Mass transport to streambed biofilms

Wat. Res. Vol. 22, No. 6, pp. 709-722, 1988 Printed in Great Britain. All rights reserved

0043-1354/88 $3.00 + 0.00 Copyright © 1988 Pergamon Press plc

MASS TRANSPORT TO STREAMBED BIOFILMS CHARLES J. GANTZER 1, BRUCE E. RITTMANN2{~ a n d EDWIN E. HERRICKS2(~ IDepartment of Civil and Mineral Engineering, University o f Minnesota, Minneapolis, M N 55455 and 2Department o f Civil Engineering, University of Illinois at U r b a n a - C h a m p a i g n , Urbana, IL 6 ! 801, U.S.A.

(Received May 1987; accepted in revisedform December 1987) Abstract--This study developed a mass transfer equation for the movement o f biodegradable materials from the water column of shallow streams to the biofilm-colonized surfaces of sand-free gravel and cobble streambeds. The equation was developed from a series of well-controlled, batch-biodegradation tests performed in an artificial stream with streambeds between 1.5 to 2 rock layers thick. The batch tests determined the sensitivity of substrate flux into the streambed biofilms to short-term changes in water velocity. Experimental results indicated that substrate flux into the cobble-streambed biofilms was more sensitive than flux into the gravel-streambed biofilms to short-term changes in water velocity, and that the cobble streambed had faster removal rates. Rates o f substrate removal by both streambeds were m u c h more sensitive to short-term changes in water velocity than would be predicted by previous mass transport models, which only addressed the transport o f materials from the water column to the external (exposed) surface o f the streambed. This greater than expected sensitivity to changes in water velocity suggests that interstitial biofilms play an important role in determining substrate removal rates in streams with sand-free gravel and cobble streambeds.

Key words--biofilm kinetics, mass transport, streambed biofilms, water quality modeling.

Qfa = Volumetric rate o f feed addition (cm s h - m)

NOMENCLATURE a = Specific surface area (cm -I) A = Cross-sectional area available for flow in stream channel (cm 2) Ap = Biofilm covered surface area in recycle pipe (cm 2) d = Streambed particle size (cm) dp = Inside diameter of recycle pipes (cm) D b = Diffusion coefficient in bulk solution (era 2 h - I ) D f = Diffusion coefficient within biofilm (cm 2 cm - l ) D L = Longitudinal dispersion coefficient (cm 2 h - ~) f = Friction factor (dimensionless) H = Depth o f flowing water (cm) Jo = Flux o f substrate at surface o f biofilm (mg s cm-2h-I) k b = Bulk liquid phase mass transfer coefficient ( c m h -I ) kb, p = Bulk liquid phase mass transfer coefficient within recycle pipe, (cm h - i ) Kr = First-order flux constant ( o n h - ~) K s = Half-velocity coefficient (mg~ o n - 3 ) K I = Obscrved first-order rate constant for removal of C O D in artificial stream (h -I) K~ f = Apparent first-order rate constant for removal o f C O D by streambed biofilms (h - I ) Kip = Apparent first-order rate constant for removal o f C O D by recycle pipe biofilms (h - l ) K 2 = Mixed second-order rate constant (cm 3 mg~- l h - i ) L c = Characteristic length (cm) Lf = Biofilm thickness (on) L s = Length of streambed (cm) n, hi, n 2 = Empirical constants (dimensionless) n 3 = Empirical constant (cm) m = Empirical constant (dimensionless) P = A m o u n t of biofilm-covered surface area per unit stream length (on) q ~ = M a x i m u m specific rate of utilization (mg~ m g f i h - l) *Address all correspondence to: Dr Charles J. Gantzer, 122 Civil and Mineral Engineering Building, 500 Pillsbury Drive, SE, Minneapolis, M N 55455, U.S.A. 709

r = Rate of substrate utilization within biofilm (m& cm-3 h - l ) r b = Rate of bulk substrate concentration reduction due to suspended microorganisms (mg~ cm -3 h -t ) rf = Rate of bulk substrate concentration reduction due to biofilms (mg s cm -3 h - I ) R h = Hydraulic radius (cm) Re = Shear Reynolds n u m b e r (dimensionless) R% = Reynolds n u m b e r for flow in recycle pipe (dimensionless) S = Bulk or water column substrate concentration (mg~ cm -3) S(o) = Bulk C O D concentration at t = 0 for the batch test (mg s cm -3) Sr = Substrate concentration at point within biofilm

(mg~ Cff1-3)

S/d = C O D concentration o f feed solution (mg~ cm -3) So = Substrate concentration at surface o f biofilm (mg~ cm -3) Sc = Schmidt n u m b e r (dimensionless) t = Time (h) tfd = Length of time for feed addition (h) T = Temperature (°C) u = Water velocity (cm s - t) up = Water velocity in recycle pipe ( o n h - t ) us = Shear velocity ( o n s -~ ) V = Volume o f water in artificial stream (cm 3) W = Channel width (cm) x = Longitudinal distance in stream channel (cm) X b = Concentration of biomass in water column (mg x cm -3) Xf = Biofilm density (mg~ cm -3) y = Curve fitting parameter (dimensionless) z = Distance into biofilm (cm) v = Kinematic viscosity of water (cm 2 h - l ) = Characteristic biofilm kinetic parameter (cm - t )

Subscripts b = Bulk solution f = Biofilm

710

CHARLESJ. GANTZERet al. fd = Feed solution o = Biofilm/fluidinterface p = Recycle pipe s = Substrate x = Biomass 1 = First-order 2 = Second-order

