Towards a better understanding of high rate biological film flow reactor theory

Water Research Pergamon Press 1973. Vol. 7, pp. 1561-1588. Printed in Great Britain

T O W A R D S A BETTER U N D E R S T A N D I N G OF H I G H RATE BIOLOGICAL FILM FLOW REACTOR T H E O R Y JOHN ROBERTS University of Newcastle, Department of Chemical Engineering, New South Wales, Australia

(Received 9 April 1973) Abatract--On the assumption that performance of biological film flow reactors is independent of oxygen transfer, a theoretical extension of a mathematical model (after Ames) is described. This predictive and interpretive model incorporates both mass transfer-limitations between biomass and liquid film, and kinetic biological reaction rate of organic "food" utilization. Given general boundary conditions for the differential equations describing the mass transfer process, it is shown that: C, = C, + (Cl -- C,).exp(--Km D/Q) where by definition: C, = a C~ + C,

IlK, = I/KLAv + a/Kx. For an influent concentration biochemical oxygen demand (C~) and resultant effluent concentration (6",) obtained during film flow through a packed media depth (D), the Model proposes that the residual concentration (C,) is a function of surface irrigation rate (Q) and biomass activity. If this term is negative, adsorption occurs; while if positive, desorption from the biomass film at concentration (Cs) takes place. An overall mass transfer coefficient (K,) is defined by a series equation where the usual mass transfer coefficient (KD is primarily a function of Reynolds Number [surface irrigation rate (Q) and specific surface area (,'Iv)I, Sehmidt Number (diffusivity of organic "Food") and concentration. "Food" utilization at active sites on the biological film is governed by a specific adsorption coefficient (a) and explained by a Langmuir analogy. Biological conversion of "food" is described by a kinetic rate constant (K), while the necessary oxygen is defined by (X). This predictive model was developed from a wide range of pilot plant data, successfully tested further on a variety of published results and on actual full scale operating plants. Parameters derived from this Model, in terms of Height of Transfer Unit and Kinetic Reaction coefficient, characterize organic "treatability" for a variety of wastes.

Au

C D G h k kL

k. K

KL

K. m n

N

NOTATION Specific surface area of packing Concentration Depth of packing Liquid phase diffusion coefficient Liquid film turbulent shear or velocity gradient Holdup per unit volume Specific activated adsorption rate Volumetric reaction rate coefficient Surface reaction rate cx)ct~ient Quasi-first order biological rate constant Liquid pha~ film mass transfer coefficient Ovexall mass transfer coef~ient Experimental coefficient Experimental coei~ient Recycle ratio 1561

(L-t) (ML- 5) (L) (L2T - ') (T- ~) (ML -3) (T- t) (T- ') (LT- ~) (T-~) (ML-2 T - t ) (ML-3 T - t ) (--)

1562 N'~, N,, a R S t

T U

V t.o

X o,

v

P Scripts

e i L r s *

JOH~ ROBERTS Modified Reynolds Number Liquid phase Schmidt Number Hydraulic irrigation rate Kinetic reaction parameter Total active surface area Time Temperature Dimensionless distance Packed volume Volumetric flow rate Dimensionless distance Dissolved oxygen concentration Specific adsorption coefficient Distribution coefficient between liquid and biomass Liquid film thickness Packing void space Surface fraction covered with adsorbed food molecules Streeter-Phelps temperature coefficient Liquid viscosity Unit rate of desorption Kinematic viscosity Buckingham pi Liquid density

(-) (-) (ML-2 T-t) (-) (L2) IT) (:C) (- ) (L 3)

(L3 T- t) (-) (ML- 3) (-) (-) (L) (-) (-) (-) (NIL- t T- t) (T- ~) (L2 T-~) (--) (NIL- 3)

Effluent Influent Liquid Residual portion of influent organic "feed" Surface Liquid-biomass interface

INTRODUCTION THE TRICKLING filter has become one of the most widely used secondary treatment processes for liquid organic wastes. It is also one o f the oldest engineered biological waste treatment systems. Low rate filters were first used in the late 1800s in Europe and North America. U.S.A. experimental filters were first constructed at Lawrence Experimental Station, Massachusetts, in 1889 and in Madison, Wisconsin in 1901. Low-rate trickling filters have been extensively investigated and general theories proposed to explain their operation. Since the early 1950s modification o f conventional trickling filter construction and operation have shown much promise in overcoming many of the inherent disadvantages of rock-packed media. High-rate trickling filters or "biological film-flow reactors" have provided a fertile area of fundamental and applied research into their mode of operation. Although many models have been proposed to describe the efficiency of removal of Biochemical Oxygen Demand (BOD), as yet a wholly satisfactory model has not been developed. There still remains a large gap in current knowledge regarding the true effect of temperature, hydraulic and organic loadings or loading intensity, mass and type of biological life within high rate filters, transfer and absorption of oxygen and " f o o d " material, together with contact time between suspended/soluble organics and filter biomass. An historical outline of existing correlations and mathematical models, following, shows the development in thinking towards a better understanding of variables which affect trickling filter performance. Where possible, relationships are expressed in the same form so that direct comparisons of appropriate variables can be made.

High Rate Biological Film Flow Reactor Theory

1563

DEVELOPMENTS IN T H I N K I N G

D t m e ~ , in 1900, assumed that complete oxidation of the organic matter could not simply occur in a short passage through the filter. Therefore, Dtme~a~ stated (1928): (1) suspended matter is removed by the attraction of the media; (2) dissolved matter is absorbed by the slime on the media; (3) the matter thus held by the slime is chemically as well as biologically oxidized and the end products are washed out of the filter by the passing sewage; (4)',the absorptive process is sustained by aerobic microorganisms; (5) there is a residue left in the filter that accumulates and is resistant to further degradation. Since this early beginning, many attempts have been made to relate performance to process variables. TABLE I shows in summary, many relationships describing performance. Particular note is made of the effluent designated and the definition used for the equation coefficient. TABLE 1

Relationships describing tricklefilter performance NATIONAL RESEARCH COUNCIL U.S.A. (1946)

( W~ °'s

c.

o.o561

C'~ = I

+ 0-0561(~F) °',

(I)

where C, = effluentB O D (mg I-i) from the secondary settlingtank C~ = raw influentB O D (mg l-I) W ----applied organic loading in pounds of B O D d- t of settledwastewater at 20oc -_ V = volume of filter medium in 1000's ft 3 F = recirculation factor and I+N F= (2) [I + (l - - j ) iV] 2 N = recirculation ratio equal to the ratio of recireulation flow to plant influent flow IN = (R]I)] i= weighing factor, usually assumed to be equal to 0.90 which recognized the change in character of the wastewater during treatment, or a decrease in "treatability". The analysis of performance data of individual plants indicates that j will range from 0.81 and 0-95 with an average of 0"90. An equation proposed for a second stage treatment was:

[

w

]o,

C,t 0"0561 LVF(CJCt)J -C, = 1 + 0.0561 !" W ]o.s

vF(-CJc,)J where C,: = effluent BOD (mg 1-:) from the final settling tank.

(3)

1564 VELZ

Joreq ROBERTS

(1948) c~ = 0 " 7 8 1 0 -'~:o° Cl

-

(4)

where D = filter depth (It) Ce = final clarifier effluent K2o = removal rate constant (=0.15). Velz postulated that: "The rate of extraction of organic matter per interval of depth of a biological bed is proportional to the remaining concentration of organic matter, measured in terms of its removability." The effect of temperature was allowed for by: Kr = K_,o.(I'047) r - ' ° . GEBER (1954)

c,

= 0-0161

__Q_Q+

K2oD

0"069

(5)

and

KT = K2o. (1"047) T- 2o

(6)

where K2o = BOD reaction rate constant @ 20°C in units of d a y - I KT = rate constant at any temperature (T) Q = hydraulic irrigation rate mgd (Imp). FAIRALL (1956)

c,

(

Q ~o.39o

C-]---- 1-244 V(1 +

N)]

(7)

where C, ---- effluent BOD from the secondary settling tank Q --- volume flow of raw sawage mgd (Imp) V = volume of filter media (× 1000's) ft 3. SCHULZE (1957, 60) C,_ =

10_o.2~6,/Qo.,,

(8)

C, where C, = effluent BOD from secondary settling tank Q = hydraulic irrigation rate mgd (Imp). The coefficient (0.266) was assumed to be dependent on temperature, active surface per unit volume and degree of treatability or biodegradability. HOWLAND (1953, 58, 60) C_., _ exp (-C,

KuoD (1 + N)÷/Q~) and Kr = K2o (1 "035) r-2°

where K = first order reaction constant N = recycle ratio which affects liquid film thickness.

