MARINE ECOLOGY PROGRESS SERIESMar Ecol Prog Ser

Vol. 303: 195–212, 2005 Published November 21

INTRODUCTION

Benthic ecology is typified by a strong interplaybetween the ‘biology’ of the bottom-dwelling organ-isms and the ‘physics’ of the sediment environment(Herman et al. 1999, Murray et al. 2002, Reise 2002). Itis well recognized that physical parameters, such asgrain size, porosity and permeability, strongly con-strain the distribution and abundance of benthicmacrofauna. However, it is also understood that thisphysical control is not exclusive and unidirectional.

Benthic organisms can actively alter the physical stateof the sediment environment to enhance their own liv-ing conditions and influence those of other organisms(Levinton 1995, Reise 2002), a concept more generallyknown as ‘ecosystem engineering’ (Jones et al. 1994).

An important example of ecosystem engineering inthe benthic environment is the process of burrow ven-tilation (Aller 1980, 2001, Herman et al. 1999, Meile &Van Cappellen 2003). Infaunal polychaetes, crusta-ceans and bivalves create burrows that deeply pene-trate into the anoxic zone of the sediment (e.g. Gust &

© Inter-Research 2005 · www.int-res.com*Email: f.meysman@nioo.knaw.nl

Irrigation patterns in permeable sediments induced by burrow ventilation: a case study

of Arenicola marina

Filip J. R. Meysman*, Oleksiy S. Galaktionov, Jack J. Middelburg

The Netherlands Institute of Ecology (NIOO-KNAW), Centre for Estuarine and Marine Ecology, Korringaweg 7, 4401 NT Yerseke, The Netherlands

ABSTRACT: In sandy sediments, a strong connection exists between the physics of flow and the ecol-ogy of burrow-ventilating macrofauna. We developed a general modelling procedure that quantifiesthis link involving 3 steps. (1) Burrow-ventilating organisms can be described as mechanical pumps.(2) The pumping of burrow water into blind-ending tubes induces advective flow in the sediment.(3) The resistance to pore water flow is governed by the friction between solid and fluid, i.e. Darcy’slaw. This analysis allows the determination of the operation point of an ‘organism pump’ under in situconditions, and we applied it in a detailed modelling study of the lugworm Arenicola marina. A3-dimensional finite element model encompasses the lugworm’s J-shaped burrow and represents atypical lugworm territory at in situ density. We simulated the associated flow patterns in the sedimentand analysed the factors that influence the lugworm’s ventilation rate. Since the lugworm’s oxygensupply critically depends on the burrow ventilation rate, we advance the following 2 ecologicalhypotheses: (1) decreasing the permeability of the burrow lining greatly increases the efficiency ofoxygen supply, as it prevents the re-entry of anoxic pore water; and (2) the permeability of the bulksediment constrains the lugworm’s habitat. When permeability falls below a critical threshold, thesediment’s resistance becomes too high, thus resulting in an insufficient oxygen supply. Overall, weshow that permeability exerts an important control on ventilation activity, and hence resource avail-ability, in sandy sediment ecosystems. From an evolutionary point of view, we anticipate biologicalfeedbacks on this physical control — in particular, behavioural adaptations that increase the perme-ability in the bulk sediment but decrease the permeability near the burrow wall.

KEY WORDS: Bio-irrigation · Burrow ventilation · Arenicola marina · Permeable sediments · Modelling

Resale or republication not permitted without written consent of the publisher

Mar Ecol Prog Ser 303: 195–212, 2005

Harisson 1981, Ziebis et al. 1996, Koretsky et al. 2002).The metabolic need for oxygen is satisfied by ventila-tion of these burrows with oxygen-rich water from theoverlying water column. Due to this ‘active’ burrowventilation, the organisms are no longer restricted tothe narrow zone near the sediment surface where oxy-gen penetrates via ‘passive’ diffusion.

One important issue, which has not received muchattention in past studies, is that the mechanism of bur-row ventilation crucially depends on the permeabilityof the sediment. One can consider 2 end-member situ-ations (Fig. 1). In muddy environments, the pressuresrequired to force a flow of pore water through the sed-iment are typically beyond the physiological capabili-ties of benthic fauna. To enable burrow ventilation,burrows must have at least 2 connected openings tothe sediment surface, to ensure a free conduit for theventilated burrow water (Fig. 1a). So, in muddy sedi-ments, advective flows are generated within the bur-row, but these flows do not penetrate the surroundingsediment. Therefore, the bio-irrigational exchange ofsolutes between burrow water and pore water princi-pally occurs by diffusion across the burrow walls. Thisdiffusive mechanism creates distinct geochemical gra-dients around the burrow structures (Aller 1980). Insandy environments, the effect of burrow ventilationcan be equally pronounced, though the connectionbetween ventilation and bio-irrigation is different. Dueto the higher permeability, organisms can activelypump water across blind ends of burrows into the sur-rounding sediment (Fig. 1b), and, as a result, burrows

no longer need a 2-way connection to the surface (Fos-ter-Smith 1978). So, in sandy sediments, the flows thatare generated within the burrow can penetrate the sur-rounding sediment, and solute transfer between bur-row water and the pore water is due to an advectivemechanism. The advective flows that are generated inthe pore water can have an important influence on theoverall biogeochemistry and microbial ecology of thesediment (e.g. Huettel 1990, Banta et al. 1999).

Here, we propose a modelling procedure to quanti-tatively expose the pore water flow patterns generatedby burrow ventilation in permeable sediments. Theaim is to investigate the ecological implications of thisadvective irrigation, especially the consequences forburrow construction and habitat selection. Our ap-proach focuses on the lugworm Arenicola marina as arepresentative example of a burrow-ventilating organ-ism and derives flow patterns from a comprehensive3D model of the organism’s burrow and the surround-ing sediment.

We selected Arenicola marina as our study speciesfor 2 specific reasons. Firstly, arenicolid polychaetesconstitute a dominant type of bio-irrigators in temper-ate, near-shore, sandy environments (Reise 1985). Sec-ondly, being a well-studied benthic organism, a sub-stantial amount of background information on theecology and ventilation of Arenicola has been gath-ered (see review by Riisgård & Banta 1998). Likewise,the reason for our exclusively modelling-based ap-proach is principally the lack of appropriate experi-mental techniques. With present-day technology, it is

196

Ventilationburrow

water flow

Ventilationburrow

water flow Bio-irrigationadvective pore

water flow

Bio-irrigationdiffusion across

burrow walls

Advective transferDiffusive transfer

(a) Muddy sediments (b) Sandy sediments

Fig. 1. The link between burrow ventilation (the bulk flow of burrow water) and bio-irrigation (the transport of solutes in the porewater) depends on the permeability of the sediment. (a) Muddy sediments: burrows have 2 or more connections to the surface;bio-irrigational transport is driven by diffusion across the burrow walls. (b) Sandy sediments: burrows may end blindly within the

sediment; bio-irrigational transport is driven by advective flows of pore water

Meysman et al.: Bio-irrigational flow in permeable sediments

not yet possible to quantify the pressure and velocityfield with a satisfactory resolution on the scale of thelugworm. Even if sufficiently small pressure transduc-ers and flow probes were available, they would onlyprovide point measurements, which would reveal littleinformation on the complex 3D pressure or flow field.Faced with this lack of experimental capabilities,numerical modelling offers an opportunity to investi-gate sediment irrigation at high resolutions.

VENTILATION ACTIVITY

Ecology

The polychaete taxon Arenicolidae, commonlyknown as lugworms, comprises a group of deposit-feeding polychaetes with a worldwide occurrence(Rouse & Pleijel 2001). One member, Arenicola mar-ina, is a large head-down deposit feeder (12 to 24 cmlong) inhabiting the intertidal sand flats of westernEurope. This polychaete can be found in considerabledensities (up to 50 ind. m–2) in clean to muddy sandthroughout most of its geographical range from theArctic to the Mediterranean (Riisgård & Banta 1998).Sometimes, it represents half of the total macrofaunalbiomass on the lower shore (Cadee 1976, Beukema &De Vlas 1979).

Lugworms dwell in J-shaped burrows (Fig. 2a) thatmay reach depths of up to 20–40 cm, depending onage and size-class (Wells 1945, Kruger 1959). Whenfeeding, the worm resides in the lower part of the bur-row called the ‘gallery’. Positioned head down, Areni-cola marina ingests sediment from a feeding pocket atthe closed end of the gallery, which is enveloped bycoarse-grained sediment particles. This feeding modecauses a downward transport of sediment above thefeeding pocket, and leads to the formation of a so-called ‘quicksand column’, a cylinder of loosened sedi-ment that is sometimes visible on the sediment surfaceas a funnel (Jakobsen 1967, Rijken 1979, Retraubun etal. 1996). When defecating, the worm moves back-wards along the burrow until its tail reaches the sur-face. At the open end of the burrow, the residual sedi-ment is ejected, which produces the characteristicfaecal mounds.

