- Email: [email protected]
Gross solids transport in small diameter sewers
8)
Pergamon
Wat. Sci. Tech. Vol. 33, No.9, pp. 25-30, 1996. Copyright © 1996 IAWQ. Published by Elseviet SCIence Ltd Printed In Greal Bntaln. All nghts reserved. 0273-1223/96 $15'00 + 0·00
PH: 50273-1223(96)00366-6
GROSS SOLIDS TRANSPORT IN SMALL DIAMETER SEWERS D. M. Brown*, D. Butler*, N. R. Orman** and 1. W. Davies***
* Depanment of Civil Engineering, Imperial College ofScience, Technology and Medicine, London SW7 2BU, UK ** WRc pic, Frankland Road, Swindon SN5 8YF, UK *** School ofArchitecture and Engineering, University of Westminster, London NWI5LS, UK ABSTRACf Currently, little is known about the properties of sanitary gross solids or their transport mechamsms in sewers. This paper describes a project designed to study solids movement in small gravity sewers by laboratory, field and modelling work. Results of laboratory tests on gross solids' transport under steady flow conditions are presented. An 'idealised' field-based sewer has been constructed and will be used to momtor solids' movement under non-steady, intermittent flow. A computational model based on a method of characteristics solution of the St Venant equations has been produced. This will be extended to account for solids' erosion, transport and deposition. Copyright © 1996 IAWQ. Published by Elsevier Science Ltd.
KEYWORDS Domestic wastewater; foul/combined sewers; gross solids; gross solids transport; solids. INTRODUCfION Despite making up a significant proportion of domestic wastewater, little is known about the properties of sanitary gross solids or the detailed mechanisms of their movement in foul and combined sewers. Information and experience that does exist has been gained from building drainage systems (Swaffield and Galowin, 1992) and by Butler and Graham's (1995) work on domestic dry weather flow modelling. Gross solids enter the system via the we and are initially transported by an attenuating flush wave. At some distance along the pipe the solid is deposited on the invert and remains at rest until re-eroded by another flush wave. Further downstream, it is presumed that there is sufficient continuous baseflow to maintain the solid in motion until it is removed from the system, either at a eso, sea outfall, or sewage treatment works. Particular interest in gross solids transport in small sewers is now emerging for the following reasons: solids are known to be implicated in small gravity sewer blockages, although the exact causes and mechanisms are still uncertain. water conservation measures are now being more widely adopted and the effects of reducing the we flush volume on in-sewer solids movement is unknown. 25
D. M. BROWN t!/ al.
26
it is not known how long individual solids remain in the sewer system, or indeed if the sewer acts as a net solids sink.
This paper describes a research project which has been developed to explore the issues associated with gross solids transport in the region lying between building drainage and large diameter sewers. The aim of the project is to gain an understanding of gross solids transportation in small diameter sewers. This will be achieved by: undertaking a fieldwork programme to examine and record the phenomenon. building a computational model based on the 5t Venant equations to model the fluid flow and solids transportation. validating this model with data obtained from laboratory work and fieldwork. Initial tests have been completed in a 13m, artificially roughened uPVC pipe laboratory flume with an artificial faecal stool, to investigate its properties under a variety of steady flow conditions. Results from these tests are presented and compared with earlier experiments with sanitary products. The fieldwork programme consists of two phases. In the first