(9)

High Rate BiologicalFilm Flow Reactor Theory

ECI~LDER

1565

(1961) C,

-- = c, I+N.

I

I+2.283

D ~7\

(10)

0. , ) _ u

where C. = effluent BOD from the filter alone Q = hydraulic irrigation rate mgd (Imp). The coefficient (2-283) for domestic sewage can vary, dependent on the active surface area of biomass, type of waste and temperature. Eckenfelder states that BOD removal is probably not a first order reaction but a retardant form of a first order reaction. He suggests that as the time of contact progresses the more readily treatable BOD is already removed and a so-called reduction on "treatability" of BOD remaining occurs; therefore, the first order reaction is retarded to the form: C, Ct

1/(1 -k- CtDl-"] Q-~ /"

It becomes more obvious that this is a retardant form of: exp (-- C 1D 1- .,/Q.) if it is expanded to: exp(--

C1DX-"/Q ") = exp( -- x) ---

1 1 -F x -F (x2/2) q- (xa/3) + . . .

and the first two figures of the denominator are only considered. GALL~R and GOTAAS(1964) as modified by BLAIN (1965)

C, C,

0"878 G °'31 QO.11 {I -F N)°'aST°'SVD°'6s

(II)

where Ct, (7, = influent,finaleffluentB O D (rag I- i) of domestic sewage Q = mgd (Imp) T = degrees Celcius. G ~ M A I N (1966)

c.

C--~= exp (--

O'090D/Q °'')

(12)

where C, = final effluent after secondary settlement of domestic sewage Q = mgd (Imp). The coefficient (0.090) was termed a treatability factor HAMMAM(1968)

C, 0"07 W°'s. CL°'12(37 -- 2")°'ss (I + N) C--~= D 1"°' (2 + N) 2 where C,, 6", = influent, final effluent BOD (rag I-1) of domestic sewage W = organic surface loading (kg BOD m - " day -1) D = depth (m).

(13)

1566

JOHN ROBERts

BALAKRISHNANet al. (1969) and GRO.~IIECet al. (1970, 72) Ce

C,

exp(-- KD/Q") (i + N) -- N.exp(-- KD/Q")"

(14)

Evaluated Eckenfelder-type parameters (K.n) for a wide variety of modular and random packings, treating domestic sewage. It was also shown that the rate coefficient (K) increased with increase in specific surface area of packing media; a result verified by BRUCE (1970). THEORETICAL CONSIDERATIONS A theory, presented in MCKINNEY'S book (1962) states that filter performance is based on the rate of oxygen transfer from the atmosphere to the sewage as well as on the rate of organic removal. It was theorized that the moving liquid film mixes with the fixed liquid film as it passes. If the concentration of organic matter is less in the fixed layer, removal will occur. Therefore, a high concentration of organic matter in the wastes is beneficial by insuring a steep concentration gradient. McKinney suggests that the concentration of organisms is far greater than the concentration of organic food, therefore, the organic matter is quickly oxidized before the next surge of sewage passes. It was further assumed that the removal of organic matter or BOD reduction is a function of the microorganisms present, the organic concentration applied, the biological slime surface area, the time of contact between sewage and slime, and the temperature. AMEs (1962) presented a mathematical model of a trickling filter based onhtypotheses that are similar in character to those that occur in chemical engineering reatment of packed beds. The BOD component was assumed to be transferred from the liquid phase to the solid phase by some mechanism of transport that was thought to be absorption. First order kinetics were used to describe the biochemical reactions that take place in the surface layer of the slime. A set of simultaneous partial differential equations describing the transient operation of the trickling filter were formulated and solved. These material balance equations were also based on the assumption of a linear equilibrium relation between the mole fraction of BOD in the liquid-solid interface and the mole fraction of BOD in the solid. AMAOO (1964) further extended this work in rearranging the form of differential equation solution to incorporate by definition, an overall mass transfer coefficient, i.e. Ce = 6", -- (C, -- Cr) exp (--K,.D/Q)

(15)

where K,. = overall mass transfer coefficient. ATKINSON (1963) described the model of the trickling filter based on the following assumptions: (a) The process is at steady state. (b) The rate of reaction is sufficiently slow that it is the limiting factor, i.e. the concentration gradients of both " f o o d " and oxygen are zero. (c) The process may be described by first order irreversible reaction kinetics of the form A ~ B where B is an acceptable product. (d) Both components A and B are soluble in the carrier liquid.

High Rate BiologicalFilm Flow Reactor Theory

1567

(e) The reaction occurs at the liquid-solid interfaces throughout the liquid film as though the liquid was flowing through a spongy mass, and (f) the liquid film thickness is not influenced by the presence of the microbial population. SWlLLEY (1963) considered an inclined plate model of the trickling falter from the point of view of the transport phenomena which involved the heterogeneous reaction at the interface between bacterial film and a flowing liquid film. Surface reaction models which included a reaction controlled heterogeneous model and a diffusioncontrolled surface reaction model with and without mixing were proposed. In these models oxygen transfer through the flowing film was not limiting and the availability of "food" at the reaction surface was the controlling factor. In the reaction-controlled model the diffusional resistance was assumed to be negligible. In the diffusion-controlled model, the rate of removal and oxidation of substrate was considered to be sufficiently fast that the diffusional resistance within the liquid film becomes important. All these models assumed independence efficiency and organic loading. MAIER (1966) and MAIER et al. (1967) simulated the trickling filter process by an inclined flat surface covered with a biological slime. A theoretical description of this physical model was developed, assuming mass transfer and the rate of growth of micro-organisms to be the main factors affecting purification. A mass balance is taken over the control surface, on the assumption that no growth occurs in the liquid film, i.e. all metabolic activity takes place in the slime layer. Using glucose as the sole food source under laminar flow conditions, studies on the effect of feed rate, glucose concentration and temperature, show that mass transfer of biodegradable material is rate limiting. GULEVICH(1967) examined the rate of uptake of nutrients by micro-organisms on a rotating disc with respect to the external velocity field, since this system could be represented mathematically as the simplest surface for mass transfer. Experiments in the laminar flow range, with glucose as nutrient, showed that the overall biological uptake rate was of the same order of magnitude as the theoretical diffusional mass transfer rate to the biological surface. This implies that the biological reaction rate may not be the controlling factor within the range studied. Another similar theory is presented in Fair, GEYER and OKUN'S book (1968). The theory states that the major operation is the transfer of organic waste from the sewage to the slime by adsorption and absorption. The process proceeds at a faster rate as the interfacial area increases and as the concentration gradient across the sewage-slime interface becomes steeper. ATKINSON,DAOUD and WILLIAMS(1968) developed a theory for the biological film reactor which allowed prediction of performance on the basis of physical and biological variables. The model incorporated diffusion in both the liquid and active biomass phases, following on from the work of ATKINSON(1963, 1967). A similar differential equation to SW1LLEa' (1963) was used but with modified boundary conditions, allowing for the reaction rate at the interface between the liquid and biological active surface. This new model purports the physical situation in the biological film based on diffusion with heterogeneous chemical reaction. When the active film thickness is small, the controlling factor is that of chemical reaction.