mass transfer coefficients and the amount of biofilm surface area presented by natural streambeds are not known. For three reasons, the problem is especially acute for shallow streams that are lined with gravel and cobble. First, biofilms located on the interstitial surfaces of the streambed may significantly contribute to the removal of biodegradable contaminants from the stream's water column. Thus, active biofilm INTRODUCTION surface area can be greater than the vertically Streambed biofilms often determine the rate at which projected surface area. Second, the actual amount of biodegradable materials are removed from the water surface area colonized by biofilms varies with streamcolumn of streams, especially in shallow rock-lined bed particle size. Larger streambed particles, such as streams. Wuhrmann (1972) estimated that between cobble, tend to have a greater portion of their surface 90 and 99.9% of the bacterial biomass in streams area covered by biological growths than smaller < 1.5 m deep existed as biofilms. Lock and Hynes stream particles, such as gravel (Novotny, 1969). (1976) observed that streambed biofilms were pre- Third, equations have not been developed that dedominantly responsible for the removal of leaf leach- scribe the mass transport of biodegradable materials ates from shallow unpolluted streams. Tuffey e t al. from the water column to interstitial streambed (1974) determined that nitrifying bacteria attached to biofilms. the streambed were predominantly responsible for Because of the complex hydraulics within a streamthe removal of ammonia from shallow streams. bed, the relationship between stream velocity and the Srinanthakumar and Amirtharajah (1983) reported mass transport of materials to interstitial biofilms is that streambed biofilms determined the rate of total also complex. Stream flow--as advection eddies, vortiorganic carbon removal in a shallow cobble-lined ces and other forms of turbulence--penetrates the stream below a point source. Several other authors entire depth of the porous layer of rocky streambeds. (Kittrell and Kochtitzky, 1947; Velz and Gannon, Within this porous layer, interstitial water velocities 1964; HarremoEs, 1982; Boyle and Scott, 1984) have sharply decrease with increasing depth into the attributed the rapid rates of soluble BOD removal streambed. Because local mass transport rates are a immediately below point sources in shallow streams function of the local water velocities, the biofilms to streambed biofilms. attached to rock surfaces found in the upper portion In situations where streambed biofilms are predom- of a streambed experience faster mass transport than inantly responsible for determining the removal rates do biofilms found at the bottom of the streambed. of biodegradable contaminants, water quality models While the upper streambed biofilms may always based on suspended-growth kinetics have poor pre- experience faster mass transport than the lower dictive capacity. Thomann (1982) observed that while stream bed biofilms, the ratio between substrate BOD-oxygen models based on suspended-growth uptake rates for biofilms located at different depths kinetics provided reasonable predictions of oxygen in the streambed can change with stream velocity. At levels in large rivers (mean relative error of 10%), slower stream velocities, the upper portion of a such models were unable to predict oxygen levels in streambed accounts for almost all of the substrate small, shallow streams (mean relative error of 60%). removal from the water column, because interstitial Games (1982) reported that suspended-growth mod- water velocities are very slow. As stream velocities els were inappropriate in predicting the removal of increase, the interstitial water velocities also increase. trace concentrations of organic compounds from Incremental increases in interstitial velocities should streams in which hetrotrophic activity was predom- have a greater effect on substrate flux into the lower inantly attached to the streambed. streambed biofilms (previously exposed to very low Because the activity of streambed biofiims cannot mass transfer rates, i.e. mass-transported-limited) be modeled by suspended-growth kinetics, the predic- than on substrate flux into the biofilms located in the tion of contaminant removal rates in shallow streams upper layers of the streambed (previously exposed to should be based, at least in part, on biofilm kinetics. higher mass transfer rates, i.e. approaching kineticConceptually, applying biofilm kinetics to streams is limited condition). Thus, at high stream velocities, similar to their application to wastewater-treatment substrate flux into the lower streambed biofilms will processes. In particular, Gantzer e t al. (1988) demon- approach that of the upper streambed biofilms. strated that an existing mechanistic biofilm kinetic The response of biofilms located at various layers model could predict the rates at which naturally within a porous streambed to increases in stream occurring biofilms removed trace-organic velocity can be represented by the concept that compounds--provided that the mass transfer increasingly deeper portions of the streambed become coefficients and specific surface area of the modeled important in determining the rate at which streambed system were known. biofilms remove contaminants from the water colThe problem with applying biofilm kinetics to umn. At low stream velocities, only the biofilms stream-water-quality modeling is that the required located in the upper portion of the streambed are

Mass transport to streambed biofilms

exposed to high mass transport rates and are active in removing water column contaminants. As stream velocities increase, the biofilms located in the lower regions of the streambed experience increased mass transport and become increasingly important in removing water column contaminants. Thus, the rate at which streambed biofilms remove biodegradable contaminants from the water column of a stream should be more sensitive to changes in stream velocity than would be expected based solely on changes in local mass transport coefficients at the external surfaces of the streambed. The objective of this study was to develop a mass transfer equation that describe the sensitivity of substrate flux to short-term changes in stream velocity. This sensitivity was expressed in terms of an apparent, overall mass transfer coefficient. The mass transfer equation was developed from a series of well-controlled, batch biodegradation tests performed at different stream velocities in an artificial stream. Before and after each batch test in a series, the streambed biofilms were grown and acclimated to a specific water velocity, which created a steady-state biofilm. Individual batch tests were conducted at water velocities greater than, less than and equal to the acclimation velocity. Because the batch tests were of short duration, streambed biofilm biomass did not change from the steady-state value during each batch test. Therefore, any changes in the rate at which streambed biofilms removed substrate from the water column between batch tests conducted at different water velocities was due only to external masstransport-related effects. THEORETICAL BACKGROUND

Stream-water-quality model The mass balance equation for a one-dimensional, steady-state stream-water-quality model that includes biodegradation of contaminants by suspended and attached microorganisms can have the following form:

d2S

dS

DL ~'SX2 -- U~X -- r b -- r r = 0

(1)

in which D E is the longitudinal dispersion coefficient (cm 2 h-l), S is the water column concentration of the contaminant (mgs cm-3), x is longitudinal distance down the stream channel (cm), u is the average stream velocity (cm h - l ) , r b is the rate at which suspended microorganisms are reducing contaminant concentrations (rags cm -3 h-1) and r r is the rate at which attached microorganisms, the streambed biofilms, are reducing water column contaminant concentrations (mg s cm -3 h -~). Because equation (1) includes rf in the liquid control volume material balance and not as a boundary condition, the influence of streambed biofilm kinetics of S is modeled as a pseudohomogeneous reaction. Equation (1) assumes that variations in S across the cross-section of the stream

711

are small and not of interest, i.e. a uniform value of S is assumed in the vertical (depth) and horizontal (width) directions, except near to biofilm-covered surfaces. The variations in stream velocity across the stream's cross-section will cause diffusion-like mixing in the x direction, which is accounted for by the first term in equation (1). The steady-state condition assumes that S is not changing with time at any point in the stream. As written, equation (1) is applicable only to short stream reaches, because the values of DL, u, r b and rf will vary with x. For relatively low contaminant concentrations, rb can be described by mixed second-order kinetics (Baughman et al., 1980), rb =

K2 X b S

(2)

in which Kz is the mixed second-order rate constant (cm 3 mg~-1 h - l ) and Xb is the concentration of suspended microbial biomass (mgx cm-3). For any biofilm reaction, the rate of contaminantconcentration reduction can be described by (Rittmann, 1982), rf = J0 a

(3)

in which J0 is the representative flux of contaminant into the biofilm (rags cm -2 h -1) and a is the specific surface area, or biofilm-covered surface area per total liquid volume (era-l). For a stream, equation (3) takes the form, P rf= J0~

(4)

in which J0 is the representative flux, A is the cross-sectional area available for flow (cm 2) and P is the amount of biofilm-covered surface area per unit stream length, or the amount of wetted perimeter covered with biofilms per unit stream length (cm). The value of P includes external and interstitial surface areas of the streambed, as long as it is covered by biofilms. For wide stream channels, A can be approximated by, A = H W

(5)

in which H is stream depth (cm) and W is stream channel width (cm). Substituting equation (5) for A into equation (4) and dividing both the numerator and denominator by W gives the following equation:

P/W

rf = J 0 -

H

(6)

The P / W term is a useful dimensionless parameter that accounts for the amount of wetted perimeter covered by biofilms per unit channel width. If a stream is lined with a flat, smooth surface, such as bedrock, and is entirely covered with biofilms, then P / W = 1. For gravel and cobble streambeds whose interstitial voids are free of sand and silt, P / W values can be substantially > 1, because biofilms can be found on the interstitial surfaces, as well as the exposed (external) surfaces of the streambed.

