- Email: [email protected]
Laboratory study and computer model development related to gross solids' movement in combined sewers
~
Pergamon
Wal. Sci. Ttclt. Vol. 33. No.9. pp. 39-47.1996. CoPyriiht «'J 1996IAWQ. PIIblished by Elsevi... Scitnce LId Printed in Oreat Britain. All rights reserved. 0273-1223/96 51 HlO + 0-00
PH: S0273-1223(96)OO368-X
LABORATORY STUDY AND COMPUTER MODEL DEVELOPMENT RELATED TO GROSS SOLIDS' MOVEMENT IN COMBINED SEWERS John W. Davies*, Yanli Xu* and David Butler** • School 0/ Architecture &: Engineering. University o/Westminster, 35 Marylebone Road. London NWI 5LS. UK •• Department 0/ Civil Engineering, Imperial College 0/ Science, Technology and Medicine, London SW7 2BU. UK
ABSTRACf Significant problems in sewer systems are caused by gross solids, and there is a strong case for their inclusion in computer simulation models of sewer flow quality. The paper describes a project which considered methods of modelling the movement of gross solids in combined sewers. Laboratory studies provided information on advection and deposition of typical gross solids in part-full pipe flow. lbeoretical considerations identified aspects of models for gross solids that should differ from those for dissolved and fine suspended pollutants. lbe proposed methods for gross solids were incorporated in a pilot model, and their effects on simple simulations were considered. Copyright @ 1996 lAWQ. Published by Elsevier Science Ltd.
KEYWORDS Advection; combined sewers; computer modelling; deposition; gross solids; laboratory studies. INTRODUCTION The problem The Urban Pollution Management Manual (Foundation for Water Research, 1995) promotes the use of computer simulation models of flow quality in sewer systems, as part of a series of models covering rainfall, sewer-flow quality, sewage treatment and river quality. Sewer flow quality models that have been developed for use in the UK are MOSQITO (Moys et al., 1988), which has been available for practical use since 1993 but will shortly be replaced by HydroWorks QM; and MOUSETRAP (Crabtree et al., 1994), which has been available since 1994. A major use of sewer flow quality models is in the design or improvement of combined sewer overflows (CSOs). If storage is to be provided at a CSO in order to contain the most polluted early storm flow, the quality model can simulate pollutographs at the CSO and thus facilitate economic and effective design. A 39
J. W. DAVIES
40
~'QI.
major measure of effectiveness is the extent to which the storage provision reduces pollution of the watercourse. A form of pollution that is particularly distasteful to the public is aesthetic pollution involving solids obviously derived from sewage. The term "gross solids" is generally used for solids in sewer flow having two dimensions greater than 6 mm (Jefferies, 1992). Many such solids are introduced to the system via the we, including faecal malter, women's sanitary products, condoms, and general bathroom litter; and these are a major component in aesthetic pollution. Yet none of the sewer flow quality models in use in the UK includes gross solids. This means, for example, that simulations carried out to optimise the size of additional storage at a eso (using existing sewer quality models) would not directly take account of gross solids or the aesthetic pollution they might cause. The potential solution A model of the production, movement and degradation of gross solids would therefore be of great value in operating combined sewer systems and minimising the pollution they cause. This paper makes proposals related to one aspect: movement of solids. The proposals are based on work that included laboratory studies of the advection and deposition of gross solids in a part-full pipe. The results, in conjunction with those of earlier experiments, were used in the development of a pilot model of gross solids movement. This differs in a number of significant ways from the current models of dissolved and fine suspended pollutants. The pilot model is intended as a means of testing the suitability of the proposed methods, not as a working tool for actual sewer system modelling. Recent studies Gross solids at esos have been studied by Jefferies (1992). The types of solids found to be most common, and most likely to contribute to aesthetic pollution, were plastic and paper strips. Faecal matter, plastic sticks and tampons were also present but less significant. The transport of solids in small sewers (up to 300 mm diameter) is the subject of a current study (Brown et al., 1995). One element has been a laboratory study which is closely related to the study described in this paper. Previous research at the University of Westminster has considered the movement of solids in part-full pipe flow in steady and unsteady conditions. Laboratory experiments (Davies, 1990) involved small particles in a 100 mm diameter perspex pipe. Steady flow particle velocities showed the expected relationship with mean flow velocity: floating particles faster than mean velocity, suspended particles close to mean velocity, bedload particles slower. In unsteady flow experiments, particles were overtaken by a "storm" wave. Analysis of the results led to the proposal of the following characterisation: that the relationship between particle velocity and mean flow velocity is the same for unsteady flow as for steady flow. LABORATORY STUDIES
In order to acquire information on the advection and deposition of typical gross solids, a programme of laboratory studies was carried out. The studies took place in a half-round channel with a diameter of 300 mm, representing the bottom half of a sewer pipe. The plastic pipe material was artificially roughened by a layer of sand fixed to the surface, giving a roughness close to that of a concrete pipe. The gradient was adjustable and the total pipe length was 13 m. Gross soUds The soUds in the experiments were mostly typical items of sanitary refuse, including most of the solids commonly observed at esos. The following were included: cotton buds, panty-liners, the protective paper strips from panty-liners, sanitary towels, tampons, the cardboard applicators for tampons, and toilet paper.
