to hydraulic-resistance

sealing occurs in the fault fill and the upper part of the

membrane seal acts like a hydrodynamic seal (Figure 4).

Hydrodynamic sealing is caused by bending the

free-water level and petroleum-water contact in re-

sponse to change in potentiometric gradient (Hubbert,

1953). Fault fill has a lower effective water permeabil-

ity than the reservoir; thus, potentiometric gradient and

hydrodynamic tilt are steeper in the fault fill than in

the reservoir (Figure 4). Contact tilting is independent

of rock wettability; thus, hydrodynamic membrane

seals can develop in petroleum- and mixed-wettability

rocks. The intersection of the tilted petroleum-water

contact in the fault fill with the aquifer marks the

transition from hydrodynamic sealing to hydraulic-

resistance seal. If the petroleum column is too thin for

hydraulic-resistance sealing to develop, hydrodyna-

mic sealing prevents cross-fault leakage. Petroleum

will be lost up the fault unless fault fill above the

reservoir acts as a hydraulic-resistance or membrane

seal.

386 Capillary Effects on Fault-Fill Sealing

Table 2. Effects of Excess Pressure on Membrane Fault-Fill Sealing

Sealing interface position and effect

of excess pressure on sealing

Valid elevation range,

overpressured fault fill (DP t > 0)

Valid elevation range,

underpressured fault fill (DP t < 0)

Seal at reservoir-fault interface:

column height is affected by excess pressure:

H t = (P tf + DP t )/DUg

H si < P tf /DUg H si < (P tf + DP t )/DUg

Seal within fault fill:

column height is affected by excess pressure:

H t = (P tf + DP t )/DUg

P tf /DUg < H si < (P tf + DP t )/DUg not possible

Hydrodynamic sealing within fault fill:

column height is affected by excess pressure:

H t = (P tf + DP t )/DUg

H si > (P tf + DP t )/DUg not possible

Seal at reservoir-fault interface:

column height is unaffected by excess pressure:

H t = P tf /DUg

not possible H swi > (P tf + DP t )/DUg

Underpressured fault fill may or may not affect seal

capacity, depending on presence of cross-fault flow (Table

2). Where water does not flow across the fault, column

height is described by equation 3, withDP =DP t (Figure

5C, case 1). Sealing is always at the reservoir interface

if fault fill is homogeneous. Cross-fault flow causes

infinitesimal excess pressure at the fault-reservoir in-

terface; thus, seal capacity is unaffected by flow (Figure

5C, case 2). Fault-fill hydrodynamic sealing is impos-

sible where the fault fill is underpressured.

Hydraulic-Resistance Sealing

Basic Concepts for Hydraulic-Resistance Sealing

Hydraulic-resistance sealing occurs where rocks are

permeable to petroleum, but petroleum permeabil-

ity is so low that petroleum can be trapped for geo-

logical lengths of time (Heum, 1996). The base of the

hydraulic-resistance sealing zone is the elevation where

capillary pressure equals the threshold capillary pres-

sure and petroleum permeability is zero. Excess pres-

sure changes the elevation of this threshold, as discussed

in the previous section. Petroleum-wet rocks (such as

fault fill containing mature source rocks) spontaneously

imbibe petroleum; thus, hydraulic-resistance sealing

begins at negative or zero capillary pressure.

Hydraulic-resistance seals fail when leakage be-

comes geologically significant. Leakage rate must be

less than charge rate; otherwise, the accumulation will

not form. When leakage rate exceeds charge rate after

formation of the accumulation, the leakage must be

sufficiently slow to preserve the accumulation since

trapping, a time span measured in millions to hun-

dreds of millions of years. Sealing, therefore, depends

on timescale of interest, area of leakage, and effective

petroleum permeability of the seal.