The direction of the water flow generated by Areni-cola marina is opposite to the sediment transport byingestion–egestion. Residing in the gallery, the lug-worm pumps water by means of piston-like waves thatrun along its dorsal surface (Kruger 1971). The suctioncreated by these peristaltic motions takes in oxy-genated water from the overlying water column. Pass-ing through the burrow and over the lugworm’s gills,this water is subsequently pumped through the porouswalls of the feeding pocket into the surrounding sedi-

197

Tailshaft

Quicksandcolumn

Lugworm

Funnel

Sedimentmovement

Waterflow

Fecalmound

Sediment

Water

Gallery

Feeding pocket

Fig. 2. (a) Schematic representation of the counter current flows of water and sediment induced by Arenicola marina. The linkbetween burrow ventilation and bio-irrigation is the advective mechanism depicted in Fig 1b. (b) Finite element mesh around thelugworm burrow used in the simulations. Due to symmetry only half of the domain needs to be meshed. A finer mesh resolution

is adopted near the burrow wall

a b

Mar Ecol Prog Ser 303: 195–212, 2005

ment. The latter then results in an upward, advectivetransport of pore water through the sediment to thesediment surface. Our aim is to quantify this irrigationpattern using a 3D flow model.

Modelling approach

Past studies of lugworm ventilation have primarilyfocused on the organism itself, while devoting far lessattention to its environment. Particularly, the pumpingactivity of Arenicola marina has been characterised ingreat detail in glass tubes under laboratory conditions(Foster-Smith 1978, Baumfalk 1979, Riisgård et al.1996). Yet, to transpose these results to the field situa-tion, highly simplified models of the sediment environ-ment were used. In these models, the flow patterncaused by A. marina is a priori assumed to be 1D, i.e.pore water moves uniformly upwards through a core ofconstant radius (Riisgård et al. 1996, Timmermann etal. 2002, 2003).

Here, our ambition is to implement the availableinformation on Arenicola pumping in a more sophisti-cated model of the lugworm’s sediment habitat. Ratherthan imposing a preconceived flow pattern, the idea isto obtain this pattern as the output of the model. Forthis purpose, we propose a detailed 3D finite elementmodel (FEM) of the lugworm burrow and the sur-rounding sediment. The driving force that generatesflow in porous media is not the fluid pressure p, but thepressure in excess over the hydrostatic pressure, whichis typically expressed as the hydraulic head H (Bear1972, Freeze & Cherry 1979). The precise relationbetween H, p and the pore water velocity vector v isdetailed below. Accordingly, we will develop a modelthat describes the spatial variation of H and v within aspecific 3D lugworm territory. In this model descrip-tion, we implement the following idealisations: (1) thelugworm’s ventilation rate is constant over time; and(2) the sediment surrounding the burrow has homoge-neous properties. These assumptions will be discussedin detail below.

THE ARENICOLA PUMP

To investigate the pumping activity of benthicorganisms, one can apply the same engineering prin-ciples as in the analysis of (abiotic) mechanicalpumps (Foster-Smith 1979). To this end, one needs toidealize the lugworm’s ventilation activity with anappropriate pumping mechanism, and, subsequently,translate the technical concepts ‘pump characteristic’and ‘system characteristic’ in terms of the lugworm’ssituation.

Pumping mechanism

Riisgård et al. (1996) made a detailed analysis of whatis referred to as the ‘Arenicola pump’ in order to assessthe energetic costs of pumping. Basically, the Arenicolapump was found to approximate an ideal, closed, posi-tive-displacement pump. In general, a pump is termedideal when it possesses perfect piston seals and showsno leakage to the suction section (i.e. no slippage). Thisimplies that a constant displacement volume Vd ismaintained irrespective of the flow resistance in thesystem in which the pump is operating. Accordingly,the frequency f at which an ideal pump operates is theonly factor that affects the flow rate Q, i.e. Q = fVd. Inthe case of Arenicola, the term f denotes the stroke fre-quency of the peristaltic tail-to-head undulations.

As noted above, we assume that the lugworm contin-uously pumps with a steady pumping rate. However, inreality, the lugworm’s ventilation activity shows 2 char-acteristic scales of temporal variability. Firstly, on ashort time-scale, the peristaltic undulations generate apulsed flow with a typical stroke frequency of f =7 min–1 (Riisgård et al. 1996). Piston pumps pulsate bynature, and, in this regard, the Arenicola pump doesnot differ from its mechanical counterparts. However,in technical calculations, this high-frequency pulsatingflow is generally replaced by its time-averaged value.The latter approach is equally justifiable for the Areni-cola pump. Due to the linearity of Darcy’s law (see sec-tion ‘System characteristic’), the time-average of thesediment pressure loss will scale with the time-aver-age of the pulsating flow. Accordingly, no major (non-linear) deviations in the flow pattern are expected dueto the pulsations. Secondly, the pumping rate alsovaries on a longer time-scale, as the lugworm’s ventila-tion activity proceeds in regular cycles of 40 to 60 minthat are probably under the control of a pacemaker inthe nervous system (Wells 1949, Kruger 1971). Thisventilation pattern differs in 2 ways from that of otherburrow ventilators. Firstly, Arenicola shows long peri-ods of continuous pumping, only interrupted by shortperiods of inactivity related to defecation at the surface(Baumfalk 1979). This contrasts markedly to othertube-dwelling organisms, such as thalassinideanshrimp (Forster & Graf 1995) and nereid polychaetes(Kristensen 2001), which show intermittent ventilation,i.e. far longer periods of rests interspersed by shortbursts of ventilation activity. Secondly, during ventila-tion, the pumping rate is almost steady, which con-trasts strongly with the irregular ventilation pattern ofnereid polychaetes (Kristensen 2001). Together, thesearguments indicate that the lugworm’s ventilationactivity can be acceptably characterised in terms of amechanical piston pump that operates in a steady andcontinuous fashion.

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Meysman et al.: Bio-irrigational flow in permeable sediments

Pump characteristic

A pump’s performance is typically summarised in apump characteristic, a curve that plots the flow rate Q,which a given pump can develop against a certainpressure difference across the pump. This pressure dif-ference across the pump is expressed as a difference inH, i.e. the pump head ΔHp (cm H2O). For mostpumps — whether mechanical or biological — there is amarked trade-off between the variables in the pumpcharacteristic. Higher flow rates can only be pumpedover smaller pressure differences, i.e. ΔHp decreaseswhen Q increases.

Employing an inventive experimental set-up, Riis-gård et al. (1996) monitored the stroke frequency andthe pumping rate of individual Arenicola marina. Forthis purpose, the organisms were enclosed in a hori-zontally placed Plexiglas tube. For a given pressuredifference ΔHp imposed between the inlet and outlet ofthe glass tube, Q was measured. Based on measure-ments for 3 separate worms, the following relation wasobtained as the Arenicola pump characteristic:

(1)

where ΔHpmax is the pump’s maximal reachable pump

head (i.e. when the flow rate vanishes) and Qmax refersto the maximal obtainable flow rate (i.e. when thepressure difference that needs to be overcomeapproaches zero). In fact, many benthic bio-irrigatingorganisms show a similar quadratic pump characteris-tic with the species-specific parameters ΔHp

max andQmax (Foster-Smith 1979). Riisgård et al. (1996) foundthat both parameters had remarkably similar values fordifferent Arenicola individuals. This led these authorsto introduce the concept of a ‘standardArenicola worm’, characterised byΔHp

max = 20 cm H2O and Qmax = 1.5 mlmin–1 (see Riisgård et al. 1996 for theexperimental data upon which thesevalues are based). This ‘standard pumpcharacteristic’ is used in all simulationsbelow (Table 1).

System characteristic

Technically, a pump can operate indistinct environments, each characteri-sed by a different resistance to flow.This dependence is captured by a sec-ond curve, termed the system charac-teristic, which depicts the system’spressure loss as a function of Q. Thesystem’s pressure loss is expressed by

system head ΔHs, which typically will increase with theflow. In the case of the Arenicola pump, ΔHs originatesfrom a number of factors: (1) the resistance to waterflow in the tail shaft tube; (2) the frictional loss whenthe water passes between the worm’s body and thegallery wall; and (3) the pressure drop in the sedimentbetween the feeding pocket and the sediment surface.Riisgård et al. (1996) estimated that the total pressuredrop due to the first 2 factors only amounts to about0.01 cm H2O, which can be neglected as compared tothe flow resistance in the sediment. Hence, we equatethe system’s pressure loss solely to the frictional resis-tance to pore water flow in the sediment surroundingthe Arenicola burrow.