1568

JoHN ROBERTS

KEHRBERGER and BUSCH (1969) summarize results of a theoretical analysis of the effect of recirculation on removal of total soluble organic carbon from film flow reactors. Three film flow models are discussed for the case where the biochemical reaction occurring in the reactor can be represented by consecutive first order reactions. The general heterogeneous model assumes no micro-organisms in the liquid phase with biochemical reaction occurring only at the liquid microbial mass interface. Organic compounds are transported by liquid film movement and diffusion into the active biomass. Partial differential equations with variable coefficients are coupled with boundary conditions and solved by computer finite difference methods. The reaction control model is a limiting case of the general heterogeneous model, above. It is assumed that the reaction rate at the active biomass surface is the controlling mechanism. First order ordinary differential equations, on intregation yield C'--~= exp

(16)

+ N) Q

where ks, = surface reaction rate coefficient. Both the heterogeneous and reaction control models depict a decrease in removal efficiency with increase in recirculation ratio. A film flow system for a pseudo homogeneous model, in which liquid entering the reactor, flows through or contains the microbial mass and reacts at all points in the liquid phase, is described by

ce

(-- k, Aoa D]

C--~---- exp \ ( 1 + ' ~ - Q

/

(17)

where kL = volumetric reaction rate coefficient 8 = liquid film thickness. The essential difference between this homogeneous model and the two former models is the dependence of effluent concentration on liquid film thickness. Because the biochemical reaction occurs throughout the liquid phase, an increase in film thickness has a significant effect on overall efficiency. Thus an increase in recycle ratio, increases the resident liquid volume and therefore film thickness, and increases removal efficiency. MONADJEMI and BEHN (1970) developed a model mechanism of substrate purification in a trickling filter, with the following assumptions: (a) Liquid flow over individual surface elements is laminar, with molecular diffusion being the mode of mass transfer (b) Mixing occurs at point of each element. (c) Available active surface slime film is constant on each element. (d) The biochemical oxidation is not rate determining. (e) The substrate is a single soluble compound. The functional form of the developed mathematical expression is similar to that of SWILLEY(1963). From a variety of laboratory experiments it was found that the removal rate coefficient reflects two aspects; the first is the type and quality of microorganisms responsible for substrate transfer to their active surface, the second is the type and quality ofsubstrate and the ease with which it can be adsorbed. Also, within

High Rate BiologicalFilm Flow Reactor Theory

1569

experimental limitations, mass transfer was the controlling mechanism which could be enhanced by surface discontinuities. LAMB (1970) developed a simple model of a mature high rate trickle filter which incorporated the usual engineering process parameters. C~=

(18)

1+

VA.] = 1/(1 + KQ!

(19)

where K = quasi-rate coefficient ( T L - 1 ) Q = volume flow rate ( L 3 T - 1) V = packed bed volume (L3). This equation excluded packed depth and irrigation rate (involving cross section area) from its development. The author extracted literature data and attempted to show agreement with this proposed equation. Actual correlation is poor, with the parameter (K) being a function of packing media, substrate type and irrigation rate. KEHRBERGER and BUSCH (1971) further extended their theoretical work noted previously, with experimental results. Mass transfer effects on removal of total soluble organic carbon down an inclined plate with glucose as primary substrate was studied. Reynold's numbers ranged between 9 and 125 for the liquid film with no rippling. Their experimental study showed that liquid phase mass transfer of substrate and organic intermediates are the controlling variables. Also, these mass transfer effects can result in decreased effectiveness of the biological process of a trickle filter. The build up of intermediates was suggested to have been due to oxygen rate limitations. Enhanced mass transport may occur over modular type packing media due to internal mixing at surface discontinuities. ATKINSONand WILLIAIVIS(1971) used the theoretical developments of ATKINSONel al. (1968) to hypothesize the performance of the pilot plant trickle filter described previously (I 967). It was suggested that efficiency was influenced by hold up of microbial mass within the filter. Performance of a filter was found to be independent of oxygen transfer but influenced by diffusional limitations in both the microbial and liquid films. The general model also allowed for biological rate in the microbial kinetics. Inherent coefficients and functional form are not know a priori. The problem has to be approached by efficiency asymptotes at low and high substrate concentrations. A computer iteration sequence is involved in the general solution since the coefficients are partially dependant upon mean interfacial substrate concentration. Prediction was reasonable at low concentrations but inaccurate at high substrate concentrations. TU~EK et al. (1971) developed dimensional equations for plug flow activated sludge and by analogy for trickle filter processes. The following dimensionless numbers were introduced for the latter: C! ~ Ce. =1 =

Ct

'

=2 = k D / Q

and

~'t = f(~2).

Using early stone media results the functional form was described by:

1570

Jom~ ROSERTS 7-r 2 ,/71 ~

a +

b~- 2

and the coefficient [a] defined to be:

a=m.~

Ct

+n.

with m, n being experimental coefficients. These equations can then be rearranged to become ~rl = 1/ 1 + ~r2A~+

for b = 1

which on substitution of the original variables becomes C,

1

C,

1 + [kD/Q(mC,/A~ + n)]

(20)

This equation (20) is quite similar to Eckenfelder's retardant equation (10) and Lamb's derivation, equation (19). BRowN (1971) suggests that the factors which affect the transfer rate are: (1) The concentration of organic matter in the liquid. (2) The time the liquid is in contact with the slime. (3) The degree of turbulence in the liquid. The resulting expression is of the familiar first order form:

--dc = KoCG dt where G = the internal shear within the liquid which is directly related to turbulence Ko = constant upon integrating: C, -- = exp (--KoGt). C, A general relationship was developed for the variable (G, t) as functions of depth, surface area and hydraulic surface loading. Substitution into the above equation yields the trickling filter model expression for laminar flow: C,

=

KLAo÷D]

exp

C, _ exp {-- 5 D A ° ' ~ Ct

\

Qk/zk

]

(21) (22)

where KL., = laminar or turbulent functional coefficients, dependent on Q. Brown suggests that recirculation acts as a dilution of the filter influent. As with many of the other trickling filter models proposed in the past, Brown's equation or the U N C Wastewater Research model implies that BOD removal is independent of the organic loading, but dependent on the hydraulic loading and resultant turbulence.

High Rate Biological Film Flow Reactor Theory

1571

MEHTA, DAVISand KINGSBURY(1972) considered biodegradation of organic wastes to be made up by three simultaneous activities:

(1) The transfer of oxygen from the gas phase to and through the liquid to the bacterial sites on the media surface. (2) Transfer of organic compounds from the liquid phase to the bacterial sites. (3) The kinetics of the biochemical reaction in the active biomass. The authors postulated that the controlling mechanisms to be that of oxygen mass transfer. Forced convection mass transfer of oxygen into the falling liquid film was described by a model similar to MONADJEMIand BErrt~ (1970). A design expression is then developed for prediction of BOD reduction from known systems physical properties and process parameters. The authors note in their conclusion that in some situations, mass transfer of "food" may be the rate limiting step. LITERATURE EVALUATION

The broad objective of the above historical review was to analyse trickling falter models in an attempt to highlight the understanding at various periods in time. TABLE2 presents some of the stepping-stones in developing a more theoretical approach to the study of trickling filters. From this brief summary it is hoped that a better insight will be gained into the controlling factors which define the capabilities and limitations of this process. As noted in TABLE 1, many of the relationships describe overall performance including the secondary settling tank. Because of the residence time within this tank, some BOD, usually between 10 and 20 per cent of the influent load, is subsequently removed. The actual performance and behaviour of the filter alone is then disguised by the characteristics of the settling tank. Real cause and effect relationships due to temperature, flow rate, organic loading, for example are clouded. Most of the relationships describing performance are modifications of the theory presented by VELZ (1948), which assumed that the rate of BOD removal at specific depths of packing media can be represented by a first order reaction, in a plug flow reactor. SCHULZ~. (1957) made a major contribution in setting down the criteria governing trickle filter performance by (a) the amount of active biomass film per unit filter volume, and ~'b) the contact time between the substrate food and this film. This contact time is best described by the depth of filter and hydraulic characteristic of the packing media in terms of irrigation rate and liquid holdup; the amount of active film being dependent upon free surface of media available and the supply of food and oxygen. Recent research suggests that this active film has a maximum aerobic depth and that the amount of biomass can vary with applied hydraulic loading and characteristics of substrate. The quantity and activity of biomass may also vary with media depth for a complex substrate food source. AMES(1962), SWILLEr(1963) and subsequently Atkinson et al. in a series of publications used the chemical engineering science approach in allowing for diffusional mass transfer of food into the surface layer of biomass. As pointed out by Ames, factors involved should include basic mechanisms and kinetics, the role of residence times, possible departure from plug flow by longitudinal mixing and short circuiting and influence of mass balances on the differential model characterizing performance.