CHARLESJ. GANTZERet al.

712

Substituting equation (2) for r b and equation (6) for rf into equation (1) produces the following equations:

d2S dS DL -~x2 -- u-d~x

. P/W K2 Xb S - . t o y =0

(7)

which can be used to described contaminant concentrations as a function of distance down the stream channel.

(Atkinson and Daoud, 1968; WiUiamson and McCarty, 1976a; Harremo~s, 1978; Grady and Lim, 1980; Gantzer et al., 1988) Jo = So Df ~b tanh (~b Lf)

in which tanh is the hyperbolic tangent and $ is a characteristic biofilm kinetic parameter (cm-l) that is defined by

Biofilm kinetic model

=FK2XfT :.

For relatively low contaminant concentrations, contaminant flux into natural biofilms can be approximated by the first-order flux model (Gantzer et al., 1988). The first-order flux model is a steady-state mechanistic biofilm kinetic model that describes substrate flux into an ideal biofilm as first-order with respect to bulk concentration of the substrate. The model assumes that substrate flux is a function of three mechanisms: (1) mass-transport from bulk liquid to the outer biofilm surface, (2) mass-transport within the biofilm, and (3) microbial transformation of the substrate within the biofilm. The two masstransport mechanisms are represented mathematically as diffusion processes; consequently, they are sensitive to the substrate gradient within the biofilm. The driving force in the formation of the concentration gradients is the rate at which biofilm microorganisms transform the substrate. The first-order flux model assumes the rate of microbial transformation at any point within the biofilm (r, mgs cm 3 h J) follows mixed second-order kinetics, r = K 2 Xf Sf

d 2Sf

Dr ~

Equation (10) has limited direct applicability, because in situations where bulk-phase mass-transport resistance is significant, the concentration of substrate at the outer surface of the biofilm (So) is unknown. Since bulk (water column) substrate concentration (S) is usually known, it is desirable to modify equation (10) such that flux is a function of S and not of So. The biofilm-surface substrate concentration is a function of bulk substrate concentration and bulkphase mass transport. When no transformation of substrate occurs within the effective diffusion layer, the flux of substrate from bulk solution to the outer biofilm surface can be defined by (FrankKamenetskii, 1969) J0 = kb (S - So)

(9)

in which D r is the diffusion coefficient for the substrate within the biofilm (cmZh 1) and z is distance in from the outer surface of the biofilm (cm). Equation (9) is subject to the following two boundary conditions: the substrate concentration at the outer surface of the biofilm (z = 0) equals So (mgs cm-3), and the substrate concentration gradient at the inner biofilm surface (z = Lf, where Lr is biofilm thickness in cm) is zero (dSf/dz = 0), i.e. the surface to which the biofilm is attached is impermeable and does not adsorb the modeled substrate. Based on equation (9) and the two boundary conditions described above, the flux of substrate into the outer layer of a biofilm can be described by

(12)

in which kb is the bulk-phase mass-transfer coefficient (cm h - l ) . By rearranging equation (12), So can be determined from

J0

So = S - - - . kh

(13)

Substitution of equation (13) for So in equation (10) produces J0

kb Df 4' tanh(q~ Lf) S kh + Dr ~b tanh(~b Lf)

(14)

which defines flux as a function of bulk substrate concentration (S). For constant values of kb, Of, Lf and 4', substrate flux is first-order with respect to S,

Jo= KrS -- K2 Xf Sf = 0

(11)

LD~j

(8)

in which K2 is the mixed second-order rate constant (cm 3 mgx 1 h - l ) , Xf is the biofilm density or the concentration of biomass within the biofilm (mgx cm -3) and Sf is substrate concentration at a point within the biofilm (mg s cm-3). Equation (8) is first-order with respect to S t, as well as Xf. The steady-state differential equation describing the substrate concentration profile within a biofilm is

(10)

(15)

in which Kf is the first-order flux constant (cm h - ' ) and is defined by kb Df q~ tanh(~b Lf)

Kf = kb + Or~b tanh(~b Lf)"

(16)

When the first-order flux model [equations (15) and (16)] is applied to streambed biofilms, the various biofilm kinetic parameters are representative of the entire streambed biofilm community: J0 is the representative flux, S is contaminant concentration in the water column, q~ is representative of the entire streambed biofilm community and kb is the apparent, overall mass transfer coefficient that describes mass transport from the water column to the outer surfaces of the streambed biofilms.

Mass transport to streambed biofllms 100

i

m

713

external flow regimes, the mass transfer coefficients can be described by equations of the following form (Frank-Kamenetskii, 1969):

!

80kb = n Re m Sc m D-2

Lc

.B e~

>, 60" n

40E O ix .~ 20-

o

I

I

0.01

0.1

I

I

1.0 HK2X b K~P/W

10

100

Fig. 1. Percent of total contaminant removal rate due to streambed biofilms as function of ratio between suspended and attached microbial removal rates.

Functional dominance o f streambed biofilms

Substitution of equation (15) for J0 in equation (7) results in the following steady-state, stream-waterquality model: d2S dS .. P~ W DL - - ~ -- U~ x - K2 Xb S - t~f - - ~ ~ = O. (17)

The relative importance of streambed biofilms compared to suspended microorganisms in determining contaminant removal rates for a stream reach can be estimated by comparing the biofilm rate to the sum of both rates. % of Total removal rate due to streambed biofilms . P/W 100/~f - ~

100 =

KrP / W - - - ~ + K2Xb

(18) H K2 Xb l + Kfp/-------~

Equation (18), which is plotted on Fig. 1, indicates that the following stream conditions favor the functional dominance of streambed biofilms over suspended microorganisms in determining contaminant removal rates: (l) shallow streams (small H ) , (2) porous streambeds with interstitial surfaces covered with biofilms (large P / W ) , and (3) low concentrations of suspended biomass (small Xb). In addition, if streambed biofilms are better acclimated for degrading the contaminant than are the suspended microorganisms (i.e. larger K2 value in Kr than in the suspended kinetic term), biofilm degradation is more dominant. Mass transfer equations

The hydraulic regime to which streambed biofilms are exposed can be represented as a complex combination of flow around particles and flow through porous media. For these flow regimes and many other

