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Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/watres
A mathematical model to predict the effect of heat recovery on the wastewater temperature in sewers David J. Du¨rrenmatt*, Oskar Wanner Swiss Federal Institute of Aquatic Science and Technology, Eawag, 8600 Du¨bendorf, Switzerland
article info
abstract
Article history:
Raw wastewater contains considerable amounts of energy that can be recovered by means
Received 5 August 2013
of a heat pump and a heat exchanger installed in the sewer. The technique is well
Received in revised form
established, and there are approximately 50 facilities in Switzerland, many of which have
29 September 2013
been successfully using this technique for years. The planning of new facilities requires
Accepted 4 October 2013
predictions of the effect of heat recovery on the wastewater temperature in the sewer
Available online 17 October 2013
because altered wastewater temperatures may cause problems for the biological processes used in wastewater treatment plants and receiving waters. A mathematical model is
Keywords:
presented that calculates the discharge in a sewer conduit and the spatial profiles and
Sewer
dynamics of the temperature in the wastewater, sewer headspace, pipe, and surrounding
Modeling
soil. The model was implemented in the simulation program TEMPEST and was used to
Wastewater temperature
evaluate measured time series of discharge and temperatures. It was found that the model
Heat transfer
adequately reproduces the measured data and that the temperature and thermal con-
Heat recovery
ductivity of the soil and the distance between the sewer pipe and undisturbed soil are the most sensitive model parameters. The temporary storage of heat in the pipe wall and the exchange of heat between wastewater and the pipe wall are the most important processes for heat transfer. The model can be used as a tool to determine the optimal site for heat recovery and the maximal amount of extractable heat. ª 2013 Elsevier Ltd. All rights reserved.
1.
Introduction
Wastewater released into the sewer from showers, sinks and washers is an attractive source of energy. It is permanently available almost everywhere, has temperatures of 10e20 C throughout the year and contains considerable amounts of energy. If 1 m3 of water is cooled down by 1 C, 1.16 kWh of heat energy can be gained. If in the city of Zurich, Switzerland, the dry weather wastewater discharge of 230,000 m3/s were continuously cooled down by 1 C, the heat energy theoretically gained would correspond to a continuous delivery of 10 MW. At present, approximately 50 facilities are operating in
Switzerland, extracting heat from the wastewater by means of heat pumps and heat exchangers installed in the sewer; among these are three facilities in Zurich that produce a total power of 5 MW (EWZ, 2008). One of these facilities heats 800 apartments, and another heats and cools the largest building in Switzerland. There is a facility in Norway that heats and cools an entire district of the city of Oslo (Schmid, 2008). Basically, there are two techniques to recover heat from the sewer. The conventional technique is to install a heat exchanger at the bottom of the sewer pipe. This technique is simple and well established, but the efficiency of the heat exchanger will be reduced drastically if its surface is covered
* Corresponding author. Tel.: þ41 58 765 5297. E-mail address: [email protected] (D.J. Du¨rrenmatt). 0043-1354/$ e see front matter ª 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.watres.2013.10.017
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Fig. 1 e Top view of a section of the sewer between the villages of Ru¨mlang and Oberglatt in the Canton of Zurich, Switzerland.
by sediments or biofilms or is not completely submerged. An alternative and newer technique is to pump the wastewater through a heat exchanger installed outside the sewer. This technique makes it easier to control fouling of the heat exchanger, but it requires that the wastewater be filtered and leads to higher installation and pumping costs.
From an ecological point of view, it is logical to close energy cycles by bringing the energy back to the original user to reuse the energy disposed with the wastewater a second time instead of warming the environment (Olsson, 2012). The economic competitiveness of heat extraction from wastewater depends on the price of oil and gas, on the distance between the recovery site and the user of the energy and on the availability of alternative ambient energy sources (Ghafghazi et al., 2010). Facilities using wastewater for both heating and cooling are usually very economical. However, there are legal constraints in most countries on the permitted temperature changes for influents of wastewater treatment plants and receiving waters (AWEL, 2010; Wanner et al., 2005). Therefore, successful planning and operation of heat recovery facilities require that their effect on the wastewater temperature be quantifiable. In this paper, a model is presented to calculate the dynamics and spatial profiles of wastewater temperature in a sewer pipe as a function of wastewater discharge, airflow in the sewer and heat transfer between the sewer, soil and atmosphere. The model is implemented in the simulation program TEMPEST (temperature estimation) and is calibrated and
Table 1 e Overview of the information required to model the wastewater temperature in a sewer. Parameter Sewer pipe Length Nominal diameter Friction coefficientb,h Slope Wall thickness Wall thermal conductivityb, h Wall thermal diffusivityb, h Soil Undisturbed temperaturee, h Penetration depthh Thermal conductivityf, h Thermal diffusivityf Wastewater Discharge at influentc Temperature at influentc COD degradation rated, h Fouling factorh Densityg Thermal conductivityg Specific heat capacityg Air Ambient temperaturec Ambient pressurec Ambient relative humidityc Density Thermal conductivity Specific heat capacity a
Symbol
Value
Unit
Source a
L D kst S0 s lP aP
1845 0.9 70 0.0091 0.1 2.3 1,106
m m m1/3 s1 e m W/(mK) m2/s
IP IP L IP IP IP/L IP/L
TS,inf dS lS aS
5.5 0.1 1.1 0.2,106
C m W/(mK) m2/s
M/E E IP/L IP/L
QWin TWin rCOD f rW lW cp,W
0.03 12 2.8 200 998.2 0.60 4181
m3/s C mgCOD/(m3 s) W/(m2 K) kg/m3 W/(mK) J/(kg K)
M M E L L L L
TA pA 4A rL lL cp,L
8.3 966 0.75 1.19 0.0257 1007
W W W L L L
C mbar e kg/m3 J/(kg K) J/(kg K)
Key: IP ¼ implementation plan, E ¼ estimate, L ¼ literature, M ¼ field measurement and W ¼ weather station. Typical parameter for concrete reinforced with 1% steel (e.g., Hager (2010) for friction coefficient and DIN (2000) for thermal properties) selected according to the implementation plan. c Average during calibration period. d Based on studies by Huisman et al. (2004) and Flamink et al. (2005). e Estimate based on measurements with temperature probes buried in the soil. f Typical parameter for clay (Unsworth and Monteith, 1990), which is prevalent according to the implementation plan. g Physical properties of wastewater approximated by clean water values at 10 C. h Parameter subject to calibration. b
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validated with data obtained from a field study in the sewer of Ru¨mlang, Switzerland. The model is then used to identify the processes and environmental conditions that primarily determine the wastewater temperature in the sewer, to predict the effect of heat recovery on the downstream wastewater temperature and to discuss various scenarios for the recovery of heat energy.
