Generation of overpressure and compaction-driven fluid ... · evolution of pressure and porosity in this system. If reversible ( elastic) compaction is assumed, sediment loading is

Basin Research (1998) 1O, 177-196

Generation of overpressure and compaction-drivenfluid flow in a Plio-Pleistocene growth-faulted basin,Eugene Island 330, offshore LouisianaDavid S. Gordon* and Peter B. FlemingsPenn State University, Department of Geosciences,

University Park, PA 16802, USA

ABSTRACT

The complex pressure and porosity fields observed in the Eugene Island (EI) 330 field(offshore Louisiana) are thought to result from sediment loading of low-permeability strata. Inthis field, fluid pressures rise with depth from hydrostatic to nearly lithostatic, iso-pressuresurfaces closely follow stratigraphic surfaces which are sharply offset by growth-faulting, andporosity declines with effective stress. A one-dimensional hydrodynamic model simulates theevolution of pressure and porosity in this system. If reversible ( elastic) compaction is assumed,sediment loading is the dominant source of overpressure (94%). If irreversible (inelastic)compaction and permeability reduction due to clay diagenesis are assumed, then thermalexpansion of pore fluids and clay dehydration provide a significant component of overpressure( > 20%). The model is applied to wells on the upthrown and downthrown sides of the majorgrowth fault in the EI 330 field. Assuming that sediment loading is the only pressure sourceand that permeability is a function of lithology and porosity, the observed pressure andporosity profiles are reproduced. Observation and theory support a conceptual model wherehydrodynamic evolution is intimately tied to the structural and stratigraphic evolution of thisprogradational deltaic system.

diagenetic expulsion of pore fluids during the smectiteto illite transition adds fluid to a finite pore volumethereby increasing fluid pressure. Advocates of the secondhypothesis suggest that heating during burial causes porefluid expansion and a resulting increase in fluid pressure.Finally, advocates of the third hypothesis suggest thatthe inability of low-permeability sediments to expel theirpore fluids in response to sediment loading generates

overpressure.The debate is significant because the three hypotheses

result in strongly divergent views on how fluid pressuresevolve in sedimentary basins. Based on the sedimentloading hypothesis, permeability and sedimentation rateare the primary controls on the evolution of fluid pressure(e.g. Bredehoeft & Hanshaw, 1968; Keith & Rimstidt,1985; Bethke, 1986; Harrison & Summa, 1991; Melloet al., 1994). Thus, according to this view, the evolutionof fluid pressure is inextricably tied to the stratigraphichistory of the basin. In contrast, some advocates of theother hypotheses subscribe to the idea that the fluidpressure field can be independent of the stratigraphicand structural history of the basin. These authors proposethe existence of 'perfect' or 'near perfect' seals which canisolate 'compartments' of sediment from the surroundingmaterial (e.g. Barker, 1972; Hunt, 1990; Powley, 1990).

INTRODUCTION

Fluid pressures in excess of hydrostatic are commonlyobserved in sedimentary basins. Great attention has beenfocused on characterizing these pressures and on under-standing their origin and evolution. At the most practicallevel, it is critical to understand overpressures in orderto drill wells safely and economically. At a more funda-mental level, overpressures are coupled to compactionand, therefore, influence acoustic properties of sediments,the stress field and permeability.

Despite, or perhaps because of, the need to understandoverpressures, there continues to be debate over theirorigin. In the Tertiary Gulf Coast, the focus of thisstudy, there are three hypotheses for the dominant causeof overpressure: (I) diagenetic reactions which releasepore fluids (Powers, 1967; Burst, 1969; Bruce, 1984); (2)

aquathermal pressuring (Barker, 1972; Powley, 1990;Hunt, 1990); and (3) sediment loading (Bredehoeft &Hanshaw, 1968; Magara, 1975; Keith & Rimstidt, 1985;Bethke, 1986; Harrison & Summa, 1991; Mello et al.,1994). Advocates of the first hypothesis propose that

.Now at Woodward-Clyde International-Americas, 1400 UnionMeeting Road, Suite 202, Blue Bell, PA 19422-1972, USA.

177@ 1998 Blackwell Science Ltd

D. S. Gordon and P. B. Flemings

Finally, we apply the forward model to four wells in theEI 330 field and compare the model results to theobserved data in those wells. Our results show that a1-0 hydrodynamic model, in which permeability is tiedto the large-scale stratigraphic architecture of the basin,can simulate the evolution of the pressure and porosityfields to their observed states.

HYDRO STRATIGRAPHICCHARACTERIZATION OF THEEI 330 FIELD

The EI 330 basin is a Plio-Pleistocene salt withdrawalshelf basin which is located offshore, Louisiana (Fig. 1).Alexander & Flemings (1995) provide a geological charac-terization which we summarize here. The basin is com-posed of three hydrostratigraphic units: a Plioceneprodelta unit, a Pleistocene proximal deltaic unit and aPleistocene and younger fluvial unit. This regressivesequence grades from clay-dominated to sand-dominatedsediments. Sand units which were deposited duringgrowth-faulting are thicker in the down thrown blockthan in the upthrown block (Fig. 2). Offset due togrowth-faulting causes the sand-dominated unit to extenddeeper into the downthrown block (Fig. 2). Over the past2.2 million years, sedimentation rates in this basin havevaried from less than 2 mm yr-1 to 2.4 mm yr-I,

In the EI 330 field, as is common in much of theTertiary Gulf Coast province (e.g. Harrison & Summa,1991), pressures rise with depth from hydrostatic tonearly lithostatic (Fig. 3D) and are closely correlated tolithology. The fluvial deposits are hydrostatically press-ured, the proximal deltaic deposits record the transitionto overpressure and the prodelta deposits are marked bystrong overpressures (Fig. 3D). The transition from clay-to sand-dominated sediments marks the transition fromhydrostatically pressured to overpressured sediments(Fig. 3A,B). Porosity and overpressure are intimatelyrelated in the EI 330 field (Fig. 3C,D). Hart et al. (1995)suggested that porosity «j» is an exponential function of

Ortoleva et al. (1995) state that 'the pattern of basincompartrnentation need not simply be the result of animposed "template" such as stratigraphy or faults.'Following the reasoning of Hunt (1990), Roberts & Nunn

(1995) perform modelling studies of clay-dominated sedi-ments, in which they impose a horizontal clay seal witha permeability of 10-25 m2, two orders of magnitudelower than the lowest observed shale permeabilities

(Neuzil, 1994).We believe that this debate persists because many of

the previous studies failed to integrate careful characteriz-ation of stratigraphy and overpressure with dynamicmodels of their evolution. Bethke (1986) performed aseries of one-dimensional inverse simulations and com-pared his results to a data set which represents a largearea of the Gulf Coast. Harrison & Summa (1991) used2-D numerical simulations to reproduce the observedpressure field from the Gulf Coast, and to explain lateralvariation in that pressure field. The scope of their studywas the 1000-km scale. By considering such large areas,Bethke (1986) and Harrison & Summa (1991) lose thedetail which we observe over the kilometre scale. Finally,Mello et al. (1994) used lithology data from the SouthMarsh Island area, offshore Louisiana, to reproduce thegeneral features of the pressure and porosity fields inthat area. However, that study did not consider the roleof clay dehydration or any lateral variation in I the pressureand porosity fields. While our I-D study necessarilyignores lateral flow, we consider lateral variations in thepressure field by performing a series of I-D simulationsalong a cross-section through the EI 330 basin.