(19)

in which k b is the bulk-phase mass-transfer coefficient (cm h -1), n is a dimensionless constant, Lc is the characteristic length (cm), the Reynolds number (dimensionless) is calculated based on L o m typically ranges in value from 1/4 to 2/3 (dimensionless), Db is the diffusion coefficient for the modeled material in bulk solution (cm 2 h - l ) and Sc is the Schmidt number (dimensionless) and is equal to the kinematic viscosity of the solvent (v, cm 2 h - l ) divided by D b . While the values of Re, Sc, D b and k b are a function of temperature, the empirical constants n and m are insensitive to changes in temperature. When particle diameter (d) represents L c and when Re values are large, equations similar to equation (l 9) described k b for flow around spheres (Bird et al., 1960; Cussler, 1984), flow through a fixed bed biological reactors (Rovita and Kittrell, 1973; Traber and Kittrell, 1974), and flow through fluidized-bed biological reactors (Jennings, 1975; Rittmann, 1982). However, in situations where Re is small, a better description of k b often is provided by m l/3 Db k b = [ n I +n2Re Sc ] ~ -

(20)

in which n~ (dimensionless) would correct kb for small Re values and n 2 is also dimensionless. For example, an equation similar to equation (20) is used to describe kb for flow around individual spheres at small Re values (Bird et al., 1960; Cussler, 1984). The initial objective of this study was to determine the values of nl, n2 and m, such that an equation similar to equation (20) would describe the apparent, overall mass transfer coefficient (kb) as a function of the shear Reynolds number for sand-free gravel and cobble streambeds. The shear Reynolds number (Re) is defined as (Henderson, 1966) Re

3600 u, d

(21)

V

in which u, is the shear velocity (cm s-t). Describing streambed mass transport in terms of shear velocity, instead of average stream velocity, reduces the problem of site and flow specificity. As discussed above, streambed mass transport rates are a function of the water velocities at streambed surfaces. Railsback (1981) observed that water velocities at gravel and cobble streambed surfaces could be described as a function of shear Reynolds number [equation (21)], regardless of average water column velocity (u) or stream depth (H). Water column velocity and depth showed little correlation with water velocities at streambed surfaces. Therefore, a streambed mass transport equation defined as a function of shear velocity (u,) should be applicable to

CHARLES J. GANTZER et al.

714

a wider range o f streams than an equation defined as a function o f water column velocity (u). F o r the results presented in the following, equation (20) provided reasonable descriptions o f mass transport in the gravel and cobble streambeds separately. However, one set o f nl, n2 and m values could not adequately describe the apparent, overall masstransport rates for both streambeds. A modified version o f equation (20) in which one set o f constants did describe both the gravel and cobble streambed data was kb=

n,+dRe

m

13 q Db Sc' J~-

(22)

in which n 3 has the units o f cm. The rest o f this paper centers on the determination o f n], n3 and m in equation (22). MATERIALS AND METHODS

Description of artificial stream The experimental determinations of nj, n3 and m in equation (22) were performed in a 10-m long Frigid-Units (tm) fish raceway. The fish raceway was modified such that water was recycled through a system of centrifugal pumps and pipes (Fig. 2). The use of return pipes and associated pumps allowed water velocities to be much higher in the artificial stream than would have been allowed with the traditional false bottom recycle. Water velocities in the artificial stream were controlled by varying stream discharge either by altering the number of recycle pumps in operation or by adjusting discharge for individual pumps via valves on each pump's discharge pipe. There were four separate recycle pumps and recycle pipes. The total volume of water in the artificial stream ranged from 90 to 2001. Two different sizes of sieved calcareous rock were used to represent two types of natural streambeds. Gravel and cobble streambeds were represented by rocks with a mean diameter of 1.6 and 6.0 cm, respectively. Both the gravel and cobble streambeds were 1.5-2 layers of rock thick. The rocks were placed in a lined rectangular channel that was

27.5 cm wide. The length of the gravel and cobble streambeds were 690 and 730 cm, respectively. Streambed slope was 2.9°/.. Sufficient water flowed over the gravel and cobble streambeds to completely cover all of the rocks.

Velocity determinations Prior to biofilm colonization of a streambed, average stream velocities (u) were determined from tracer studies for several different pump combinations and settings. A NaCI solution was step-fed to the head of the streambed, and travel time was observed with a conductivity probe located at the end of the streambed (procedure described in following section). For steady, uniform flow in the artificial stream, shear velocities could be calculated from the following modified version of the Keulegan equation (Bray, 1979): u~ -

U

6.25 + 5.75 log(Rh/d )

(23)

in which u~ is the shear velocity (cm s ~), u is the average stream velocity (cm s ~), log is the base 10 logarithm, d is the median diameter of the streambed particles (era) and Rh is the hydraulic radius of the artificial stream channel (cm). Rh for the rectangular channel was obtained from

HW 2H+W

RI, . . . . . . . . . . . .

(24)

in which W is the width of the channel (27.5) cm) and H is the depth of flowing water (cm).

Tracer studies NaC1 tracer studies were conducted to determine average stream velocities and the amount of time required for batch additions of feed solutions to be uniformly distributed throughout the artificial stream. The step-fed NaC1 tracer studies were performed under the same time and physical constraints as were the COD bateh-biodegradation tests. The tracer (200 g of NaC1 in 91. of water) was added at the same rates at which the glucose was added to the stream during the COD batch tests, i.e. 30-120 s to add the 91. of solution. For determination of stream velocities and mixingtime requirements, NaCI concentrations were monitored by a Yellow Springs Instruments conductivity probe located at the end of the streambed just before the stream water fell into the sump. This location was comparable to where the

t

pump Fig. 2. Schematic diagram of the artificial stream reactor.

Mass transport to streambed biofilms water samples for the COD batch-biodegradation tests were collected. Tracer studies were also conducted to see if any vertical concentration gradients existed in the cobble streambed. These studies were conducted as above, but with two conductivity probes. One probe was located at the end of the streambed, as above, while the second probe was buried at the bottom of the cobble streambed midway down the streambed. The conductivity peaks for the two probes should be out of phase by the time required for stream water to travel one-half the length of the streambed. If the magnitude of the two peaks were equal, then the tracer study would suggest that there is no vertical concentration gradient within the cobble streambed, i.e. there is rapid mixing between water column and interstitial voids in the cobble streambed. Growth o f streambed biofilms

The artificial stream was initially inoculated with the microorganisms found in water pumped from a 46 m deep well. The well water also functioned as the nutrient media for the streambed biofilms. The concentrations of the major inorganic nutrients were as follows: ammonium I. 1 mg l-i, nitrate 1.5 mg l- t, sulfate 1.2 mg l-I and phosphate 0.03 mg 1-I. The well water was also moderately hard and had a total organic carbon concentration of 3.54.0 mg l-i (Randtke and Jepson, 1981). The artificial stream was covered and located in a dark room to prevent the growth of phototrophic microorganisms. Each day, 501. of artificial stream water (25-50% of the total amount of stream water) was replaced with fresh well water to maintain nutrient concentrations and to reduce any existing suspended pupulations of microorganisms. As a carbon source for the streambed biofilms, an acidified (pH = 3) glucose solution of 75rag COD1 -l was added to the stream at the rate of 0.751 h - t - - a rate that was approximately equal to the rate of water lost due to evaporation. With the stream water lacing recycled at flows of at least 30501 h - l, recycle rates during periods of biofilm exceeded 4000. Therefore, during biofilm acclimation to a stream velocity, the artificial stream approximated a completely-mixed reactor, which meant that physical biofilm characteristics could be assumed uniform over the length of the streambed. Streambed biofilm communities were acclimated to stream flows that completely covered all of the rock surfaces. For the gravel streambed experiments, the biofilm community was acclimated to an average stream velocity (u) of 17.7 cm s -l (us = 2.5 cm s-I). For the cobble experiments, the streambed biofilms were acclimated to an average stream velocity of 13.2 cm s - l (us = 2.2 cm s- t ). The biofilm community was considered to be acclimated to a stream velocity when the ability of the streambed to remove COD was constant for a 2-week period. Streambed biofilm model