Effective petroleum permeability is the product of

absolute permeability and relative petroleum perme-

ability. No siliciclastic rock has been identified with

zero absolute permeability (Neuzil, 1994); thus, all

siliciclastic rocks (including fault fill) are potential

hydraulic-resistance seals where capillary pressure is

sufficiently large. Absolute permeability is controlled

by the pore network. Absolute permeability can be

estimated from the threshold pressure (Smith, 1966;

Jennings, 1987). Relative permeability is best consid-

ered a function of capillary pressure for sealing studies

because saturation is a function of capillary pressure

(Figure 6). Petroleum saturation increases during trap

charging; thus, injection relative permeability is appli-

cable during charging. Injection relative permeability

can be calculated from the injection capillary-pressure

curve (Jennings, 1987; see Appendix). When leakage

rate exceeds charge rate after the accumulation forms,

Brown 387

Res

ervo

ir

Fau

lt fil

l

H = Ptr/(∆ρg)(Tilted reservoir

PWC)

Lines ofequal waterexcesspressure

H = Ptf/(∆ρg)

Waterflow

Tilted fault-fillPWC

H = (Ptf + ∆P)/∆ρgHyd

raul

ic-

resi

stan

cese

al

Mem

bran

e se

al

Figure 4. Section along the fault fill (left) and adjacent res-ervoir (right), showing distribution of petroleum with hydro-dynamic sealing in the upper part of membrane-sealing zone.Capillary pressure varies laterally at the same elevation, andthus, all fluid contacts tilt. Low fault-fill permeability amplifies thehydrodynamic tilt, and thus, the oil-water contact tilts steeply.The tilted oil-water contact intersects the juxtaposed permeablebed at the transition to hydraulic-resistance sealing. Symbols areidentified in Table 1.

the capillary pressure decreases; thus, relative perme-

ability follows withdrawal curves (Figure 6).

Modeling Hydraulic-Resistance Sealing

Cross-fault petroleum leakage is modeled as a function

of height above the free-water level. Details of the mod-

eling are presented in the Appendix, and properties of the

modeled petroleum fluids are given in Table 3. Fault fill is

assumed homogeneous and water wet. Water pressures

are assumed hydrostatic. The height of the fault through

which petroleum flows (transmissive height of the

fault) is normalized to the height of membrane sealing.

Leakage is calculated as petroleum transmissivity, the

volumetric flow of petroleum across the entire height

of the homogeneous fault above the free-water level per

lateral unit length of fault (Figure 7B). Transmissivity

multiplied by the fault length gives the petroleum

leakage across the fault.

Transmissivity is found to be a function of normal-

ized transmissive height, capillary-pressure curve shape

factor (l), and petroleum fluid characteristics (Figure 7A).

Normalization of the petroleum column height removes

dependence on threshold pressure. This simplifies anal-

ysis of hydraulic-resistance sealing. The four trends

on Figure 7A show the range of oil and gas transmis-

sivity for fault fill with a reasonable range of l and

typical oil and gas fluid properties (Table 3). The shape

factor affects transmissivity by a factor of about two.

Gas and oil have transmissivities differing by about an

order of magnitude due to different viscosity, density,

388 Capillary Effects on Fault-Fill Sealing

Figure 5. Fault-seal mechanisms with negative fault-fill excess pressure. (A) Section along fault fill (left) and adjacent reservoir(right) showing distribution of petroleum saturation as a function of height (H). Reservoir irreducible water develops below H = (P tf +DP)/(DUg). Trapped petroleum column is reduced by H = (DP)/(DUg). (B) Same as A, with reservoir irreducible water developingabove H = (P tf + DP)/DUg. Membrane-seal capacity is unaffected by pressure difference. (C) Horizontal pressure cross sectionsacross the reservoir/fault fill/aquifer applicable to underpressured faults. Cross section pressure behavior is referenced in A and B bythe numbers at the left of each cross section. Symbols are identified in Table 1.

and interfacial tension. Hydraulic-resistance sealing is

evaluated for three settings: during charge, after charge,

and during production.