Gross solids movements
41
The solids were soaked in clean water for 24 hours before use in the experiments. The exception to this was the toilet paper. For this, a standard length was lightly crushed by hand, and squeezed under water to remove air. The cotton buds floated in water, all the other solids had a density close to that of water but sank in still water when soaked. In addition to the items of sanitary refuse, an artificial solid was considered. This was a cylinder of ABS plastic (Specific Gravity, 1.07): length 43 mm, diameter 20 rom. It was intended to represent a faecal solid, denser than water, after some physical degradation in the sewer. It allowed comparison with the results for the sanitary refuse items and with the results of a parallel study (Brown et al., 1995) which took place in the same experimental installation, using an NBS (US National Bureau of Standards) artificial faecal solid. This was a plastic cylinder with length 80 mm, diameter 37.5 mm, and specific gravity 1.05. -
-
-
melln
n.",
n'lO/cit)'
IIJI
cuttun hlld I'''pcr .trip
-
ABS c)'linder
~
t·
.~
;; ,
11.4
fl
0.2
0.4
deplh (1ll"Oportioll of dillllll·ter) Figure I. Solids velocities.
Advection The speed of longitudinal movement of the solids carried with the flow was studied in steady conditions for a series of water depths. Solids were introduced singly, and timed over a IO m length. Gradients of 1:100, 1:200 and l:5oo were studied. Sample results are given in Fig. I. This gives the velocity of selected solids plotted against depth, together with mean water velocity. Figure 1 is for a gradient of 1:500. The behaviour of the solids was as follows.
Cotton buds. These floated in all conditions and travelled at the water surface. Paper strips. Though these items sank when soaked in still water, they tended to move with the flow in partial contact with the water surface, under the influence of surface adhesion forces. This occurred at all gradients and all depths, and caused the velocity of the solids to be greater than mean velocity, as shown in Fig. 1. When studied in a channel with much lower roughness (a rectangular glass-sided flume) and at greater depths, they moved with the flow with no contact with the water surface, at velocities close to the mean water velocity.
42
J. W. DAVIES n al.
ASS cylinder At lower values of water velocity, these solids moved with the flow near the pipe bed with their length in the direction of flow. At higher velocities they tended additionally either to roll with their length perpendicular to the direction of flow, or to rotate end-over-end. At 1:500, their velocity was lower than mean velocity (as shown in Fig. I). At 1:100 their velocity was higher than mean velocity since their movement within the flow area brought them into greater contact with the higher water velocities further from the pipe bed. Most of the other solids moved at velocities greater than mean velocity. This was partly a consequence of the problems of surface adhesion described above, and also of the fact that some of the particles were large in relation to the pipe diameter and therefore tended to be forced into contact with the water surface. This is not necessarily representative of their behaviour in actual sewers. The cardboard applicators moved at velocities close to mean velocity (slightly lower at 1:500 and slightly higher at 1:1(0). After 24 hours of .soaking they had became unwound, and the resulting thin cardboard strips moved within the flow area, without contact with the surface. Advection of the NBS solid in the same pipe system is discussed by Brown et al. (1995), and is compared with the results for some of the sanitary solids described above. Deposition At sufficiently low depths the solids became stationary, in contact with the pipe wall. The general word "deposition" will be used for this effect, though floating particles were stranded rather than deposited in the usual sense. At a series of steady flow depths, a fixed number of solids of each type were introduced to the flow one by one, by being laid gently on the bed. The percentage of the particles that did not reach the end of a 10 m length was recorded. This was taken as the percentage of particles "deposited". These experiments were carried out at gradients of 1: 100, 1:200, 1:300 and 1:500. In addition to the items of sanitary refuse already listed, an NBS solid (described above) was included. For each solid type the hydraulic conditions associated with 50% deposition at the different gradients were investigated, in order to identify the parameters most strongly associated with deposition. The hydraulic conditions considered were depth, mean flow velocity, and shear stress over the wetted perimeter. It was found that deposition was associated more strongly with particular values of depth and velocity than with particular values of shear stress. The following is therefore proposed as a simplified representation, suitable for inclusion in the initial model of solids' movement: deposition of a solid type takes place when the value of either depth or mean velocity goes below a critical value, and re-erosion takes place when that level is subsequently exceeded. The experiments did not consider interaction between solids, or the effects of an existing sediment bed or pipe imperfections. Further work is needed to consider these aspects. EXISTING SEWER QUALITY MODELS MOSQITO, HydroWorks QM and MOUSETRAP model the movement of pollutants with the flow using forms of pollutant continuity equation. The equation in MOSQITO and HydroWorks has the general form: (I)
()
where c = concentration, u = mean velocity, x = distance and t MOUSETRAP has the general form:
= time.