phase, tests will be carried out in real small diameter sewers in order to evaluate the attenuation of multiple flush waves, and to compare these results with those predicted by an existing model based on a method of characteristics solution of the St Venant equations. In the second phase, a 25m long vitrified clay channel flume will be used to examine gross solids transport in a controllable environment. This work will provide additional data to extend the model ultimately to simulate multiple (solid and liquid) inputs in a dendritic network. Input data on domestic appliance flow and solids generation will also be incorporated. GROSS SOLIDS INPUTS Surprisingly little is known concerning the characteristics of gross solids or indeed the nature of their input into sewerage systems through the WC, despite their composing a significant proportion of domestic wastewater. In particular, in the context of this work, there is a lack of quantitative information on the rates of solids' entry. Recent work (Friedler et al., 1995) has attempted to fill some of the information gaps by providing data on WC derived solids. Averaged results from this work are contained in the paper mentioned, but detailed statistical analysis has yet to be completed. Some statistical information on WC input flows is, however, available (Friedler and Butler, 1995). Information from both of these studies will be incorporated into a stochastic generator of solids and WC wave inputs, which will be used in association with the wave attenuation and solids transport computational models. INITIAL TESTING OF SOLIDS Solids transport under steady open channel flow conditions has been investigated in a 13m, 289mm ID artificially roughened uPVC pipe flume. The solid used was an 'NBS' solid (artificial faecal stool) which is a plastic cylinder 38mm diameter by 76mm long, and a specific gravity of 1.05. The average velocity of this solid was recorded under a series of flows with different depths and velocities by timing its movement over a measured 10m distance. Each test was repeated ten times. The flow rate was adjusted by means of a butterfly valve, and the discharged volume was measured over a timed period. This procedure was carried out three times at each flow setting, and the mean flow was calculated. Earlier experiments have been carried out in the same apparatus (Xu, 1994) using a variety of other gross solids, that had previously been soaked for 24 hours prior to the experiment. Examples of solids tested include various sanitary towels and tampons, backing strips from towels, cotton buds and toilet tissue. These were chosen to represent typical solids that spill through a CSO during a storm event. Combined test results
Gross solids transport
21
are shown in Figure 1A and 1B, where the proportional depth of the flow in relation to the diameter of the pipe is plotted against the ratio of the mean solid velocity to the mean velocity of flow. 1.4 T - - -
- ------
-
- ------------------- -- -------
---
----I
I I
12
A1
OS
f.. .
~.8
..
I
!.61
1
~
.-+- NBS S~iid - ,
;g
~.41 ~ j
-6-TOJlet Paper I
i- - Panty Liner ! ~-:-o-::-]:am~n_ '
0.2 , 1
o
+----.-..----------r• I
o
O.OS
~-----r-
0.1
O.IS
-- - - - - ....... --- - - - ---- ---T-
~--
0.2 0.2S Proportional Depth
- - --.-- ~ -
OJ
----,--------
0.3S
04
Figure IA. Ratio of solid to flow velocities against proportional depth at a gradient of 1:100_ 1.4
~--
1.2:
~
OS 1 l
f
-----------
- -- -- --- - - - -
:
: ~I
~
~:.-.==--.
~.8 J
..
I
I
.@
I
~ ••
I'
..
j).61
'
...
I
'"
,.::;::NBS S~iid
}.4 ~
,
I
--:
,
1-6- Toilet Paper,
~
I--
Panty Liner
I
;-0- T!..mpon ..J
0.2
o +-------,----,---• O.OS 0.1 O.IS o
--
~---_.~--..,-._-----,-----
0.2 0.2S Proportional Depth
0.3
0.3S
Figure IB. Ratio of solid to flow velocities against proportional depth at a gradient of I: 1500.