We first characterize the geological setting and thepressure and porosity fields of a Plio-Pleistocene growth-faulted basin, the Eugene Island (EI) Block 330 field(Fig. 1). We then present a I-D forward model whichincorporates each of the proposed sources of overpres-sure. We show simple examples of how pressure andporosity evolve in a clay-dominated system and in a

progradational system (represented by clay-dominatedsediments overlain by sand-dominated sediments).

Fig. 1. Position of A-A' cross-sectionshowing wells used in study. Inset:position of Eugene Island Block 330, onthe Louisiana Continental Shelf.

178 (i:;, 1998 Blackwell Science Ltd, Basin Research, 10, 177-196

Generation of overpressure

Fig. 2. Dip-line well-log cross-section (A-A' located in Fig. 1). Logs on the left in the individual wells are either gamma ray orspontaneous potential logs. Logs on the right are resistivity logs. Well correlations are tied to the lithology (gamma ray orspontaneous potential) logs. The faults shown here are interpreted from a seismic line running from A to A'.

330#8-13

Percent Shale PorositySand 70 0.10 0.40 0

Pressure (MPa)20 40 60

Gamma20 Ray 120 0

0 --I' :-- 80

~500-

II--I: ~~ -

I~1000

K~ 1500I- l'"

0c:

2000

lISQ)(/).a::J(/)

I1I2500

I

3000

3500

ABC 0

Fig. 3. (A) Gamma ray log, (B) smoothed per cent sand log, (C) porosity and (D) fluid pressure vs. subsea true vertical depth inthe 330 B-13 well. (A) The gamma ray log shows the distribution of sands and shales with the sands identified by kicks to theleft. (C) Porosity is plotted on a logarithmic scale. (D) Pressure is predicted from drilling mud density. Direct measurements ofpressure are shown as stars; these measurements were made in individual sand units. Six stratigraphic surfaces with the ages inmillions of years are shown.

179(i:) 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


overpressured prodelta deposits are generally not encoun-tered until 2000 ffi.

effective stress (cr). The linear porosity trend (on asemilog plot) in the shallow hydrostatically pressuredsediments of EI 330 support this interpretation (Fig. 3C):

 = <1>0 e-J}a (1)

where <1>0 is the initial sediment porosity and J3 definessediment compressibility. While the shallow sediments(0-1000 m) follow the normal compaction trend (porosityexpected at hydrostatic conditions), the deeper sediments(1100-1800 m) are undercompacted relative to the normalcompaction trend and effective stress is lower thanexpected at hydrostatic conditions (Fig. 3C,D). The verydeep sediments (below 1800 m) are further undercom-pacted, and have higher porosities and lower effectivestresses than the overlying sediments (Fig. 3C).Throughout this basin, porosity decreases to the top ofthe strongly overpressured sediments; often a 'rollover'occurs where porosities increase and effective stressesdecrease with depth.

The offset in stratigraphic architecture is reflected inthe offset of the overpressure field (Fig. 4). The fluvialphase is hydrostatically pressured, and thicker and deeperin the downthrown block than in the upthrown block(Fig. 4). The transition to overpressure is thicker in thedown thrown block where the proximal deltaic depositsare thicker than in the upthrown block. Strong overpres-sure is generally encountered in the prodelta phase(beneath C.mac) which is 1500 m below sea level in theupthrown block, whereas in the down thrown block, the

A

OlA'

-400

~

~P.lac.A 1;, f+ J_-

~ +"+ "P.lac.B +

.~ 2la~~-

; --y.;!~.~--800

-1200

--1600

E"-..c: -2000+-'0-0)

0 -2400 +6, ';;"c¥" '~~ .

stratigraphic surfaces

-20 -pressure contours

(MPa)

-2800

-3200

-3600 1km..-

-

-4000

Fig. 4. Cross-section along A-A I (located in Fig. 1) of overpressure predicted from drilling mud density. Data points are shown

as + symbols. These points come from wells within 100 m on either side of the line of section. The contour interval is 2 MPa.Dashed lines represent surfaces of known age which were interpreted from well log and seismic data. Fault is assumed to be abarrier to lateral fluid flow and contours are projected toward the fault from both upthrown and down thrown sides. The result isa sharp lateral pressure gradient at the fault.

180 @ 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


pressure through time comprises four components: (1)fluid flow (the Darcy term), (2) sediment loading, (3)thermal loading and (4) clay dehydration. Overpressuredevelops when the flux from the Darcy flow term cannotbalance pore pressure generated by the combined effectsof the three source terms: sediment loading, aquathermalpressuring and clay dehydration. In basins where hydro-carbon generation may be an important source, a fourthsource term may be added to Eq. (2) which would besimilar for the clay dehydration source term (seeBredehoeft et at., 1994). Equation (2) differs from thepresentations of Palciauskas & Domenico (1989) and ofMello et at. (1994) in the treatment of the matrixcompressibility (13), and in the inclusion of a source termfor clay dehydration (Appendix).

a kinetic transfornlation of smectite to illite (Bekins et at.,

1994):

OS-= -A e-D/TSS (7)Ot

where the rate of change in the mole fraction of smectite(S) in the mixed-layer clay (smectite plus illite) is anexponential function of temperature (T). A and Dareempirically defined fitting parameters from Bekins et at.(1994). Equation (7) was shown by Bekins et at. (1994)to reproduce Hower et at.'s (1976) observed smectite/illite profile from the Gulf Coast. Huang et at. (1993)were able to reproduce the observed smectite/illite profilein the Gulf Coast using a similar approach. Typicalvalues for bulk volume fraction of mixed-layer clay (S)in EI 330 muds is approximately 0.60, and initial valuesfor illite fraction of mixed layer clay is 0.20 (S. Losh,pers. comm.). Once we know from Eq. (7) how muchsmectite has dehydrated, we calculate how much pressurewas generated by that process:

OP clay Sled ' cl>micro 'dpc OS-='-. (8)

Ot S, Ot

Permeability as a function of porosity and

lithology

Our goal is to find an expression for the bulk verticalpermeability of sediment which approximates the effectof the large-scale change from clay-dominated to sand-dominated sediment. Intrinsic permeability is modelledas a function of lithology and porosity:

ksand = G .e<."'+b) (4)

kclay = G. e(e++d) (5)

k .- 10[(1- ji)log("c!ay) + filog("sand).sediment - (6)

Equation (8) describes the pressure generated by claydehydration as a function of the volume fraction ofsmectite and illite in the sediment, the microporosity ofsmectite «I>micro), the amount of smectite which hasdehydrated, the density contrast between clay-boundwater and pore water, and the storage capacity (S,) ofthe sediment.

We equated the smectite/illite transition to the claydehydration process. We assumed the clay portion of thesediment to be originally composed of 50% smectite and0% illite. We used the observed geothermal gradient forthe EI 330 field of 33 °C km -1 (Holland et al., 1990) and

a clay-bound water density of 1.15 g cm-3 (Colten-Bradley, 1987). We assume that all pressure generationis due to the higher density of clay-bound water comparedto free water. The value of clay-bound water densitywhich we use (1.15 g cm-3) is at the high end of whatis published in the literature (1.02-1.4 g cm-3) (Powers,

1967; Burst, 1969; Bruce, 1984; Colten-Bradley, 1987).When making these estimates of clay-bound water densityand bulk volume fraction of smectite and illite, we hopedto calculate the maximum reasonable contribution of claydehydration to the fluid pressure field. Table 1 gives thevalues for all constants used in our simulations.