The frictional resistance to pore water flow in sedi-ments is generally modelled by Darcy’s law. Whenapplying Darcy’s law to a particular sediment domain,one always obtains a linear relation between the sys-tem’s pressure loss and the flow rate, referred to as thesystem characteristic:

ΔHs (Q) = CfQ (2)

where Cf is termed the resistance coefficient. Theactual proof that Darcy’s law always yields a linear sys-tem characteristic (Eq. 2) is discussed in detail below.Note that the system characteristic (Eq. 2) applies to aspecific sediment domain. In other words, to establishthe system characteristic for the Arenicola pump undernatural conditions, we need to delineate a suitable‘Arenicola territory’, i.e. a representative sedimentdomain that sufficiently encompasses the pore waterflow pattern near the burrow of an individual lug-worm. In contrast to the pump characteristic (Eq. 1),which incorporates 2 parameters, the system charac-teristic (Eq. 2) only features 1 parameter, Cf. Remark-

Δ = Δ − ( )⎡

⎣⎢

⎤

⎦⎥H Q H

QQp p( ) max

max1

2

199

Table 1. The default parameter set employed in the simulations. The parametervalues represent an average lugworm (a ‘standard Arenicola worm’) with atypical burrow structure (a ‘standard Arenicola burrow’) in a typical sediment

territory (a ‘standard Arenicola domain’)

Parameter Description Value Unit

Pump characteristicQmax Maximal obtainable flow rate 90 cm3 h–1

ΔHpmax Maximal reachable pump head 20 cm H2O

TerritoryLL Length lugworm territory 20 cmLW Width lugworm territory 20 cmLD Depth model domain 25 cmφ Porosity 0.5 –k Permeability 2.5 × 10–11 m2

Burrow Lshaft Length tail shaft 15 cmLgal Length gallery 9 cmRb Radius burrow 0.25 cmRfp Radius feeding pocket 0.25 cm

Mar Ecol Prog Ser 303: 195–212, 2005

ably, this implies that all the factors that influence theresistance to flow in a particular Arenicola territory arecondensed into a single proportionality constant. Asshown below, the resistance coefficient Cf is depen-dent on the territory’s geometry (determined by‘biological’ parameters such as organism density andburrow shape), as well as on intrinsic resistance to flowin the sediment (determined by ‘physical’ parameterssuch as sediment permeability and pore water vis-cosity).

Operating point

The pump’s actual operating point is where thepressure difference generated by the pump matchesthe pressure difference due to frictional loss in thepump’s environment. Graphically (Fig. 3), this operat-ing point can be determined as the intersection of thequadratic pump characteristic (Eq. 1) and the linearsystem characteristic (Eq. 2). Analytically, the pump-ing rate at the operating point (denoted Qop) can bederived by equating the pump characteristic (Eq. 1)and the system characteristic (Eq. 2), yielding thequadratic equation:

(3)

As noted above, Riisgård et al. (1996) determined theparameters ΔHp

max and Qmax for a representative lug-worm individual, a so-called ‘standard Arenicolaworm’ (Table 1). Accordingly, the only unknown para-

meter in Eq. (3) is the resistance coefficient Cf. In otherwords, the problem of finding the operation point ofthe Arenicola pump in the sediment comes down to thedetermination of Cf for a suitable Arenicola territory.This calculation procedure is detailed in the followingsections. To simplify terminology, we will from now onrefer to Cf as the ‘resistance coefficient’, while actuallymeaning ‘the frictional resistance coefficient in thesystem characteristic for a representative Arenicolaterritory’.

1D MODEL APPROACH

To date, only crude approximations have been pre-sented to obtain specific Cf values. Typically, onedefines a so-called ‘representative percolation volume’(RPV) above the feeding pocket through which theburrow water flows back to the sediment surface (e.g.Riisgård et al. 1996, Timmermann et al. 2002). Assum-ing a laterally uniform flow field in this column, oneapplies the 1D version of Darcy’s law (Bear 1972,Freeze & Cherry 1979):

(4)

where K denotes the hydraulic conductivity, while LRPV

and ARPV, respectively, denote the depth and cross-sectional area of the RPV. Comparing Eqs. (2) & (4)yields:

(5)

where we have introduced the proportionality constantα1D = LRPV/ARPV, which characterises the geometry ofthe RPV. Eq. (5) shows that sediment resistance isdependent on the geometrical factor α1D and on K.Consequently, one can explicitly calculate Cf, providedthat accurate values can be determined for each of theparameters in Eq. (5). K is a physical parameter that isreadily amenable to experimental evaluation. Forexample, Riisgård et al. (1996) determined a K-value of5 × 10–4 m s–1 for the sediment from which Arenicolaspecimens were collected. Furthermore, LRPV is typi-cally taken to be equal to the depth of the gallery in theArenicola burrow (Riisgård et al. 1996, Timmermannet al. 2002). Nevertheless, the specification of an ap-propriate value for the ‘representative area’ ARPV isproblematic. The principal difficulty is the inherentsubjectivity associated with the selection of the RPVabove the feeding pocket. In reality, the feedingpocket is a 3D object, and, hence, the velocity fieldnear the feeding pocket is likely to be 3D in nature.The RPV concept greatly simplifies this complex flowpattern by mapping it into an averaged 1D representa-

C KL

AKf = =− −1 1

RPV

RPV 1Dα

QAL

K H= ΔRPV

RPV s

Q

Q

C

HQf

op

p

opmax max

⎛⎝⎜

⎞⎠⎟ +

Δ− =

2

1 0

200

Qop

ΔHsim

Qmax

ΔHop

Auxiliary point

Pump characteristic

System characteristic

Operating point

Fig. 3. Procedure to arrive at the operating point of the lug-worm pump. In a first step, the pressure head ΔH sim that cor-responds to the maximal pumping rate Qmax is obtained fromthe simulation output. Subsequently, the system characteristicis drawn as the line through the origin and the auxiliary point(Qmax, ΔH sim). Finally, the operation point of the lugwormpump is determined as the intersection between system

characteristic and pump characteristic

Meysman et al.: Bio-irrigational flow in permeable sediments

tion with unidirectional flow. Consequently, the extentof ARPV cannot be assessed experimentally, as it hasonly a conceptual meaning. Therefore, any Cf valuescalculated from Eq. (5) must be regarded as approxi-mate and qualitative, as they are based on an ‘intelli-gent guess’ for ARPV. For example, Riisgård et al. (1996)postulated a value of 5.5 cm2 for ARPV in order to arriveat resistance coefficients, while Timmermann et al.(2002) estimated ARPV values (5.5 to 29 cm2) by fitting a1D reactive transport model to experimental tracerprofiles.

3D MODEL APPROACH

The 1D application of Darcy’s law (Eq. 4) provesunsatisfactory, as it specifies the flow pattern a prioriand employs a subjective delineation of the percolationvolume. In reality, the flow pattern induced by Areni-cola ventilation is 3D in nature, and therefore we nowapproach the problem of determining Cf in a full 3Dfashion. To this end, we will (1) demarcate a suitable3D sediment domain enclosing the Arenicola burrow,(2) apply Darcy’s law to this 3D setting, (3) specifyappropriate boundary conditions and (4) solve the cor-responding equation set. In this way, the flow pat-tern — or equally the ‘percolation volume’— is nolonger imposed a priori, but is obtained a posteriori asthe output of the model.

3D model domain

Assuming non-overlapping territories of equal size, arectangular sediment block surrounding the J-shapedArenicola burrow was selected as the 3D model sedi-ment domain (Fig. 2). On top, the model domain isdelineated by the sediment–water interface (SWI). Weneglect the depression of the feeding pit and the pro-trusion of the defecation mound, so the SWI is mod-elled as a flat surface. The size of this ‘Arenicoladomain’ should correspond to representative lugwormdensities on intertidal flats. Adopting an average wormdensity of 25 animals m–2 (Beukema & De Vlas 1979),we arrive at a horizontal square cross-section of lengthLL = 20 cm and width LW = 20 cm (Fig. 2).