0.4
28
D. M. BROWN tl at.
Figure IA and lB illustrate the ratio of solid to flow velocities for a range of proportional depths and two gradients. I: 100 and I:500. Figure IA shows that the NBS solid has a much lower velocity than other solids at lower depths of flow. Observations in the laboratory suggest that the NBS solid is in contact with the pipe invert and/or wall, and hence subject to frictional resistance during its transportation. This is in contrast to the other solids which tend to travel in the centre of the flow, even at low proportional depths. The differences in NBS solid velocity is still apparent at the lower gradient in Figure lB, but less pronounced. Both figures IA and lB show clearly that some solids travel at velocities which exceed the mean velocity. It is well known that a uniform distribution of velocity does not occur in open channel flow, due to the effects of the solid boundaries and the free surface. Nalluri and Alvarez (1992) have further shown how this distribution is distorted by the presence of a sediment bed. The maximum velocity occurs at a point below the free surface, along the centre line of a circular pipe, and is 20-30% above mean velocity. It is in this position that many solids were seen to flow down the flume. LEVEL MONITORING SYSTEM A series of level monitors has been obtained for use during the planned fieldwork. An ultrasonic emitter sends a pulse in the direction of the surface that is being measured which partially reflects the pulse to the sensor, where the emitter now acts as a microphone. The time taken between the emission and the reception of the pulse is recorded, and thus the distance of the surface from the sensor can be determined. This is carried out approximately at 10 Hz by the converting unit, also known as the transmitter. The transmitter produces a continuous 4-20mA signal, which can be readily logged by a PC using a conversion board and suitable software. The software and hardware combination used can sample this signal at a rate of over 50Hz, although this is not necessary due to the lower sampling rate of the sensor. In practice the signal is sampled at around 2Hz in order to keep the data logging files to a manageable size. WAVE ATTENUATION FIELDWORK A set of field experiments has been designed to validate the wave attenuation model in sewers. A. combination of up to three WC flushes and a baseflow may be discharged into a series of sewer pipes, ranging from lOOmm ID to 225mm 10. Up to three level monitoring sensors (described above) will be placed in manholes, and the results will be compared with those predicted by the computational model. The detectors have a small enough measuring cone to ensure that flow widths as low as 42mm can be recorded which equates to a depth of 5mm in a lOOmm 10 pipe. ' SOLIDS TRANSPORTATION FIELDWORK As there are currently no known data on the nature of solids transport in small diameter foul sewer pipes an experimental flume was devised to produce such data. This flume has been designed to reproduce field conditions in an idealised environment. The flume consists of twenty five l.Om long 150mm 10 vitrified clay (VC) channels. These are placed on top of a 200mm wide by 300mm deep glass reinforced plastic (GRP) channel. The GRP sections are connected by adjustable mild steel brackets to brick piers. This arrangement allows the gradient of the whole system to be infinitely adjusted between I :50 and flat. This will ensure that experimental work can be carried out at both sub- and super-critical flows. Repeatable waves are generated using an electrically activated ball valve connected to a programmable electronic sequence controller. A 4-20mA output from this ball valve is logged, and indicates the position of the valve, and the level of flow passing through it. This valve is supplied by a constant head tank, that is pumped from a downstream sump, and flows back from the tank to the sump through the GRP channel, beneath the clay channels. These waves are designed to represent typical outputs from a WC at the base of a drainage stack. Once a profile is built up of this wave at 20m from the stack using the level monitoring equipment described later in this paper, then the wave generator is reprogrammed to produce this wave. Again this may be profiled, and a similar generation procedure may be undertaken. This procedure is
Gross solids transport
29
repeated for each set of experiments until a representation is made of conditions at up to 100m from the drainage stack. When each wave has been successfully profiled and reproduced with the level monitoring equipment. solid transport experiments will be undertaken using this wave. Solids will initially be placed at a fixed point at the beginning of the flume. and the distance that they travel will be recorded in a defect free pipe. This work will then be extended to study the action of various defects on the transportation distance of the solid. The action of the deposition of the least transportable solid placed at a fixed point on the flume. will be studied to see how it interacts with the solid under investigation. A further set of experiments will discover the likely percentage of different solids that will be eroded by a given flush wave at varying distances from the discharge stack. It is expected that solids will not be eroded or left deposited on an entirely predictable basis. and so the computational model will be programmed to reflect this. Joint deformations up to around l5mm may be prepared in the clay channels. together with other construction defects that are thought to initiate blockages. such as mortar intrusion. The ultrasonic level detecting equipment described earlier will record the profiles of the waves generated. COMPUTATIONAL MODEL Mathematical models. based on the method of characteristics have been used extensively for the solution of the full St Venant equations. This method of solution of the quasi-linear hyperbolic partial differential equations (pde's) is particularly favoured because of its applicability to the rapidly varying waves studied. It is a technique which transforms the full pde's into total derivatives. which are known as 'characteristics'. and appear as lines in the x-t plane. They allow the prediction of flow depth and velocity and hence flow at a particular location and particular time based upon adjacent flow conditions one step in the past. Thus suitable boundary conditions must therefore be made for the first and last node simulated. As the discharge to the pipe is known at each timestep, then the flow. velocity and depth is assumed to enter at normal depth. The downstream end is assumed to act as free outfall. and thus the flow will exit at the critical depth. which may be readily calculated. Currently a first order or linear approximation is used in the FORTRAN 77 model to calculate the depth and velocity at the adjacent nodes. It is based on the expression:
1"...
f(x) dx .. f(x o) (XI - xo) This will be replaced in the future by the better approximation:
J''1o1
f(x) dx ..