For a batch-biodegradation experiment, the rate at which streambed biofilms reduced the COD concentrations was equal to mass flux into the streambed biofilms times the specific surface area of the artificial stream channel, dS P Li - - = -- K f S - (25) dt V in which Kf times S equals the mass flux, S is the COD concentration in the artificial stream (mg~cm-3), t is time (h), Kr is the representative first-order flux constant for the streambed biofilms (cm h -I ) as defined by equation (16), P is the geometrically available surface area for biofilm colonization per unit length of streambed (cm), Ls is the length of the streambed (cm) and V is the volume of water in the artificial stream (cm3). The geometric P values for the gravel and cobble streambeds were 192 ( P / W = 7.0) and 170cm ( P / W = 6.2), respectively.

715

The derivation of equation (16), i.e. the definition of the first-order flux constant (Kf), assumes steady-state conditions within the biofilm [equation (9)]. A steady-state substrate-concentration profile can be obtained when the bulk substrate concentration is at steady-state or when bulk substrate concentrations are changing sufficiently slowly to provide a pseudo-steady-state [the case described by equation (25)]. For the first-order flux model to be appropriate for a pseudo-steady-state situation, two conditions must be met. First, the characteristic time associated with establishing the steady-state substrate-concentration profiles within the biofilm must be considerably shorter than the characteristic time associated with biofilm growth, i.e. changes in biofilm thickness (Rittmann and McCarty, 1981; Kissel et al., 1984; Wanner and Gujer, 1986). Second, the characteristic time for the substrate profile within the biofilm must also be considerably shorter than the characteristic time associated with changes in bulk substrate concentration (Kissel et al., 1984). The first-order flux model was used to describe biofilm kinetics during the COD batch tests, because both of the above pseudo-steady-state conditions were met. The first condition was met, because the batch tests were of short duration ( < 20 min) and did not allow time for microbial growth. The second condition was met, because timedependent numerical simniations indicated that the streambed biofilms developed a new steady-state profile virtually instantaneously in response to any observable changes in bulk COD concentrations, i.e. substrate-profile characteristic times were much shorter than the characteristic times for bulk COD changes. Direct calculation of characteristic times also indicated that substrate-profile characteristic times were shorter than bulk-COD characteristic times. Based on the equations presented by Kissel et al. (1984), the minimum bulk-COD characteristic time was 0.36 h, while the maximum substrate-profile time was approx. 0.005 h. Equation (25) indicates that COD removal by streambed biofilms is first-order with respect to COD concentration and that the corresponding first-order rate constant (Kmr) can be defined by P LI Klf = Kf T

(26)

in which Klf has the units h -I. COD batch-biodegradation tests

A batch-biodegradation test consisted of three steps. First, the background COD concentrations were reduced by stopping the addition of the 75 mg COD 1-1 feed solution. Second, the COD concentration in the artificial stream was rapidly increased to between 30 and 45 mg COD l -I by adding 9 I. of concentrated glucose solution; the actual concentration of this feed solution varied with the volume of water being recycled in the artificial stream. The 91. of glucose solution were added at a uniform rate for 30-120 s. The time at which the entire 91. of the feed solution had been added to the artificial stream corresponded to t = 0. Third, the rate of COD removal from the waters of the artificial stream was determined by measuring COD concentrations in stream water samples that were collected at regular time intervals. Replicate stream water samples were collected as the stream water fell into the artificial stream's sump and not from the sump itself (Fig. 2). The first stream water sample was collected after the time required for the COD concentrations to become uniform throughout the artificial stream. The NaC1 tracer studies indicated that 3 recycle times after feed addition were required for uniform distribution. The water samples were filtered through a 0.45 #m membrane filter. COD analysis of the water samples followed the low-level procedure described in Standard Methods (APHA, 1978).

716

CHARLES J. GANTZER et al.

The initial rate of C O D removal was first-order with respect to C O D concentration, dS dt=

-K~S

(27)

in which t is time (h), and K 1 is the experimentally observed first-order rate constant (h -~) and is equal to the slope of the line produced when the natural logarithm of S (In S ) is plotted vs time (least-squares fit). During the gravel streambed tests, water was recycled through clean pipes, which made K~f = K~. However, during batch tests with the cobble streambed, water was recycled through at least one pipe that had been colonized with biofilms. Then, Kjr was calculated from Ktf = K I - KIv (28) in which K~_ is the first-order rate constant for C O D removal by the recycle pipe biofilms (h -~ ). For the cobble batch tests, the Ktp value for each recycle pipe colonized with biofilms was calculated from kb.pDr¢ Ap kb.p + Dfdp V

KiP

(29)

in which kb, p is the bulk-phase mass-transfer coefficient for the movement of C O D from bulk solution in the pipe to the outer surface of the biofilms in the pipe ( c m h i), Ap is a m o u n t of pipe surface area colonized by biofllms (cm2), and V is the a m o u n t of water being recycled in the artificial stream (cm3). Equation (29) assumed that the pipe biofilms were deep with respect to COD, i.e. C O D concentrations approached zero within the biofilms and tanh(q~ Lf) was The volume of water being recycled in the artificial stream (V) was not determined by volumetric means, because the a m o u n t of water retained in the false bottom of the artificial stream reactor was not measurable. Instead V was obtained from the following equation:

Qfd Sfd

V=KIS(o)[I

-- exp(

K 1 tfd)]

(30)

in which Qfd is the volumetric rate at which the C O D feed was added to the stream (9000 cm 3 tfd- ~), tfd is the length of time over which the C O D feed was added to the stream (h), St.d is the C O D concentration of the glucose feed (rag 1- i) and S (o) is the C O D concentration at t = 0 for the batch test and is calculated from the ),-intercept (t = 0) for the straight line produced when In S is plotted vs t (leastsquares fit). Equation (30) assumed that the C O D feed was added to a completely-mixed reactor at a uniform rate (Qfd) for a known length o f time (trd) and that some C O D was biodegraded during tfd. Determination o f constants in mass transfer equation

As described above, each C O D batch test experimentally determined a value of Kif. After an appropriate value of K t. was calculated from (a rearrangement of equation (26)], KIf V Kf = - L~ P

(31)

the apparent, overall mass transfer coefficient (kb) for the batch test was calculated from the following rearrangement of equation (16):

Kt Dfdp

kb - - (32) Dr dp - Kf in which k b has the units cm h - t . Equation (32) assumed that the streambed biofilms were deep with respect to COD, i.e. C O D concentrations approached zero within the biofilms and tanh(¢ Lr) was ~ I. This was a realistic assumption, because of the large ~ values (e.g. 253 cm-*) and the presence of macroscopically visible streambed biofilms (e.g. L r values > 0.01 era). Thus, the values of tanh(¢ Lr) were greater than 0.98.