Bl~uCt and MEaKBNS MImTA et aL l e t BUCKFIdtTLgIGH

Vm.z Gm~dt SO~LZ~ EOI~NFELDER SWILLtV AJkIADO GAI.LtP. and GOTAAS M M n et al. ATICINdlONet aL A r r J m o N and DAOUD ~ l C and IMiALINA MOt~DII~I and B ~ N

Reaearcher(s)

1948 1954 1957°60 1961 1963 1963 1964 1967 1968,71 1967,70 1970 1970 1970 1973 1972 1972

Year

32'0 29"2 27.5 62.5 3! ' 0 158.0 24.0 34.7 30"0 65-0 188"0

16-7 13"7 25 '0 233"0

mgad

kg m -2 h - *

gal y d - 3 day-1

0"27 780 1750 0'22 641 1180 0"40 1170 2560 3"8 10,900 8025 Theoretical model 50 < N~, < 900 0"51 1500 2480 0-46 i 365 2235 0.43 1290 -1.0 2930 19,400 0"49 145 ! 2"51 7395 46"50 0-38 1120 3300 0-55 1620 4000 0-48 1408 2710 1.04 3040 2500 3.00 8807 6480

gal ft -2 m i n - ~

27.6 19.6 23-8 16' I 14-8 38-5

115.0

14'7 13"3

10.4 6'9 15"2 47"0

m -3 m -a day -~

TABLE 2. MAXIMUM LIQUID LOADING CONSIDERED IN IMPERIAL AND S I

Study

BOD experiments--l.5 in. packed spheres Regression analysis o f plant data Glucose breakdown on inclined llat plate Glucose breakdown using packed 2 in. spheres Glucose breakdown on inclined flat plate Surfpac pilot plant Glucose using packed 2 in. spheres Various modular packings Various random and modular packings Various modular packings Flocor pilot units--domestic-itldustrlal sewage

Simple experiments using rock packing Simple experiments using rock I - I . 5 in. BOD experinlents on vertica| screens Regression analysis o f plant data

UNITS

O

"r'

High Rate Biological Film Flow Reactor Theory

1573

Ames and Atkinson et al. also allowed for biochemical reaction at the active film surface in conjunction with mass transfer. All these models state that the overall process is independent of oxygen concentration and transfer in so far as the process describes "food" exchange, not oxygen transfer, between the liquid and active film surface. A major difficulty in using the simple model of Velz or that developed by ECKEN~LDER (1961) and further extended by others, is in the definition of the rate constant (K). GROMIEC et al. (1972) clearly point out that the so-called rate constant (K2o) is dependent upon the units of flow rate, depths and whether with reference to the logarithmic base [e] or 10. Note has been made in the TABLE 1 summary of particular definitions describing this parameter (K2o). It can be seen that as early as 1946, the NRC Committee considered some change in treatability of the waste material on passing through a unit. Subsequently, Schulze and most other workers who introduced a (K2o) parameter into their particular equation, called it a coefficient, not a constant. This coefficient was then considered to vary with temperature, active surface area of biomass per unit volume and type of waste, that is, its biodegradability or "treatability". Velz' rate constant could then be placed by an overall mass transfer coefficient which is primarily a function of Reynolds' number (surface irrigation rate) and Schmidt's number (diffusivity of food). Biological conversion of food would be described by a kinetic rate term, for simplicity first order, because of mathematical convenience and interpretation of BOD rate-time data. It is apparent that the theoretical aspects of high rate trickling filters have not progressed to the point where the design engineer can dimension a tower for given waste and predict in advance the results to be expected. The number of real process variables and their interrelationships have complicated the development of a complete fundamental theory. Any general model put forward to describe the process should include such variables as irrigation rate (flow per unit cross-sectional area), depth of packing media, characteristics of media (specific surface area, orientation), liquid temperature, food characteristics of broadly "treatability", and possible organic loading. Once the interaction of these parameters has been determined, the general model should then explain and predict satisfactorily a number of previously unexplained anomalies. These include: (1) Why the relationship between efficiency and BOD load or concentration is a curve and not independent of load or concentration; (2) Why a new filter does not perform as efficiently as a conditioned or "mature" one; (3) Why stage efficiency of a series combination of filters may decrease; (4) Why the effect of temperature is much less than that expected for a biological rate process; (5) Why either heavy metal ions or gross high food concentration markedly decrease filter performance for a time. The later models noted above became much more sophisticated, requiring iterative computer solution to complex simultaneous differential equations. Interpretation and cause-and-effect relationships have become extremely difficult to understand or predict. Of the models noted here, the one which simply and directly can develop w.!~. 7 / 1 1 ~ D

1574

JOHN ROBERTS

this understanding without recourse to a computer is that of Ames. On the assumption that film flow reactor performance is independent of oxygen transfer, the Ames approach incorporates both mass transfer limitations between active bacteria and liquid film and biological kinetic reaction rate of food utilization on the active bios surface. DESCRIPTION

OF

MATHEMATICAL

MODEL

AFTER

AMES

The development of this model was based on certain hypotheses, resulting from theoretical considerations of film flow reactor operation. This hypothetical reactor consists of a cylinder filled with an oriented or random packing covered with a biological slime (bios). Influent solute organic "food" having a Biochemical Oxygen Demand (BOD) flows downward through the column, with the liquid and bios exchanging material. BOD is transferred from the liquid to the slime layer by some adsorption process. A continuous biochemical reaction occurs on the bios surface and an equilibrium exists between BOD in the solid phase and BOD in the solidliquid interface. Differential material balances of the adsorpable "food" component in the liquid and bios are produced which result in a set of simultaneous partial differential equations. Ames' original work is summarized below: dC In the Bulk Liquid phase -- ~p ~zz

dc Kt.A~ (C-C*) = hr. ~ .

In the Active Biomass phase -- K. C,. X + Kt.Ao (C-C*) = h,

(23)

dC~

(24)

and C* -----a C, + C,

(25)

by analogy with gaseous adsorption as a linear equilibrium relationship for a first approximation. Utilizing equation (25), equations (23) and (24) are re-arranged into: d_c =

dt

_

~

. d_c _

hL dz

KLAo

. (C-C*)

(26)

hr.

and dc* dt

KLA~ (C-C*) -- K X (C*-C,).

(27)

These equations (26) and (27) are transformed by using dimensionless variables into dc

--

(28)

(C-C*)

du and

dc*

_

(c-c*)

dw

-

KX

. fC*-C,)

(29)

aKt.Ao

where u =

KL,4.Z/~

(30)

High Rate Biological Film How Reactor Theory

w =

h--"~- "

1575

@/

By definition, one "transfer Unit" is (~t,/Kt.Av) and the kinetic reaction parameter is

(,Using Laplace transforms on equations (28) and (29) a unique solution can be obtained which rearranged into original variables, becomes:

C, + (C,- C,).exp (.__-qR .

KLAoDI.

(32)

\/~+1 From the limit of D ~ o o , equation (32), becomes Ce ~ C, that is C, may be interpreted as the non-degradable fraction of "food" whilst (C,I-C,) may be considered the degraded and assimilated fraction of "food" presented to the biological film by the flowing liquid. The complete bracketed exponential term can be rearranged into the following form by substitution for R, above so that an overall mass transfer coefficient need be defined as 1

K,,,

--

1

KLAo

+

a

K. X

(33)

i.e. (overall) = (mass film transfer) + (kinetic) terms contained within the exponential term exp(--K,D[Q). Equation (32) can now be re-written as

Ce = C, + (CcC,) exp [(--/i'm D/Q)].

(34)

Ames derived the mathematical equation (32) and Amado equation (33), but no published data have appeared as to its application in using the series term equation (33) or its interpretation. Prior information is lacking as to the effect of flow rate and temperature on liquid phase film mass transfer coefficient or on the magnitude of the individual parameters contained within the kinetic term. AN I N T E R P R E T A T I V E T H E O R E T I C A L EXTENSION

Equation (34) is identical in form to : c, = a + bG

(35)

C, = 6", [1 -- exp (--K,. D/Q)] + exp[--K,,(D/a)]. C,.