The equation used in
Gross solids movements
43
(2) where D = dispersion coefficient. Values of mean velocity must be supplied by the hydraulic model upon which the quality model is based. Equation (I) represents only advection: movement of pollutant at the mean velocity. Equation (2) additionally includes dispersion: spreading out of pollutant relative to mean velocity. In most sewer flow cases, dispersion of dissolved and fine suspended material is not thought to be significant (Davies, 1993). Equation (2) assumes that dispersion is mathematically analogous to diffusion according to Fick's law: flux proportional to concentration gradient. This longitudinal dispersion arises when a pollutant is fully mixed laterally and vertically over the area of flow under the influence of turbulent diffusion, and experiences water velocities throughout the cross-section. The average longitudinal velocity of pollutants equals the mean velocity of the water. PROPOSED APPROACH TO MODELLING GROSS SOLIDS' MOVEMENT The proposed methods are based on: - theoretical consideration of the difference between the movement of gross solids and of dissolved and fine suspended pollutants (those covered by existing sewer quality models). - the results of the laboratory studies. Theoretical considerations As the laboratory results have demonstrated, many types of gross solid move with the flow at velocities that do not equal the mean velocity. Some move faster, and some slower, giving rise to a form of longitudinal dispersion of gross solids. Let us consider the possible approaches to modelling this effect. The use of Fickian dispersion coefficients is not appropriate because gross solids do not necessarily experience water velocities throughout the cross-sectional area of flow, or have an average velocity that equals the mean flow velocity. Longitudinal dispersion of gross solids results from differential advection, and does not conform with the Fickian model. The normal representation of pollutant advection in sewers is by equation (1). Advection of dissolved and fine suspended matter is assumed to be at the mean flow velocity, so U in equation (1) represents both mean flow velocity and pollutant velocity. Using equation (I) with u set to any value other than mean velocity (solid velocity for example) would be incompatible with the equation for water continuity that would exist in the hydraulic model. Therefore a different method of modelling gross solids advection is proposed, which involves "tracking" individual solids or groups of solids through the system. Details are given later.
In a normal sewer quality model, quantities of dissolved and fine suspended material are calculated in terms of concentration (mass of material per volume of water). For gross solids which move at speeds other than the mean velocity, the use of concentration is not necessarily appropriate. This is because a mass of material cannot be associated directly with a volume of water since the two are moving at different speeds. It is proposed therefore that load-rate of gross solids be used in this model rather than concentration. Alternative forms of load-rate would be mass per unit time or number of solids per unit time. The choice must be influenced by the importance of physical degradation of solids in the system, about which little is currently known. The form of load-rate at present proposed for the model is number per unit time.
44
J. W. DAVIES et al.
Use Qf labQratOlY results Results from the earlier study Qf unsteady flQW (Davies, 1990) suggest that, fQr any particular SQlid type, the modelling Qf advectiQn in unsteady flQW can be based Qn a relatiQnship between SQlid velocity and mean flQW velocity fQr steady flow. The laboratory studies Qn grQss sanitary SQlids described in the paper suggest the fQlIowing.
1. Gross solids of different types move with the flow at a range of different longitudinal velocities, and the difference between SQlid velocity and mean flQW velocity can be significant. 2. Deposition of gross solids can be related to depth and velocity. MODEL DETAILS A pilQt model using the principles described above has been developed and tested. The purpose is to test the effect and suitability Qf the propQsed methQds of mQdelling gross SQlids' mQvement. The outcome is not, at present, a finalised wQrking tool for actual sewer system modelling. Hydraulic model A model of gross solids' movement, as with all models of sewer water quality, should be based on a hydraulic model of the sewer system. In this case, the hydraulic model is one in which the full Saint-Venant equations are solved using an explicit finite difference method (Davies, 1993). This hydraulic model performs well in mass balances checks and in comparison with experimental unsteady flow data. The model can represent a main sewer with lateral inflows but not a fully branched sewer system. Representin& different types of solid The following is proposed as an appropriate method of representing the range of gross solids fQund in practice. The full range can be divided into an appropriate number of types according to advective behaviour in steady flow. Such a division is inevitably artificial, but aims to give a simple representation of the full range. For each type, a particular relationship between solid velocity and mean flow velocity is specified, together with particular values of depth and velocity associated with deposition. Trackin& The advection of gross solids is modelled by "tracking" individual solids or groups of solids. At any point in distance and time, the mean flow velocity is known from the hydraulic model. This can be converted to solid velocity using the specified relationship for the particular solid type. Each specified relationship between solid velocity and mean velocity is assumed (on the basis of the earlier laboratory results) to apply in steady and unsteady conditions. The velocity of a solid at any instantaneous position is thus known, and this can be used progressively to track its movement through the system. If depth or velocity over any section decreases to the level specified as causing deposition, the progress of solids in the section is halted until this level is again exceeded. Simulation A simulation starts with a steady baseflow with a constant load-rate of solids for each solids type. Inflow hydrographs are specified for the inflow points, together with relationships between solids input load-rate and time. At a specified PQint at the downstream end of the system, the resulting solids load-rate graphs are given by the model.