Many authors approximate permeability as a log functionof porosity for a given lithology (e.g. Archie, 1950;Harrison & Summa, 1991; Mello et al., 1994). Theseauthors divide stratigraphic sequences into distinct units(with a specific value for per cent sand (fi», each withits own fitting parameters in Eqs (4) and (5) (e.g. Harrison& Summa, 1991; Mello et al., 1994). We extend thisapproach by modelling permeability as a continuousfunction of both lithology (per cent sand (fi» andporosity «I» (Nelson, 1994; Panda & Lake, 1994). Thisis a first approximation to permeability measured overthe metre and decametre scale.

Line A in Fig. 5B shows permeability as a function ofporosity for sediment with 10% sand, and line B for 0%sand. In our examples, where we average lithology overlarge vertical distances (450 m), there are virtually nosediments modelled with less than 10% sand. Thus, lineA acts as an effective minimum bound to the permeabilityfield. The shale permeability model used in this studyfalls within the limits for shale permeability found byNeuzil (1994) (shaded grey area in Fig. 5B). We assumeviscosity varies as a function of temperature (Mello et al.,

1994; Mercer, 1973) (Appendix).

THEORETICAL SIMULATIONS

In order to evaluate the relative roles of sediment loading,aquathermal pressuring, clay dehydration and lithology,we now consider four simulations of fluid pressureevolution in an aggrading basin. We display our resultswith an upper boundary fixed in space (the basin surface).Sediment is continually added at the upper surface witha surface porosity of 0.40, and typical quartz and seawater densities. We derive the surface porosity «1>0) and

Clay diagenesis and dehydration

The pressure generated by clay dehydration is calculatedaccording to two equations. The first equation describes

181co 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


Fig. 5. (A) Log of permeability (m1plotted as a function of per cent sandand porosity. (B) Sand-shalepermeability model used in this study(solid lines), from Mello et al. (1994)(dashed lines) and from Harrison &Summa (1991) (dashed-dotted lines).Lines A, Band C (this study) arepermeability as a function of porosityfor sediment with 10% sand, 0% sandand 100% sand, respectively. Line D(this study) represents permeability ofsediment with 10% sand in theupthrown block (see Application ofModel to Field Data). The shaded areais the range of shale permeability foundby Neuzil (1994).