(36)

if the equation is rearranged to:

Equation (35) can be rearranged to define fraction efficiency of a film flow reactor

1 -- C_,= 1 - - b - - a / C , . C,

(37)

If coefficient (a) in equation (37) is negative and (b) positive, a curved efficiency decrease with increase in concentration is described as is shown for full scale units by CmemmHt=LV (1968). For coefficient (a) to be negative, the parameter ((7,) must correspondingly be negative, that is, a state of adsorption onto the active

1576

Joan ROSERTS

biomass which may be a function of surface irrigation rate and bios activity. FACTORS I N F L U E N C I N G ADSORPTION Characterization of a particular biomass system may be given in terms of the nature and properties of three general components: the absorbant or food source, the adsorbent or biosphere of film and the solution carrying the food source. Three important properties of the adsorbent are (i) surface area (ii) actual site distribution and (iii) active film thickness: adsorption rate exhibiting an increase with decrease in biomass filament thickness. The rate of transfer is complicated by the complex mechanism of the process. A postulated mechanism could consist of the following steps: (1) Movement of the food from the bulk liquid phase to the surface of the biomass. (2) Movement of the food from the surface into the areas of active sites. (3) Activation of the food at these active sites. (4) Exchange of food and expiration products at these sites. (5) Movement of the expiration products from the active sites to the external surface of the biomass. (6) Movement of these products from the surface into the bulk liquid. Any one of the six steps may be a rate limiting factor. The rates for steps (3) and (4) can best be described by an overall kinetic rate term, whereas the rate for the movement of food and products may be described by the usual rate equations for counter mass transfer and an appropriate mass transfer coefficient need be defined. If the activation and exchange of material at the active sites is very fast compared to the mass transfer steps, then mass transfer considerations are of dominant importance such as surface area, concentration difference and liquid velocity. However, if the rate controlling step is activation and exchange of material at active sites then kinetic factors are dominant such as surface active sites--their number and size, temperature. One consequence of mass transfer controlling limitations is a relative decrease in mass transfer coefficient for a gross concentration difference. POSTULATED LANGMUIR TYPE ANALOGY OF BIOMASS ADSORPTION Consider unit area of biomass surface in contact with a single food source of concentration (C~). Let (0) be the fraction of surface covered with adsorbed food molecules, then (1 -- 0) is the remaining bare surface. Let the unit rate of desorption be (v) and that of adsorption (/~). Suppose a fraction (a) of these adsorbed food molecules are subsequently "activated" and then consumed by the biomass. This rate of disappearance of material over the surface not already covered is a/z(1 -- 0), while the rate of desportion is (vO). At equilibrium, this rate of disappearance will equal the rate of desorption. Thus ~(1 - - O)---- v 0

(38)

therefore a/~ --

vO 1--0

(39)

High Rate Biological Film Flow Reactor Theory.

1577

Further, let (~ tz) the rate of adsorption be proportional to the food source concentration (C~). Therefore, ~/~ = kCt where k = proportional constant (40). From equation (39) vO

kC, = i---~--~

(41)

or

kC, 1 1 ----v + kC, 1 + (v/k) C/

0= ~

(42)

Let us now redefine (k) as the "specific activated adsorption rate" with respect to the particular food source. Then the ratio (v/k) is the parameter which dictates the amount of food molecules that will be absorbed. In general then, the amount of food absorbed is greater the smaller the value of (v/k); either low rate of desorption, high specific activated adsorption rate or high concentration. Three other particular situations may be noted: Case 1 low Cv From equation (42) for C~ ~ 0; 0 = (k/v) C~. Thus the amount of food absorbed is proportional to the food concentration. Case 2 high C~. From equation (42) when C~ >> v/k; 0 ~ 1. That is, the amount of food absorbed is independent of concentration and v/k. Case 3 low v. When k >> v such that v/k ~ 0 the surface is nearly covered and the amount of vacant space available for further adsorption being (1 -- (9) tends to zero. From equation (42) l

--

0

~

V

v + kCi and for lowv,

1 -- 0 - - kCt" v

(43) (44)

This situation is important for describing the mode of action of nonbiodegradable materials which may be preferentially adsorbed at the available surface active sites as below. P R E F E R E N T I A L A D S O R P T I O N OF HEAVY M E T A L IONS OR N O N - F O O D

Consider the case of two species in the food source (v/k)~ and concentration Cl are with respect non-food such as strongly adsorbed heavy metal ions or foodlike material with similar adsorption properties to the food source but not biodegradable; (v/k)z and concentration C2 are with respect the food source. The fraction of surface not covered by the food species 1, available for further adsorption. 1

--

Oi

--

(v/k)~ C1

from equation (44) and this may be equated to the fraction of surface to be covered by adsorbed food species. Thus 1 -- O~ = 02 02 -

(v/k)~

Cl

=

C~

C2 + (v/k)z"

1578

JOHN ROBERTS

If C2, the biodegradable food concentration is low, 02 _ (v/k), _ C2 C, (dk)2

(45)

That is, the remaining unoccupied space available for biodegradable food to be adsorbed is inversely proportional to the non-food concentration and its rate of specific activated adsorption, either of which could be quite high. Rearranging equation (45) C1 Ca (v/k)2 = (v/k),"

(46)

The amount of biodegradable food that can be adsorbed, from equation (46) can be large only when (v/k)~ is relatively large and/or the product CIC2 is small. As a consequence Ct must be small. Conversely if (v/k), is small, with preferred adsorption of non-food and/or the product C~C2 is large, the amount of biodegradable food adsorbed will be small. FULL SCALE E X P E R I M E N T A L SUMMARY Since the autumn of 1964, Buckfastleigh, a small English village, has been the site of a multiple ICI pilot plant. These units have been used for the evaluation of "Flocor'" as an oriented packing and compared with various stone and synthetic random media. The plant has, at various times, consisted of up to 20 units, all about 1 1112. with packed depths between 1.21 and 5-48 m. Units have been irrigated with macerated crude sewage, settled effluent or other tower effluent, at rates that have ranged between 1"1 and 290 m 3 m - 2 day - ', over packings of specific surface area from 35 to 190 m 2 m - 3. Parameters that have been measured regularly on the feed and effluents are BOD, N H , , and NOn ions concentrations, together with local rainfall, air and sewage temperatures. Regression analyses on feed and effluent data have been computed for all units. Performances determined from these calculations have enabled the postulated model to be tested and particular parameters evaluated. To further compare the magnitude of these parameters, published data of BRucE (1972) and QUXRK (1972) have been utilized. One aspect of the overall development of this interpretive model is illustrated in the following section. Order o f magnitude o f model parameters For a particular organic waste [from BRUCE (1972)] individual terms of equation (33) have been evaluated by solving the overall mass transfer coefficient equation simultaneously at several temperatures and specific surface areas for constant depth TABLE 3. INDIVIDUAL PARAMETERS FOR SETTLED DOMESTIC SEWAGE AT 15°C

Oxygen concentration (X) Biological rate constant (K) Specific adsorption coefficients(a) Overall biological rate term (KX/a) Liquid film mass transfer coefficient(KD Height of transfer unit (Q = 500 kg m -2 h; Av = 85 m2 m -3) Kinetic reaction parameter (R)

(×10 -3 ) (×10 -3) (xlO -s) (HTU)

6"12 7-95 2"03 2397 1-97 3.00 14-4

kgm -3 h -z (--) kg m -3 h kg m -2 h m (--)

High Rate Biological Film Flow Reactor Theory

1579

and hydraulic loading. TABLE 3 shows one unique set of parameters at a hydraulic irrigation rate of 12 m a m - 2 d a y - i . TABLE 4 compares these parameters, evaluated for a variety of organic wastes [from Qtnr, K (1972)] highlighting the differences and trends with change in biological "treatability". TABLE 4. COMPARISONOF PARAMETERS F O R SEVERAL O R G A N I C W A S T E S

Basis, Q = 70-5 m 3 m -2 day at 20°C; Av = 89 m 2 m-a;

KX

Waste

X = 5"0 × 10-a kg m -a

K

a

a

KL

(h-t)

(-)

(kgm-~h)

(kgm-2h)

(m)

2-6 × 10-a 4-1 5"3 5-4 5.8 6.9

2550 1170 560 730 645 480

13"1 7.5 5.5 5.4 4"9 3.9

2.5 4.4 6.0 6.2 6-7 8-4

Ragmill 13.2 x 10-a Slaughterhouse 9"6 Kraft papermill 8-1 Whey-sewage 7-9 Boxboard mill 7.5 Canning 6"6

HTU

K.