45
Gross solids movements
MODEL OPERAnON Two simple examples of output from the pilot model are now given. Both are for simplified fictitious catchments. The first example (Fig. 2) demonstrates the representation of gross solids' advection. The main sewer has no lateral inflows. The hydrograph has a trapezoidal shape, and the input load-rate of gross solids is constant. Solids are represented by five types - two that move at velocities faster than mean flow velocity, one that moves at mean velocity, and two that move at lower velocities. There is no erosion or deposition. 100 80 -;
eo. 80
..
..........,
011
:;
40 20 0 0
--'S.
20
40
80
..
-
&ross solids suspended solids
:0
~
. :s ... '0
.. f
800
-. ~ ~
~
f\
24
~
• oS
120 1000
'i::
."
tOO
40
.c 32 E
.s-
80
rime (min)
8cto
18
400
8
200
o ."
.
• oS
.
:'5! '0
..... ..
'2 ."
c.
:0
a
a
0
20
40
80
80
100
120
rime (min)
Figure 2. Advection.
The resulting graph of gross solids' load-rate at the downstream end of the system, for the five types combined, is given on Fig. 2. It is compared with the equivalent graph for suspended solids (also resulting from a constant input load-rate) modelled using equation (I). The scales on the load-rate graph have been drawn so that the input rates for gross solids and suspended solids coincide. For both gross solids and suspended solids there is a first flush resulting from the overtaking of the pollutants by the storm wave. The gross solids variations are attenuated by the effect of the range of velocities for the solids types. In the example on Fig. 3, the conditions created by the hydrograph cause depth and velocity to decrease, for a short period. below the level associated with deposition for one of the solids types. This causes a reduction in load-rate while the conditions prevail and a small peak resulting from the later erosion. After the peak, the load-rate continues to rise gradually with increasing flow.
J. W. DAVIES el al.
46
SO 40
......
~ ...
.
u
30 20
,
~
10
1 0
.
.....
/
l
0
·si::
.,..........-"
20
40 60 time (min)
60
100
80
100
8
..
,Q
E
.:."
. . .. :=
8
~
'l'
"0
4 i'/
.2
....
Q
..
/'-.
2
co
0 0
20
40 60 time (min)
Figure 3. Deposition/erosion.
CONCLUSIONS
Methods of modelling gross solids' movement in combined sewers have been considered. Laboratory studies have given information on the advection and deposition of gross solids. Theoretical considerations have suggested that: - the Fickian model is not suitable for representing longitudinal dispersion of gross solids - a pollutant continuity (advection) equation may not be suitable for representing advection of gross solids - load-rate is more suitable than concentration for expressing quantities of gross solids. The proposed method of modelling gross solids' movement entails: - representing the range of solids found in actual sewers by an appropriate number of types - tracking solids by successively converting mean flow velocity to solid velocity using a relationship specified for each type, assumed to apply in steady and unsteady conditions - halting the progress of solids while depth or velocity is below the level associated with deposition.
Gross solids movements
47
These proposals relate simply to modelling gross solids' movement in sewers and do not take account of the influences of physical degradation or interaction with other material. The next stage in practical application should be to determine appropriate values for the physical parameters associated with advection, deposition and re-erosion in actual sewers.
REFERENCES Brown. D. M.• Buller. D., Onnan. N. R. and Davies. J. W. (1995). Gross solids transport in small diameter sewers. In: Proceedings of lnt~mationolConfu~rrc~ on S~w~r Solids. Dundee. Crabtree. R.. Garsdal. H., Gent. R., Mark, O. and Dorge, J. (1994). MOUSETRAP - A detenninistic sewer flow quality model. In: Proceedings of lA WQ 17th Bitnnial Confu~nce. Budapest Davies. J. W. (1990). Laboratory study related to the modelling of slonnwater quality in combined sewers. In: Proceedings of 5th lrrumatiolUll Confu~nct on Urban Storm DraiJlag~. Osaka, Japan, 215-219. Davies, J. W. (1993). Modelling of stonnwater quality in combined sewers. In: Proceedings of 6th lnt~mational Confu~nc~ on Urban Storm Drairrag~, Niagara Falls, Canada. 1254-1259. Foundation for Water Research (1994). Urban Pollution Manag~m~rrt (UPM) Manual, FRlCL 0002. Jefferies. C. (1992). Methods of estimating the discharge of gross solids from combined sewer systems. Wat. Sci. T~ch .• 26(5/6), 1295-1304. Moys. G. D.. Osborne. M. P. and Payne. J. A. (1988). MOSQrrO 1 • Design Sp~cification. HR Wallingford. Report SR 184.