2.
Experimental
2.1.
Site description
The investigated sewer line is 1845 m in length; lies parallel to the river Glatt; and has a circular cross-section, uniform geometrical and material properties, and no tributaries (cf. Fig. 1). A manhole, consisting of a cover with a small opening, was built approximately every 60 m. The surrounding soil is homogenous along the sewer line; however, the groundwater table varies with time. Upstream of the considered section, at a distance of 75 m, there is a combined sewer overflow, while downstream, at a distance of 120 m, there is an inverted siphon; both allow for free air exchange with the atmosphere.
2.2. Field measurements of wastewater discharge and temperature A data acquisition campaign was carried out from February 14 to March 22, 2008, during which the wastewater discharge was measured with two Nivus PCM 3 ultrasonic flow meters in the upstream manhole (RS 4943) and in the downstream manhole (RS 3096). Temperature was logged using Onset TMC6-HD temperature probes mounted in both manholes. To obtain a good estimate for the soil temperature, another temperature logger was buried at a depth of 1.2 m and a distance of 2 m from the sewer at manhole RS 4943.
2.3.
Sewer properties and ambient conditions
Modeling of the spatial profiles and dynamics of the wastewater temperature in a sewer conduit requires information on the sewer pipe properties, soil properties and influent and ambient conditions.
Information on the geometry, thermal properties and friction coefficient of the sewer pipe and on the properties of the surrounding soil can be extracted from implementation plans or from the literature. Ambient data were taken from a meteorological station located nearby. Table 1 gives an overview of the values of the parameters and ambient conditions used for modeling of the wastewater temperature in the sewer of Ru¨mlang.
3.
Modeling
A pseudo two-dimensional mathematical model of a sewer conduit is designed in which the compartments “wastewater”, “sewer headspace”, “pipe” and “surrounding soil” are distinguished (Fig. 2). The model contains one-dimensional balance equations that describe the changes in flow direction and in time of discharge, water temperature, air temperature and water vapor, and it contains one-dimensional balance equations that describe the radial profiles and changes in time of the temperature in the pipe wall and soil. The processes considered in the model are the flow of water and air, the heat flux between wastewater and soil and between sewer headspace and soil, the latent and convective heat exchange at the water surface and at the pipe wall, the latent and sensible heat transfer in the sewer headspace, and the heat production by biochemical reactions in the water body. The conduit is assumed to be a prismatic pipe with a circular cross-section and with no discontinuities.
3.1.
Wastewater
The wastewater discharge QW in the sewer conduit is modeled by the well-known de St. Venant equations (Cunge et al., 1980) as 2 vQW v QW vh ¼ gAW þ gAW S0 Sf vx AW vx vt
(1)
and rW
vAW vQW ¼ rW jeW P vt vx
(2)
where AW is the wetted cross-sectional area, h is the water depth, g is the gravitational force, S0 is the sewer slope, rW is the wastewater density, P is the water level width, t is time, x is the spatial coordinate in the longitudinal direction, and Sf is the friction slope, which can be expressed as Sf ¼
QW jQW j 2 2 4=3 AW kst RW;hy
(3)
where kst is the Strickler friction coefficient, RW,hy ¼ AW/UW is the hydraulic radius and UW is the wetted perimeter (Cunge et al., 1980). The specific mass flux of evaporation or condensation at the water surface, jeW, is modeled as jeW ¼ aeW psat ðTW Þ pL hfg Fig. 2 e Compartments, processes and state variables considered in the model of wastewater temperature dynamics and spatial profiles in a sewer conduit.