The worm burrow is placed in the middle plane ofthe sediment block, and its dimensions are chosen torepresent a ‘standard Arenicola burrow’. Note that byplacing the burrow in the middle plane, the Arenicoladomain becomes symmetrical, and hence only half ofthe sediment block has to be effectively modelled. TheJ-shaped burrow has a curved cylindrical form of con-stant radius Rb = 2.5 mm. The horizontal gallery has alength Lgal = 9 cm and is located at a depth of Lshaft =

15 cm (Fig. 2). The feeding pocket is a sphere of radiusRfp at the end of the gallery. In the absence of geomet-rical data on the feeding pocket, we assume that it hasthe same radius as the burrow, i.e. Rfp = Rb. The bur-row’s shape was described analytically using the stan-dard geometrical shape functions available in FEM-LAB (www.comsol.com). Note that the burrow itselfconsists of water, and hence does not belong to themodelled sediment domain. The positioning of the bur-row within the middle plane is to some extent arbi-trary. We opted for the most central position, placingthe gallery symmetrically around the central verticalaxis. In this arrangement, the tail shaft and feedingpocket are at equal distance from this central axis. Thesensitivity of the model results to this particular burrowarrangement was checked a posteriori. Small horizon-tal translations (<3 cm) of the burrow to either side ofthe central axis did not influence the results signifi-cantly. Larger translations did have an effect, causingboundary effects when either the feeding pocket or thetail shaft were too near to the lateral side of thedomain. However, since the lugworm is a territorialorganism, we consider such arrangements not repre-sentative for actual conditions in the field. The lowerboundary of the model domain was chosen to be LD =25 cm. By setting this lower boundary sufficiently deep(i.e. 10 cm below the gallery depth), we found that thesimulation results are virtually the same for a semi-infinite domain, and thus boundary effects wereavoided.

As a simplifying idealisation, we assume that thesediment has uniform properties (porosity, permeabil-ity) within the Arenicola domain. However, under nat-ural conditions, it has been observed that sedimentreworking by benthic organisms has an influence onsediment properties (Meadows & Tait 1989). For thespecific case of A. marina, 2 types of spatial hetero-geneity are generally put forward. Horizontally, acoarse sediment layer is often observed at the level ofthe gallery and the feeding pocket, attributed to selec-tive particle ingestion (Reise 2002). Because the lug-worm selectively ingests the smaller particles, thecoarser ones (e.g. shell fragments, small stones) accu-mulate (Jones & Jago 1993, Reise 2002). Vertically, thezone beyond the feeding funnel, where sedimentslopes downwards to the feeding pocket, is consideredto have a higher porosity and permeability (Jones &Jago 1993, Riisgård & Banta 1998). Following the mod-elling principle of Occam’s Razor, we have chosen notto incorporate this heterogeneity. Instead, our aim is toinvestigate to what extent the first-order assumption ofhomogeneity can explain observations. Moreover, pastdiscussions on the spatial variation of sediment proper-ties within the Arenicola habitat were typically veryqualitative and not supported by actual measurements.

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To our knowledge, no data are presently available onthe porosity and permeability deviations within thepermeable shell layer or the feeding funnel, nor arethere any data on the extent of these zones. Thisabsence of data is mainly because the correspondingporosity and permeability measurements wouldrequire a millimeter-scale resolution, and such resolu-tion is presently not experimentally accessible (Rochaet al. 2005). Therefore, the inclusion of a more perme-able shell layer and feeding funnel would extend themodel by at least 4 unknown parameters, without anydata constraint on these extra degrees of freedom. Inthe absence of such data, the assumption of homo-geneity emerges as the most parsimonious startingpoint for model development.

3D flow model

In a 3D setting, the resistance to flow in the sedimentis described by the following generalised form ofDarcy’s law relating the velocity vector vd to the gradi-ent of the pressure p (Bear 1972, Bear & Bachmat1991).

(6)

where ∇ ≡ [∂/∂x, ∂/∂y, ∂/∂z] is the gradient operator, vd isthe Darcy velocity vector, k denotes the permeability ofthe sediment, μ is the dynamic viscosity of the porewater, ρ is the density of the pore water, g is the gravi-tational constant and p is the pressure. The z-coordi-nate represents the depth measured downwards fromthe SWI. vd is related to the actual pore water velocityvector v such that vd = φv, where φ is the porosity. Thedensity ρ of the pore water is primarily dependent ontemperature and salinity. Assuming an isothermal sed-iment and no salinity gradients, ρ remains constantover the model domain, i.e. ∇ρ = 0. Under this condi-tion, Darcy’s law (Eq. 6) can be rewritten in the alter-native form:

vd = –K ∇H (7)

where K = kρg/μ. Eq. (7) is the conventional presenta-tion of Darcy’s law in hydraulic problems. As notedabove, it features H = p/ρg – z rather than p. Eq. (7)must be combined with the continuity equation for theincompressible pore water:

∇ · vd = 0 (8)

Direct substitution of Eq. (7) into Eq. (8) yields:

∇ · (K ∇H) = 0 (9)

Eq. (9) exemplifies the central role of K, or equally k,in the determination of flow patterns in the sediment.Note that Eq. (9) still allows the permeability to be spa-

tially variable over the model domain. Given such apermeability ‘heterogeneity’, Eq. (9) calculates thespatial distribution of the hydraulic head, from whichone can subsequently calculate the flow field via Eq.(7). As noted above, we consider the permeability ofthe sediment to be uniform over the Arenicola domain.Implementing this most parsimonious model assump-tion, Eq. (9) reduces to:

∇2H = 0 (10)

which is commonly referred to as the Laplace equa-tion. The solution of this equation is a function H (x,y,z)that describes the value of the hydraulic head at anypoint in the Arenicola domain. Via Eq. (7) one can sub-sequently calculate the associated flow pattern, i.e. thevector function vd (x, y, z).

3D boundary conditions

A crucial step in the modelling process is the specifi-cation of proper boundary conditions. This task provesfairly straightforward for the external boundaries ofthe Arenicola domain. At the SWI we assume that porewater can freely flow out of the sediment. This is emu-lated by stating a constant hydraulic head condition(i.e. H ≡ 0) along this boundary. Laterally, we assume afull periodic coverage of the tidal flat by adjacentArenicola domains. Consequently, at the boundary of 2adjacent domains we impose a no-flux boundary con-dition (i.e. vd × n ≡ 0, where n is the normal vector to thesurface). Furthermore, it is assumed that advectiveflow does not penetrate the sediment below, andhence the same no-flux condition is also imposed at thedomain’s lower boundary.

The conditions specified at the internal boundariesof the Arenicola domain, i.e. along the shaft, thegallery and the feeding pocket, require more consider-ation. Firstly, the flow rate Q pumped by the lugwormshould leave the feeding pocket, and hence the follow-ing integral relation holds:

(11)

where Afp denotes the surface area of the feedingpocket and n is the normal vector to this surface(pointing outwards). Two types of boundary condi-tions are possible along the feeding pocket. In the-ory, the lugworm imposes a constant pressure inexcess over the hydrostatic pressure, resulting in aconstant Hfp along the surface of the feeding pocket.However, parameter values for this excess pressureare typically not available in the literature, and Q isreported instead. So rather than imposing an isobaricsurface, we assume that the discharge of water

Q AA

= ∫ v nd dfp

i

vd = − ∇ − ∇( )kp g z

μρ

202

Meysman et al.: Bio-irrigational flow in permeable sediments

occurs uniformly over the surface of the feedingpocket. Eq. (11) then allows the calculation of themagnitude of vd normal to the surface of the feedingpocket for a given pumping rate Q, i.e. ⏐⏐vd⏐⏐ = Q/Afp.Note that in the case of Arenicola, the distinctionbetween uniform discharge and isobaric conditionsalong the feeding pocket is rather academic. Effec-tively, the feeding pocket constitutes a small void rel-ative to its depth location in the sediment (i.e.Lshaft/Rfp > 10). Under such conditions, the feedingpocket becomes an isobaric surface, and hence bothtypes of boundary conditions will produce the sameflow pattern (this was verified by simulations, resultsnot shown).

With regard to the conditions along the burrowwall, the gallery and the tail shaft need separate con-sideration. The gallery is where the worm remainswhile pumping. If the gallery were to have perme-able walls, the lugworm’s peristaltic pumping wouldbe highly ineffective, as water forced between thebody and the gallery’s wall would immediately leakto the surrounding sediment, rendering the Arenicolapump utterly inefficient. Therefore, it seems a justifi-able assumption to consider the gallery wall a no-flux boundary. Yet, in the case of the tail shaft wall,it is not as clear a priori whether the walls should beconsidered open or closed to advective flow. In otherwords, the costs versus the benefits of insulating thetail shaft wall remain to be determined. To this end,we will explore 2 end-member cases, i.e. fully per-meable and completely impermeable shaft walls. Inthe case of permeable walls, the pressure at the bur-row wall is set to the hydrostatic pressure, neglectingthe small pressure drop due to flow within the bur-row. In the case of impermeable walls, the flow inthe burrow is completely de-coupled from the flow inthe surrounding sediment, i.e. no-flux boundary con-ditions along the complete burrow surface. For anillustration of both types of boundary conditions, seeFig. 5.