Pergamon
Wal. Sci. Ttclt. Vol. 33. No.9. pp. 39-47.1996. CoPyriiht «'J 1996IAWQ. PIIblished by Elsevi... Scitnce LId Printed in Oreat Britain. All rights reserved. 0273-1223/96 51 HlO + 0-00
PH: S0273-1223(96)OO368-X
LABORATORY STUDY AND COMPUTER MODEL DEVELOPMENT RELATED TO GROSS SOLIDS' MOVEMENT IN COMBINED SEWERS John W. Davies*, Yanli Xu* and David Butler** • School 0/ Architecture &: Engineering. University o/Westminster, 35 Marylebone Road. London NWI 5LS. UK •• Department 0/ Civil Engineering, Imperial College 0/ Science, Technology and Medicine, London SW7 2BU. UK
ABSTRACf Significant problems in sewer systems are caused by gross solids, and there is a strong case for their inclusion in computer simulation models of sewer flow quality. The paper describes a project which considered methods of modelling the movement of gross solids in combined sewers. Laboratory studies provided information on advection and deposition of typical gross solids in part-full pipe flow. lbeoretical considerations identified aspects of models for gross solids that should differ from those for dissolved and fine suspended pollutants. lbe proposed methods for gross solids were incorporated in a pilot model, and their effects on simple simulations were considered. Copyright @ 1996 lAWQ. Published by Elsevier Science Ltd.
KEYWORDS Advection; combined sewers; computer modelling; deposition; gross solids; laboratory studies. INTRODUCTION The problem The Urban Pollution Management Manual (Foundation for Water Research, 1995) promotes the use of computer simulation models of flow quality in sewer systems, as part of a series of models covering rainfall, sewer-flow quality, sewage treatment and river quality. Sewer flow quality models that have been developed for use in the UK are MOSQITO (Moys et al., 1988), which has been available for practical use since 1993 but will shortly be replaced by HydroWorks QM; and MOUSETRAP (Crabtree et al., 1994), which has been available since 1994. A major use of sewer flow quality models is in the design or improvement of combined sewer overflows (CSOs). If storage is to be provided at a CSO in order to contain the most polluted early storm flow, the quality model can simulate pollutographs at the CSO and thus facilitate economic and effective design. A 39
J. W. DAVIES
40
~'QI.
major measure of effectiveness is the extent to which the storage provision reduces pollution of the watercourse. A form of pollution that is particularly distasteful to the public is aesthetic pollution involving solids obviously derived from sewage. The term "gross solids" is generally used for solids in sewer flow having two dimensions greater than 6 mm (Jefferies, 1992). Many such solids are introduced to the system via the we, including faecal malter, women's sanitary products, condoms, and general bathroom litter; and these are a major component in aesthetic pollution. Yet none of the sewer flow quality models in use in the UK includes gross solids. This means, for example, that simulations carried out to optimise the size of additional storage at a eso (using existing sewer quality models) would not directly take account of gross solids or the aesthetic pollution they might cause. The potential solution A model of the production, movement and degradation of gross solids would therefore be of great value in operating combined sewer systems and minimising the pollution they cause. This paper makes proposals related to one aspect: movement of solids. The proposals are based on work that included laboratory studies of the advection and deposition of gross solids in a part-full pipe. The results, in conjunction with those of earlier experiments, were used in the development of a pilot model of gross solids movement. This differs in a number of significant ways from the current models of dissolved and fine suspended pollutants. The pilot model is intended as a means of testing the suitability of the proposed methods, not as a working tool for actual sewer system modelling. Recent studies Gross solids at esos have been studied by Jefferies (1992). The types of solids found to be most common, and most likely to contribute to aesthetic pollution, were plastic and paper strips. Faecal matter, plastic sticks and tampons were also present but less significant. The transport of solids in small sewers (up to 300 mm diameter) is the subject of a current study (Brown et al., 1995). One element has been a laboratory study which is closely related to the study described in this paper. Previous research at the University of Westminster has considered the movement of solids in part-full pipe flow in steady and unsteady conditions. Laboratory experiments (Davies, 1990) involved small particles in a 100 mm diameter perspex pipe. Steady flow particle velocities showed the expected relationship with mean flow velocity: floating particles faster than mean velocity, suspended particles close to mean velocity, bedload particles slower. In unsteady flow experiments, particles were overtaken by a "storm" wave. Analysis of the results led to the proposal of the following characterisation: that the relationship between particle velocity and mean flow velocity is the same for unsteady flow as for steady flow. LABORATORY STUDIES
In order to acquire information on the advection and deposition of typical gross solids, a programme of laboratory studies was carried out. The studies took place in a half-round channel with a diameter of 300 mm, representing the bottom half of a sewer pipe. The plastic pipe material was artificially roughened by a layer of sand fixed to the surface, giving a roughness close to that of a concrete pipe. The gradient was adjustable and the total pipe length was 13 m. Gross soUds The soUds in the experiments were mostly typical items of sanitary refuse, including most of the solids commonly observed at esos. The following were included: cotton buds, panty-liners, the protective paper strips from panty-liners, sanitary towels, tampons, the cardboard applicators for tampons, and toilet paper.