Table I. Constants,

Constant Value Units References

3.86 X 10920.0-0.436.0-22.3190961150

Bekins et al., 1994this studythis studythis studythis studyBekins et al., 1994Cohen-Bradley, 1987

~~~i~:ti

..,~J~Aabc

dD

clay-boundwater density

kg m-r

G

g

Ssed

U

ab

as

af

13

I3f

<Pmicro

<Po

Pf

Ps

L\tma

9.87 X 10-169.810.502.193.34 x 10-53.27 X 10-5

5.00 X 10-43.68 X 10-85-10

0.300.4010252650220

2 d -1mm-2ms

bulk v lume fraction

°c-1

°C-I

°C-IPa-1Pa-1bulk-v lume fractionm3m 3

kgmkgmIts m

de Marsily, 1986Fetter, 1988this studyIssler, 1992Palciauskas and Domenico, 1982Palciauskas and Domenico, 1982de Marsily, 1986Hart e1 a/., 1995de Marsily, 1986from Colten-Bradley, 1987Hart e1 a/., 1995Fetter, 1988de Marsily, 1986Issler, 1992

the sediment compressibility (~) from previous studiesof the pressure-porosity relationship in EI 330 (Hartet al., 1995). Because we are relating empirically observedporosity -effective stress relationships (Hart et al., 1995)with a uniaxial compaction model (Appendix), we arenecessarily making several assumptions: (I) the observedporosity -effective stress profiles record only uniaxialstrain, and (2) all compaction is mechanical. The formeris a simplifying assumption made by most compaction-driven fluid-flow models (e.g. Harrison & Summa, 1991).The latter assumption relies on the observation of

IPleistocene and younger sediments in EI 330 which showno evidence of significant chemical processes (e.g. dissolu-tion or cementation).

The upper boundary is set to a constant overpressure(p.=O). The lower boundary is a no flow boundary{OP'

/011 = 0). Two types of results are shown for each

simulation. First, we display the final states of the pressure,porosity and hydraulic conductivity fields as a function ofdepth (solid lines, Figs 6, 8, 9 and 11). Second, we showthe evolution of a single unit of sediment deposited early inthe simulation (arrows, Figs 6, 8, 9 and 11).

182 ((;) 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


Clay deposition at a constant rate

We first consider three cases where clay is deposited ata constant rate of I mm yr-1 for 4.4 million years. Weuse these three examples to show the effects of mineral-ogical-dependent permeability and of reversible versusirreversible compaction.

the simulation does not track precisely along the present-day fields. The particle first experiences overpressure ata slightly greater depth than overpressure is encounteredtoday (Fig. 6A). The particle followed the normal com-paction trend (dashed line) to a depth of about 300 m(Fig. 6B). From 300 m to 1500 m, compaction continued,but it deviated from the normal compaction trend. Below1500 m, compaction nearly halts (Fig. 6B). Particlesdeposited early in the simulation which lie at the base ofthe sediment column experience sediment loading but,due to the lower boundary condition (no flow), theyexperience no pressure addition from below. In contrast,particles deposited later in the simulation experience flowfrom below as well as sediment loading. Therefore,sediment deposited later in the simulation encountersoverpressure at a shallower burial depth than the sedi-ment deposited early in the simulation.

For one unit of sediment deposited early in thesimulation, Fig. 7 A shows the accumulated pressure gen-erated by each process in this simulation. Sedimentloading accounts for more than 94% of the overpressurewhile clay dehydration and aquathermal pressuring eachaccount for less than 3% of the total pressure (Fig. 7 A).Almost all of the pressure from the clay dehydrationreaction is added after 2.5 million years of simulationtime. Figure 7B shows the change in pressure with timeand the relative contributions of sediment loading, claydehydration, aquathermal pressuring and Darcy flow withtime. As the permeability is reduced by compaction, theDarcy flow decreases. Mter 3.1 Myr of simulation time,the Darcy flow term approaches a constant rate ofpressure removal. As the Darcy flow approaches thisconstant rate, the system approaches a pseudo-equilib-rium where the rate of pressure addition becomesconstant.

Simulation 1.. constant rate clay deposition

In the first example, permeability varies only as a functionof porosity, according to line A (Fig. SB). In this simu-lation, the sediment compacted normally in the shallowzone, but below about 300 m, the clay was not permeableenough to expel its formation fluids in response to furthersediment loading (Fig. 6A). Thus, at approximately300 m depth, overpressures developed and compactionwithin the shale deviated considerably from the normalcompaction trend (Fig. 6A). The porosity field (solidline) deviates almost immediately from the normal com-paction trend (dashed line) (Fig.6B). The hydraulicconductivity of the shale in the overpressured zone isapproximately 10-12 m S-I, but it decreases slightly withdepth (Fig. 6C). Since the sediment is all one type, thesedecreases in hydraulic conductivity are due to decreasesin porosity. Figure 60 shows the particle evolution ofporosity and effective stress. The time elapsed betweeneach point is 0.9 Myr. The virgin compaction trendshows the relationship between effective stress andporosity as sediment is compacted. In Fig. 60, thedecreasing distance between points indicates that fromTime 2 to Time 3, the sediment has experienced lesscompaction relative to the normal compaction trend thanfrom Time 1 to Time 2.

The history of a particle which was deposited early in

O.4~

.,

0.35

\1

~2

~4-

\~J" \ I

Fig. 6. Simulation of clay deposition at1 mm yr-1 for 4.4 Myr. The solid linerepresents the present state of the field,and the arrows represent the evolutionof a particle deposited early in thesimulation. (A) Overpressure.

(B) Porosity. (C) Hydraulicconductivity. (D) Porosity of a particleplotted as a function of effective stressthrough the simulation. The numbersrepresent the relative time of equallyspaced measurements. Normalcompaction is represented by equallyspaced points along the virgincompaction trend (solid line). Thedecreasing interval between points alongthe curve is indicative of slowed

compaction.

J

20O.15~ 10

Sigma (MPa)

DA B

183@ 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


'(U'e:.

Fig. 7. (A) Accumulated contributionsof sediment loading (solid line), clay

dehydration (dashed-dotted line),temperature loading (dashed line) andDarcy flow (dotted line) for Simulations1 and 2. For comparison Darcy flow isshown as an absolute value; the sign ofDarcy flow is opposite that of the threesource terms and the total pressureapplied to the system. (B) ForSimulation 1: contribution of sediment

loading, clay dehydration, aquathermalpressuring and Darcy flow (reversedsign) at each timestep. The aquathermalpressuring line is horizontal, showingthat the burial rate is nearly constant,and that the temperature gradientincreases linearly with depth. Likewise,the sediment loading line is horizontalbecause sedimentation is constantthrough the simulation. The totalpressure line (solid grey line) reaches abalance with the loading terms and thepermeability field after 3.1 Myr. (C) ForSimulation 2: contribution of each termto the total pressure. When the totalpressure line (solid grey line) exceeds(crosses) the sediment loadingcontribution, pressure is increasing at arate faster than the lithostatic gradient.This crossover records a decrease ineffective stress with time.

a function of clay mineralogy in the following manner:

.4ksediment = ksediment X S .(9)

This has the effect of reducing permeability by up totwo orders of magnitude (we assumed that 10-22 m2 wasa lower limit on permeability (Neuzil, 1994)). We applyEq. (9) in two simulations to demonstrate the effect of apermeability reduction due to clay dehydration.

Role of mineralogical-dependent permeabilityand reversible versus irreversible compaction

We were particularly interested in examining under whatconditions it is possible for sediment to experience adecrease in effective stress through time. Plumley (1980)and Hart et at. (1995) both suggest that a late-stagepressure generation source may have this effect. FromSimulation 1, we found that inclusion of clay dehydrationand aquathermal pressuring alone were not sufficient togenerate a decrease in effective stress. Assuming thatthere are no other pressure sources, the only way togenerate a decrease in effective stress with the three givensources is to decrease the sediment permeability. Oneway to justify a reduction in permeability is to tie thatreduction to a change in mineralogy. Bethke (1986) andColten-Bradley (1987) suggest that permeability is sub-stantially reduced by the transformation of smectite toillite. We found no information to quantify this relation-ship, but we did find that it is possible to decreaseeffective stress through time by reducing permeability as

Simulation 2: constant rate clay deposition with permeabilityreduction due to clay diagenesis