Eqs. (6) to (11) completely specify our model ofpore water flow induced by lugworm bio-irrigation.Flow fields vd (x, y, z) over the Arenicola domain areobtained by numerical solution of this equation setfor a suitable set of parameters. From such a flowfield, one can construct the associated flow-line pat-tern, which consists of curves that are tangential tothe velocity vector. All flow lines start from the feed-ing pocket, i.e. an isobaric surface at H = Hfp, andarrive at the tail shaft or the SWI, i.e. an isobaric sur-face at H ≡ 0. Consequently, ΔHs = Hfp and is thesame for all flow lines. Effectively, the quantity ΔHs

specifies the actual sediment resistance that the lug-worm pump needs to overcome to maintain the flowrate (see Eq. 2).

Influence of pumping rate and permeability on theflow pattern

Even without actually solving the model, one candraw relevant conclusions with respect to lugwormbio-irrigation. By simple inspection of Eqs. (6) to (11),one can assess how crucial model parameters, such asQ and K, will influence the flow field and flow-linepattern. Effectively, one can prove that both para-meters will modulate the flow field without affectingthe flow-line pattern. In other words, the adaptation ofQ or K will cause a change in the magnitude, but not inthe direction of vd.

To show that a change in the lugworm’s pumpingrate does not affect the flow-line pattern, consider acertain lugworm that has created a particular burrowsystem and pumps at a particular flow rate Q. For theseconditions, assume that the corresponding solution ofthe Laplace equation (Eq. 10) is given by the functionH (x, y, z), from which the flow field vd(x, y, z) and theassociated flow-line pattern have been derived. Nowassume that the lugworm remains within the same bur-row system, but changes its pumping rate to a newvalue Q*. In terms of the model, this comes down to anadaptation of the boundary condition (Eq. 11) alongthe feeding pocket. Due to the linearity of the Laplaceequation, one can easily verify that the hydraulic headfunction H* = (Q*/Q)H (x, y, z) forms a solution for thisnew set of boundary conditions. This relation alsoapplies to the surface of the feeding pocket, and so wefind that Hs* = (Q*/Q)Hs. In other words, when chang-ing the pumping rate, the sediment resistance withinthe Arenicola domain will be proportionally rescaled:

(12)

Furthermore, due to the linearity of Darcy’s law , thecorresponding velocity field will also be rescaled bythe same factor, i.e. v*d = (Q*/Q)vd(x, y, z). This rescal-ing by a scalar factor changes the magnitude, but notthe direction, of the velocity vector, and hence achange in the lugworm’s pumping rate will not influ-ence the flow-line pattern.

In a similar way, one can also show that a change inthe hydraulic conductivity (or equally the permeabil-ity) does not affect the flow-line pattern. To this end,consider a certain sediment with hydraulic conductiv-ity K, in which lugworms attain a certain density, con-struct a specific burrow system and maintain a givenpumping rate Q. Again, assume that the correspondingsolution of the Laplace equation (Eq. 10) is given byH(x, y, z), while the associated velocity field becomesvd(x, y, z). Now consider a separate sediment environ-ment with a different hydraulic conductivity K*. Sup-pose that within this new environment lugworms

ΔΔ

=HH

QQ

* *s

s

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Mar Ecol Prog Ser 303: 195–212, 2005

adopt the same density, construct exactly the sameburrow system and maintain the same pumping rate.In other words, neither the burrow geometry nor thepumping rate is affected by the texture of the sedi-ment. Because the flow model (Eqs. 7 to 10) comprisesa linear model with respect to the permeability, onecan show that the hydraulic head function nowbecomes H* = (K/K*)H(x, y, z). As a consequence, adecrease in the sediment permeability will lead to aproportional increase in the sediment resistance, gov-erned by:

(13)

However, when implementing H* into Darcy’s law(Eq. 9), one finds that the velocity field remainsunchanged, i.e. v*d = vd(x, y, z). Effectively, when thelugworm is able to maintain a fixed pumping rate, achange in the sediment permeability does not affectthe flow field, and hence the flow-line pattern remainsunchanged as well. In reality, however, when the sedi-ment resistance increases, the lugworm’s pumpingrate will decrease. In other words, one will observe ashift of the operation point of the lugworm pump, andthe flow field will be modified (this scenario is exam-ined below). However, the resulting change in thepumping rate will still not affect the flow-line patternas shown in the discussion of Eq. (12).

Linearity of the system characteristic

The analysis of the previous section reveals that inthe 3D pore water flow model, ΔHs is proportional to Q(Eq. 12) and inversely proportional to K (Eq. 13). Com-bining both propositions, we obtain:

ΔHs = α3DK –1Q (14)

where α3D is a certain proportionality constant. Eq. (14)effectively confirms that also in the 3D case, Darcy’slaw leads to a linear system characteristic (Eq. 2) aswas adopted earlier without proof. By comparingEqs. (14) and (2), we obtain the following decomposi-tion of the resistance coefficient:

Cf = α3DK –1 (15)

The scaling factor α3D designates the sensitivity of Cf

to changes in hydraulic conductivity. This proportion-ality constant is only dependent on those parametersthat were kept invariant in the model analysis of theprevious section. In other words, α3D only depends onthe specific geometry of the Arenicola territory, whichis determined by the lugworm density and the 3Dgeometry of the burrow. If one adopts the simplifyingassumption that the shape of the Arenicola domain is

not significantly affected by sediment type (i.e. the lug-worm density and the burrow geometry do not dependon the permeability), the domain’s resistance to flowscales inversely with the hydraulic conductivity.

The introduction of the geometrical factor α3D viaEq. (15) ultimately results from the application ofDarcy’s law in 3 dimensions. As such, Eq. (15) formsthe 3D counterpart of Eq. (5), which produces a verysimilar decomposition of Cf. The latter equation fea-tures the similar geometrical factor α1D and resultsfrom the 1D application of Darcy’s law. There is, how-ever, a fundamental difference between Eq. (5) andEq. (15). In the 1D approach, the value of α1D needs tobe fixed a priori. To this end, one requires a certainvalue for ARPV, which is a conceptual quantity that can-not be constrained by data. In contrast, in the 3Dapproach, the value of α3D is obtained a posteriori fromthe model output. In other words, we can derive theappropriate values for Cf and α3D from the pressureand velocity fields that are simulated numerically.

To this end, we can take advantage of the linearity ofthe system characteristic (Eq. 14) to determine theoperating point of the Arenicola pump for a specificArenicola domain and a given hydraulic conductivity.This modelling procedure is illustrated in Fig. 3. First,Qmax = 1.5 ml min–1 is imposed via the boundary condi-tion (Eq. 11). The resulting pressure difference ΔH sim

between the SWI and the feeding pocket is obtainedfrom the simulation output. Subsequently, the resis-tance coefficient is calculated as the slope of the linearsystem characteristic via:

(16)

Then, by substituting Eq. (16) into the quadraticequation (Eq. 3), the pumping rate Qop at the operatingpoint can be determined. Graphically (Fig. 3), this cor-responds to finding the intersection point between thelinear system characteristic (Eq. 2) with slope Cf andthe parabolic pump characteristic (Eq. 1).

Numerical solution procedure

Over the Arenicola domain, the Laplace equation(Eq. 9) is solved using a finite element approach imple-mented in the Chemical Engineering Module of FEM-LAB®. The simulation output consists of the steady-state field of the hydraulic head, the associatedvelocity field and the flow-line pattern. Fig. 2b showsthe unstructured finite element mesh used in thenumerical simulations. Note that a finer mesh resolu-tion is implemented near the burrow wall and the feed-ing pocket, since the largest pressure gradients occurin those zones.

CH

Qf max= Δ sim

ΔΔ

=HH

KK

**

s

s

204

Meysman et al.: Bio-irrigational flow in permeable sediments

SIMULATION RESULTS

The above 3D modelling procedure was implemen-ted to derive the system characteristic (i.e. to calculateCf) for a representative Arenicola territory. Table 1summarises the default parameter set used in the sim-ulations, which reflects the ventilation activity of astandard Arenicola worm (sensu Riisgård et al. 1996)in a standard Arenicola domain (i.e. a territory withtypical burrow at a typical lugworm density). Thespecification of this default parameter set is not in itselfsufficient to constrain a solution. As noted before, theboundary conditions along the tail shaft part of theburrow need to be decided upon first. To this end, wesimulated the flow patterns for both end-member con-ditions using the default parameter set. Subsequently,we used the default parameter set as the starting pointfor a sensitivity analysis with respect to sediment per-meability.