.x [f(xo) +
f(x l )]
(XI
-
x o)
based on the trapezoidal rule, where represents a derivative present in the characteristic equations. This second order approximation should allow better volume conservation which is important considering the limited flow often found in small diameter foul sewers. This model effectively routes non-steady flow down a single pipe from the upstream end. and provides detailed node information as the simulation progresses. Other workers (Swaffield et al., 1982) have successfully applied this technique to unsteady open channel flow problems, particularly internal building drainage systems. As this model is intended for use in small diameter sewer systems. which are potentially quite different to internal building drainage systems. the wave attenuation model will be validated using results from the field referred to earlier. Fok (1990) and Campbell (1991) used a specific energy approach to develop the solid transport model SOLNET. a simple model used to predict the distances various solids are transported by a WC flush. Later work at Heriot-Watt (McDougall and Swaffie1d. 1993. 1994) has used a solid velocitylflow velocity decrement model to extend the work into defective building drainage systems. This is because a depth only model would not be able to represent backwater conditions that may exist in a network where the velocities
D. M. BROWN el al.
30
would decrease as depths increase. A tractive force approach has not been ruled out. This may be based on the forces necessary to cause a solid to either deposit or erode; further work will identify if this approach is appropriate. CONCLUSIONS The work described should allow a computational model to be built representing the mechanisms of gross solids transport in small diameter pipes. The model will incorporate a stochastic generator of flushes and solids, based on the results of a recent survey. The attenuation of these waves will be modelled by a second order approximation of a method of characteristics solution of the St Venant equations. Field work obtained from sewers will be used to validate this method before the transportation of solids is considered. Results from experiments carried out in real sewer channels, although in an idealised field environment, will be used to build and verify a solids transportation model. Development of the model will allow experimentation with the major variables to predict the movement of solids through the system, and allow exploration of scenarios which increase the propensity for blockage formation. ACKNOWLEDGEMENTS The first author is in receipt of a Postgraduate Training Partnership Award funded by EPSRC, WRc pIc and the Department of Trade and Industry REFERENCES Butler, D. and Graham, N. 1. D. (1995). Modeling dry weather wastewater flow in sewer networks, J. Env. Eng. ASCE, 121(2), 161-173. Campbell, D. P. (1991). Development and validation of the solid transport model SOLNET, Laboratory Report, Heriot-Watt University, Edinburgh. Friedler, E., Brown, D. M. and Butler, D. (1995). A study of solids input into sewer networks from the WC, International Conference on Sewer Solids, Dundee. Friedler, E. and Butler, D. (1995). Quantifying the inherent uncertainty in the quantity and quality of domestic wastewater. Proc Inter-disciplinary Int. Symp. on Uncertainty, Risk & Transient Pollution Events, Exeter, July. Fok, C. M. R. (1990). Solid transport studies in partially filled pipe flows, MSc Dissertation, Heriot-Watt University, Edinburgh. McDougall, J. A. and Swaffield, J. A. (1993). Transport of solids in defective building drainage systems, CIBW62 Conference, Oporto. McDougall, J. A. and Swaffield, 1. A. (1994). Assessment of WC performance using computer based prediction techniques, CIBW62 Conference, Brighton. Nalluri, C. and Alvarez, E. M. (1992). The influence of cohesion on sediment behaviour, Wal. Sci. Tech., 25(8), 151-164. Swaffield, 1. A., Galowin, L. S. and Bridge, S. (1982). Mathematical modelling of time dependant wave attenuation in gravity driven partially filled pipe flow, 4th Int Conf on Finite Elements in Water Resources, Hanover, June. Swaffield, J. A. and Galowin, L. S. (1992). The Engineered Design ofBuilding DraillDge Systems, Ashgate. Aldershot, UK. Xu, Y. (1994). Study of gross solids in drainage flow, Laboratory Report, University of Westminster, London.