The maximum possible leakage rate during charge

is the charge rate. Charge rates are estimated by dividing

the petroleum-in-place by the charge duration for

traps that have little documented leakage. The highest

observed charge rates are approximately 500 m3

petroleum per year, calculated for giant Pleistocene

accumulations with minor leakage. Assuming sealing

faults 1 km long, leakage equals charge rate when

transmissivity is 0.5 m3 petroleum per meter of fault

length per year (m3/m/yr). At this transmissivity, the

ratio of height of hydraulic-resistance sealing to height

of membrane sealing for gas accumulations is about

0.2; that is, about 15% of the total sealing height is

caused by hydraulic-resistance sealing (Figure 7A).

Height ratio for oil accumulations at this transmissiv-

ity is about 0.5; that is, hydraulic-resistance sealing

accounts for about one-third of the trapping height. The

charge rate used here is the maximum realistic possi-

ble rate. It is at least an order of magnitude higher

than that of the vast majority of accumulations. Slow-

er charged accumulations with lower petroleum vol-

umes will have a much smaller fraction of hydraulic-

resistance sealing, in the range of 1–10% of the

trapping height caused by hydraulic-resistance sealing.

To evaluate dominant sealing type after charge

stops, trap geometry and fault length must be assumed.

Trap geometry and fault length were scaled to a

truncated pyramid with variable height to edge-length

ratio (Figure 7D, Appendix). Different trap lifetimes

were assumed to determine a reasonable range of

maximum leakage rates for accumulations with the

assumed lifetime (Appendix). Leakage rate is the

moveable petroleum divided by life span. To estimate

maximum leakage rates, consider the shortest reason-

able lifetime (3 m.y.) and the largest reasonable accu-

mulation (2 � 109 m3 petroleum). With this trap size

and lifetime, transmissivity is 0.03 for trap height/side

length ratio (h/L) of 0.01 and 0.1 for h/L of 0.1. These

transmissivities correspond with gas height ratio near

0.1 (9% hydraulic-resistance sealing) and oil height

ratio near 0.2 (16% hydraulic-resistance sealing). The

assumed leakage rate is much higher than those ex-

pected for accumulations with longer life and smaller

reserves; thus, the estimated height ratios are near the

maximum that could be expected for homogeneous,

water-wet fault seals.

Production rates can be used to determine signifi-

cance of hydraulic-resistance sealing during production.

Assume a field production rate of 1,000,000 m3/yr,

with one-tenth of this volume crossing a 1-km fault bar-

rier within the field. Transmissivity is about 100 m3

petroleum per meter of fault length per year. Height

ratio for gas accumulations at this transmissivity is

Brown 389

Figure 6. Relative permeability vs. capillary pressure. Gaspermeability increases during injection (thin solid line) as waterpermeability (heavy solid line) decreases. Gas withdrawal-secondary injection hysteresis loops are shown by dashed lineswith arrows showing direction of permeability change. Non-wetting phase permeability is lower during withdrawal thanduring injection. Secondary and primary injection have similarthreshold pressures (P t). Gas relative permeability data arefrom Colonna et al. (1972). The water relative permeabilitycurve is generic.

Table 3. Model Parameters

Property Oil Gas

Capillary-pressure gradient, 0.003 (0.13) 0.008 (0.347)

MPa/m (psi/ft)

g cos u, dyn-cm 26 33

Viscosity, cp 1 0.02

Fault width, m (ft) 1 (3.3) 1 (3.3)

about 1; that is, about 50% of the petroleum-water

contact elevation difference developing across the bar-

rier during production is caused by hydraulic-resistance

sealing. Height ratio for oil accumulations at this

transmissivity is about 4; that is, hydraulic-resistance

sealing accounts for about 80% of oil-column height

differences that develop during production.