Flow patterns

Flow patterns are obtained for both the case in whichthe tail shaft walls are permeable to advective flow(Fig. 4a) and for the case of fully insulated (i.e. non-permeable) shaft walls (Fig. 4b). Similar in both sce-narios is the clear 3D nature of the flow pattern. Flowlines irradiate from the feeding pocket, and, whilediverging, these flow lines rise to the sediment surfaceover an increasingly large area. This pattern deviatessignificantly from the classical 1D representation(Benoit et al. 1991, Timmermann et al. 2002, 2003),which assumes a percolation column of constant cross-section, through which the burrow water migratesupwards along parallel flow lines. A second strikingfeature in Fig. 4 is that flow lines also head downwardsfrom the injection point. This implies that a zoneunderneath the burrow will also be flushed. In otherwords, the sediment below the feeding depth is not

205

Fig. 4. Simulated flow-line patterns for a standard Arenicola domain (parameter set in Table 1). (a) Flow lines short-circuit backto the burrow when the burrow walls are open to advective flow. (b) Flow lines rise parallel to the sediment surface pattern whenthe burrow walls are impermeable to advective flow. (c,d) Patterns of the pore water velocity perpendicular to the sediment–

water interface corresponding to the simulations (a,b). The plot mimics an aerial view of the sediment surface

a

c

b

d

Mar Ecol Prog Ser 303: 195–212, 2005

only affected by diffusive transport, but also by advec-tion, i.e. by bulk pore water flow. This aspect is notaccounted for in the conventional 1D modellingapproach to burrow water injection.

In addition to similarities, Fig. 4 also shows somestriking differences between the 2 end-members ofshaft wall permeability. In the case of permeable bur-row walls (Fig. 4a), some flow lines curve back to theburrow wall. This implies that a certain amount of thewater pumped by the lugworm effectively re-entersthe burrow. Integrating this advective flux, our simula-tions show that the return flow of anoxic pore waterconsititutes 40% of the total pumping rate (Fig. 5a).Conversely, in the case of impermeable burrow walls(Fig. 4b), all flow lines eventually ‘line up’ in paralleland arrive at the sediment–water surface, since in thisscenario it is the only boundary open to flow (Fig. 5b).So, the flow-line pattern now consists of 2 separatezones: (1) a lower ‘irradiation’ zone (heterogeneous,3D), where flow lines irradiate from the feedingpocket, and (2) an upper ‘percolation’ zone (homoge-neous, 1D), where flow lines align in parallel to thevertical. Effectively, the conventional 1D approach(Benoit et al. 1991, Timmermann et al. 2002, 2003)assumes that the lower 3D irradiation zone is negligi-bly small as compared to the upper 1D percolationzone. However, our simulations show that both zonesare of the same extent. Consequently, in order to rep-resent the irradiation zone in a 1D reactive transport

model, one needs to take account of an appropriatemapping of the 3D advective transport within this zonein a 1D model formulation.

The difference between the 2 flow scenarios is alsoevident from the velocity field at the SWI (Fig. 4c,d). Inthe case of permeable burrow walls, there are distinctgradients in velocity at the SWI (Fig. 4c). Velocities arehigher in the area above the feeding pocket, indicativeof an increased upwards percolation in this zone.Around the entrance to the burrow, velocities are low.When burrow walls are open to advective flow, the bur-row acts as a sink, and so velocity vectors are normallyoriented to the burrow surface. Accordingly, the verti-cal component of the velocity vectors at the SWI van-ishes when approaching the burrow entrance. In con-trast, for the case of impermeable burrow walls, theflow across the SWI is almost uniform over the domain(Fig. 4d), with a Darcy velocity of around 2000 cm yr–1.This is indeed the expected average velocity, obtainedwhen dividing the lugworm’s yearly pumping rate, i.e.Qmax × 24 × 365 = 7.9 × 105 cm3 yr–1, by the surface areaof the Arenicola domain, i.e. 400 cm2. Note that theeffective velocity in the pore water is higher, i.e. vSWI ≈4000 cm yr–1 (the Darcy velocity must be divided by theporosity). These velocity values are 3 orders of magni-tude higher than those in muddy sediments (Boudreau1997), but similar to those observed in groundwatertransport (Bear 1972, Freeze & Cherry 1979). Assumingan irrigated zone of 20 cm, i.e. irrigation extends to 5 cmbelow the feeding depth, the frequency at which thelugworm flushes the pore water becomes 200 yr–1. Thisresults in an average residence time of <2 d for the porewater within the bio-irrigated zone. Such high flushingrates have a considerable impact on the biogeochem-istry of the sediment (Huettel 1990, Banta et al. 1998).

Sensitivity to permeability

We used the above simulation procedure to deter-mine the operation point of the Arenicola pump for dif-ferent sediment types (Table 2, Fig. 6). To this end, wevaried the permeability, while all other parametersretained the value of the default parameter set(Table 1). The selected permeability range is charac-teristic for Arenicola habitat, i.e. from clean, coarsesand (k = 2.5 × 10–11 m2) to silty, fine sand (k = 1.0 ×10–13 m2). Simulations were performed for both end-member conditions of burrow wall permeability, butonly results for impermeable burrows are shown.Remarkably, Cf, and hence the lugworm’s operatingpoint, did not significantly depend on the type ofboundary condition employed at the tail shaft wall. Toexplain this, we need to analyse where the actual resis-tance to flow occurs in the Arenicola domain. Pressure

206

100%

100%

60%

40%60%

Impermeable burrow wallsPermeable burrow walls

a b

Fig. 5. Dependence of the sediment irrigation pattern on theboundary conditions at the burrow walls (solid lines, boundariesare closed to flow; dashed lines, boundaries are open to flow).(a) When the tail shaft wall is open to flow, the return flow ofanoxic pore water constitutes 40% of the total pumping rate.Only 60% of the burrow water flow is derived as fresh oxy-genated water from the overlying water column. (b) When thetail shaft wall is closed to flow, no return flow to the burrowexists. All irrigated pore water eventually crosses the sedi-ment–water interface, and all burrow water originates from the

overlying water column

Meysman et al.: Bio-irrigational flow in permeable sediments

distribution plots (results not shown) reveal that thehighest pressure gradients occur close to the feedingpocket. These same plots also show that pressure gra-dients quickly drop when moving away from the feed-ing pocket. This implies that the resistance to flow ispredominantly concentrated in a relatively small zonearound the feeding pocket. In other words, the irradia-tion zone centralises almost all resistance, while thepercolation zone does not significantly influence theoverall resistance. As this irradiation zone is very simi-lar in both situations (only the percolation zone is dif-ferent), the overall sediment resistance is very similar.This explains the insensitivity of Cf with respect to theboundary condition at the shaft wall.

As expected, Qop decreases with decreasing K(Fig. 6a). An increase of the intrinsic sediment resis-tance (lower K values) shifts the operation point of thelugworm pump to lower pumping rates (lower Qop val-ues). However, the relation between these variablesshows 2 specific trends. Below a threshold value of K =1.0 × 10–4 m s–1, the operational pumping rate decreaseswith the logarithm of the hydraulic conductivity. So de-creasing the sediment’s permeability will markedly in-

fluence the operation point of the lugworm pump. Forexample, at a value around K = 1.0 × 10–5 m s–1, the op-erational pumping rate only attains 50% of the maximalpumping rate (Fig. 6a). Yet, above a threshold hydraulicconductivity of K = 1.0 × 10–4 m s–1, the operational fluxdoes not increase any longer and almost equals themaximal pumping rate. Accordingly, any further in-crease of the sediment permeability will no longerinfluence the operation point of the lugworm pump.