R

(kgm-)h) (-) 800 425 298 290 260 201

2-2 1.75 1.55 1.5 1.45 1.4

It is immediately apparent that the chemical engineering approach can explain the trends in parameter values. The film mass transfer (KL) is primarily a function of Reynolds' N u m b e r (surface irrigation rate), Schmidt N u m b e r (diffusivity of organic "feed" molecules) and concentration differences between " f o o d " source (Ct) and bios surface (C,). Biological conversion of the degradable organic material is described by the kinetic rate constant (K), while the necessary dissolved oxygen in excess is described by (X). " F o o d " utilization is governed by a Langmuir type specific adsorption coefficient (a). This term can be affected by bios film ecology and maturity or preferred adsorption of non-degradable foodlike matter or heavy metal ions.

Summary of pilot plant performance Several consecutive years results were collated for a number of 1"83 m and 5.48 m Flocor units, operating at Buckfastleigh. TASL~ 5 lists the range of conditions applicable in the comparison. TABLE 5. RANGE OF OPERATING CONDITIONS

Packed depth 1.83 m 5.48 m Irrigation rate (Q)

Lowest 337 821 Highest 2250 8840 Common Feed BOD (CJ 50 to 700 with a mean of 230 mg 1- * Common Feed temperature 8-18 with a mean of 13"5°C Number of pilot units 5 5 Number of data pairs (C~.C,) 2700 3700

kgm-" h

Correlations were developed for mean performance, by using equation (34). The assumption made was that over the two year period, the term (C,) would be zero as

1580

JOHN ROBERTS

an average result. Using the following rearranged equation, correlation parameters were obtained. From equation (34), on rearrangement, became log[log(cC---~)/D ] = log A + (n + 1) l o g ( Q )

(47)

where K., ~ AQ".

(48)

The correlation coefficient obtained was (r = 0"87) and slope (n = 0.56 ± 0.055). An improved correlation could have been developed if a Streeter-Phelps temperature dependence had been incorporated into the original data comparison, and residual concentration (6",) allowed to vary with flow rate and biomass seasonal acclimatization. For average performance of these units, an equation of the form

Ce

- - ~ exp ( -- K,.D/Q) Ct

(49)

where Km ~- Ax/(Q) is proposed. This equation (49) is similar in form to the original equation of Eckenfelder, Germain, Gromiec and Balakrishnan et al. However, a completely different interpretation is placed on the overall coefficient (K.,), to their rate coefficient (K,). VARIATION

OF

LIQUID

PHASE MASS TRANSFER WITH FLOW RATE

COEFFICIENT

Many attempts have been made throughout the years to develop theoretical relationships in describing the functional behaviour of liquid phase mass transfer coefficients. The transfer of matter between liquid and film surface in a packed bed is one of the fundamental problems in unit operations. CARBE~a~V(1960) proposed that the boundary layer develops and collapses over a finite short distance. TAKESm et al. (1972) used a laminar regime model incorporating a developing velocity profile and mixing after each surface element for Schmidt Number greater than (1000) and Reynolds Number greater than (0.1). From TAKESHI(1972) jL' = (1---~') + • KrNSC÷Q/, -- l'85/NRe '÷.

(50)

From CARBERRY(1960) = 1.15/NR, '~

(51)

where for random packed beds or modular type packing, TREYBEr~(1955) defines NR,' -and

Q rAy(1 -- e)

(52)

High Rate Biological Film Flow Reactor Theory

(c,-c. t ~,c,-c,l

KL = -~ where

1581

(53)

S total active surface area V = mass flow rate C, = surface concentration of organic " f o o d " at the biomass. Experimental data from a variety of sources are shown by Takeshi et al. to closely follow equation (50) for (NR,' < I0) and equation (51) for (NR/ > 100). This implies that =

KL oc D~Q *

for

NRe' < I0

Kt, oc D÷Q*

for

Nae' > 100.

and

0"6 r \ \

"-'~

'

0"4~'~t,~ " ~ .

-:

0.2

,~

D

o oo.o,

~

-

0"04 I0

Y/)'////,~/~~ ..... Spread of Buckfa$lloigh data F--""T"'I , I i I iI I 20 30 40 60 80 I00 2.00 N'Re Modified Reynolds number,

log

t 300 400

scale

FiG. 1. FIGURE 1 shows the particular range of jL~ VS N~e' of interest as an extension and application to biological processes. The solid line represents the theoretical prediction after Carberry-Takeshi while the dashed upper and lower boundaries show the spread of experimental data for such systems as ~-naphthol-water; succinic acid-nbutyl-alcohol and benzoic acid-water. Superimposed on this graph are the range of results for Buckfastleigh Flocor pilot units for which Appendix 1 provides the details. The near match between organic " f o o d " mass transfer and organic dissolution mass transfer in terms of Reynolds and Schmidt Number variables is in excellent agreement. An independent check on the approximate value of liquid phase mass transfer coefficient can be made through equation (53), for example, at Q -- 1468 kg m -2 h - x and Ao = 88 m 2 m -3 for D = 5.48 m, V = 1230 kg h - l ; S = 404 m ' then from equation (53) KL -- 1230 In (C,-C,~

404

\C~-Cd

for

Ce_

C,

0.355.

1582

JOHN ROBERTS

If the log term is assumed equal to 1.036, implying (C~ -~ 0) then KL = 3.14 kg m h - 1 which compares favourably with a value of KL = 3-64 kg m - 2 h - ~ as determined in Appendix 1.

Magnit,~de of oxygen and organic mass transfer coefficients The main premise of this mass transfer model as described by equations (33 and 34) is the fact that oxygen transfer is very much faster than that for organic " f o o d " molecules from the liquid film into the actual biomass. To illustrate the relative magnitude of the liquid phase oxygen and liquid phase film mass transfer coefficients, two examples are given in Appendix 2. The calculations show at least an order of magnitude range between oxygen and organic " f o o d " mass transfer coefficients. Therefore, provided there is necessary oxygen in the thin liquid film, the controlling mechanism is that of organic molecule mass transfer into the active bios. This conclusion supports the statements of most recent researchers noted previously, excepting that of MEHTA et al. (1972).

Interpretive application of this model To illustrate the versatility of this interpretive model, several examples are cited below which gives an indication of its usefulness. Individual coetticients contained within equations (33 and 34) cannot at present be known a priori. There is a need to characterize different substrates and necessary active biomass in building up families o f individual parameters of which TABLES 3 and 4 are examples. 1. Eckenfelder-type reaction coefficient change with Av. It has been implied from most published work that the Eckenfelder-Schuize type reaction codficient incorporates specific surface area within its definition, see for example equations (8 and 14). Thus, C " ' - - e)x p ( -c- K 2 ,° - ~ and/('2o = k2o Avm, with m normally taken as unity. An attempt was made by BALAKRISHNANet al. (1969) to correlate Kao with specific surface area and applied load because of the non-linear trend in the above assumed relationship. A different explanation can be offered through the use of equations (33), (34) and (50). F r o m the data given in Balakrishnan for a flow rate of 47 kg m -2 h-1, independent values of liquid phase mass transfer coefficient (Kt3 can be determined and this approximated to an overall mass transfer coefficient (K~). TABLE 6 shows TABLE 6. CHANGEIN REACTIONCOEFFICIENTWITHSPECIFICSURFACEAREA Specific surface areaA~(m2m -a) 49-2 88-5

91-9 95"1 131 249

Film mass transfer Overallcoeff. K2o coeff. KL(kgm-ah-1) KMkg(m-ah -1) 0-275 0-359, 0"357 0"33, 0-395 0-31 0"46 0"55

0"55 0-90 0-91 0"94 1-17 1-79

21 45-4 46-7

Predicted /('2° 0-25 0"358 0"37

48-3

0-38

62"3 85-1

0.44 0"55

High Rate Biological Film Flow Reactor Theory

1583

the original data together with coefficients determined from equations (33), (34) and (50). A direct correlation exists between (K2o) and (K,,) values, resulting in predicted reaction coefficients being a close match to those published. 2. Predictive capability. Recent research by ATKXNSONet al. (1968, 1971) and MAXER et al. (1966, 1967) for example, offer sufficient data to test the proposed equations (33 and 34) and their predictive accuracy. In simultation of the trickling falter process, Maier et al. used an inclined flat plate covered with biomass. Glucose was used as a single food source in a mixed nutrient solution. Liquid feed rate markedly affected glucose removal in agreement with predictions assuming diffusion controlling limitations. Differential equations describing the process required numerical computer evaluation. Once appropriate coefficients were determined a predicted response could be made as shown in FIG. 2. Using full equation (34) with ((7,) a

@,,p,s *~" // ~c,

2

_

/ /

~9 0

Moieret ol experimental data Maler et al computer prediction Equ (33, :54) prediction

•

/ . . . . .