(4)
where pL and psat are the water vapor partial pressure in the headspace and saturation partial pressure at the water surface, respectively; TW is the wastewater temperature; and
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hfg ¼ 2.453 106 J/kg (Incropera and DeWitt, 2002) is the enthalpy, which is approximated by the evaporation enthalpy. The partial pressure is calculated as pL ¼ 4Lpsat(TL) using the relative humidity 4L and temperature TL of the air in the sewer, and the saturation partial pressure at temperature T is calculated as psat ðTÞ ¼ pso e
Tso T
(5)
where pso ¼ 1.73 109 mbar and Tso ¼ 5311 K (Bischofsberger and Seyfried, 1984). The transfer coefficient aeW has units of W/m2/mbar and can be modeled by the equation of Trabert (Bischofsberger and Seyfried, 1984) as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aeW ¼ 8:75 juL uW j
(6)
where uL and uW are the velocities of the sewer air and wastewater, respectively, which must have the units m/s when used in Eq. (6). The solution of Eqs. (1) and (2) requires initial and boundary conditions for QW and AW. In the case of sub-critical flow, a downstream and an upstream boundary condition are required, whereas in the case of super-critical flow, two upstream boundary conditions must be provided (Cunge et al., 1980). If pressurized flow can occur in the sewer, an additional assumption such as the Preissmann slot (Cunge et al., 1980) must be introduced to solve Eqs. (1) and (2).
paper are functions of uL. According to Fischer et al. (1979), uW,c of a circular conduit is uW;c ¼ uW þ
uW 3 2h0 þ 2:30log k 2 D
Airflow
uW ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gRW;hy S0
vAL vQL ¼ vt vx
(7)
where AL is the cross-sectional area of the headspace. Because AL ¼ A AW, where A is the cross-sectional area of the sewer pipe, substitution for AL in Eq. (7) followed by integration yields QL ðt; xÞ ¼ 0
vAW ðt; xÞ dx þ QL0 vt
(8)
where k z 0.4 is the von Karman constant, D is the nominal diameter of the sewer pipe, and h0 ¼ h if h D/2 or h0 ¼ D h if h > D/2. Eq. (8) is based on the assumption that the airflow only depends on the geometric and hydraulic quantities of the conduit considered, i.e., it is independent of the airflow in the upstream and downstream conduits and external forces. This assumption is fulfilled if the upstream and downstream ends of the conduit are chosen at locations where differences of the airflow in subsequent conduits are equilibrated by free exchange of air between the sewer and the atmosphere.
3.3.
Temperature and humidity
Models of temperature and humidity are based on mass balance equations for the water vapor X in the sewer headspace, which is defined as the loading of water per unit mass of dry air,
0:856 L
(12)
vðAW TW Þ vðQW TW Þ 1 ¼ þ q_ UW q_ WL P q_ eW P vt vx cp;W rW PW 0 þ q_ COD AW ;
(13)
for the air temperature TL in the sewer headspace vðAL TL Þ vðQL TL Þ 1 ¼ þ q_ UL þ q_ WL P þ q_ 0cL AL vt vx cp;L rL PL
(14)
for the temperature TP in the pipe wall vTP 1v vTP r ¼ aP r vr vt vr
(15)
and for the temperature TS in the surrounding soil
The effect of changes of the water depth on the airflow is modeled by the first term on the right-hand side of Eq. (8). In a steady state situation, this term is zero, and QL(x) ¼ QL0 throughout the conduit. To determine QL0, the model of steady airflow suggested by Edwini-Bonsu and Steffler (2004) is used in a modified version in which the airflow in a sewer conduit with a backwater curve can be calculated as QL0 ¼
(11)
and the heat balances for the wastewater temperature TW
Assuming that the air is incompressible, the mass balance of the airflow QL in the headspace of a sewer conduit is
Zx
(10)
with
vðAL XÞ vðQL XÞ 1 ¼ þ jeW P jcP UL j0cL AL ; vt vx rL
3.2.
551
ZL AL 0
P uW;c dx UL þ P
(9)
where L is the length of the sewer conduit, UL is the headspace perimeter and uW,c is the wastewater velocity at the water surface. According to this model, uL ¼ QL0/AL is determined by the friction at the pipe wall and at the moving water surface and usually has a value of approximately 0.5$uW,c. This factor is relevant because several transfer functions used in this
vTS 1v vTS r ¼ aS r vr vt vr
(16)
where j and q_ are mass and heat fluxes per unit area, respectively; j0 and q_ 0 are mass and heat fluxes per unit volume, respectively; r are densities; cp are heat capacities; a are thermal diffusivities; and r is the radial distance from the sewer pipe center. Longitudinal dispersion in the wastewater and headspace was found to be small compared to advective transport. The transfer rates used to model the exchange of mass and heat between the various compartments were taken from the literature. The condensation rate q_ cP at the pipe wall in the sewer headspace is q_ cP ¼ 0 if pL ðTL Þ < psat ðTPL Þ q_ cP ¼ acP pL psat ðTPL Þ if pL ðTL Þ psat ðTPL Þ
(17)
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where TPL is the pipe temperature at the interface between the sewer pipe and headspace, and the heat transfer coefficient acP is modeled as pffiffiffiffiffiffiffiffi acP ¼ 8:75 juL j
(18)
and has the units W/m2/mbar if uL has the units m/s (Bischofsberger and Seyfried, 1984). Mass and heat transfer are proportional because they depend on the same boundary layer properties (Incropera and DeWitt, 2002). Thus, the condensate mass flux of water vapor at this interface, jcP, can be modeled by jcP ¼ q_ cP =hfg
(19)
It is assumed that the condensate flows back into the wastewater, but this flux is very small compared to the discharge and can therefore be neglected in Eq. (2). The proportionality between mass and heat transfer is also used to model condensation and evaporation at the water surface analogous to Eqs. (4) and (19) as q_ eW ¼ aeW psat ðTW Þ pL