In this first application of Eq. (9), we repeat Simulation1 and assume compaction is completely reversible(Fig. 8). Within the zone of the smectic to illite transition(below 2300 m), there is a dramatic decrease in per-meability (Fig. 8C). Figure 80 shows the evolution ofporosity and effective stress through the simulation.Effective stress is lower at Time 5 than at Time 4, andeffective stress is lower at Time 4 than at Time 3. Thecompressibility (j3) does not change; thus, as effective

(!;) 1998 Blackwell Science Ltd, Basin Research, 10, 177-196184


0O4Ff:Tl

,

\2,5~\

~

Fig. 8. Simulation of clay deposition atI mm yr-1 for 4.4 Myr with apermeability reduction associated withthe clay dehydration reaction.Compaction is considered an elasticprocess (see Fig. 6 caption). Theeffective stress at time 5 is less than attimes 3 and 4.

20K(m/s)

{'A B D

stress decreases, the particle tracks back up the virgincompaction trend (reversible compaction) (Fig. 80). Theparticle evolution shows a porosity minimum at 2600 mbelow which there is a very small increase in porosity(Fig. 8B). This increase in porosity can also be observedin Fig. 80, where porosity increases from Time 3 toTime 5.

Again in this simulation, sediment loading accountsfor greater than 94% of the total pressure applied to thesystem, and aquathermal pressuring and clay dehydrationeach account for less than 3% (Fig. 7 A). Figure 7 A isthe same for Simulation I and Simulation 2 becausethere is no change in compressibility during the simu-lation; the same amount of sediment is added, the elementexperiences the same amount of heating and the sameamount of clay dehydrates. As the permeability is reducedby compaction and the clay dehydration process, theDarcy flow in the system decreases more than inSimulation 1 (Fig.7B for Simulation 1; Fig.7C forSimulation 2). When the Darcy flow term drops belowthe sum of the clay dehydration and .aquathermal pressur-ing terms (approximately 3.1 Myr into the simulation),the change in pressure per time step exceeds the contri-bution of sediment loading (Fig. 7C). Effective stressdecreases when the total change in pressure exceeds thepressure added by sediment loading (from 3.1 Myr to

the end of the simulation) (Fig. 7C).

increasing (estimated from Corbet & Bethke, 1992).Similar to Simulation 2, there is a dramatic decrease inhydraulic conductivity within the zone of the smectite toillite transition (Fig. 9C). Figure 9A illustrates that theparticle experiences increasing pressure at a higher gradi-ent than the lithostatic gradient; this corresponds to adecrease in effective stress. When effective stressdecreases, the porosity departs from the virgin com-paction curve (from Time 4 to Time 5, Fig. 9D). Thelength (amount of effective stress reducl;ion) and slope(amount of porosity increase for a given decrease ineffective stress) of the line connecting points 4 and 5 isdependent upon the compressibility (expandability) ofthe sediment (Fig. 9D).

In this simulation aquathermal pressuring accounts for8% of the total pressure applied to the system, and claydehydration accounts for nearly 13%. Figure 10 showshow the decrease in effective stress and the correspondingdecrease in matrix compressibility (at 3.1 Myr) causesthe relative roles of clay dehydration and aquathermalpressuring to increase, while the relative role of sedimentloading decreases. The point at which the total pressurecurve crosses the sediment loading curve corresponds tothe abrupt change in the clay dehydration and aquather-mal pressuring contributions (Fig. 10).

Clay-dominated deposition followed by

sand-dominated deposition

Simulation 4

The EI 330 region, like much of the Tertiary Gulf Coast,is characterized by a progradational history where earlydeposition is clay-dominated and late deposition is sand-dominated. We approximate this depositional history by

Simulation 3: constant rate clay deposition, permeabilityreduction and irreversible compaction

We now repeat Simulation 2, except that we assume thatcompaction is primarily inelastic; if the effective stressdecreases, the compressibility of the sediment is assumedto be one-tenth what it is when effective stress is

185II:> 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


O.4r-

.1 "

~!\ Fig. 9. Simulation of clay deposition atI mm yr-1 for 4.4 Myr with a

penneability reduction associated withthe clay dehydration reaction (see Fig. 6caption). Compaction is considered tobe a largely inelastic process. Theeffective stress at times 4 and 5 is lessthan at time 3, and during this period of

decreasing effective stress, the sedimentdeviates from the virgin compactioncurve (solid line).

0.150.2 03

Porosity10-'0 10 20

Sigma (MPa)K(m/s)

A B c D

Fig. 10. Pressure sources as a functionof time for Simulation 3 (see Fig. 8Bcaption). When the total pressure lineexceeds (crosses) the sediment loading,there is an abrupt shift in each curve.This shift is due to the fact that as thetotal pressure line crosses the sedimentloading curve, the compressibility('expandability') of the sedimentdecreases by an order of magnitude.

repeating Simulation 1, but after 2.2 million years ofsimulation time, we assume deposition goes from clay-dominated to sand-dominated. The permeability rule forthe clay-dominated sediment is represented by line A,and that for the sand-dominated sediment is representedby line C in Fig. 5B (there is no mineralogical controlon permeability resulting from clay alteration). The depthto the top of overpressure is controlled by the depth tothe transition between the sand and shale intervals(Fig. 11). Within the upper sand-dominated unit, nooverpressure develops (Fig. l1A) and the porosity followsthe normal compaction trend (Fig. lIB). Even at lowporosities, the sand was permeable enough to expel itsformation fluids in response to further sediment loading.Within the clay unit, porosity is virtually constant at27.5%, and the fluid pressure gradient is nearly lithostatic(Fig. lIA,B). Once again, the hydraulic conductivityof the overpressured shale is between 10-12 m S-1 and10-13 m S-I. While the porosity decreases and thenincreases with depth, the particle did not experience thisevolution. It decreased to a minimum value at whichpoint compaction effectively ceased.

Discussion of constant rate depositionsimulations

These simulations illustrate that clay compaction is thekey control on the development of overpressure. For theassumed porosity-permeability behaviour and the appliedsedimentation rates, the clay compacts until its per-meability is reduced to the point at which fluid cannotescape at the rate necessary for the sediment to compactnormally and, consequently, overpressure develops. Thehigher the sedimentation rate, the shallower the depth tooverpressure. Keith & Rimstidt (1985), Bethke (1986)and Harrison & Summa (1991) observed this behaviourin their compaction-driven fluid-flow models. Similarly,the lower the sediment permeability-porosity relation-ship, the shallower the depth to overpressure.

Our quantification of the three major source termsillustrates that for the observed sedimentation rates,sediment loading is the dominant source of overpressure.Clay dehydration and aquathermal pressuring are import-ant only when we assume mineralogical permeabilitydependence and inelastic sediment behaviour. While we

186 ~ 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


Fig. 11. Simulation of clay-dominateddeposition for 2.2 million years, andthen sand-dominated deposition for 2.2million years (see Fig. 6 caption).(D) The decreasing interval betweenpoints along the curve is indicative ofslowed compaction. A 8 D

(~t )I/U = 1 --ff (10)

recognize that there are certain conditions under whichanyone of these sources might be the dominant mechan-ism in overpressure generation, in rapidly depositedsedimentary basins, sediment loading is the dominantsource.

We have explored conditions under which it is possiblefor sediments to experience a decrease in effective stressthrough time. We suggest that a rapid decrease inpermeability which is coincident with the smectite-illitetransition could cause this effect. Under these conditions,the magnitude of the decrease in effective stress dependson the extent to which the medium behaves elasticallyversus inelastically.

We emphasize that permeability reduction is only onepossible mechanism for generating a decrease in effectivestress. Alternatively, a large fluid source entering frombelow or an in-situ source that we have not consideredcould cause this effect. Fluid expulsion at depth by anyof a range of processes (e.g. compaction, hydrocarbongeneration) might cause the former effect. An in-situsource that we have not considered is biogenic gas (e.g.Hedberg, 1974). We can estimate what the magnitude ofthese sources would need to be by pointing out that apermeability reduction of two orders of magnitude wasrequired to generate a decrease in effective stress giventhe source terms we considered. If only a fluid sourcewere called upon, we would need an increase in the fluxof fluids of several orders of magnitude. This new sourcewould then dwarf the role of sediment loading. Biogenicgas production is an appealing mechanism because itrepresents a source of pressure and may cause a decreasein effective permeability due to the relative permeabilityeffects of multiphase fluid flow. We do not believe thatthere is in-situ thermogenic hydrocarbon generationbecause the sediments are immature (Holland et al.,