Representative percolation area

As noted above, the classical 1D approach is basedon the specification of a so-called ‘representative 1Dpercolation volume’, characterised by the geometricalconstant α1D. An important problem was that α1D

needed a priori specification, and hence required thedebatable determination of ARPV. This arbitrariness inthe specification of the representative percolation vol-ume can now be removed. Eq. (15) predicts that, for afixed model geometry and a fixed pumping rate, Cf

should linearly scale with the inverse of K. Our numer-

207

Table 2. Simulation results for a range of sediment permeabilities

Permeability k m2 2.5 × 10–11 1.0 × 10–11 1.0 × 10–12 1.0 × 10–13

Hydraulic conductivity K m s–1 2.46 × 10–4 9.82 × 10–5 9.82 × 10–6 9.82 × 10–7

Simulated pressure ΔH sim cm H2O 0.93 2.24 13.5 19.9

Frictional resistance coefficient Cf cm–2 min 0.63 1.58 15.8 158

Flow at operation point Qop cm3 min–1 1.47 1.41 0.85 0.13

Scaling factor α3D cm–1 0.93 0.93 0.93 0.93

Representative percolation area ARPV cm2 16.0 16.1 16.1 16.2

0.5

1.0

1.5

2.0

2.5

3.0

1 2 3

Inve

rse

Cf (

10–6

m2

s–1)

slope = 1.07 x 10–2 m

0.0

0.5

1.0

1.5

10–6 10–5 10–4 10–3

Hydraulic conductivity (m s–1) Hydraulic conductivity (10–4 m s–1)

Op

erat

iona

l pum

pin

g r

ate

(cm

3 min

–1)

50% of maximal pumping rate

maximal pumping rate ba

Fig. 6. Dependence of the operation point of the lugworm pump on the hydraulic conductivity of the sediment: summary of modelresults. (a) Below K = 1 × 10–4 m s–1 the operational pumping rate scales with the logarithm of the hydraulic conductivity. Above K = 1 × 10–4 m s–1 the operational pumping rate remains roughly invariant with the hydraulic conductivity. (b) The inverse of the

frictional resistance of the sediment scales linearly with hydraulic conductivity as predicted by theory

Mar Ecol Prog Ser 303: 195–212, 2005

ical simulations corroborate this theoretical relation-ship, as shown in Fig. 6b, which plots Cf

–1 as a functionof K. The scaling factor α3D can be calculated by takingthe inverse of the slope of this graph and using theproper unit conversion. We obtained the value of0.93 cm–1 for our standard Arenicola domain (Fig. 6b,Table 2). As discussed above, this value of α3D is notdependent on the permeability of the sediment (Table2). By setting α1D to the value calculated for α3D fromthe model, we effectively map the (real) 3D flow pat-tern into a corresponding (virtual) 1D flow pattern thathas the same resistance to flow. This way, using Eq. (5),it becomes possible to quantify the cross-sectional areaof this representative 1D percolation volume as:

(17)

where Lshaft is the tail shaft length, i.e. the depth ofgallery and feeding pocket. For the standard Arenicoladomain employed in our simulations (Table 1), weobtained ARPV = 16 cm2, implying a representative per-colation column of 4.5 cm in diameter (Table 2). Thisvalue for ARPV deviates markedly from the value of 5.5cm2 postulated in Riisgård et al. (1996). Yet, it lieswithin the range of 5.5 to 29 cm2 obtained from fittinga 1D injection model to Br

–profiles, as reported by

Timmermann et al. (2002).

Influence of quicksand column

The value of ARPV is obtained for an Arenicola domainwith a uniform permeability. However, in the field, ob-servations indicate that lugworms create a so-called‘quicksand column’, i.e. a loosened cylinder sedimentthat is assumed to have a significantly higher permeabil-ity (Jakobsen 1967, Rijken 1979, Retraubun et al. 1996).In this view, the quicksand column may act as a ‘porewater highway’, i.e. a zone of high permeability thatchannels and facilitates the upward flow of pore water.In a qualitative sense, one can expect that the inclusionof the quicksand column will result in a concentration offlow lines and a reduction in the value of ARPV in Eq. (17).Provided one has a description of the associated spatialvariation in permeability, one could consider the quick-sand column as part of the Arenicola domain and inves-tigate its influence on the pore water flow pattern usingthe modelling approach as outlined above. As discussedabove, this was not done here, but is scheduled to be in-cluded in a further sensitivity analysis of the model.

However, Eq. (17) does allow a crude estimate of theinfluence of the quicksand column on the overall per-meability. To this end, one can assume a representa-tive 1D percolation zone with 2 concentric zones, i.e.an outer zone of bulk sediment (BS) and an inner

quicksand column (QC). Applying the theory of paral-lel resistances, the apparent conductivity Kapp of thisheterogeneous percolation zone can be calculated as:

(18)

where ARPV is the cross-sectional area of the percola-tion zone and KBS is the hydraulic conductivity of thebulk sediment. Furthermore, AQC is the cross-sectionalarea of the quicksand column, and ξ = K QC/K BS repre-sents the relative enhancement of the permeabilitywithin this column (ξ > 1). At present, both parametersAQC and ξ are poorly constrained by data. For thediameter of the quicksand column, we only found avalue of 5 mm, as reported by Rijken (1979), which wasderived from tracer experiments with glass beads. Forξ, we did not retrieve any information. However, con-sidering a 10-fold increase in the permeability andusing the value of 16 cm2 for ARPV as derived above,Eq. (18) leads to a factor of 1.44. In other words, thepresence of the quicksand column enhances theapparent hydraulic conductivity of the sediment by44%. Because the hydraulic conductivity in naturalsediments effectively varies over several orders ofmagnitude (Freeze & Cherry 1979), i.e. from 10–10 m s–1

(marine clay) to 10–2 m s–1 (clean coarse sand), a 1.44increase due to the presence of the quicksand columnis a rather small effect. In other words, one requireswider columns, with higher enhancement factors (ξ) tosubstantially influence the bulk permeability.

ECOLOGICAL IMPLICATIONS

Permeability of burrow walls

Our model simulations show that a reduction of theadvective flow through the burrow wall provides aclear ecological advantage for the lugworm. Hydrody-namic insulation of the burrow walls prevents theshort-circuiting of flow lines, and thus shuns the inflowof pore water into the burrow. Without this insulation,40% of the burrow water is derived from pore waterand only 60% originates from the overlying water col-umn (Fig. 5a). Obviously, such recirculation wouldhave an adverse effect on the oxygen supply to the lug-worm. According to Zebe & Schiedek (1996) Arenicolamarina is able to extract between 32 and 40% of theoxygen under natural conditions. Once injected intothe sediment, the remaining oxygen is rapidly con-sumed by the microbial community, and hence anywater re-entering the burrow will be anoxic. Assumingthat oxygen uptake is a function of the concentrationdifference across the gill surface, this dilution of freshoverlying water with anoxic pore water will reduce the

K

K

A

A

A

A

app

BS

QC

RPV

QC

RPV= + −⎛

⎝⎜⎞⎠⎟ξ 1

AL L

C Kf

RPV shaft

D

shaft= =α3

208

Meysman et al.: Bio-irrigational flow in permeable sediments

lugworm’s oxygen intake by 40%. In other words, thelugworm would have to increase its pumping rate by afactor of 1.67 to obtain the same oxygen supply.

Two mechanisms can be envisaged to prevent thisre-entrance of anoxic pore water, i.e. active and pas-sive burrow insulation. In the case of active insulation,the lugworm will invest resources to reduce the advec-tive inflow of pore water into its burrow. Obviously,from an evolutionary perspective, the benefits of thisinvestment in terms of enhanced oxygen supply haveto outweigh the costs. In the passive case, no additionalresources are invested, and the decreased burrow wallpermeability simply originates as a side-effect of bur-row ventilation activity.

There are indications that 2 types of active insulationmight be operating, i.e. the lining of burrow walls withmucus and the mechanical re-enforcement of burrowwalls. In muddy sediments, organic burrow liningshave been shown to reduce the diffusive permeabilityof burrow walls, so that diffusion coefficients are only10 to 40% of their corresponding value in free solution(Aller 1983). Accordingly, one might expect similaradaptations to reduce the advective flow throughburrow linings in permeable sediments. Evidence ofactive burrow insulation has been reported by Huettel(1990), who observed that sediment particles in theburrow wall of the tail shaft are tightly cemented bymucus. This mucus layer was estimated to be about1 mm thick and relatively impermeable for the advec-tive flow of pore water. Furthermore, Atkinson & Nash(1990) observed that Callianassa subterranea producesa mucus lining when burrowing in sandy sediments,but not in muddy environments. It was argued that thislining provided structural stability in the less cohesivesandy substrate. However, our link between oxygensupply and wall permeability provides an additionalexplanation for this observation.