(20)
Condensation in the air of the sewer headspace occurs if the water loading of the air, X, is equal to or greater than the saturation value Xsat. This process is modeled by an empirical function j0 cL, which is zero if X < Xsat or is given a value such that v(ALX)/vt in Eq. (12) is equal to zero if X Xsat. The heat transfer associated with this process is modeled as q_ 0cL ¼ 0 if XðTL Þ < Xsat ðTL Þ q_ 0cL ¼ hfg j0cL if XðTL Þ Xsat ðTL Þ
(21)
The water vapor loading is related to the relative humidity
4L psat ðTL Þ pL 4L psat ðTL Þ
(22)
where psat is given by Eq. (5) and pL is the air pressure (Wanner et al., 2004). For 4L ¼ 1, Eq. (22) yields the water vapor saturation value Xsat. The convective heat transfer rate q_ WL between wastewater and sewer air is modeled as q_ WL ¼ aWL ðTW TL Þ
(23)
with the heat transfer coefficient aWL
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 5:85 juL uW j
aPW ¼
1=3 0:023Re4=5 W PrW lW RW;hy
(27)
where lW is the thermal conductivity as given in Table 1. The heat flux q_ PL between the pipe wall and the sewer air is modeled as q_ PL ¼ aPL ðTPL TL Þ
(28)
where the heat transfer coefficient aPL can be calculated using Eq. (27) by substituting the values for air for all parameters instead of those for water, i.e., aPL ¼
1=3 0:023Re4=5 L PrL lL : RL;hy
(29)
Heat produced by biochemical reactions in the nutrient rich wastewater is modeled by the heat production rate q_ 0COD ¼ eCOD rCOD
(30) 6
where eCOD ¼ 14 10 J/kgCOD is the reaction enthalpy (Wanner et al., 2005) and rCOD is the degradation rate, which has values of the order of 106 kgCOD/m3/s (Huisman et al., 2004). The solution of Eqs. (12)e(16) requires initial values TW ðt ¼ 0; xÞ; TL ðt ¼ 0; xÞ; TP ðt ¼ 0; rÞ; TS ðt ¼ 0; rÞ and Xðt ¼ 0; xÞ; upstream boundary conditions TW ðt; x ¼ 0Þ ¼ TWin ; TL ðt; x ¼ 0Þ ¼ TLin and Xðt; x ¼ 0Þ ¼ Xin ; continuity conditions for the temperature and heat flux between the wastewater and the pipe wall,
by XðTL Þ ¼ 0:622
turbulent flow, with Reynolds numbers ReW 10000 and Prantl numbers in the range 0.7 PrW 160 (Incropera and DeWitt, 2002) is modeled as
TP ðt; r ¼ D=2Þ ¼ TPW and lP
vTPW ¼ q_ PW ; vr D=2
between the headspace and the pipe wall, TP ðt; r ¼ D=2Þ ¼ TPL and lP
vTPL ¼ q_ PL q_ cP ; vr D=2
(32)
and between the pipe wall and the soil, TP ðt; r ¼ D=2 þ sÞ ¼ TPS and lP
(24)
(31)
vTPS ¼ q_ PS ; vr D=2þs
(33)
which has the units W/m /K if uL and uW have the units m/s (Bischofsberger and Seyfried, 1984). The heat flux q_ PW between the pipe wall and the wastewater is modeled as
where lP is the heat conductivity of the pipe; s is the wall thickness; and TPS is the pipe temperature at the interface between pipe and soil; and a boundary condition at the interface between the disturbed and undisturbed soil
q_ PW ¼ kPW ðTPW TW Þ
TS ðt; r ¼ D=2 þ s þ dS Þ ¼ TS;inf
2
(25)
where TPW is the pipe temperature at the interface between the pipe wall and the wastewater, and the heat transmission coefficient kPW is calculated as 1 1 1 ¼ þ kPW aPW f
(26)
where f is a fouling factor whose reciprocal value can be interpreted as a heat transfer resistance caused by biofilm growth on the pipe wall. The heat transfer coefficient aPW for
where D/2 þ s þ ds is the radius from the pipe’s center, at which the soil is assumed to have the undisturbed soil temperature TS,inf. If TW and TL change along the flow direction (x), the radial profiles of TP and TS also change along the flow direction. Changes of the soil temperature during a simulation period usually are small. If this is the case, TS can be modeled by radial steady state profiles that depend on the actual TPS and TS,inf; for vTS/vt ¼ 0, there is an analytical solution to Eq. (16):
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TS ðrÞ ¼ TPS þ TS;inf
r ln D=2þs
; TPS S ln D=2þsþd D=2þs
(34)
q_ PS ¼ lS
dTS lS TPS TS;inf
: ¼ dr D=2þs D=2 þ s ln D=2þs
The simulation program TEMPEST
The presented model was implemented in an interactive simulation program for temperature estimation in sewers, TEMPEST (Du¨rrenmatt and Wanner, 2008), which was developed to facilitate the application of the model and which was used for all simulations presented in this paper. The program can be obtained from the authors free of charge (Du¨rrenmatt and Wanner, 2013). In TEMPEST, the balance equations are integrated by the two-step LaxeWendroff algorithm (Press, 2005). Discretization in space can be specified by the user, who defines the number of spatial grid points in the flow direction and in the radial direction in the pipe wall. Integration over time is controlled by the program, which continuously optimizes the length of the integration time step according to the CouranteFriedrichseLevy criterion (Press, 2005). The heat exchange between sewer and soil is calculated separately for the wastewater and the headspace according to the actual water depth, which is limited to 0 < h hmax ¼ 0.95*D. The necessary input data include the wastewater discharge and temperature at the upstream end of the sewer, which are QWin and TWin, respectively; the ambient temperature TA, which is used to approximate TLin; and the ambient humidity and pressure, 4A and pA, which are used to approximate Xin by Eq. (22). To provide the initial conditions needed, a steady state solution is calculated by TEMPEST, and the thermal properties of various soil types and sewer pipe materials can be found in a small database. For the simulations presented in this paper, the discretization in space was gradually refined until its effect on the results became negligible. This was the case with a discretization along the flow axis of 50 m, and a pipe wall with five radial layers.