1990).

where u and Atma are empirical parameters for shalesderived by Issler (1992) (Figs 12A2, H2, C2, 02).

We predicted fluid pressures from three sources: sonic-derived porosity measurements, drilling mud weights andreservoir pressure surveys. Assuming porosity is anexponential function of effective stress, we calculate fluidpressure after (Hart et al., 1995)

In ( ~).(11)p= i -+ O"L

':,pwhere the overburden stress (crL) is calculated from anaccumulated density log (Figs 12Al, Bl, Cl, Dl).

As a second approximation of the fluid pressure, weuse the weight of the muds used to drill the wells (Figs12Al, Bl, Cl, Dl). Finally, we used bottom hole pressuresurveys to determine fluid pressure in individual reservoirsands (black asterisks, Figs 12Al, Bl, Cl, Dl). Wecalculated sedimentation rates according to Eq. (12)


CHARACTERIZATION OF PRESSUREAND POROSITY IN EI 330 FIELD

We now characterize lithology, pressure and porosity infour wells, two in the upthrown block (329 #3 and 330#3), and two in the downthrown block (330 #1 and 330B-13) (Fig. 1). We converted gamma ray logs to per centsand logs by linear interpolation between minimum andmaximum gamma ray response values. We smoothed theper cent sand curve over a window of 450 m to use asan input parameter in the model (Figs 12A4, B4, C4, 04).

We used the sonic log to calculate shale porosityaccording to Issler's (1992) equation:

(A) 329_3 (Upthrown)

P .lac.A

(0.46)

P .Lac.B

(0.65):[InIn.,c-5:2l-E.,E'C.,cn

Sm.Gep.1(0.90)

H.Sellii(1.27)

C.Mac.(1.50)

0 50 0 1 2Sed Rate (mm/yr)

0 50 100Percent Sand (%)Pressure (MPa)

2

(8) 330_3 (Upthrown)

-l-I

I

P.Lac.A(0.46)

:[InInOJC~"Ef-EOJE'COJ

cn

~

i~I :

P.Lac.B(0.65)

91-iF

~i!\\~(- -

'.

Sm.Gep.1(0.90)

H.Sellii(1.27)

--;':~;A. B

C.Mac.(1.50)

0 20Pressure (MPa)

40 0.2 0.3Shale Porosity

0.4 0 1 2Sed Rate (mmiyr)

0 50 100Percent Sand (%)

1 2 3 4

Fig. 12. For each simulated well, we plot measured and simulated fluid pressure (1), measured and simulated porosity (2),calculated sedimentation rate (3) and per cent sand, smoothed per cent sand and the depth of the known age surfaces (4). Wells:(A) 329_3, (B) 33o_3, (C) 33o_1, (D) 330_B-13. In per cent sand figures, the dotted lines represent the assumed sedimentcomposition over intervals where no log was available. The pressure figures (1) show the hydrostatic and lithostatic gradients,pressure measured from mud weight data (solid line), pressure predicted from sonic porosity (grey + 's), direct reservoirpressure measurements (black asterisks) and the simulated pressure field (dashed lines). The porosity figures show porositycalculated from the sonic log (grey + 's) and simulated porosity (dashed lines). For each upthrown well, 12A, and 12B, twosimulations are shown, A and B. Simulation A uses the same permeability models as used in the downthrown wells, andSimulation B uses a modified permeability model.

188 @ 1998 Blackwell Science Ltd, Basin Research, 10, 177-196

0.2 0.3 0.4Shale Porosity


(Figs 12A3, B3, C3, D3):

1 -<l>ave

1-<1>0SedRate = AccRate x (12)

not strongly dependent on mineralogy, then the previoussimulations show these processes to be insignificant. Weused the smoothed per cent sand curves (Figs 12A4, B4,C4, D4) to constrain the lithology in each simulation. Inorder to approximate the effects of depositing sedimentinto an already overpressured basin, we began eachsimulation by depositing 500 m of sediment (10% sand)at 1 mm yr-I. Then we continued the simulation usingthe sedimentation rates and lithology data from each well.

In the downthrown block wells, the model predictionsprovide an excellent match for the data. The modelreproduces both the character and magnitude of thepressure and porosity fields (Figs 12Cl, C2, Dl, D2). Inthe upthrown block, using the same permeability rulesas in the downthrown block, the model reproduces thegeneral character of the pressure and porosity fields (Figs12Al, A2, Bl, B2, line A). It accurately predicts thedepth of the three distinct pressure regimes, and itcorrectly predicts the depth to the rollover in the porosityfield. However, it underestimates the magnitude of theoverpressure and, therefore, it overestimates the amountof compaction which takes place.

The permeability model used successfully in the down-thrown block predicts permeabilities which are too highto reproduce the magnitude of overpressuring observedin the upthrown block. There is greater structural reliefto sands in the downthrown block due to the largeanticlinal structures present (Alexander & Flemings,1995). In addition, there is significant lateral variation insand thickness throughout the downthrown block(Alexander & Flemings, 1995). We infer that as a resultof these factors, there is greater effective vertical per-meability in the down thrown block than in the upthrown.We found that by dividing the permeability field bythree, we could capture the character and magnitude ofthe overpressure (Fig. 12Al, line B; A2, line B; Bl; andB2). Line D (Fig. 5B) shows the permeability for sedi-ment with 10% sand in the upthrown fault block. Theneed to manipulate the permeability rules from one blockto the other illustrates a limitation of one-dimensionalmodelling. It is difficult to approximate the three-dimen-sional vertical interconnectivity of sand bodies based ona single variable such as per cent sand in a given well.These results suggest that interconnectivity can vary overdistances of less than 1 km. Lines A and B in Figs 12Aland A2 give some indication of the sensitivity of themodel to changes in the porosity-per cent sand-per-

meability relationship.

where Q>ave is the average porosity over the intervalbetween surfaces of known age.

Figures 12A4, B4, C4, D4 each show that the averageper cent sand gradually increases from approximately10% at depth to approximately 50% near the sedi-ment-water interface. This gradual increase in per centsand is characteristic of a regressive sequence. The sand-dominated sediments extend to nearly 2000 m depth inthe down thrown block (Figs 12A4, 12B4), and to only1500 m in the upthrown block (Figs 12C4, D4), reflectingoffset due to growth faulting (Fig. 2). The shale porosityprofiles show a decrease to a minimum of approximately0.20 which corresponds to the bottom of the sand-dominated unit, and then an increase below that depthto nearly 0.30 (Figs 12A2, B2, C2, D2).

The pressure profiles each show three distinct pressureregimes: a shallow hydrostatic zone, a deeper moderatelyoverpressured zone and a deep strongly overpressuredzone (Figs 12A1, B1, C1, D1). In the upthrown block,the moderately overpressured zone tends to be only acouple of hundred metres thick, and it runs from 1100 mor 1300 m down to 1500 m or 1600 m (Figs 12A1, B1).In the downthrown block the transition zone is500-1000 m thick. It is encountered at shallower depths(1000 m), and it extends to nearly 2000 m (Figs 12C1,D 1). In both blocks, within the strongly overpressuredzone the fluid pressure gradient is nearly lithostatic.

In general, we observe good agreement between mudweight-predicted pressure, sonic porosity-predictedpressure and direct reservoir pressure measurements.However, in the upthrown wells, the direct-reservoirpressure measurements fall below the pressure predictedby mud weight and sonic data. We attribute this discrep-ancy to the fact that these- measurements were madefrom reservoirs in which fluid pressure is decreasing dueto hydrocarbon production.

The observed agreement between the drilling mud-predicted pressures, the porosity-predicted pressures anddirect reservoir pressure measurements show that thecurrent effective stress field is equal or similar to themaximum effective stress field to the depth that we havedirect measurements of pressure.

APPLICATION OF MODEL TO FIELDDATA

We apply our forward modelling approach to simulatethe evolution of pressure and porosity in the four wellsdiscussed above. The boundary conditions were the sameas in the previous simulations. We do not consideraquathermal pressuring or clay dehydration for tworeasons. First, our data show no evidence for significantlate-stage pressure generation or for a departure fromthe virgin compaction trend. Second, if permeability is

DISCUSSION

We have characterized the geological and hydrodynamicstate of the £1-330 field, a young Plio-Pleistocene basin.We have developed a one-dimensional model that incor-porates sediment loading, clay dehydration and aquather-mal pressuring to illuminate the hydrodynamic evolutionof this basin. The results show that a simple model wheresedimentation rate and permeability are constrained by

190 ({:) 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


observed accumulation rates and lithologies successfullysimulates present-day pressures and porosities.