Capillary Hysteresis and Fault Sealing

Capillary pressure decreases during production or nat-

ural trap leakage. Relative permeability changes with

decreasing capillary pressure are different from those

with increasing capillary pressure (Figure 6). At first,

petroleum relative permeability does not decrease sig-

nificantly as capillary pressure decreases. As capillary

pressure approaches the threshold pressure, petroleum

relative permeability drops abruptly with decreasing

capillary pressure. Permeability drops to zero (mem-

brane sealing) at a withdrawal capillary pressure about

half to a quarter of the injection threshold pressure.

This matches withdrawal seal capacity predicted from

theoretical analysis of the snap-off process (Petroleum

Research Corporation, 1959). Mercury, secondary-

injection entry pressure on hysteresis loops indicates

that the original seal capacity is restored once the

390 Capillary Effects on Fault-Fill Sealing

Figure 7. Hydraulic-resistance–sealing model. (A) Calculated normalized transmissivity as a function of height of transmissive faultnormalized to height of membrane-sealing zone. This is a function of the capillary shape factor, l, fluid density, surface tension, andwettability (Table 3). (B) Expected transmissivity as a function of accumulation size and accumulation life, based on trap geometricmodel shown in D. Dot shows example discussed in text. (C) Definition of transmissivity. Total petroleum loss rate is calculated bymultiplying the transmissivity by the length of the fault. (D) Trap geometry assumed to estimate transmissivity from accumulationlifetime and size. See Appendix.

capillary pressure has dropped sufficiently. Healing of

seal capacity is also reported in other studies (e.g., Co-

lonna et al., 1972; Schowalter, 1979).

Relative permeability hysteresis affects petroleum

column height when charge rate to a leaking accumu-

lation slows. This can be illustrated with a simple,

hydrostatic fill-and-leak charge history (Figure 8). As

the trap fills, it is initially membrane sealed. Leakage is

zero and the petroleum column increases until the

capillary pressure exceeds the seal threshold pressure.

Initial leakage rate is slower than charge, and thus, the

petroleum column and capillary pressure continue to

increase. As capillary pressure increases, effective seal

permeability increases until leakage rate equals charge

rate (Figure 8A). Leakage rate cannot exceed charge

rate as long as charge rate, petroleum type, seal phys-

ical properties, and hydrodynamic setting remain

constant.

As the charge rate begins to slow, the seal’s effec-

tive permeability remains about the same (Figure 6);

thus, leakage rate now exceeds the diminished charge

rate. The free-water level rises and capillary pressure

decreases (Figure 8B). Leakage rate decreases in re-

sponse to the lower capillary pressure, until leakage

equilibrates with the lower charge rate at a thinner

petroleum column. If charge stops, leakage will con-

tinue until membrane sealing is reestablished at a cap-

illary pressure one-half to one-quarter of the original

membrane-sealing height. Most of the petroleum ac-

cumulation will be lost and the thinned accumulation

will have a thick, residual-oil–saturation zone (Figure

8C). Once membrane sealing is reestablished, later

Brown 391

Figure 8. Effect of petroleum perme-ability hysteresis on seal failure. The leftfigures show fluid contacts and trap con-figuration; right figures are effective per-meability of seal and reservoir (horizontalaxis) plotted against capillary pressurescaled for height (vertical). (A) Leakagerate equals charge rate. Seal permeabilityis on injection curve (i). (B) As chargerates slows, the oil column shrinks andcapillary pressure decreases to a newequilibrium. Oil relative permeabilityis on the withdrawal curve (w), andinitial decrease in permeability is modest.(C) If charge stops, the FWL rises untilwithdrawal-oil-permeability of the sealdrops to zero. This reduces the columnto about one-half to one-fourth of itsoriginal height before membrane sealingis reestablished. (D) Threshold pressure isrestored to approximately the originalthreshold pressure and additional chargecan build petroleum column to a heightnear the original column without leaking.

charge can refill the trap to its original membrane-seal

capacity (Figure 8D).

DISCUSSION

Cross-Fault Water-Pressure Differences and Sealing

The conflicting interpretations by Heum (1996) and

Bjorkum et al. (1998) arise in overpressured reservoirs

(‘‘water-drive leakage’’ of Heum, 1996, and ‘‘under-

pressured seals’’ using the terminology of this article).