The k b values obtained from the gravel and cobble-batchbiodegradation tests were used to determine the values ofn~, n 3 and m in equation (22),

k~ = [n~ + ~ RemSc ~3] Db / d 3d

(22)

For a given value of n~, the values of n 3 and m were determined from a least-squares fit of the following equation: log y = logn 3 + m log Re

(33)

in which log is the base 10 logarithm and

y

=[k~d L - ~ n,]dSc ,3.

(34)

Thus, the values of n 3 and m were obtained by fitting a straight line to the set of ordered pairs [log Re, log y] obtained from both the gravel and cobble experiments. By trial and error, different values of n~ were used in calculating y [equation (34)] until the best linear correlation was obtained between log Re and Iog y. Since each value of ku was determined experimentally at a specific water temperature, the corresponding values of Re, Sc and D b were corrected for temperature effects. The values of nt, n 3 and m were not affected by temperature. Determination ~ff' biofilm kinetic' parameters

The diffusion coefficient of glucose (i.e. the C O D source) in water was determined from the W i l k e ~ h a n g expression (Perry and Green, 1984) and was estimated to be 0.025 cm 2 h-~ at 20°C. Diffusion coefficients were corrected for small changes in temperature by (Rittmann et al., 1983) D h = 0.025 exp[0.0421 (T - 20)]

(35)

in which D b is the diffusion coefficient for glucose in water (cm2h -~) at the temperature T(°C). The diffusion coefficient for glucose within the biofilm (Dr) was assumed to be 0.8 times D b (Williamson and McCarty, 1976b). Based on data presented in Streeter and Wylie (1975), the variation in the kinetic viscosity of water with temperature (between 15-30°C) was described by v = 36.25 exp[ - 0.0233 (T - 20)]

(36)

in which v is the kinematic viscosity of water (cm 2 h t) at the water temperature 7'. and 36.25 cm 2 h -~ is the kinematic viscosity of water at 2if'C. The sensitivity of characteristic biofilm kinetic parameter [~b, equation (11)] to changes in temperature was a combination of the effects of temperature on Df and the mixed second-order rate constant (K2). The value of K 2 was assumed to double for every 10°C increase in temperature; thus (Rittmann et al., 1983). K 2 = K2,2o exp[0.0693 (T - 20)]

(37)

in which K 2 is the mixed second-order rate constant (cm 3 rag? ~ h - J ) at a water temperature of T, and K2,20is the mixed second-order rate constant at 20°C. Biofilm density (X0 was assumed to be insensitive to temperature changes. Based on equations (35) and (37), the value of ~b (cm ~) at the water temperature T was obtained from (h = 4)20exp[0.0137 (T

20)]

(38)

in which ~b20is the value of lhe characteristic biofilm kinetic parameter at 20°C. The value of q~20was calculated from the experimentally determined first-order rate constants for the removal of C O D by recycle pipe biofilms (Kip). During gravel streambed acclimation, the inside surface of the recycle pipe became covered with biofilm. The pipe biofilm was assumed to have the same bacterial composition and the same ¢ value as the streambed biofilm community. Two batch tests were needed to experimentally determine Kip. The first

Mass transport to streambed biofilms

717

batch test determined the first-order rate constant for COD removal by both strearnbed and recycle pipe biofilms (K l) by routing water over the gravel streambed and through bioffim-colonized recycle pipes. The second batch test determined the first-order rate constant for COD removal by streambed biofilm (Kif) by recycling water through clean pipes after the water flowed over the gravel streambed. The value of Kip was calculated from

sitive to increases in f A sensitivity analysis for the experimental conditions used (Gantzer, 1986) indicated that a 75% increase in f would result in only a 5% overestimate

Kip = Ki -- Klf.

The N a C i tracer studies performed on the cobble streambed suggested that there was no signifcant difference in bulk concentrations of a conservative material between the water column and the bottom of the cobble streambed. As shown on Fig. 3, the magnitude of the conductivity peaks for the water column and interstitial probes were the same. Therefore, the rate of mixing between the water column and the interstitial voids in the cobble streambed was rapid. The same result was observed for all stream velocities at which the cobble batch tests were conducted. The cobble NaC1 tracer studies suggest that interstitial biofilm activity was controlled by the mass transport at the biofilm-covered surfaces (micro-scale conditions) and not by the rate of mixing between the bulk water and voids in the cobble streambed (macroscale conditions). Thus, the sensitivity of streambed biofilm activity to changes in average stream velocity probably was more a function of interstitial water velocities than a function of the vertical mixing rate. Conductivity probes could not be placed in the gravel streambed without disrupting normal flow patterns. Because of the smaller interstitial voids in the gravel streambed, the rate o f macro-scale mixing between bulk water and the bottom of the gravel streambed may have been slower than in the cobble streambed.

(39)

The value of 4, was obtained from ~b

kb'p KIp V kb, p DfAp -- DfKlp V"

(40)

Equation (40) assumed a deep biofilm. The value of ¢~0 for each pair of batch tests was calculated from equation (38). The pipe mass transfer coefficients (k~ p) used in equations (29) and (40) were calculated from (Bi~:d et al., 1960)

f.p

(41)

kb, p = Sc2/3

in which kb,p has the units cm h -I, f is the friction factor for flow past the wall of the pipe (dimensionless), up is the average water velocity in the pipe (cm h - l) and is equal to stream flow divided by the cross-sectional area of the recycle pipe and Sc is the Schmidt number. The friction factor was calculated from the Blasius formula (Chow, 1959), f = 0.316 Re~-I/4

(42)

in which Rep is the pipe Reynolds number (dimensionless), Rep = Updp

(43)

V

and dp is the inside diameter of the pipe (cm). The Blasius formula is considered valid in smooth pipes up to Rep values of 100,000 (Bird et al., 1960). The experimental Rep values ranged from 24,000 to 78,000. The use of equations (40), (41) and 42) had the potential to overestimate ¢, because the presence of biofilms inside of a pipe can increase the pipe's friction factor to values greater than those predicted by the Blasius formula. Characklis (1973) reported that the result of biofilms colonizing the inner surface of a 36 in. dia pipe was a decrease the capacity of the pipe by 23%, which corresponded to a 73% increase in f However, during the ¢ experiments, the calculated kb.p values were > 70 cm h - 1. The insertion of these large mass transport coefficients into equation (16) suggested that the recycle-pipe biofilms were not mass-transport limited. Thus, the experimental determination of ~bwas considered insen-

of ¢.