Pergamon
Wat. Sci. Tech. Vol. 33, No.9, pp. 25-30, 1996. Copyright © 1996 IAWQ. Published by Elseviet SCIence Ltd Printed In Greal Bntaln. All nghts reserved. 0273-1223/96 $15'00 + 0·00
PH: 50273-1223(96)00366-6
GROSS SOLIDS TRANSPORT IN SMALL DIAMETER SEWERS D. M. Brown*, D. Butler*, N. R. Orman** and 1. W. Davies***
* Depanment of Civil Engineering, Imperial College ofScience, Technology and Medicine, London SW7 2BU, UK ** WRc pic, Frankland Road, Swindon SN5 8YF, UK *** School ofArchitecture and Engineering, University of Westminster, London NWI5LS, UK ABSTRACf Currently, little is known about the properties of sanitary gross solids or their transport mechamsms in sewers. This paper describes a project designed to study solids movement in small gravity sewers by laboratory, field and modelling work. Results of laboratory tests on gross solids' transport under steady flow conditions are presented. An 'idealised' field-based sewer has been constructed and will be used to momtor solids' movement under non-steady, intermittent flow. A computational model based on a method of characteristics solution of the St Venant equations has been produced. This will be extended to account for solids' erosion, transport and deposition. Copyright © 1996 IAWQ. Published by Elsevier Science Ltd.
KEYWORDS Domestic wastewater; foul/combined sewers; gross solids; gross solids transport; solids. INTRODUCfION Despite making up a significant proportion of domestic wastewater, little is known about the properties of sanitary gross solids or the detailed mechanisms of their movement in foul and combined sewers. Information and experience that does exist has been gained from building drainage systems (Swaffield and Galowin, 1992) and by Butler and Graham's (1995) work on domestic dry weather flow modelling. Gross solids enter the system via the we and are initially transported by an attenuating flush wave. At some distance along the pipe the solid is deposited on the invert and remains at rest until re-eroded by another flush wave. Further downstream, it is presumed that there is sufficient continuous baseflow to maintain the solid in motion until it is removed from the system, either at a eso, sea outfall, or sewage treatment works. Particular interest in gross solids transport in small sewers is now emerging for the following reasons: solids are known to be implicated in small gravity sewer blockages, although the exact causes and mechanisms are still uncertain. water conservation measures are now being more widely adopted and the effects of reducing the we flush volume on in-sewer solids movement is unknown. 25
D. M. BROWN t!/ al.
26
it is not known how long individual solids remain in the sewer system, or indeed if the sewer acts as a net solids sink.
This paper describes a research project which has been developed to explore the issues associated with gross solids transport in the region lying between building drainage and large diameter sewers. The aim of the project is to gain an understanding of gross solids transportation in small diameter sewers. This will be achieved by: undertaking a fieldwork programme to examine and record the phenomenon. building a computational model based on the 5t Venant equations to model the fluid flow and solids transportation. validating this model with data obtained from laboratory work and fieldwork. Initial tests have been completed in a 13m, artificially roughened uPVC pipe laboratory flume with an artificial faecal stool, to investigate its properties under a variety of steady flow conditions. Results from these tests are presented and compared with earlier experiments with sanitary products. The fieldwork programme consists of two phases. In the first phase, tests will be carried out in real small