Heum (1996) assumes no flow through the seal, and

thus, total water-pressure difference is concentrated at

the sealing interface, as shown in Figure 5C (case 1).

Bjorkum et al. (1998) assume that water will always

flow through the entire oil-saturated reservoir under

hydrodynamic conditions; thus, the pressure drop is

distributed across the seal (Figure 5C, case 2). Water

only flows through petroleum reservoirs that have not

reached irreducible water saturation. Tall petroleum

columns in a good-quality reservoir are generally docu-

mented to reach irreducible water saturation (Mor-

row, 1971) and the Bjorkum et al. (1998) analysis

only applies to thin columns in poor-quality reser-

voirs. Although both interpretations are correct in the

proper setting, settings favoring reduction of petro-

leum columns by underpressured seals are more likely

in large petroleum accumulations.

Interaction of Capillary Pressures across Faults

Seal capacity has been interpreted to equal the total

cross-fault pressure difference where petroleum col-

umns lie on both sides of the fault (e.g., Yielding et al.,

1997; Grauls et al., 2000). This interpretation under-

estimates injection seal capacity. As pointed out by

Fisher et al. (2001), once seal effective permeability to

petroleum is greater than zero, petroleum columns will

communicate across the fault fill. Pressures equalize if

capillary pressure does not drop below the withdrawal

threshold pressure of the fault fill at the communication

point. Older works (e.g., Smith, 1980) have long rec-

ognized this fact. Where petroleum-water contacts are

different, the fault is sealing by either membrane or

hydraulic resistance. Seal capacity is estimated from the

capillary pressure calculated for the tallest petroleum

column.

This misinterpretation is based on Watts’s (1987)

conclusion that free-water level elevation differences

across a leaking fault will be maintained during cross-

fault leakage at a value where the difference in capillary

pressure equals the threshold pressure of the fault.

Watts’s (1987) interpretation is incorrectly cited to

Smith (1966, 1980). Smith’s (1966) figure 7, upon

which Watts’s (1987) figure 11 is based, clearly states

that differences in petroleum-water contact are caused

by differences in threshold pressure of sandstones

across the fault, not the entry pressure of the fault

fill.

Although the effects of differences in drainage and

imbibition relative permeability were discussed by

Watts (1987), the effects of permeability hysteresis

on reservoir behavior differences across a leaking fault

were not discussed. Free-water levels equalize once

capillary pressure exceeds fault threshold pressure,

assuming that capillary pressure does not drop below

the withdrawal threshold pressure. The reservoir that

leaked petroleum will have effective petroleum perme-

ability that lies along the withdrawal curve, whereas

effective petroleum permeability in the reservoir that

was charged by the leakage lies along the injection

curve. The reservoir that leaked petroleum has higher

effective petroleum permeability than that across the

fault at the same elevation, assuming equivalent rock

properties. The reservoir that leaked petroleum will

also have water-free petroleum production lower in the

accumulation and a thicker nonproductive residual oil

zone below the petroleum-water contact. Residual oil

zones at the base of the accumulation can be used to

identify which reservoir has leaked across the fault. If

trap compartments were charged separately, the fault

seal may not have leaked. This can be confirmed by

evaluating the thickness of the transition zone where

reservoir rock properties are similar on both sides of

the fault.

Membrane vs. Hydraulic-Resistance Seals

Hydraulic-resistance sealing in homogeneous, water-wet

faults does not substantially increase the membrane-

sealed height before leakage becomes geologically

significant. In most natural settings, fault fill will leak

at geologically significant rates once the petroleum

column is a few percent greater than the height of

the membrane-sealing zone (Figure 7). Hydraulic-

resistance sealing does not double the membrane-

sealed height even under worst-case natural scenarios,

given homogeneous, water-wet seals. This result is

consistent with caprock sealing models by Ingram

et al. (1997) and consistent with the conclusion that

hydraulic resistance is not significant for sealing fault

392 Capillary Effects on Fault-Fill Sealing

traps (Fulljames et al., 1997). Hydraulic-resistance

sealing of water-wet, homogenous, fault-fill seals is

uncommonly important because the transmissivity

required for geologically significant leakage is small.