Gross solids movements
41
The solids were soaked in clean water for 24 hours before use in the experiments. The exception to this was the toilet paper. For this, a standard length was lightly crushed by hand, and squeezed under water to remove air. The cotton buds floated in water, all the other solids had a density close to that of water but sank in still water when soaked. In addition to the items of sanitary refuse, an artificial solid was considered. This was a cylinder of ABS plastic (Specific Gravity, 1.07): length 43 mm, diameter 20 rom. It was intended to represent a faecal solid, denser than water, after some physical degradation in the sewer. It allowed comparison with the results for the sanitary refuse items and with the results of a parallel study (Brown et al., 1995) which took place in the same experimental installation, using an NBS (US National Bureau of Standards) artificial faecal solid. This was a plastic cylinder with length 80 mm, diameter 37.5 mm, and specific gravity 1.05. -
-
-
melln
n.",
n'lO/cit)'
IIJI
cuttun hlld I'''pcr .trip
-
ABS c)'linder
~
t·
.~
;; ,
11.4
fl
0.2
0.4
deplh (1ll"Oportioll of dillllll·ter) Figure I. Solids velocities.
Advection The speed of longitudinal movement of the solids carried with the flow was studied in steady conditions for a series of water depths. Solids were introduced singly, and timed over a IO m length. Gradients of 1:100, 1:200 and l:5oo were studied. Sample results are given in Fig. I. This gives the velocity of selected solids plotted against depth, together with mean water velocity. Figure 1 is for a gradient of 1:500. The behaviour of the solids was as follows.
Cotton buds. These floated in all conditions and travelled at the water surface. Paper strips. Though these items sank when soaked in still water, they tended to move with the flow in partial contact with the water surface, under the influence of surface adhesion forces. This occurred at all gradients and all depths, and caused the velocity of the solids to be greater than mean velocity, as shown in Fig. 1. When studied in a channel with much lower roughness (a rectangular glass-sided flume) and at greater depths, they moved with the flow with no contact with the water surface, at velocities close to the mean water velocity.
42
J. W. DAVIES n al.
ASS cylinder At lower values of water velocity, these solids moved with the flow near the pipe bed with their length in the direction of flow. At higher velocities they tended additionally either to roll with their length perpendicular to the direction of flow, or to rotate end-over-end. At 1:500, their velocity was lower than mean velocity (as shown in Fig. I). At 1:100 their velocity was higher than mean velocity since their movement within the flow area brought them into greater contact with the higher water velocities further from the pipe bed. Most of the other solids moved at velocities greater than mean velocity. This was partly a consequence of the problems of surface adhesion described above, and also of the fact that some of the particles were large in relation to the pipe diameter and therefore tended to be forced into contact with the water surface. This is not necessarily representative of their behaviour in actual sewers. The cardboard applicators moved at velocities close to mean velocity (slightly lower at 1:500 and slightly higher at 1:1(0). After 24 hours of .soaking they had became unwound, and the resulting thin cardboard strips moved within the flow area, without contact with the surface. Advection of the NBS solid in the same pipe system is discussed by Brown et al. (1995), and is compared with the results for some of the sanitary solids described above. Deposition At sufficiently low depths the solids became stationary, in contact with the pipe wall. The general word "deposition" will be used for this effect, though floating particles were stranded rather than deposited in the usual sense. At a series of steady flow depths, a fixed number of solids of each type were introduced to the flow one by one, by being laid gently on the bed. The percentage of the particles that did not reach the end of a 10 m length was recorded. This was taken as the percentage of particles "deposited". These experiments were carried out at gradients of 1: 100, 1:200, 1:300 and 1:500. In addition to the items of sanitary refuse already listed, an NBS solid (described above) was included. For each solid type the hydraulic conditions associated with 50% deposition at the different gradients were investigated, in order to identify the parameters most strongly associated with deposition. The hydraulic conditions considered were depth, mean flow velocity, and shear stress over the wetted perimeter. It was found that deposition was associated more strongly with particular values of depth and velocity than with particular values of shear stress. The following is therefore proposed as a simplified representation, suitable for inclusion in the initial model of solids' movement: deposition of a solid type takes place when the value of either depth or mean velocity goes below a critical value, and re-erosion takes place when that level is subsequently exceeded. The experiments did not consider interaction between solids, or the effects of an existing sediment bed or pipe imperfections. Further work is needed to consider these aspects. EXISTING SEWER QUALITY MODELS MOSQITO, HydroWorks QM and MOUSETRAP model the movement of pollutants with the flow using forms of pollutant continuity equation. The equation in MOSQITO and HydroWorks has the general form: (I)
()
where c = concentration, u = mean velocity, x = distance and t MOUSETRAP has the general form:
= time.