diameter sewers in order to evaluate the attenuation of multiple flush waves, and to compare these results with those predicted by an existing model based on a method of characteristics solution of the St Venant equations. In the second phase, a 25m long vitrified clay channel flume will be used to examine gross solids transport in a controllable environment. This work will provide additional data to extend the model ultimately to simulate multiple (solid and liquid) inputs in a dendritic network. Input data on domestic appliance flow and solids generation will also be incorporated. GROSS SOLIDS INPUTS Surprisingly little is known concerning the characteristics of gross solids or indeed the nature of their input into sewerage systems through the WC, despite their composing a significant proportion of domestic wastewater. In particular, in the context of this work, there is a lack of quantitative information on the rates of solids' entry. Recent work (Friedler et al., 1995) has attempted to fill some of the information gaps by providing data on WC derived solids. Averaged results from this work are contained in the paper mentioned, but detailed statistical analysis has yet to be completed. Some statistical information on WC input flows is, however, available (Friedler and Butler, 1995). Information from both of these studies will be incorporated into a stochastic generator of solids and WC wave inputs, which will be used in association with the wave attenuation and solids transport computational models. INITIAL TESTING OF SOLIDS Solids transport under steady open channel flow conditions has been investigated in a 13m, 289mm ID artificially roughened uPVC pipe flume. The solid used was an 'NBS' solid (artificial faecal stool) which is a plastic cylinder 38mm diameter by 76mm long, and a specific gravity of 1.05. The average velocity of this solid was recorded under a series of flows with different depths and velocities by timing its movement over a measured 10m distance. Each test was repeated ten times. The flow rate was adjusted by means of a butterfly valve, and the discharged volume was measured over a timed period. This procedure was carried out three times at each flow setting, and the mean flow was calculated. Earlier experiments have been carried out in the same apparatus (Xu, 1994) using a variety of other gross solids, that had previously been soaked for 24 hours prior to the experiment. Examples of solids tested include various sanitary towels and tampons, backing strips from towels, cotton buds and toilet tissue. These were chosen to represent typical solids that spill through a CSO during a storm event. Combined test results
Gross solids transport
21
are shown in Figure 1A and 1B, where the proportional depth of the flow in relation to the diameter of the pipe is plotted against the ratio of the mean solid velocity to the mean velocity of flow. 1.4 T - - -
- ------
-
- ------------------- -- -------
---
----I
I I
12
A1
OS
f.. .
~.8
..
I
!.61
1
~
.-+- NBS S~iid - ,
;g
~.41 ~ j
-6-TOJlet Paper I
i- - Panty Liner ! ~-:-o-::-]:am~n_ '
0.2 , 1
o
+----.-..----------r• I
o
O.OS
~-----r-
0.1
O.IS
-- - - - - ....... --- - - - ---- ---T-
~--
0.2 0.2S Proportional Depth
- - --.-- ~ -
OJ
----,--------
0.3S
04
Figure IA. Ratio of solid to flow velocities against proportional depth at a gradient of 1:100_ 1.4
~--
1.2:
~
OS 1 l
f
-----------
- -- -- --- - - - -
:
: ~I
~
~:.-.==--.
~.8 J
..
I
I
.@
I
~ ••
I'
..
j).61
'
...
I
'"
,.::;::NBS S~iid
}.4 ~
,
I
--:
,
1-6- Toilet Paper,
~
I--
Panty Liner
I
;-0- T!..mpon ..J
0.2
o +-------,----,---• O.OS 0.1 O.IS o
--
~---_.~--..,-._-----,-----
0.2 0.2S Proportional Depth
0.3
0.3S
Figure IB. Ratio of solid to flow velocities against proportional depth at a gradient of I: 1500.