5.
Results and discussion
5.1.
Model calibration
To test the ability of the model to adequately reproduce the temperature profiles in the Ru¨mlang sewer, a simulation was performed, and the measured and calculated time series of discharge and wastewater temperature were compared. The quality criteria employed were the rootmean-squared error
RMSD ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP u ðTm;t Ts;t Þ2 t t n
P
(37)
t
(35)
D=2þsþdS
4.
and the NasheSutcliffe coefficient of efficiency ðTm;t Ts;t Þ2 t E¼1P 2 Tm;t Tm
which can be used to calculate q_ PS as
553
(36)
where Tm,t and Ts,t denote the measured and simulated temperatures at time t, respectively; Tm is the mean of the measured temperature; and n denotes the number of data pairs. The NasheSutcliffe coefficient has an optimum value of E ¼ 1, whereas E < 0 indicates that the approximation of the measured series Tm,t by Ts,t is worse than the approximation by Tm . The parameters TS,inf, lS, dS, lP, aP, kst, rCOD and f were chosen for model calibration and will later on be examined by a sensitivity analysis. These parameters were selected according to the following criteria: parameters that have a dominant effect on the result, are difficult to measure, or can vary with time and space were included, whereas parameters that are readily available and have reliable values, such as sewer material properties and geometry, were not included to keep the number of fitted parameters as low as possible. Influent and effluent discharge and wastewater temperature data measured on February 26 and 27, 2008, were used for the calibration. A comparison of the measured and calibrated discharges, QWout and QWout, calib, reveals that a satisfactory correspondence can be reached (Fig. 3, top). A comparison of the effluent wastewater temperature TWout, apriori, which was simulated with the a priori parameter values of Table 1, and the temperature TWout, calib, which was simulated with the
Fig. 3 e Influent and effluent discharge and wastewater temperature time-series measured in the sewer conduit and effluent discharge and wastewater temperature calculated with a priori and calibrated values of the model parameters.
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calibrated parameter values, shows that the pattern of the measured effluent temperature TWout is adequately reproduced by both simulations (Fig. 3, bottom). However, the values of the quality criteria from the calibration, RMSD ¼ 0.14 C and E ¼ 0.97, were significantly better than those of the a priori simulation, RMSD ¼ 0.35 C and E ¼ 0.79. For the model parameters, the calibration yielded TS,inf ¼ 5.2 C, lS ¼ 0.65 W/m/K, dS ¼ 0.11 m, lP ¼ 2.3 W/m/K, aP ¼ 0.6*106 m2/s, kst ¼ 70 m1/3/s, rCOD ¼ 2.8 mgCOD/m3/s and f ¼ 200 W/m2/K. These values differ between 0 and 41% from the values of the a priori model parameters of Table 1. By a local sensitivity analysis the quantitative effect of the model parameters on the wastewater temperature was assessed. The analysis was performed for a steady state situation and included the calibrated model parameters, except for aP, since the thermal diffusivity is related to changes of the amount of stored heat and does not affect TW in a steady state situation (Eq. (15)). The most sensitive parameters are the temperature of the undisturbed soil, TS,inf; the thermal conductivity lS of the soil; and the soil penetration depth dS, which represents the distance at which the soil temperature can be assumed to be independent of the heat exchange with the sewer (Fig. 4). Thus, the processes and conditions in the soil surrounding the sewer are of primary importance when modeling the heat exchange between sewer and soil and will be discussed in detail in a subsequent section. The thermal diffusivity of the soil, aS, was not included in the calibration or the sensitivity analysis because these were performed using Eq. (35). The COD degradation rate rCOD and the fouling factor f do not have a significant effect on TW; therefore, it is usually not worthwhile to determine their values with high accuracy. However, these parameters vary with time, and f can change by more than 10% if sediments and biofilms that developed during long dry weather periods are suddenly washed off by a storm event (Wanner, 2004).
5.2.