RESULTS

Tracer study

Appearance of streambed biofilms After a 4-month acclimation period to an average stream velocity of 17.7 cm s -~, macroscopically visible biofilms were evident as patches on the upper-

1000

"E°800' -= 600' .r400. u 0C

&-water

c~ 200'

!/,

,

60

"120

,

columnn a l a r

"""P cobl~e V- 17.4 m / u e

o

....

I 0

180 240 Time (sec)

300

360

Fig. 3. Results of NaCI tracer study performed on cobble streambed at an average stream velocity (u) of 17.4cms -l.

718

CHARLES J. GANTZER et al.

most surfaces of the gravel streambed. Brown patches were most prevalent immediately behind the ridges found on the surfaces of individual pieces of gravel. The macroscopic biofilm colonies represented less than 50% of the projected surface area of the gravel streambed. However, thinner, macroscopically invisible biofilms existed elsewhere within the gravel streambed. In contrast, after a 3 month acclimation period to an average stream velocity of 13.2cm s ~, all of the external and interstitial surfaces of the cobble streambed were uniformly colonized with macroscopic biofilms. Novotny (1969) reported that a greater fraction of the available surface area was colonized with thick growths for larger streambed particles. The percentage of the vertically projected surface area of streambeds covered by thick biofilms could range from 100% for particles > 4 c m , 50-80% for particles between 1 and 4 cm and 30-50% for particles between 0.5 and I cm. Thus, our data conforms to the general observation concerning macroscopic biofilm colonization. First-order COD removal In all cases, the results for the initial rate of COD removal conformed to the first-order assumption, because straight lines were produced when the natural logarithm of stream COD concentrations were plotted vs time. Figure 4 provides three examples for the gravel streambed. The first-order rate of COD removal suggests that streambed-biofilm activity was limited by bulk-phase mass transport rates, glucose utilization within the streambed biofilms followed mixed second-order kinetics [equation (8)] or both. Dissolved oxygen concentrations During several cobble COD batch-biodegradation tests, water column dissolved oxygen (DO) levels were monitored with a Yellow Springs Instrument Model 54 oxygen meter that had been calibrated via the Winkler-Azide method (APHA, 1978). During the time period in which water samples were collected for COD analysis, water column DO levels did not fall more than I mg 1-~ below saturation in the cobble stream. The main reasons that water column DO levels stayed high during the sampling period were that the cobble stream had calculated reaeration coefficients greater than 5 h -~ based on the Owens equation (Thomann, 1972) and the duration of high COD-utilization rates was short, < 20 min. The high DO levels in bulk solution make oxygen limitations within the streambed biofilms unlikely. Value o f c~ The average value of the characteristic biofilm kinetic parameter at 20°C (¢P20) for three sets of batch tests with colonized and uncolonized recycle pipes was 253 _+ 29cm -1. This average q~20value was used in calculating the apparent, overall mass-transport

1.0

!

!

0

\.\

0.9"

0

a

U= 9.Sl era~lee

,, o-..T o,./.o

0.8-

o o 2

o z-

,,.,, 0 (...)

0.6-

o.5

I I 0.1 0.2 Time ( hr )

0

0.3

Fig. 4. Effect of short-term changes in average stream velocity on the rate of COD removal by the gravel streambed. The streambed was acclimated to an average stream velocity of 17.7 cm s-L

coefficient (kb) for each batch test performed on the gravel and cobble streambeds. Mass transfer equation Short-term increases in the average stream velocity (u) increased the rate at which COD was removed from the artificial stream, e.g. note the increasing slope with increasing u in Fig. 4. The effect that short-term changes in water velocity had on COD removal rates was expressed in terms of the apparent, overall mass transfer coefficient (kb). The ,calculated values of kb for representative batch tests performed on the gravel and cobble streambeds are listed in Table 1. The determination of the constants in equation (22) was dependent on producing a straight line when log y [defined by equation (34)] was plotted vs log Re [defined by equation (21)]. By trial and error, it was observed that when nj was set equal to 88, the best linear regression coefficient (least-squares fit) was obtained for the set of ordered pairs [log Re, log y] (Fig. 5). The slope of the line (m) was 4.33, the intercept (log n3) w a s -- 10.96, and the square of the regression coefficient (r 2) was 0.989. Substitution of the appropriate values into equation (22) yielded the following mass transfer equation: kb =

[

88 +

1"11×10 t' ] d Re433 ScU3 -2Db

(44)

in which kb is the apparent, overall mass-transport coefficient (cm h -~) that describes the transport of biodegradable material from bulk solution (i.e. the water column) to the streambed biofilms, Re is the shear Reynolds number [equation (21)], Sc is the Schmidt number, Db is the diffusion coefficient for the material in bulk solution (cm h - ~), d is the streambed particle size (cm) and the n 3 constant (1.1 ! x 10 - n )

Mass transport to streambed biofilms 50

Table I. Results of gravel and cobble streambed experiments u (em s - l )

u, (ellis -I )

T (°C)

Kf (cm h - l )

Re

kb ( c m h -I )

719 I

i

/

cobble data 40"

~

/

equation [ 4 4 )

Gravel streambed

9.9 17.7" 23.0 28.8 31.4 40.6

1.5 2.5 3.1 3.7 3.9 4.9

24.5 24.5 24.0 25.0 25.7 25.0

265 441 541 660 708 875

1.3 1.6 1.9 2.6 3.2 3.8

1.7 2.1 2.7 4.3 6.0 8.7

30"

.c

E 20"

I

Cobble streambed

/

3

10"

8.8 1.5 21.0 915 0.6 0.7 9.9 1.7 23.0 1086 1.1 1.4 10.2 1.8 22.0 1124 1.3 1.7 11.6 2.0 21.5 1234 1.8 2.8 13.2" 2.2 22.0 1373 2.4 4.1 16.6 2.7 22.0 1685 4.0 13.7 25.2 4.0 22.0 2497 5.0 45.1 * Acclimation velocity for each streambed. Values of Re, Kf, and kb represent experimental temperatures.

o

I 1000

2000

3000

Re

has the units cm. Equation (44) provided very good descriptions of both the gravel and cobble experimental data (Figs 6 and 7, respectively).

Fig. 7. Relationship between the apparent, overall bulkphase mass transfer coefficient (kb) and shear Reynolds number (Re) for the cobble streambed experiments. Temperatures for the experimental data points ranged from 21 to 23°C. The line representing equation (44) assumed a temperature of 22°C.

DISCUSSION

Comparison with another mass transfer equation 0 gravel 3-

D cobble

,

f/

2-

1-

/

-88 -

nI m • 4.33 Log n 3,

10.96

f 2l 0 . 9 8 9

0-

-1

I

I

I

3

4

log Re Fig. 5. Relationship between log Re and log y values for gravel and cobble streambed experimental data when n~ was set equal to 88. The straight line was determined by method of least-squares applied to equation (33).