Most faults that leak at geological flow rates will act

as hydraulic-resistance seals during production, because

rates sufficient for geological leakage are much lower

than production rates (Fulljames et al., 1997). Prepro-

duction membrane seals may also become hydraulic-

resistance seals during production unless their displace-

ment pressures are very high and field water-drive is

strong. As water pressure in the fault fill drops with

production, capillary pressure at the interface between

the fault fill and an undrained compartment increases

until petroleum invades the fault and the fill leaks.

Models to date are relatively primitive, including

the one presented here, and the significance of model-

ing results may change with further investigation. Cur-

rent models do not account for fault-fill heterogeneity,

which is certainly significant. Fault-fill heterogeneity

will cause leakage rates to vary independent of elevation.

The thickness of the zone of membrane sealing will

thin, and the zone of hydraulic-resistance sealing may

thicken or thin. Leakage rate is also affected by the

threshold pressure of the aquifer into which petroleum

leaks. Fault-fill transmissivity may also be lower in het-

erogeneous faults than that modeled for homogeneous

faults, because the vertical fraction of the fault actually

leaking is smaller than modeled.

Pulsed Seal Leakage

Petroleum permeability hysteresis dampens pulsed

leakage through intact fault-fill and matrix seals. Leak-

age rate is relatively insensitive to minor changes in cap-

illary pressure. Petroleum permeability at membrane-

seal failure is infinitesimal and increases only if capillary

pressure increases significantly above the threshold

pressure (Figure 6). Petroleum permeability remains

almost unchanged during the initial stages of decreas-

ing capillary pressure (Figure 6). The leakage rate of an

intact membrane seal exceeds the charge rate only if

the charge rate drops (Figure 8). Once the leakage rate

exceeds the charge rate, the trap will drain to a low

capillary pressure before initial sealing capacity is

reestablished. Although hysteresis may seem to en-

hance pulsed leakage, the charge-rate variation causes

variable leakage rate. Overall, hysteresis dampens mi-

grating petroleum flux variations and causes leakage-

rate variation to lag behind charge-rate variation. These

effects push petroleum migration through porous media

such as fault fill or sedimentary strata toward steady flow.

Pulsed leakage does occur in nature. The best example

is leakage by natural hydraulic fracture (e.g., Nunn and

Meulbroek, 2002). Pulsing is caused by gravitational

instability of individual hydraulic fractures. This flow

mechanism does not involve matrix porosity; thus,

matrix capillary properties do not dampen pulsing.

Harris et al. (1999) propose that pulsed water-

pressure changes in the reservoir will cause pulsed

leakage through matrix pore systems. They assumed an

abrupt water-pressure change at the fault-reservoir

interface, incompressible fluid behavior, and abrupt

change in permeability at the threshold pressure. These

assumptions favor cross-fault leakage and leakage rate

independent from pulse duration. Relative permeabil-

ity variation and fluid and frame compressibility sig-

nificantly lower and smooth fault leakage rates. If water

pressure changes are caused by dilation or compression

of the rock pore space (during earthquakes, for exam-

ple), then water-pressure differences between the res-

ervoir and fault fill will be modest or absent, because

both pore systems will compress.

CONCLUSIONS

Capillary-pressure concepts can be used to evaluate

sealing in homogeneous water-wet fault fill. Membrane

sealing is controlled by the capillary threshold pressure,

which can be determined from capillary-pressure tests.

Absolute permeability and relative permeability can

also be estimated from the capillary-pressure curve

and threshold pressure (Appendix). Results from this

theoretical evaluation include the following:

� Relative permeability smoothes the transition from

membrane sealing to geologically significant leakage.