0.4
28
D. M. BROWN tl at.
Figure IA and lB illustrate the ratio of solid to flow velocities for a range of proportional depths and two gradients. I: 100 and I:500. Figure IA shows that the NBS solid has a much lower velocity than other solids at lower depths of flow. Observations in the laboratory suggest that the NBS solid is in contact with the pipe invert and/or wall, and hence subject to frictional resistance during its transportation. This is in contrast to the other solids which tend to travel in the centre of the flow, even at low proportional depths. The differences in NBS solid velocity is still apparent at the lower gradient in Figure lB, but less pronounced. Both figures IA and lB show clearly that some solids travel at velocities which exceed the mean velocity. It is well known that a uniform distribution of velocity does not occur in open channel flow, due to the effects of the solid boundaries and the free surface. Nalluri and Alvarez (1992) have further shown how this distribution is distorted by the presence of a sediment bed. The maximum velocity occurs at a point below the free surface, along the centre line of a circular pipe, and is 20-30% above mean velocity. It is in this position that many solids were seen to flow down the flume. LEVEL MONITORING SYSTEM A series of level monitors has been obtained for use during the planned fieldwork. An ultrasonic emitter sends a pulse in the direction of the surface that is being measured which partially reflects the pulse to the sensor, where the emitter now acts as a microphone. The time taken between the emission and the reception of the pulse is recorded, and thus the distance of the surface from the sensor can be determined. This is carried out approximately at 10 Hz by the converting unit, also known as the transmitter. The transmitter produces a continuous 4-20mA signal, which can be readily logged by a PC using a conversion board and suitable software. The software and hardware combination used can sample this signal at a rate of over 50Hz, although this is not necessary due to the lower sampling rate of the sensor. In practice the signal is sampled at around 2Hz in order to keep the data logging files to a manageable size. WAVE ATTENUATION FIELDWORK A set of field experiments has been designed to validate the wave attenuation model in sewers. A. combination of up to three WC flushes and a baseflow may be discharged into a series of sewer pipes, ranging from lOOmm ID to 225mm 10. Up to three level monitoring sensors (described above) will be placed in manholes, and the results will be compared with those predicted by the computational model. The detectors have a small enough measuring cone to ensure that flow widths as low as 42mm can be recorded which equates to a depth of 5mm in a lOOmm 10 pipe. ' SOLIDS TRANSPORTATION FIELDWORK As there are currently no known data on the nature of solids transport in small diameter foul sewer pipes an experimental flume was devised to produce such data. This flume has been designed to reproduce field conditions in an idealised environment. The flume consists of twenty five l.Om long 150mm 10 vitrified clay (VC) channels. These are placed on top of a 200mm wide by 300mm deep glass reinforced plastic (GRP) channel. The GRP sections are connected by adjustable mild steel brackets to brick piers. This arrangement allows the gradient of the whole system to be infinitely adjusted between I :50 and flat. This will ensure that experimental work can be carried out at both sub- and super-critical flows. Repeatable waves are generated using an electrically activated ball valve connected to a programmable electronic sequence controller. A 4-20mA output from this ball valve is logged, and indicates the position of the valve, and the level of flow passing through it. This valve is supplied by a constant head tank, that is pumped from a downstream sump, and flows back from the tank to the sump through the GRP channel, beneath the clay channels. These waves are designed to represent typical outputs from a WC at the base of a drainage stack. Once a profile is built up of this wave at 20m from the stack using the level monitoring equipment described later in this paper, then the wave generator is reprogrammed to produce this wave. Again this may be profiled, and a similar generation procedure may be undertaken. This procedure is
Gross solids transport
29
repeated for each set of experiments until a representation is made of conditions at up to 100m from the drainage stack. When each wave has been successfully profiled and reproduced with the level monitoring equipment. solid transport experiments will be undertaken using this wave. Solids will initially be placed at a fixed point at the beginning of the flume. and the distance that they travel will be recorded in a defect free pipe. This work will then be extended to study the action of various defects on the transportation distance of the solid. The action of the deposition of the least transportable solid placed at a fixed point on the flume. will be studied to see how it interacts with the solid under investigation. A further set of experiments will discover the likely percentage of different solids that will be eroded by a given flush wave at varying distances from the discharge stack. It is expected that solids will not be eroded or left deposited on an entirely predictable basis. and so the computational model will be programmed to reflect this. Joint deformations up to around l5mm may be prepared in the clay channels. together with other construction defects that are thought to initiate blockages. such as mortar intrusion. The ultrasonic level detecting equipment described earlier will record the profiles of the waves generated. COMPUTATIONAL MODEL Mathematical models. based on the method of characteristics have been used extensively for the solution of the full St Venant equations. This method of solution of the quasi-linear hyperbolic partial differential equations (pde's) is particularly favoured because of its applicability to the rapidly varying waves studied. It is a technique which transforms the full pde's into total derivatives. which are known as 'characteristics'. and appear as lines in the x-t plane. They allow the prediction of flow depth and velocity and hence flow at a particular location and particular time based upon adjacent flow conditions one step in the past. Thus suitable boundary conditions must therefore be made for the first and last node simulated. As the discharge to the pipe is known at each timestep, then the flow. velocity and depth is assumed to enter at normal depth. The downstream end is assumed to act as free outfall. and thus the flow will exit at the critical depth. which may be readily calculated. Currently a first order or linear approximation is used in the FORTRAN 77 model to calculate the depth and velocity at the adjacent nodes. It is based on the expression:
1"...
f(x) dx .. f(x o) (XI - xo) This will be replaced in the future by the better approximation:
J''1o1
f(x) dx ..