Model validation
To validate the model, a simulation was performed for another set of measured wastewater temperature data. This simulation was performed using the parameter values found by the calibration run and the values from Table 1 for any remaining parameters except for the ambient parameters, which had slightly different values of TS,inf ¼ 5.8 C, TA ¼ 7.2 C, pA ¼ 948 mbar and 4A ¼ 0.72 during the validation data’s time period of March 11 to March 13, 2008. Fig. 5 shows that the effluent temperature predicted by the calibrated model, TWval, corresponds quite well with the measured effluent temperature, TWout, except for the initial phase of the diagram. The values of the quality criteria found by the validation were RMSD ¼ 0.20 C and E ¼ 0.94. These values are almost as good as the values obtained by the calibration, which indicates that the model can indeed be used to predict the effluent wastewater temperatures of the sewer conduit.
5.3. Effect of heat transfer processes and environmental conditions on the wastewater temperature To assess the significance of the heat transfer processes considered in the model, steady-state simulations for typical situations with different environmental conditions were performed. These situations and the resulting model predictions are summarized in Table 2. On the left-hand side of the table, the examined environmental conditions are shown and are characterized by dS, lP, lS, f and daily averages of TWin and TS,inf. The columns in the center of the table show the difference between the calculated downstream and upstream values of wastewater temperature and heat flux, DTW ¼ TWout TWin and DQ_ W ¼ Q_ Wout Q_ Win , respectively, where the upstream and downstream wastewater heat fluxes are calculated according to Q_ W ¼ cp;W rW QW TW
(38)
The columns on the right-hand side of the table show the heat flux through the wetted perimeter (PW), the convection (WL), the evaporation (eW) and the biodegradation (COD), i.e., the processes by which heat is exchanged between the wastewater and the other compartments (cf. Fig. 1). The given
Fig. 4 e Sensitivity of the effluent wastewater temperature to the parameters used for the calibration of the model.
Fig. 5 e Influent and effluent wastewater temperatures measured in the sewer conduit and the effluent wastewater temperature predicted by the calibrated model.
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Table 2 e Change of the wastewater temperature and heat flux in the sewer of Ru¨mlang, Switzerland, for various situations and environmental conditions. Please note that negative values indicate a loss of heat from the wastewater. Situation
Calibrated model Winter (benchmark) High heat transport in pipe wall and soila Low heat transport in pipe wall and soilb Unsaturated aquifer, no groundwater flow Saturated aquifer, high groundwater velocity Wetted perimeter with biofilm Summer a b
Environmental conditions
Change in the sewer
Processes accounting for heat transfer into wastewater
TWin ( C)
TS.inf ( C)
dS (m)
lP (W/ m/K)
lS (W/ m/K)
f (W/ m2/K)
DTW ( C)
DQ_ W (kW)
PW (%)
WL (%)
eW (%)
COD (%)
12.0 11.0 11.0
5.2 5.0 5.0
0.11 0.11 0.11
2.3 2.3 2.5
0.65 0.65 2.2
200 200 200
0.63 0.55 0.98
79 77 123
75 75 86
11 12 7
20 20 11
þ6 þ7 þ4
11.0
5.0
0.11
0.17
0.25
200
0.16
20
51
26
47
þ24
11.0
5.0
1.0
2.3
0.65
200
0.19
24
50
25
44
þ19
11.0
5.0
0.01
2.3
0.65
200
1.24
155
89
5
9
þ3
11.0
5.0
0.11
2.3
0.65
20
0.46
57
70
14
24
þ8
18.7
12.5
0.11
2.3
0.65
200
0.62
77
69
10
27
þ6
Change of pipe type from 1% to 2% steel in reinforced concrete and soil type from sandy clay to saturated sand. Change of pipe type from concrete to PVC with a wall thickness of 0.079 m and soil type from sandy clay to gravel.
numbers represent the specific heat fluxes q_ integrated over the interfacial areas as percentages of DQ_ W . The environmental conditions in the first line of Table 2 are those determined by the calibration of the model with measured data from February 2008 and the a priori parameter values, as given in Table 1. In this situation, the model predicted a change of the wastewater temperature in the sewer of DTW ¼ 0.63 C and a rate of the heat loss from the wastewater of DQ_ W ¼ 79 kW. This loss is attributed 75% to the heat flux through the wetted perimeter of the sewer pipe to the surrounding soil, 20% to evaporation at the water surface and 11% to the convective heat flux across the water surface. The contribution of heat production due to the degradation of organic matter in the water is insignificant (6%). The rate of the heat loss DQ_ W in the sewer is approximately 5% of Q_ Win ¼ 1500 kW, as calculated by Eq. (38). To facilitate a discussion of the significance of the heat transfer processes and environmental conditions in the cold season, typical winter conditions are introduced and used as a benchmark. During wintertime, the wastewater temperature is usually between 10 and 20 C, depending upon the origin of the wastewater, sewer properties and ambient conditions. The model predictions based on a simulation with TWin ¼ 11.0 C and TS,inf ¼ 5.0 C were DTW ¼ 0.55 C and DQ_ W ¼ 77 kW. The predicted heat loss of the benchmark is slightly lower than that of the calibrated model, which can be explained by the smaller temperature gradient between wastewater and undisturbed soil. Because heat transfer between wastewater and the surrounding soil was found to be so important, the material properties of the sewer pipe and soil must have a significant influence on the wastewater temperature. Among the materials with the highest thermal conductivities are reinforced concrete (2% steel), with lP ¼ 2.5 W/m/K (DIN, 2000), and saturated sandy soil, with lS ¼ 2.2 W/m/K (Unsworth and Monteith, 1990). For these materials, the simulation yields DTW ¼ 0.98 C and DQ_ W ¼ 123 kW, and the dominant heat