I

200

I

4 oo

I

600

I

800

I

I000

Liquid feed rate ml 10.4 rain

FIO. 2.

negative quantity, decreasing with increase in flow rate, values of overall mass transfer coefficient were determined. Having obtained the relationship between (K,, -- Q) equation (34) and smooth coefficients which used to predict the result as Maier et al. had done using complex computer arithmetic. The comparison is made in FIG. 2. This simpler method of attack does not require computer time and yet offers very close prediction to actual data points. A similar case in point is in using the information provided by ATKINSOSet al. (1968, 1971). Biological film reactor theory is developed which results in predicting performance on the basis of physical and biological variables, incorporating diffusion in both the liquid and "solid" phases. An iterative computer solution of the general problem is required with at least four flexible coefficients to be determined. For the case--effect of organism growth, in the publications noted, a more straight forward approach is as follows: consider the biological rate term (KX/a) in equation (33) to vary with time, commencing at a low value corresponding to a thin film containing small biological colonies. As time elapses, the film thickens and a multitude of active biological colonies become established. FIGURE3 shows the assumed changed in biomass activity with time. If it is further assumed that the liquid film mass transfer coefficient(K~ remains constant, equations (33) and (34) can be solved to obtain performance at particular times. FIGURE 4 shows the end result of the calculations in predicting the effect of microorganism growth as compared to actual data. With dissolved oxygen concentration

1584

JOHN ROBERTS 4000

2000

E

,

tO00

~

400

K× E'-~-

200

o u o

"5

~oo 80 o

8

t6

24

32

40

Elapsed time, h FIG. 3.

80

O~

4j~O

6O

./

4c

./

te~e'e~ I10 p.g rnl "c glucose Atkinson et al data (1968) Equ ( 3 3 , 3 4 ) prediction

2o

E

o

I

I

I

I

8

16

24

32

40

Elapsed time, h F r G . 4.

being constant this parameter (K/a) is interpreted as varying with biological colony, film thickness and maturity. At short times, (K[a) is relatively small, implying that the distribution coefficient between biomass and liquid interface is not as efficient in collecting organic material. Therefore, the overall biological term (KX/a) is equally as important as the mass transfer term in equation (34). As time elapses, a thicker, more active, mature biological film colony is established with (K/a) re.aching its steady state value, and the overall biological term (KX/a) is an order of magnitude greater than the mass transfer term.

High Rate Biological Film Flow Reactor Theory

1585

CONCLUSION This m a s s transfer m o d e l described by e q u a t i o n s (33), (34) a n d (50) p r o v i d e s a simple m e a n s o f interpreting b e h a v i o u r o f biological film flow reactors. It has been useful in e x p l a i n i n g v a r i a t i o n s in p e r f o r m a n c e a n d as a predictive design aid in the g e o m e t r y o f high rate trickling filters. A c o m p l e t e l a c k o f c o m p a r a t i v e external d a t a o n the height o f a transfer unit ( H T U ) a n d liquid film mass transfer coefficient KL for biological processes is a p p a r e n t . F u r t h e r w o r k is necessary to evaluate a n d c o m p a r e p a r a m e t e r s f r o m a wide variety o f substrates, especially to gain a m o r e detailed k n o w ledge o f the i n d i v i d u a l coefficients (K, ~) that is, " t r e a t a b i l i t y " factors o f p a r t i c u l a r bios a n d a d d e d insight into the b i o c h e m i c a l m e c h a n i s m s involved. Acknowledgements--The major portion of this work was undertaken whilst the author was on study leave at Imperial Chemical Industries Ltd, Brixham Laboratory, throughout 1972. Sincere thanks are due to Dr P. N. J. CHIFrER.FIELDand his staff for the constructive suggestions and criticisms.

REFERENCES AMADOM. A. (1964) Analysis of BOD reduction in trickling filters. Master's Thesis, Cornell University, February. AMES W. F., BEHN V. G. and COLLINGSW. Z. (1962) Transient operation of the trickling filter. J. sanit. Engng Die. Am. See. cio. Engrs 88, 21-38. A1"KrNSONB., BUSCHA. W. and DAWKtNSG. C. (1963) Recirculation, reaction kinetics and effluent quality in a trickling filter flow model. 3". Wat. Pollut. ControlFed. 35, 1307-1317. ATKtNSON B., SWILLEYE. L., BUSCH A. W. and WILLIAMSD. A. (1967) Kinetics, mass transfer and organism growth in a biological film reactor. Trans. Inst. Chem. Engrs 45, T257-T264. ATKINSONB., DAOUD I. S. and WILLIAMSD. A. (1968) A theory for the biological film reactor. Trans. Inst. Chem. Engrs 46, T245--250. ATKINSONB. and WILLIAMSD. A. (1971) Performance characteristics of a trickling filter with holdup of microbial mass controlled by periodic washing. Trans. Inst. Chem. Eagrs 49, T205-224. BALAKR.ISHNANS., ECKENFELDERW. W. and BROWN C. (1969) Organics removal by a selected trickling filter media. War. Wustes Eagng 6, A22-A25. BENEI)ICr A. H. and CAR.LSOND. A. (1970) The real nature of the Streeter-Phelps temperature coefficient. Wat. Sewage Wks February, 54-57. BEh'N V. C. and MONADJEMIP. 0968) Developments in Biological Filtration Advances in Water Quality Improvement, Water Resources Symposium No. 1 (Edited by GLOYNA E. F. and ECr~NFELDER.W. W.) University of Texas Press, Austin and London. BLAIN A. W. arid MCDONNELL A. J. (1965) Discussion to paper by GALLERand GOTAAS(1964) Analysis of biological filter variables. 3". san. Eagng Div. Am. See. cir. Eagrs 91, SA 4, 57-61. BP.OWNJ. C. (1971) Mathematical model describing the performance of trickling filters, within M.Sc. Thesis, Dept. of Environmental Sciences, University of North Carolina. BR.UCE A. M. and MER.r,~NSJ. C. (1973) Further studies of partial treatment of sewage by highrate biological filtration. War. Pollut. Control, to be published. CHn)I)ER.FIELDP. N. J. 0968) Effluent and Water Treatment Manual 4th Edn., 60-77. Thunderbird Press, London. DUNBAR.0928) The Chemistry of Water and Sewage Treatment (Edited by BUSWELLA. M.) Chemical Catalogue Co. Inc., New York. ECKENFELDER.W. W. (1961) Trickling Filtration Design and Performance. J. sanit. Engng Die. Am. Soc. cir. Engng 87, 33-45. ECKENFELDERW. W. and BAR.NHARTE. L. (1963) Performance of a high rate trickling filter using selected media. J. War. Pollut. Control Fed. 35, 1535-1551. ECr,.ENFELDER.W. W. (1966) Industrial Water Pollution Control, 188-198 pp. McGraw-Hill, New York. FAIR G. M. and GEwR. J. C. (1954) Water Supply and Waste Water Disposal. pp. 710-716. John Wiley, New York. FAIR.G. M., GEYERJ. C. and OKUND. A. (1968) Water and Wastewater Engineering, Vol. 2. p. 34. 1-5. Wiley, New York. FAIR.ALLJ. M. (1956) Correlation of trickling filter data. Sewage Wks. 28, I069-74. GALLER.W. S. and GOTAASH. B. 0964) Analysis of biological filter variables. J. sanit. Engng Div. Am. Soc. cir. Eagrs 90, 57-79. GESER B. (1954) A new concept in trickling filter design. Sewage ind. Wastes 26, 136--139.