All homogeneous, water-wet faults have a range of

petroleum column height where leakage is slow

enough to seal by hydraulic resistance.� Higher excess pressure in faults increases the petro-

leum column regardless of cross-fault water flow, as

estimated by equation 3. Sealing occurs within the

fault fill where water flows across the fault fill; other-

wise, sealing occurs at the interface between the fault

fill and the reservoir.� Lower excess pressure in sealing faults decreases the

petroleum column where water does not flow across

the fault. When water flows across the fault, under-

pressure does not decrease the petroleum column.

Brown 393

Water flows across faults only if the reservoir is perme-

able to water; that is, water can flow when reservoir

water saturation exceeds irreducible water saturation.� Absolute permeability and relative permeability are

scaled to the capillary-pressure curve; thus, the leak-

age rate across a water-wet, homogeneous fault is a

function of the ratio of transmissive fault height to

membrane-sealing height. This ratio is independent

from the threshold pressure. The leakage rate for

normalized fault height is controlled by the capillary

shape factor and fluid properties.� Hydraulic-resistance sealing adds a relatively modest

sealing height to water-wet, homogeneous, membrane-

sealing faults. Leakage through the fault abruptly

increases with increasing column height; thus, leak-

age becomes geologically significant at a relatively

short elevation above the height of membrane seal-

ing. Membrane-seal capacity of water-wet, homo-

geneous faults can probably be estimated from the

pressure differences across hydraulic-resistance

fault seals, especially where charge rate is slow.� Charge history is an essential variable for interpret-

ing cross-fault pressure differences where petroleum

leaks. Active charge offsets the effects of leakage;

thus, petroleum column height slightly exceeds

membrane-sealing height. However, once the charg-

ing rate starts to decrease, the petroleum column

height may drop as much as 75% from its original

height, especially in settings where charge has com-

pletely stopped. Thin fault-sealed petroleum col-

umns may result from low-withdrawal threshold

pressure after an earlier stage of intense leakage, not

low-injection-threshold pressure.

APPENDIX: FAULT LEAKAGE MODEL

Estimation of Cross-Fault Transmissivity

Hydraulic-resistance leakage was modeled in the following steps. (1)Absolute permeability of a homogeneous fault fill was calculatedfrom the threshold pressure and relative permeability was calculatedfrom the pore-throat distribution. (2) Cross-fault flow at eachelevation was calculated with Darcy’s law, the effective permeability,a fixed fault width, and capillary pressure as the pressure differencedriving petroleum flow. (3) Cumulative cross-fault petroleum flowwas calculated from the elevation of the threshold pressure to anelevation of interest.

1. Absolute water permeability (in millidarcys) was estimatedfrom an empirical power law relationship between absolute perme-ability (K a) and threshold pore-throat radius (r t, in microns):

ka ¼ 0:46 � r2:2t ð4Þ

The exponent describing this relationship is approximately 2,consistent with the Kozeny-Carmen relationship. Empirical perme-ability of small threshold pore throats is lower than predicted by thismodel. This is caused by increasing tortuosity with decreasing thresh-old radius. This effect is also responsible for a power law slope greaterthan 2. Except for using an exponent greater than 2, there is nocorrection for tortuosity in the model. Absolute permeability issomewhat overestimated for samples with very small throat radii.This overestimates the significance of hydraulic-resistance sealing.

Relative petroleum permeability (K ro) was calculated from theeffective water saturation (Jennings, 1987):

Kro ¼ ð1 � Sw* Þð1 � Sw*ð2þlÞ=lÞ: ð5Þ

Lambda, l, is the capillary curve shape factor (Jennings, 1987). Thefractional effective water saturation, Sw* , is normally calculated fromempirical fractionalwater saturation (S w) using the relationship S w* =(S w � S i)/(1 � S i). This study used model capillary-pressurecurves in which capillary pressure is assumed to have a power lawrelation to S w* . It was also assumed that S w* = S w. Effective watersaturation was directly calculated from the model power lawrelationship between capillary pressure and fractional effective sat-uration (modified from Jennings, 1987):