The equation used in
Gross solids movements
43
(2) where D = dispersion coefficient. Values of mean velocity must be supplied by the hydraulic model upon which the quality model is based. Equation (I) represents only advection: movement of pollutant at the mean velocity. Equation (2) additionally includes dispersion: spreading out of pollutant relative to mean velocity. In most sewer flow cases, dispersion of dissolved and fine suspended material is not thought to be significant (Davies, 1993). Equation (2) assumes that dispersion is mathematically analogous to diffusion according to Fick's law: flux proportional to concentration gradient. This longitudinal dispersion arises when a pollutant is fully mixed laterally and vertically over the area of flow under the influence of turbulent diffusion, and experiences water velocities throughout the cross-section. The average longitudinal velocity of pollutants equals the mean velocity of the water. PROPOSED APPROACH TO MODELLING GROSS SOLIDS' MOVEMENT The proposed methods are based on: - theoretical consideration of the difference between the movement of gross solids and of dissolved and fine suspended pollutants (those covered by existing sewer quality models). - the results of the laboratory studies. Theoretical considerations As the laboratory results have demonstrated, many types of gross solid move with the flow at velocities that do not equal the mean velocity. Some move faster, and some slower, giving rise to a form of longitudinal dispersion of gross solids. Let us consider the possible approaches to modelling this effect. The use of Fickian dispersion coefficients is not appropriate because gross solids do not necessarily experience water velocities throughout the cross-sectional area of flow, or have an average velocity that equals the mean flow velocity. Longitudinal dispersion of gross solids results from differential advection, and does not conform with the Fickian model. The normal representation of pollutant advection in sewers is by equation (1). Advection of dissolved and fine suspended matter is assumed to be at the mean flow velocity, so U in equation (1) represents both mean flow velocity and pollutant velocity. Using equation (I) with u set to any value other than mean velocity (solid velocity for example) would be incompatible with the equation for water continuity that would exist in the hydraulic model. Therefore a different method of modelling gross solids advection is proposed, which involves "tracking" individual solids or groups of solids through the system. Details are given later.
In a normal sewer quality model, quantities of dissolved and fine suspended material are calculated in terms of concentration (mass of material per volume of water). For gross solids which move at speeds other than the mean velocity, the use of concentration is not necessarily appropriate. This is because a mass of material cannot be associated directly with a volume of water since the two are moving at different speeds. It is proposed therefore that load-rate of gross solids be used in this model rather than concentration. Alternative forms of load-rate would be mass per unit time or number of solids per unit time. The choice must be influenced by the importance of physical degradation of solids in the system, about which little is currently known. The form of load-rate at present proposed for the model is number per unit time.
44
J. W. DAVIES et al.
Use Qf labQratOlY results Results from the earlier study Qf unsteady flQW (Davies, 1990) suggest that, fQr any particular SQlid type, the modelling Qf advectiQn in unsteady flQW can be based Qn a relatiQnship between SQlid velocity and mean flQW velocity fQr steady flow. The laboratory studies Qn grQss sanitary SQlids described in the paper suggest the fQlIowing.
1. Gross solids of different types move with the flow at a range of different longitudinal velocities, and the difference between SQlid velocity and mean flQW velocity can be significant. 2. Deposition of gross solids can be related to depth and velocity. MODEL DETAILS A pilQt model using the principles described above has been developed and tested. The purpose is to test the effect and suitability Qf the propQsed methQds of mQdelling gross SQlids' mQvement. The outcome is not, at present, a finalised wQrking tool for actual sewer system modelling. Hydraulic model A model of gross solids' movement, as with all models of sewer water quality, should be based on a hydraulic model of the sewer system. In this case, the hydraulic model is one in which the full Saint-Venant equations are solved using an explicit finite difference method (Davies, 1993). This hydraulic model performs well in mass balances checks and in comparison with experimental unsteady flow data. The model can represent a main sewer with lateral inflows but not a fully branched sewer system. Representin& different types of solid The following is proposed as an appropriate method of representing the range of gross solids fQund in practice. The full range can be divided into an appropriate number of types according to advective behaviour in steady flow. Such a division is inevitably artificial, but aims to give a simple representation of the full range. For each type, a particular relationship between solid velocity and mean flow velocity is specified, together with particular values of depth and velocity associated with deposition. Trackin& The advection of gross solids is modelled by "tracking" individual solids or groups of solids. At any point in distance and time, the mean flow velocity is known from the hydraulic model. This can be converted to solid velocity using the specified relationship for the particular solid type. Each specified relationship between solid velocity and mean velocity is assumed (on the basis of the earlier laboratory results) to apply in steady and unsteady conditions. The velocity of a solid at any instantaneous position is thus known, and this can be used progressively to track its movement through the system. If depth or velocity over any section decreases to the level specified as causing deposition, the progress of solids in the section is halted until this level is again exceeded. Simulation A simulation starts with a steady baseflow with a constant load-rate of solids for each solids type. Inflow hydrographs are specified for the inflow points, together with relationships between solids input load-rate and time. At a specified PQint at the downstream end of the system, the resulting solids load-rate graphs are given by the model.