1586

JOHN ROBERTS

GE~MArN J. E. (1966) Economical treatment of domestic waste by plastic medium trickling filters. J. Wat. Pollut. Control Fed. 38, 192-203. GROMEC M. J., and MAUNA J. F. (1970). Verification of Trickling Filter Models Using Surfpac EHE-70-13; CRWR-60, University of Texas. GROMmC M. J. MAUNA J. E. and ECKENFELDER W. W. (1972) Performance of plastic media in trickling filters. Water Research 6, 1321-32. GULEVICH W. (1967) The Role of Diffusion in Biological Waste Treatment Ph.D. Thesis. Johns Hopkins University. HAMMAM S. (1968) An investigation into the performance of a trickling filter plant. Stuttg. Bet. SiedtWasserw. No. 36. HOWLAND W. E. (1953) Effect of temperature on sewage treatment processes. Sewage ind. Wastes 25, 161-169. HOWLAND W. E. (1958) Flow over porous media as in a trickling filter. Proc. 12th Ann. Ind. Waste Conf. Purdue University 94, 435-465. HOWLAND W. E., POHLAND F. G. and BLOODGOODG. E. (1960) Kinetics in trickling filters. 3rd Annual Conference on Biological Waste Treatment, Manhattan College, New York. KEHRBERGERG. J. and BUSCH A. W. (1969) Effects of recirculation on the performance of trickling filter models. Proc. 24th Ann. Purdue ind. Waste Conf. 37-52. KEHRBERGER G. J. and BUSCH A. W. (1971) Mass transfer effects in maintaining aerobic conditions in filter flow reactors. J. Wat. Poltut. Control Fed. 43, 1514-27. LAMB R. (1970) A suggested formula for the process of biological filtration. Wat. Pollut. Control 69, 209-220. McKINNEY R. E. (1962) Trickling Filters--~ricrobiology for Sanitary Engineers, pp. 199-212. McGraw-Hill, New York. MATER W. J. (1966) Mass Transfer and Growth Kinetics on a Slime Layer, a Simulation of the Trickling Filter. Ph.D. Thesis, Cornell University. MATER W. J., BEHN V. G. and GATES C. D. (1967) Simulation of the trickling filter process. J. sanit. Engng Div. Am. Soc. cir. Engrs 93, SA 4, 91-112. MEHTA D. S., DAVIS H. H. and KINGSLEYR. P. (1972) Oxygen theory in biological treatment plant design. J. sanit. Engng Div. Am. Soc. cir. Engrs 48, SA 3, 471-89. MONADJEMIP. and BEHN V. C. (1970) Oxygen uptake and mechanism of substrate purification in a model trickling filter. Proc. 5th Int. Hat. Pollut. Res. Conf. Paper 11-12-16. NATIONALRESEARCHCOUNOL (1946) Sewage treatment at military installations. Sewage Wks J. 18,. 787-1028. QUIRK T. P. (a) (1971) Trickling Filtration Treatment of Whey Effluents, pp. 453--494. National Symposium of Food Processing Wastes, March 23-26 Denver, Colorado. (b) (1972) Scale-up and process design techniques for fixed film biological reactors. Water Research 6, 1333-1360. SCHULZE K. L. (1957, 60) (a) Experimental vertical screen trickling filter. Sewage ind. Wastes 29, 958-967 (1957). (b) Load and efficiency of trickling filters. J. Wat. Pollut. Control Fed. 32, 245-261 (1960). SWILLEY E. L. and ATKINSONB. (1963) A mathematical model for trickling filters. Proc. 18th Ann. ind. Waste Conf. Purdue University, Lafayette, Indiana. TU(:EK F., CHUt~BA J. and MADI~RAV. (1971) Unified basis for design of biological aerobic treatment processes. Water Research 5, 647-681. TAKESHt K., HtROVNKI Y. and KORErSUNEU. (1972) Mass transfer in laminar region between liquid and packing material. J. Chem. Engng, Japan 5, 132-136. VELZ C. J. (1948) A basic law for the performance of biological filters. Sewage Wks J. 20, 607-617.

1587

High Rate Biological Film Flow Reactor Theory APPENDIX

1. E V A L U A T I O N

OF MASS TRANSFER

COEFFICIENT

(KL)

From the Buckfastleigh results, using equation (49): K , ~ 276 kg m -3 h - t at {2 = 1468 kg m -2 h - t and assume (a) a priori (KX/~) " 2000 kg m =s h - 1 , a constant, independent of flow rate, for specific surface area Ao, = 88m= m -3. On substitution into equation (33): 1

1

K. -

a

rL`4v + ~ :

1

1

1

27-'6 = Kt..8"--~-/- 2 - ~ therefore KL=3.64kgm-2h -t. Assume (b) actual void space in operation is ( = 0.92; (c) Schmidt Number N'~c = 2000; (d) Viscosity of influent v ----0.01 poise at 13.5°C. From equation (50)

(l....~t ")÷ KLNsc÷ iL'

•

=

QI~

[1 -- 0"92)* 3"64 x 2000 ~ -- k 0"92 / " 146810-92 ==0"16

NR.'=

Q v,4u(l -- ~) 1468 x 10'

(0.01 x 3600) x 88 x 0.08 =

58

Thus one coordinate is (58, 0.16) at Q -- 1468 kg m-= h -t. Since K . ~ ~/(Q), equation (33) can be solved again at extreme flow rates to obtain co-ordinates (13, 0.305 and 348, 0-075) on F[o. 1.

A P P E N D I X 2. C H E C K O N M A G N I T U D E MASS TRANSFER COEFFICIENTS

OF

Example 1 From TXeLE 3 for a temperature of 15°C, irrigation rate of (Q = 500 kg m -2 h-1) and modular packing of specific surface area (,4, = 94 m 2 m-3), depth 2 m, being fed by an influent containing 225 mg 1-1 BOD: ffL = 1.96 kg m -2 h - l ; biological rate term = 2400 kg m -3 h -1 from which K , = 171"1 kg m =a h - l ; total active surface area = 184 m 2. By definition: " exp

-- 171.1 x ~

" 0.504

therefore fraction removal ~ 0.496. The portion of BOD removed ----0.496 x 225 = 111.5 mg 1-1 i.e. quantity of BOD removed = 111.5 x 10 -6 x 500---~ 5.58/184 x 10 -= kg m -2 h - t . Let this quantity equal the necessary oxygen transferred, N o . No2 -- K o 2 • a C where AC ----the maximum oxygen driving force = 6.12 × 10 -~ from TABLe 3. Therefore minimum Ko, =

5.58 184 x 1 0 - ' / 6 . 1 2 x 10 -6

= 49.6 kg m -2 h - l .

1588

Jo~ROBERTS

This oxygen mass transfer coefficient can now be compared with the liquid film organic mass transfer coefficient i.e. minimum ratio (Koz~ _ 49...___6_-- 25:1 \KL / 1" 96 Example 2

From MEwrA et al. (1972) in their Example 1, at a temperature of 25 degrees Celcius, irrigation rate o f ( Q = 2270 kg m -2 h -1) and modular packings of specific surface area (A~ = 121 m ~ m-3), depth 5.49 m, being fed by an influent containing 279 mg 1-1 BOD and removing 187 mg 1-x BOD. Then: (

C,

C~ = 0"33 --- exp

5"49~ --Kin x 2-'~'0!

from which K,, = 459 kg m - 3 h-1. Assume a biological rate term = 5700 kg m -3 h -1. From 1 1 1 4 5 9 - - KL X 121 q- 5700

KL = 4"12 kg m - z h -1. Total active surface area = 665 m 2. The quantity of BOD removed = 187 × 10 -~ × 2270 = 0.425 kg m - 2 h - .1 665 Let this equal the necessary oxygen transferred, (Not). As before, define: No2 = Ko2. AC. At 25°C, the maximum oxygen driving force = 8.40 mg 1-1. Therefore, minimum 0.425 Koz = ~ / 8 " 4

× 10 -~

= 7 6 k g m - 2 h -1. This value may be compared with the liquid film mass transfer coefficient, estimated above: i.e. minimum ratio (K£.o2~ _ 7._6_6 _ 18:1. KL ! 4"12