Sw* ¼Pc

ffiffiffiffika

f

q

0:07g cos �

0@

1A

�l

ð6Þ

where P c is the capillary pressure for the system of interest, F is thefractional porosity, g is the surface tension, and u is the angle ofwettability. The shape factor, l, was varied between 1 and 2 to in-clude most unimodal pore-throat distributions. Capillary pressureis calculated from the height above the free-water level and thecapillary-pressure gradient. Table 3 summarizes parameters used inthe four models shown in Figure 7.

2. Cross-fault volumetric flow per unit area of fault at each heightwas calculated from the effective permeability (k ak ro), fault thickness(T ), and fluid viscosity (A) using Darcy’s law with constant assumedrelative permeability across the fault thickness. The pressure-dropdriving flow is the difference between the capillary pressure andthe fault-fill, threshold capillary pressure. Flow per unit area (Q) is

Q ¼ kakro

mPc � Ptf

Tð7Þ

Equation 7 is an approximation. First, relative permeability isassumed constant across the fault fill, but it actually drops across thefault as capillary pressure decreases.Thisassumptionoverestimates flow.The pressure-difference driving flow is probably underestimated byequation 7. The pressure change is the maximum possible pressurechange across the fault fill, because petroleum pressure less than thethreshold pressure is not possible under steady flow on the injectioncurve. The cross-fault pressure drop does not include the effects of thecapillary threshold pressure at the discharge face of the fault fill norchanges in relative permeability resulting from such changes. Thefault-fill, threshold capillary pressure exceeds that of the reservoirinto which petroleum flows; thus, the steep capillary-pressure gradi-ent partially offsets the lower relative permeability near this interface.

3. Transmissivity (volumetric flow per unit length of fault mea-sured transverse to the flow) was calculated by numerically integratingthe volumetric flow from the threshold elevation to the elevation ofinterest. Volumetric flow per unit area increases with height becauserelative permeability and capillary pressure increase upward.

394 Capillary Effects on Fault-Fill Sealing

Correlating Transmissivity with Leakage Rate

Transmissivity multiplied by the fault length gives the total leakage.Total leakage can be estimated from the trap size and the age of atrap. It is assumed that half of the petroleum will remain as residualsaturation. Accumulation life is modeled as half the accumulationpetroleum volume divided by the leakage rate. This simplisticapproach underestimates accumulation age for a given initialtransmissivity because leakage rate will decrease as the accumulationis leaked due to decreasing capillary pressure.

To correlate fault transmissivity to trap leakage rates, trap-and-fault geometry must be assumed. For this study, traps are assumed tobe truncated pyramids with the top area one-quarter the area of thebase (Figure 7D). One side of the pyramid is a leaking fault. Assumedheights of the truncated pyramid are one-tenth and one-hundredththe length of the base of the pyramid. Petroleum was assumed tooccupy 20% of the total trap volume (equals 20% porosity with 100%oil saturation). Accumulation size was varied from 0.1 million to 10billion m3. Leakage rate is calculated by multiplying the fault trans-missivity by fault length, approximated by 0.6 times the pyramid base(because most leakage occurs in the upper part of the fault).

The magnitude of geologically significant leakage depends on thelifetime of the accumulation. A model accumulation life of 3 m.y. waschosen for estimating leakage rate and transmissivity. This is about anorder of magnitude less than reported median petroleum accumulationage (Macgregor, 1996); thus, median transmissivity is about an order ofmagnitude lower than those estimated here. The lower age and highertransmissivity were chosen for the following reasons. First, the assumedlinear leakage rate underestimates accumulation age. Transmissivityestimates might err due to assumed trap-and-fault geometry; thus, ahigh threshold is likely to include geometries more favorable for leakage.Finally, the short accumulation age encompasses just about all eco-nomic accumulations, not just the median case.

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Brown 395