transfer process through the wetted perimeter becomes even more important and accounts for 86% of the heat loss. Materials with low thermal conductivities are PVC-pipes, with lP ¼ 0.17 W/m/K (DIN, 2000), and unsaturated clay soil, with lS ¼ 0.25 W/m/K (Unsworth and Monteith, 1990). For this combination of materials, DTW ¼ 0.16 C and DQ_ W ¼ 20 kW, i.e., the relative importances of convection and evaporation at the water surface of 26% plus 47% exceed that of the heat loss through the wetted perimeter (51%). In addition to the material properties, the hydraulic conditions in the aquifer surrounding the sewer pipe also have a significant effect on the heat transfer between soil and sewer, which was clearly demonstrated in an experimental study by Abdel-Aal et al. (2012). In an unsaturated aquifer or a saturated aquifer with a very low groundwater flow velocity, the transport of heat in the soil is a slow process, and the soil temperature around the sewer pipe gradually adjusts to the wastewater temperature. This situation can be modeled by a large value of the penetration depth dS, i.e., the distance between the sewer pipe and the zone where the soil temperature is assumed to be undisturbed. A change of dS from 0.11 m to 1.0 m yields model predictions of DTW ¼ 0.19 C and DQ_ W ¼ 24 kW and also leads to a lower relative contribution of heat transfer through the wetted perimeter (50% vs. 25% plus 44%). If the groundwater flow velocity is high, the convective transport of heat results in a soil temperature in the vicinity of the sewer pipe that remains close to the undisturbed temperature. This situation can be accounted for by setting dS ¼ 0.01 m, which yields model predictions of DTW ¼ 1.24 C and DQ_ W ¼ 155 kW. In this situation, the heat flux through the wetted perimeter of the sewer pipe to the surrounding soil becomes absolutely dominant and is responsible for 89% of the heat loss from the wastewater. It is well-known that in nutrient-rich raw wastewater, a biofilm rapidly develops on the wetted perimeter of the sewer pipe and creates an additional resistance to heat transfer. This
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resistance is proportional to the inverse of the so-called biofouling factor f. In an experimental study of biofilm growth in a laboratory scale sewer conduit, values of f ¼ 20 W/ m2/K were observed (Wanner, 2004). A simulation with this value yielded DTW ¼ 0.46 C and DQ_ W ¼ 57 kW. A comparison with the benchmark shows that heat resistance caused by a biofilm considerably reduces the heat loss and lowers the relative contribution of heat loss through the wetted perimeter. It should be noted that inorganic sediments deposited on the bottom of the sewer pipe can form even higher heat transfer resistances, and the extent of biofilms is usually controlled by the shear of the flowing water (Wanner, 2004). In the summertime, the wastewater and soil temperatures are usually considerably higher than in the winter. In Ru¨mlang, typical summer temperatures are TWin ¼ 18.7 C and TS,inf ¼ 12.5 C (data not shown). A simulation with these temperatures yielded DTW ¼ 0.62 C and DQ_ W ¼ 77 kW. A comparison with the benchmark reveals that only the evaporation has a higher value in the summer, while the other heat fluxes have almost identical values. The explanation of this finding is that the gradients between TWin and TS,inf are practically equal due to the relatively high soil temperature. However, it must be noted that TS,inf can be considerably lower depending on how deep the sewer pipe is buried in the soil.
5.4. Prediction of the effect of heat recovery on the wastewater temperature
treatment plant (WWTP) must not be lowered below 10 C as a consequence of the total heat recovered from upstream sewers (AWEL, 2010). The reason for this regulatory constraint is that in Switzerland, most of the sewage is treated in nitrifying activated sludge plants, and nitrification is significantly reduced at low wastewater temperatures, or the nitrifying bacteria can even be washed out from the plant (Wanner et al., 2005). This constraint is not applied to sewer lines connecting WWTP effluents and receiving waters. However, there are other constraints based on ecological considerations that limit sudden temperature changes and warming of the receiving waters. These constraints are relevant because a heat pump can be used for heating and for cooling and because the latter is very attractive economically. The best site for heatproducing facilities is at the point of WWTP effluent because the amount of heat energy that can be extracted from the wastewater is usually a multiple of that which can be extracted from the sewer upstream of the WWTP. However, if there are no consumers near the site of extraction, the loss of heat during its transport may make this solution unfeasible. To determine the optimal site for a heat recovery facility and the amount of heat that can be extracted in a specific situation and under the constraints given, it is necessary to estimate the changes in wastewater temperature at the end of the sewer. These changes occur, on the one hand, directly at the site of heat extraction and, on the other hand, in the reach between the extraction site and the end of the sewer.
To ensure successful operation of a heat recovery plant, there are some technical aspects and legal constraints that must be addressed as early as the planning stage. The Swiss canton of Zurich, in which Ru¨mlang is located, requires that the daily average of the influent temperature of a wastewater
Fig. 6 e Time course of discharge QWin and wastewater temperature TWin measured at the upper end of the sewer and the wastewater temperature directly downstream of the extraction site, TWin,rec, calculated by Eq. (39) for an assumed amount of extracted heat of 250 kW.