I

10 0

I

gravel data

1

Based on theoretical considerations, N o v o t n y (1969) derived a mass transfer equation for the transport of material from the water column to the upper (external) surfaces o f streambeds, i.e. the effect stream velocity had on interstitial biofilms was not considered. His equation was o f the same form as equation (19), with Reynolds numbers based on shear velocity [equation (21)]. However, N o v o t n y ' s equation had a m value of 1/2; a value much smaller than the 4.33 value in equation (44). Because of the non-linear relationship between flux and local mass transfer coefficients [equation (14)] and because of the complex nature of flow within the interstitial voids o f a streambed, the ability of entire streambeds to remove contaminants from the water column is more sensitive to velocity changes than can be defined by mass transfer equations for just the external surfaces of a streambed. Thus, raising Re to a power greater than 1/2 is required in order to describe the sensitivity of contaminant flux into streambed biofilms to shortterm velocity changes.

Comparison of streambed rates

o

0

I

I

300

600

90(

Re

Fig. 6. Relationship between the apparent, overall bulkphase mass transfer coefficient (kb) and shear Reynolds number (Re) for the gravel streambed experiments. Temperatures for the experimental data points ranged from 24 to 26°C. The line representing equation (44) assumed a temperature of 25°C.

Figure 8 illustrates the relative rates of streambed C O D utilization per unit of vertically projected surface area (KfP/W) for the gravel and cobble streambeds as a function of shear velocity. Equation (44) was used in the calculation of the first-order flux constants [Kf, equation (16)] for each streambed over the range of shear velocities to which both the gravel and cobble streambeds were exposed, 1.5--4.0 cm s-i. Despite the experimental gravel streambed having more surface area ( P / W = 7 . 0 ) than the cobble streambed ( P / W = 6.2), the cobble streambed had greater K r P / W values for shear velocities (us) between 1.8 and 4.0cm s -1 (Fig. 8). However, at us

720

CHARLESJ. GANTZERet al. 3Q

t

,~

1978) using assumed Ks values. The variable-order model assumes the biofilm is deep, substrate utilization follows Monod kinetics, and the steady-state substrate concentration profile can be described by

2O

d 2 Sf

Dr dz 2 .¢

o

0

I

2

I

I

4

i

6

Us (Cm sec -1)

Fig. 8. Comparison of calculated COD removal rate constants per unit projected streambed surface area (KfP/W) for the gravel and cobble streambeds as a function of shear velocity (us). A common water temperature of 20°C was assumed. values between 1.5 and 1.8 cm s -j, the gravel streambed removed COD at a faster rate than did the cobble streambed. As indicated by the slope of the lines on Fig. 8, cobble streambed activity was more sensitive than gravel streambed activity to short-term changes in shear velocity. These observations suggest that streambed particle size (d) played a more complex role in determining COD removal rates in the artificial stream than would be expected based on geometric surface area alone. Streambed particle size probably influenced COD removal rates via such parameters as interstitial void size, streambed porosity, and the percentage of available surface area covered with biofilms. Applicability o f mass transfer equation to other systems

Development of equation (44) assumed that the rate of COD utilization within the streambed biofilms followed mixed second-order kinetics and that equation (9) could be used to describe the steady-state COD concentration profile. Because Monod halfvelocity coefficients (K~) were not determined for this study, there is a possibility that COD utilization within the streambed biofilms did not follow mixed second-order kinetics. If COD utilization followed Monod kinetics instead of mixed second-order kinetics, then the kb values produced by equation (44) are functions of both bulk-phase mass transport and microbial kinetics. To be applicable for other substrates and other streambed biofilm systems, the k b values calculated by equation (44) should be corrected for any kinetic contributions, so that they are only a function of bulk-phase mass transport. The degree to which the kb values calculated by equation (44) should be corrected to account for differences between mixed second-order kinetics and Monod kinetics was assessed by recalculating the experimental values of q~20and kb with the variableorder biofilm kinetic model (Rittmann and McCarty,

qmaxXf Sf

Ks + ~

= 0

(45)

in which qmax is the maximum specific rate of substrate utilization (rags mg~-~ h - l ) , Ks is the Monod half-velocity coefficient (mg, cm -3) and the other parameters are as defined in equation (9). When the streambed biofilms were assumed to have a K~ of 1 mgs 1- ~, the variable-order model calculated k b values that were, on the average, 25% less than the values calculated by the first-order flux model (Table l). As the assumed K~ values for the streambed biofilms increased, there was closer agreement between the kb values calculated by the two models. For example, if the assumed k~ value was l0 rags l - J, the variable-order model calculated kb values that were, on the average, 15% less than the kb values calculated by the first-order flux model. Since the experimental results all exhibited first-order COD removal rates and provided no independent data to estimate the actual K~, the degree to which k b might be overestimated (if any) cannot be ascertained. Nevertheless, the sensitivity of k~ to changes in Re as described by equation (44) still are accurate. Stream water quality modeling

In calculating K r for use in a stream-water-quality model [equation (l 7)], equation (44) can be used to describe the apparent, overall mass-transport coefficients (kb) for rocky streambeds that are free of sand (upper two layers) and have particle diameters within the range of the gravel and cobble experiments. The other parameters needed to calculate K r can be obtained via the procedures presented in Gantzer et al. (1988). Because equation (44) was developed based on the shear velocity (u~) values instead of average stream velocity (u) values, it is applicable to a wide range of rock-lined streams. However, because water velocity can also have long-term effects on the accumulation of streambed-biofilm biomass (demonstrated in a subsequent paper), field application of equation (44) should be limited to streams in which the biofilm community is acclimated to shear velocities approximately equal to the acclimation velocities used in the gravel and cobble experiments (us= 2.5 and u~ = 2.2 cm s J, respectively). CONCLUSIONS

Based on experiments performed on sand-free gravel and cobble streambeds that were 1.5-2 particles thick, a mass transfer equation [equation (44)] was developed to describe the sensitivity of substrate removal rates by streambed biofilms to short-term changes in water velocity. The rates of COD removal

Mass transport to streambed biofilms by the streambed biofilms were much more sensitive to water velocity changes than would be predicted by the mass transport of materials from the water column to the external surfaces of the streambed. This greater sensitivity to flow velocity was indicated by the Reynolds number in the equation (44) being raised to the 4.33 power, which was considerably larger than the 0.5 value used by N o v o t n y (1969) for mass transport to the external surfaces alone. Because equation (44) included the mass transport o f materials from the water column to the interstitial surfaces of a streambed, as well as the external surfaces, the larger exponent reflected the complex hydraulic conditions found within porous streambeds. Equation (44) allows the incorporation of biofilm kinetics into water quality models for rocklined streams with porous streambeds (sand-free for 1.5-2 rock layers) that have been acclimated to conditions similar to those presented in this study.

Acknowledgement--This study was supported in part by a grant from the University of Illinois Water Resources Center, Project Number S-098-ILL.

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