45
Gross solids movements
MODEL OPERAnON Two simple examples of output from the pilot model are now given. Both are for simplified fictitious catchments. The first example (Fig. 2) demonstrates the representation of gross solids' advection. The main sewer has no lateral inflows. The hydrograph has a trapezoidal shape, and the input load-rate of gross solids is constant. Solids are represented by five types - two that move at velocities faster than mean flow velocity, one that moves at mean velocity, and two that move at lower velocities. There is no erosion or deposition. 100 80 -;
eo. 80
..
..........,
011
:;
40 20 0 0
--'S.
20
40
80
..
-
&ross solids suspended solids
:0
~
. :s ... '0
.. f
800
-. ~ ~
~
f\
24
~
• oS
120 1000
'i::
."
tOO
40
.c 32 E
.s-
80
rime (min)
8cto
18
400
8
200
o ."
.
• oS
.
:'5! '0
..... ..
'2 ."
c.
:0
a
a
0
20
40
80
80
100
120
rime (min)
Figure 2. Advection.
The resulting graph of gross solids' load-rate at the downstream end of the system, for the five types combined, is given on Fig. 2. It is compared with the equivalent graph for suspended solids (also resulting from a constant input load-rate) modelled using equation (I). The scales on the load-rate graph have been drawn so that the input rates for gross solids and suspended solids coincide. For both gross solids and suspended solids there is a first flush resulting from the overtaking of the pollutants by the storm wave. The gross solids variations are attenuated by the effect of the range of velocities for the solids types. In the example on Fig. 3, the conditions created by the hydrograph cause depth and velocity to decrease, for a short period. below the level associated with deposition for one of the solids types. This causes a reduction in load-rate while the conditions prevail and a small peak resulting from the later erosion. After the peak, the load-rate continues to rise gradually with increasing flow.
J. W. DAVIES el al.
46
SO 40
......
~ ...
.
u
30 20
,
~
10
1 0
.
.....
/
l
0
·si::
.,..........-"
20
40 60 time (min)
60
100
80
100
8
..
,Q
E
.:."
. . .. :=
8
~
'l'
"0
4 i'/
.2
....
Q
..
/'-.
2
co
0 0
20
40 60 time (min)
Figure 3. Deposition/erosion.
CONCLUSIONS
Methods of modelling gross solids' movement in combined sewers have been considered. Laboratory studies have given information on the advection and deposition of gross solids. Theoretical considerations have suggested that: - the Fickian model is not suitable for representing longitudinal dispersion of gross solids - a pollutant continuity (advection) equation may not be suitable for representing advection of gross solids - load-rate is more suitable than concentration for expressing quantities of gross solids. The proposed method of modelling gross solids' movement entails: - representing the range of solids found in actual sewers by an appropriate number of types - tracking solids by successively converting mean flow velocity to solid velocity using a relationship specified for each type, assumed to apply in steady and unsteady conditions - halting the progress of solids while depth or velocity is below the level associated with deposition.
Gross solids movements
47
These proposals relate simply to modelling gross solids' movement in sewers and do not take account of the influences of physical degradation or interaction with other material. The next stage in practical application should be to determine appropriate values for the physical parameters associated with advection, deposition and re-erosion in actual sewers.
REFERENCES Brown. D. M.• Buller. D., Onnan. N. R. and Davies. J. W. (1995). Gross solids transport in small diameter sewers. In: Proceedings of lnt~mationolConfu~rrc~ on S~w~r Solids. Dundee. Crabtree. R.. Garsdal. H., Gent. R., Mark, O. and Dorge, J. (1994). MOUSETRAP - A detenninistic sewer flow quality model. In: Proceedings of lA WQ 17th Bitnnial Confu~nce. Budapest Davies. J. W. (1990). Laboratory study related to the modelling of slonnwater quality in combined sewers. In: Proceedings of 5th lrrumatiolUll Confu~nct on Urban Storm DraiJlag~. Osaka, Japan, 215-219. Davies, J. W. (1993). Modelling of stonnwater quality in combined sewers. In: Proceedings of 6th lnt~mational Confu~nc~ on Urban Storm Drairrag~, Niagara Falls, Canada. 1254-1259. Foundation for Water Research (1994). Urban Pollution Manag~m~rrt (UPM) Manual, FRlCL 0002. Jefferies. C. (1992). Methods of estimating the discharge of gross solids from combined sewer systems. Wat. Sci. T~ch .• 26(5/6), 1295-1304. Moys. G. D.. Osborne. M. P. and Payne. J. A. (1988). MOSQrrO 1 • Design Sp~cification. HR Wallingford. Report SR 184.