Mechanical hardening might be a second way to ac-tively decrease the permeability of the burrow wall.The case for this type of insulation is significantlystrengthened by recent observations on intertidal sedi-ments with a novel acoustic technique (S. A. Woodinunpubl. data). Pressure sensors were placed in situ inthe vicinity of burrows of Abarenicola pacifica, arelated arenicolid polychaete with a similar ecology.Large-amplitude infrasound signals were monitoredthat are associated with macrofaunal activity. A strikingpattern of pressure pulses was recorded in a limitedtime span just after burrow construction. Closer inspec-tion revealed that this signal was associated with ‘headbanging’ behaviour, i.e. hammering mucus and sedi-ment grains tightly together in the burrow wall.

In addition to active insulation, plentiful evidence ofauthigenic mineral formation near Arenicola burrows(Gribsholt & Kristensen 2003, Nielsen et al. 2003) indi-

cates that passive insulation might be operational aswell. The transfer of oxygen across the burrow walltypically creates a 2 to 4 mm thick brownish crustaround the tail shaft, associated with the precipitationof ferric (hydr)oxides (Reise 1985, Huettel 1990).Deeper in the sediment and around the gallery thecolour of this halo may change to grey, associated withpyrite formation (Huettel 1990). Such authigenic min-eral formation (FeOOH, FeS) may result in porecementation and a reduced permeability near the bur-row wall. However, it remains to be determined towhat extent authigenic mineral formation effectivelychanges the permeability of the burrow wall.

Distribution of Arenicola marina

Surveys on the distribution of A. marina typicallyreveal the same general pattern with particle size: thelugworm is absent in fine mud, abundant in fine andmuddy sand and absent from coarse sand and gravel(Longbottom 1970). The absence of lugworms fromcoarse sand is attributed to insufficient food, sinceunder exceptional conditions lugworms have beenfound in these environments, e.g. a coarse sandexposed to sewage outflow (Longbottom 1970). Theabsence of lugworms from fine mud has beenexplained by the inability to maintain a permanentburrow in such a ‘liquid’ environment (Longbottom1970). The latter argument is rather unconvincing for anumber of reasons. (1) Other benthic macrofauna areable to create (semi) permanent burrows in muddyenvironments. (2) As discussed above, lugworms havebeen shown to exhibit adaptations (mucus production,head banging) that fortify burrow structures.

Our model analysis of burrow ventilation activity,however, offers an alternative explanation (Fig. 7). Thephysics of pore water advection causes burrow ventila-tion to become energetically costly at low sedimentpermeabilities. To show this, we have first quantifiedthe resistance to pore water flow in a representativeArenicola territory, as expressed by Cf. In a secondstep, we have evaluated Cf as a function of thesediment permeability. As summarised in Fig. 7, thesediment permeability constitutes a major factor con-trolling the lugworm’s pumping rate. Lower perme-abilities will increase Cf and shift the operation point ofthe Arenicola pump to a lower operational pumpingrate. Accordingly, the lugworm will require higherpumping pressures, and hence an increased energyexpenditure, to maintain the same burrow water flowand the same oxygen supply. One can imagine thatwhen the permeability falls below a certain threshold,Arenicola’s operating point will shift to a pumping ratetoo low to ensure its oxygen supply. Assuming (1) that

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A. marina respiration reduces the oxygen concentra-tion in the burrow water by about 40% (Zebe &Schiedek 1996) and (2) that oxygen uptake becomescritical at 10% oxygen saturation, the oxygen supplybecomes critical at 50% of its normal value. Conse-quently, allowing a 50% reduction from Qmax, we esti-mated the critical permeability to be 10–12 m2 for ourstandard Arenicola domain (Fig. 7). In terms of mediangrain size, this critical permeability is roughly associ-ated with the transition from muddy sand (Arenicolapresent) to fine mud (Arenicola absent).

The strong link between permeability and oxygenavailability also implies that there is a clear scope forhabitat improvement. This can be done in 2 ways:either affecting the bulk permeability throughout theterritory, or creating local zones of high permeability.Our model simulations indicate that by increasing thebulk permeability of its territory, the lugworm couldclearly improve its ventilation efficiency and hencereduce the energetic cost of its oxygen supply. How-ever, at present, the data to corroborate this modelhypothesis are few and indirect. In microcosm experi-ments with Arenicola marina, Kure & Forbes (1997)observed a significant increase of the porosity after36 h. Although permeability was not quantified, onemight expect a corresponding increase in the perme-ability in the microcosm sediment (assuming that the

grain size distribution has not changedin the microcosms). In situ, Jones &Jago (1993) reported a decrease in theelectrical resistivity of the sedimentwith an increasing density of lugwormburrows. This decrease was then linkedto an increase in the porosity, and, byinference, to an increase in permeabil-ity. However, the link between porosityand permeability is typically non-linearand highly dependent on the grain sizedistribution.

Furthermore, permeability may notincrease throughout the whole Areni-cola territory, but can be due to stronglocalised enhancements. In this regard,one could think of the lugworm as cre-ating a ‘pore water highway’, i.e. a zoneof high permeability that channels andfacilitates the upward flow of porewater. It has been suggested that thequicksand column fulfils this task(Jakobsen 1967, Rijken 1979, Retrau-bun et al. 1996). Within this cylinder,loosened sediment slides from the sedi-ment surface down to the feedingpocket. However, our preliminary cal-culations indicate that in order to sub-

stantially influence the overall sediment permeability,one requires substantially wider pore water highwaysthan the quicksand columns of 5 mm diameter thathave been observed in the field (Rijken 1979). Accord-ingly, direct (and preferably in situ) measurements ofpermeability are needed to confirm the occurrenceand elucidate the nature (local or bulk) of habitatimprovement through permeability modulation.

CONCLUSION

We have presented a modelling procedure that illus-trates how physical constraints of the environmentinteract with the way benthic fauna ventilate their bur-rows. This model analysis was used to explain existingobservations on the distribution and behavioural adap-tations of Arenicola marina, as well as to put forwardnew hypotheses with regard to lugworm ecology. Mostof all, our simulations show that permeability exerts animportant control on the lugworm’s ventilation activity,creating an opportunity for active habitat improve-ment. This can occur in 2 distinct ways. Firstly, the lug-worm has a clear ecological advantage in reducing thepermeability of its burrow walls. Without such insula-tion, flow lines short-circuit from the feeding pocket tothe burrow, resulting in a 40% dilution of the burrow

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0 0.5 1 1.50

5

10

15

20k = 1×10–13 m2

k = 1×10–12 m2

k = 1×10–11 m2

k = 2.5×10–11 m2

loss of ventilation efficiency

mud

sand

flow rate (ml min–1)

pum

pin

g he

ad (c

m H

20)

pump characteristic (Riisgard et al. 1996)burrow walls permeable to flowburrow walls impermeable to flow

Fig. 7. Oxygen supply as a function of sediment permeability. In the case of im-permeable burrow walls, the oxygen supply simply scales with the pumpingrate. When burrow walls are open to advective flow, anoxic flow short-circuitingoccurs and the oxygen supply is reduced by about 40% (marked as the ‘loss ofventilation efficiency’). The ‘effective’ operation point of the lugworm pump, ex-pressed in terms of oxygen supply, now lies on an effective ‘pump characteris-tic’, which depicts a lower apparent flow rate for the same pumping head

Meysman et al.: Bio-irrigational flow in permeable sediments

water with anoxic pore water. Secondly, it is clearlyadvantageous for the lugworm to increase the perme-ability of its habitat. When the permeability increases,the sediment resistance decreases, and, hence, thelugworm needs to overcome a decreased back pres-sure to maintain the same ventilation rate and oxygensupply.

The modelling approach presented here is not lim-ited to the specific case of Arenicola marina. It appliesto a general 3D sediment territory given that boundaryconditions are sufficiently similar. In other words, itcan also be used to analyse the bio-irrigational activityof other organisms, provided that burrow ventilation iscoupled to advective flows in the sediments. Extendingour conclusions from the lugworm to other burrow-ventilating macrofauna, we can claim that sedimentpermeability is an important ecological parameter insandy sediment ecosystems. This conclusion markedlycontrasts with the current practice in macrofauna fieldstudies. Unlike other geological parameters, such asgrain size distribution and porosity, benthic studiesusually do not quantify sediment permeability as anenvironmental factor.

Acknowledgements. This research was supported by grantsfrom the EU (NAME project, EVK#3-CT-2001-00066, COSAproject, EVK#3-CT-2002-00076) and a PIONIER grant fromthe Netherlands Organisation for Scientific Research (NWO,833.02.2002). This is Publication 3497 of the NIOO-KNAW(Netherlands Institute of Ecology).

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Editorial responsibility: Otto Kinne (Editor-in-Chief), Oldendorf/Luhe, Germany

Submitted: June 17, 2004; Accepted: May 16, 2005Proofs received from author(s): November 7, 2005