.x [f(xo) +
f(x l )]
(XI
-
x o)
based on the trapezoidal rule, where represents a derivative present in the characteristic equations. This second order approximation should allow better volume conservation which is important considering the limited flow often found in small diameter foul sewers. This model effectively routes non-steady flow down a single pipe from the upstream end. and provides detailed node information as the simulation progresses. Other workers (Swaffield et al., 1982) have successfully applied this technique to unsteady open channel flow problems, particularly internal building drainage systems. As this model is intended for use in small diameter sewer systems. which are potentially quite different to internal building drainage systems. the wave attenuation model will be validated using results from the field referred to earlier. Fok (1990) and Campbell (1991) used a specific energy approach to develop the solid transport model SOLNET. a simple model used to predict the distances various solids are transported by a WC flush. Later work at Heriot-Watt (McDougall and Swaffie1d. 1993. 1994) has used a solid velocitylflow velocity decrement model to extend the work into defective building drainage systems. This is because a depth only model would not be able to represent backwater conditions that may exist in a network where the velocities
D. M. BROWN el al.
30
would decrease as depths increase. A tractive force approach has not been ruled out. This may be based on the forces necessary to cause a solid to either deposit or erode; further work will identify if this approach is appropriate. CONCLUSIONS The work described should allow a computational model to be built representing the mechanisms of gross solids transport in small diameter pipes. The model will incorporate a stochastic generator of flushes and solids, based on the results of a recent survey. The attenuation of these waves will be modelled by a second order approximation of a method of characteristics solution of the St Venant equations. Field work obtained from sewers will be used to validate this method before the transportation of solids is considered. Results from experiments carried out in real sewer channels, although in an idealised field environment, will be used to build and verify a solids transportation model. Development of the model will allow experimentation with the major variables to predict the movement of solids through the system, and allow exploration of scenarios which increase the propensity for blockage formation. ACKNOWLEDGEMENTS The first author is in receipt of a Postgraduate Training Partnership Award funded by EPSRC, WRc pIc and the Department of Trade and Industry REFERENCES Butler, D. and Graham, N. 1. D. (1995). Modeling dry weather wastewater flow in sewer networks, J. Env. Eng. ASCE, 121(2), 161-173. Campbell, D. P. (1991). Development and validation of the solid transport model SOLNET, Laboratory Report, Heriot-Watt University, Edinburgh. Friedler, E., Brown, D. M. and Butler, D. (1995). A study of solids input into sewer networks from the WC, International Conference on Sewer Solids, Dundee. Friedler, E. and Butler, D. (1995). Quantifying the inherent uncertainty in the quantity and quality of domestic wastewater. Proc Inter-disciplinary Int. Symp. on Uncertainty, Risk & Transient Pollution Events, Exeter, July. Fok, C. M. R. (1990). Solid transport studies in partially filled pipe flows, MSc Dissertation, Heriot-Watt University, Edinburgh. McDougall, J. A. and Swaffield, J. A. (1993). Transport of solids in defective building drainage systems, CIBW62 Conference, Oporto. McDougall, J. A. and Swaffield, 1. A. (1994). Assessment of WC performance using computer based prediction techniques, CIBW62 Conference, Brighton. Nalluri, C. and Alvarez, E. M. (1992). The influence of cohesion on sediment behaviour, Wal. Sci. Tech., 25(8), 151-164. Swaffield, 1. A., Galowin, L. S. and Bridge, S. (1982). Mathematical modelling of time dependant wave attenuation in gravity driven partially filled pipe flow, 4th Int Conf on Finite Elements in Water Resources, Hanover, June. Swaffield, J. A. and Galowin, L. S. (1992). The Engineered Design ofBuilding DraillDge Systems, Ashgate. Aldershot, UK. Xu, Y. (1994). Study of gross solids in drainage flow, Laboratory Report, University of Westminster, London.