Our analysis builds on previous studies by Rubey &Hubbert (1959), Bredehoeft & Hanshaw (1968), Keith &Rimstidt (1985), Bethke (1986), Palciauskas & Domenico(1989), Harrison & Summa (1991), Mello et al. (1994)and Hart et al. (1995). Through theory and observation,these authors also analysed the processes which generateoverpressure in the Gulf Coast and concluded thatsediment loading of low-permeability sediments is thedominant source of overpressure. We extend their workin two ways: (1) by exploring in detail the effects ofsediment loading, aquathermal pressuring and clay dehy-dration, and (2) by integrating observation and theory atthe kilometre scale.

Keith & Rimstidt (1985), Bethke (1986) and Harrison& Summa (1991) have quantitatively considered the rolesof sediment loading, aquathermal pressuring and claydehydration. We have extended their analyses by explor-ing the effect of reversible versus irreversible compactionon the development of overpressure. This allows us toconsider the implications of observations made byPlumley (1980), Bowers (1994) and Hart et al. (1995)which documented situations where porosity does notfollow the virgin compaction curve and suggest that thereason is due to late-stage pressure sources.

A solid grasp of how sediment responds to decreasingeffective stress is fundamental to understandingporosity / pressure relationships. Significant departuresfrom a virgin compaction curve due to decreasing effectivestress mean that traditional approaches using porosityfrom core or wireline data (e.g. Hart et al., 1995) or, ata larger scale, from stacking velocities in seismic data(e.g. Louden et al., 1971) to predict pressure will beunsuccessful. At a broader scale, an understanding of thecompressibility behaviour of sediments is critical tounderstanding under what conditions sediments willfracture (as the fluid pressure exceeds the least principalstress). We have shown that if compressibility is lowduring late-state pressure generation, the result is astrong increase in pressure which will drive a rock morerapidly to fracture than if elastic behaviour is assumed.

The second contribution of our analysis is the emphasison integrating observations of pressure and porosity withdynamic simulations at the kilometre scale. Previousstudies have either not considered lateral variation in thepressure field over distances of less than 1 km (e.g. Melloet al., 1994) or have studied the problem at the 1000-kmscale (e.g. Harrison & Summa, 1991). An analysis at thekilometre scale illuminates the sharp changes in pressureand lithology that can occur laterally over distances ofless than 1 km. However, if detailed observations areincorporated into the model development, then the modelcan successfully reproduce these lateral variations in thepressure and porosity fields. Our results suggest thatthere may not be a significant component of lateral flowacross the fault system in this basin. However, our resultsdo not preclude the propositions of Roberts & Nunn

(1995) that the fault is a conduit for vertical flow, andthat it may both capture lateral flow from each faultblock and so expel fluid laterally into reservoirs.

Our modelling and observations illustrate that thehydrodynamic evolution of this basin is tied to itsstructural and stratigraphic evolution. Pressures tie tostratigraphy and the dominant source of pressure issediment loading of low-permeability strata. This viewof the subsurface as a hydrodynamic system is espousedby many previous authors (Bredehoeft & Hanshaw, 1968;Chapman, 1980; Keith & Rimstidt, 1985; Bethke, 1986;Shi & Wang, 1986; Harrison & Summa, 1991; Toth et al.,1991; Mello et al., 1994; Hart et al., 1995), and contrastsseveral recent papers that have proposed the existence ofimpermeable seals which form pressure compartmentsthat cross-cut both stratigraphy and structure in thesubsurface (e.g. Hunt, 1990; Powley, 1990; Ortolevaet al., 1995). This 'seal' approach has been extended tothe EI 330 region where Roberts & Nunn (1995) andNunn (1996) have modelled the geopressure surface as asingle horizontal low-permeability horizon, beneathwhich lie permeable strata. Both the thick transition zonefrom hydrostatic to strong overpressure and our modelresults strongly contradict the idea that there is a thinimpermeable seal in the EI 330 basin. Rather, ourobservations and modelling suggest a more appropriatepermeability structure is one that is tied to stratigraphyand where permeability generally decreases with depthdue to the regressive character of the strata. Mello et al.(1994) proposed a dynamic model in which the hydraulicdiffusivity of clays in the subsurface reaches a minimumat depths of a few kilometres due to compaction andcompressibility behaviour, and beneath that depth, diffu-sivity increases. Their result relies critically on theirassumption that porosity declines as a function of depth(as opposed to effective stress) in hydrostatically press-ured sediments. In contrast, in our approach, whereporosity is assumed to decline as a function of effectivestress, a diffusivity minimum is not required as a sealwhich marks the top of the overpressured zone.

The basic overpressure field is formed early, duringthe rapid formation of the basin. Today, because sedimen-tation rates are low, pressures are gradually dissipating.We can estimate the relaxation time through Eq. (13)(Paola et al., 1992):

S L2Te = ,Pfg (13)K .

Using a specific storage (S,) of 1.36 x 10-8 Pa-l, asediment thickness (L) of 1500 m and a bulk averagehydraulic conductivity of 10-12 m S-I, the characteristicrelaxation time for the strongly overpressured sedimentsin EI 330 is on the order of 10 million years. In EI 330,sedimentation rates have varied from 1 mm yr-1 or moreduring the salt-withdrawal of the Plio-Pleistocene to0.1 mm yr-1 or less today. This order of magnitudedecrease in sedimentation rate means that the currentpressure gradient is far greater than that called for by

191<0 1998 Blackwell Science Ltd, Basin Research, 10, 177-196


the current loading conditions. The length of timerequired for the pressures in EI 330 to dissipate untilthey are in line with the current loading conditions is onthe order of 10 million years. This number agrees withthe relaxation times calculated by Bredehoeft & Hanshaw(1968) for thick sequences of low-permeability sediment.

Although the one-dimensional model is successful incapturing the large-scale hydrodynamic behaviour of thisbasin, it is limited in its ability to represent a naturalsystem. This problem is reflected in our need to modifythe sandi shale permeability relationship in the upthrownversus the downthrown block. In addition there is stillsignificant debate as to the mechanisms for smectitedehydration. Finally, we have assumed a linear tempera-ture gradient to approximate conductive heat flow. Infact, the temperature gradient will vary as a function ofporosity, and, if there is advection present, it will alsodepend on the flow field.

R. Slingerland, R. Parizek, L. Summa, G. Garven,U. Mello, J. Nunn, B. Stump, J. Dacy and P. Hickshelped to focus our thoughts. S. Nelson and B. Stumpprovided assistance in preparing figures and editing themanuscript. Additional support is provided by a ShellFoundation Fellowship to Flemings and NSF Grant#EAR-9614689. Pennzoil and Exxon provided well log,seismic and pressure data from the EI 330 field. Wethank Mincom Ltd for the use of their software,GeologTM. Finally, we appreciate the critical review ofMark Person and three anonymous reviewers.

CONCLUSION

The complex pressure and porosity fields observed in EI330 result from sediment loading of low-permeabilitystrata. Pressures rise with depth from hydrostatic tonearly lithostatic, iso-pressure surfaces closely followstratigraphic surfaces which are sharply offset by growth-faulting, and porosity follows an exponential function ofeffective stress.

A hydrodynamic model is used to explore the evolutionof fluid pressure in a rapidly subsiding basin. If reversiblecompaction is assumed, then sediment loading is alwaysthe dominant source of overpressure. However, ifirreversible compaction and permeability reduction dueto diagenesis are assumed, then aqua thermal pressuringand clay dehydration (or other diagenetic reactions) canplay significant roles in the generation of overpressure.Application of the hydrodynamic model to four locationsin the EI 330 field, assuming that sediment loading isthe only pressure source, and that permeability is afunction of lithology and porosity, successfully repro-duces the observed pressure and porosity profiles.Observation and theory support a conceptual modelwhere hydrodynamic evolution is intimately tied to thestructural and stratigraphic evolution of the progra-dational deltaic system. Today, permeability decreasesand overpressure increases with depth because of thegreater abundance of shales deposited early in the evol-ution of this basin. Modelling suggests that these low-permeability shales developed overpressure early in theirsubsidence history (within 500 m of the surface) and thensubsided more deeply into the basin to produce thepresent observed pressure distribution.

ACKNOWLEDGMENTS

We thank Core Laboratories for their generous supportof David Gordon through the Penn State-CoreLaboratories Fellowship. Discussions with D. Elsworth,

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APPENDIX: DERIVATION OF THEMODEL EQUATION

The equations for fluid flow in a compacting mediumare derived from the conservation of mass equations forfluid moving through a porous medium and from fourconstitutive laws (Palciauskas & Domenico, 1989). Theconservation of mass for solid grains subsiding andcompacting in one dimension is

()at [(1

iJ<I»ps] + -;-: [vsp.(l -<1»] = o. (14)

vz

The conservation of mass for a fluid moving in onedimension is

(15)

Equations (14) and (15) are derived in cartesian coor-dinates. We solve these equations according to aLaGrangian formulation where the reference frame isfixed on the solid grains:

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of Mexico geopressured sediments. J. geophys. Res., 101,

2963-2970.

ORTOLEVA, P., AL-SHAIEB, Z. & PUCKETTE, J. (1995) Genesis

and dynamics of basin compartments and seals. Am. J. Sci.,

295, 345-427.PALCIAUSKAS, V.V. & DOMENICO, P.A. (1982) Characterization

of drained and undrained response of thermally loaded

repository rocks. Water Resour. Res., 18, 281-290.

PALCIAUSKAS, V.V. & DOMENICO, P.A. (1989) Fluid pressures

in deforming porous rocks. Water Resour. Res., 25, 203-213.

PANDA, M.N. & LAKE, L.W. (1994) Estimation of single-phase

Combining Eqs (15) and (16) we find

Dpc a aDt -v. a:;: (Pc<!» + a:;:(vcPc<!» = o. (17)

Simplifying Eq. (17), introducing the substantial time

193~ 1998 Blackwell Science Ltd, Basin Research, 1O, 177-196


(18)

This simplifies to

~~-~~Pc Dt Ps Dt

oP,.K-oz

<1>" OO"L-J3-+CXm:

(l-<j>T]) Ot Ot

DTi:f'~

=D11<1>11) Dt \Pfg; OZ L

where IXrn is

~

where

IXm i

1 a+;;; a; ~Pfq) = 0+ ,;,,-

(1(27)

(19)

We assume uniaxial deformation (Jacob, 1949; Palciauskas& Domenico, 1989) and express the strain of the materialelement:

where

IXm i

~

-<1>"

tX:m = <1>11 CXf -1 .CXb -<1>11 cx.

I

1 1 1

(28)

vov= <I-=-~ 0<1>,,- -p:°P..

Solving Eq. (19) for 1/(1 -<1>,,) 0<1>" and substitutingthat into Eq. (20), we find

(1 -<1>,,) Op. <1>" Opc 1 I I ~!" .-+-- .

\-'. 01 Pc 01

(20)

~ ) 1 DV+ -( -;- (Prq) = -V Dt.

Pr \ Z (21)

(23)

-I(24) l-TJ

Dlldz = ---;:- .l-'I'TJ

1 .~ , -::~;!;t"--

1I -A:C~/

n

~

Each term in Eq. (21) has units of strain rate.The strain due to fluid flow is described by Darcy's

law

The

units of each term in Eq. (27) are still strain pertime. The first term describes strain rate due to fluidand

matrix compressibility, the second, strain rate dueto fluid flow, the third strain rate due to sediment loading,and

the fourth, strain rate due to thermal loading. Thecompressibility of solid quartz is approximately 2 x10-11 Pa-l, while for water it is 5 X 10-10 Pa-1 (deMarsily, 1986) and for the matrix 3.68 x 10-8 Pa-1 (Hartet al., 1995). Therefore, we assume that the compress-ibility of the solid grains is zero. Dropping these termsand

including an internal source term in Eq. (27) givesEq.

(2).In Eq. (27), each term except the Darcy term is stated

in substantial coordinates where the reference frame isfixed on the solid grains. In contrast, the Darcy term isstated

with respect to the cartesian coordinate system(z = 0 at the sediment surface and increases with depth).To

simplify the solution ofEq. (27), we express it entirelyin substantial coordinates (11). To map between the twocoordinate

systems, we assume

rll 1z = Jo d11 (29)

K 0 KoP.Pcq= ---(P-Pcgz)= ---(22)

g oz g iJz

where p. is the overpressure.The fluid and the solid strain are assumed proportional

to changes in fluid pressure and temperature:

Dpf= I3fDP- CXrDT

~

Pc

~ Dps = f:\s DP CIs 01

~0"0"~

(30)

This is a 'fully-compacted' coordinate system wherethe length scale, 11, is the distance from the sedimentsurface

to a particular grain when no porosity is present.Figure Al shows the relationship between depth, z, and

substantial coordinates, 11.Now, the Darcy term can be restated as

./~ 'I (1-<j>,,)DI( v [ DP- ]~\a:;:(Pfq), Pfg 011 -K(l-ll)~

(31)

We combine Eqs (27) and (31) and simplify

[ ip" J DP ~ 13 + ip" 13f -ip" 13. n;

, J. ~'. .~

The bulk strain of the material element is expressedas a function of pressure and temperature. Porosity is afunction of changes in effective stress and changes in

temperature. = <1>0 e-f\("L -P)+IXb(T- TO) (25)

which when differentiated yields

D,,= -~"DO'L+~"DP+(Xb<l>"DT. (26)

The matrix compressibility (~) has been defined in amyriad of fashions. Palciauskas & Domenico (1989)assume porosity varies linearly with depth; Mello et al.(1994) assume porosity declines exponentially with depth;we assume porosity decreases exponentially with effectivestress. These differences in the definition of matrixcompressibility result in significant differences in howstorage (St) (Eq. 3) varies with depth.

For purposes of estimating porosity from effectivestress, Eq. (25) can be approximated by Eq. (1) usingthe definition of effective stress and assuming the alphaterm of Eq. (25) is negligible.

.<1>" OO"L CXm 01+-/3-+~-.\

Pcg 0112 1-<1>" Ot Ot

Equation (32) is a simple diffusion equation where the

<1>" )' (32)= (]

~ 1998 Blackwell Science Ltd, Basin Research, 10, 177-196194


0NOMENCLATURE

1

Variable Description2 Units

3 unitless

4

z

Fig. AI. Schematic showing the 'fully-compacted' coordinatesystem (11) and how it relates to depth (z).

A constant in smectic decay rate

equationa permeability constant (Eq. 4)AccRate accumulation rateb permeability constant (Eq. 4)c permeability constant (Eq. 5)D smectite decay constant (Eq. 7)d permeability constant (Eq. 5)t timez depth.Ii per cent sandchange in pressure is proportional to the change in the

spatial gradient in the overpressure field. Source termsare due to sediment loading and temperature change.The spatial variation in porosity is approximated with afinite difference approach where at each time step theequation is solved based on the spatial variation inporosity at the previous time step and then the porosityis updated given the change in pressure over the timestep. Mello et al. (1994) made a similar approximation.

Viscosity is varied in the model according to therelation used by Mello et al. (1994) and found in Mercer

(1973):

unitlessmm yr-1unitlessunitless°Cunitlesssmbulk volumefraction

conversion factor from millidarcies m2 md -I

to m2g acceleration due to gravity m S-2k intrinsic permeability m2K hydraulic conductivity m s-1k,and sand (100%) permeability m2kclay clay (100%) permeability m2ksediment permeability of sediment m2k~ediment permeability of sediment as a m2

function of per cent sandand the mole fraction of smectite inthe mixed layer clayscompacted reference depth m

I porosity in bulkcompacted reference volumeframe fraction

L thickness of low-permeability msedimentfluid pressure Pafluid overpressure Pathe flux of fluid with respect to the m S-Isolid grainsclay dehydration pressure component Pamole fraction of smectite in smectite bulk volumeillite clays fraction

Ssed volume fraction of smectite plus bulk volumeillite in sediment fraction

St storage Pa-1SedRate sedimentation rate mm yr-1T e relaxation time sT temperature °CTo initial temperature °Cu empirically defined constant for -

Issler (1992) equationV volume m3v, velocity of the solid grains m s-1Vr velocity of the fluid m 8-1~ bulk sediment thermal expansion °c-1

coefficientCXr fluid thermal expansion coefficient °c-1~ matrix thermal expansion coefficient °c-1IX, solid thermal expansion coefficient °c-113 compressibility of sediment matrix Pa-1I3r fluid compressibility Pa -I13, compressibility of solid grains Pa -I

G

'1

I/IT

(33)

where

pp'

q

p clay

S

K=~J.l

(35)

Equation (32) was solved with a fully implicit finitedifference scheme. At the upper boundary no overpres-sure is assumed (P(ll = 0, t) = 0); at the lower boundaryno flow was assumed «DP*/Dll)(ll = I, t) = 0)) where I

is the depth in fully compacted coordinates to the bottomof the basin. Model results are expressed in the uncom-pacted coordinate system (z) through Eq. (29). Themodel was validated by comparison to the analyticalsolution to a half space diffusion problem (Turcotte &

Schubert, 1982).



L\tma assumed sonic travel time for mematrix from Issler (1992)measured sonic log responseporosity

~m kgm-1 S-I,

m3 m-3

J.1

dpcviscosityvolume expansion from clay-boundwater to pore waterdensity of the fluiddensity of the solid grainseffective stresslithostatic stress

1\.t



~sm-lbulk volumefractionbulk volumefractionbulk volumefractionbulk volumefraction

kgm-3

kgm-3Pa

Pa

PrP.

0"

O"L

..e average porosity for interval betweenknown age surfacesmicroporosity of smectite

CPo initial porosity at sea floorReceived 7 February 1997; accepted 1 December 1997

({;) 1998 Blackwell Science Ltd, Basin Research, 10, 177-196

Documents

Generation of overpressure and compaction-driven fluid ... · evolution of pressure and porosity in this system. If reversible ( elastic) compaction is assumed, sediment loading is