Fig. 7 e Time course of wastewater temperatures directly downstream of the extraction site, TWin,rec, at the end of the sewer, TWout,rec and TWout,rec,var (top), and the heat transferred from the sewer headspace and pipe wall into the wastewater, Q_ TWrec , Q_ TWrec;var and the average of the latter, Q_ TWrec;avg (middle), predicted for two alternative time courses of the extracted heat, Q_ rec and Q_ rec;var (bottom).
w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
Estimates of the latter require simulations with a mathematical model, while the former can be calculated as TWin;rec ¼ TWin
Q_ rec cp;W rW QWin
(39)
and Q_ rec DTWin;rec ¼ TWin;rec TWin ¼ cp;W rW QWin
(40)
where Q_ rec is the amount of heat recovered from the wastewater per unit time; TWin and TWin,rec are the wastewater temperatures directly upstream and downstream of the site of heat extraction, respectively; and DTWin,rec is the decrease of the wastewater temperature at this site. According to Eq. (40), DTWin,rec is directly proportional to Q_ rec and inversely proportional to the wastewater discharge QWin. This mathematical relation is reflected in Fig. 6, which displays QWin and TWin measured from March 11 to 12, 2008, in Ru¨mlang and TWin,rec calculated by Eq. (39) for an assumed Q_ rec of 250 kW. For the large discharge on the right-hand side of the figure, the decrease in the wastewater temperature at the recovery site is almost null, whereas the small discharge on the left-hand side leads to a large decrease and to a low temperature TWin,rec of approximately 6 C. The smaller the ratio Q_ rec /QWin, the smaller the decrease of TWin at the site of extraction. In the early morning hours of March 12, TWin,rec also had a very low value, which was primarily due to the already low TWin. The smallest value of TWin,rec resulted from simultaneous low values of both QWin and TWin. These observations raise questions about the origin of the wastewater. Depending upon whether sewage is primarily municipal or industrial and whether it is groundwater or rain water sewage, the seasonal and diurnal variations and the average values of QWin and TWin will be different. Usually, QWin increases in the flow direction because of lateral inflows, and TWin decreases because of heat loss to the environment. Consequently, these two quantities, together with the availability of a consumer for the recovered heat, primarily determine where heat recovery from the wastewater is feasible and how much heat can be extracted. In addition to changes in the wastewater temperature resulting from the extraction of heat, there are also temperature changes due to the exchange of heat between the wastewater, sewer headspace and pipe wall in the sewer conduit. Fig. 7 displays the time course of the wastewater temperatures directly downstream of the extraction site and at the end of the sewer, TWin,rec and TWout,rec (top), respectively. The latter is the result of a simulation based on the calibrated model and parameters, and using TWin,rec and QWin, as displayed in Fig. 6, as input. As seen on the left-hand side of Fig. 7, the temperature TWin,rec decreases remarkably in the early morning hours, but TWout,rec is higher than TWin,rec, i.e., the wastewater is gaining heat in the sewer. This finding corresponds to the initially positive values of Q_ TWrec , which is the integral over the exchange area of the heat flux from the sewer headspace and pipe wall into the wastewater (middle). The explanation for this finding is that the heat stored in the pipe wall is released into the wastewater as long as TW is smaller than TP. If TWin,rec is low and then increases, Q_ TWrec is
557
negative, the wastewater is losing heat, and the pipe wall is accumulating heat. These phenomena are temporary; in a steady state situation, the direction of heat exchange is determined by the temperature difference between wastewater and the soil, TW TS,inf. If this difference has a high positive value, a large loss of heat occurs, while heat can be gained from the soil if it is negative. This gain requires a heat flux in the soil that is strong enough to maintain a stable value of TS,inf and a TWin,rec value that is constantly smaller than TS,inf. The former condition was discussed in Section 5.3, while the latter is usually feasible only if warmer lateral inflows downstream of the extraction site ensure that the daily average of the influent temperature of a downstream WWTP is above the required 10 C. For the data presented in Fig. 5, the daily average of TWout is 11.2 C; for the TWout,rec displayed in Fig. 7, it is 9.8 C. Thus, the value of the daily average of TWout,rec is critical, and the question is how the temperature can be increased above 10 C. The simplest possibility is to lower Q_ rec when the environmental conditions are critical. Usually, this can readily be achieved because almost all heat recovery facilities are bivalent, i.e., for safety reasons, they also have a conventional heater. Another possibility is to vary Q_ rec during the day according to a predefined pattern. The idea behind this strategy is to extract the heat at the time when it is abundant in the wastewater and to store it for later use. This strategy is successful if TWin follows a typical diurnal pattern, as is usually the case for municipal or industrial wastewater. Such a pattern can also be observed for the Ru¨mlang data, except on the afternoon of March 12, when a rain event led to a lower TWin (Figs. 3 and 6). To test this strategy, another simulation was performed in which Q_ rec;var was changed between a low value in the early morning hours and a high value during daytime such that the total daily amount of extracted heat remained the same as that of the constant Q_ rec case. As seen in Fig. 7, the effect of this strategy is that TWout,rec,var, which is simulated in the same way as TWout,rec, varies less and has a slightly higher daily average of 10.0 C; Q_ TWrec;var also varies less than Q_ TWrec . The wastewater discharge usually also exhibits a typical diurnal variation with low values during nighttime and a rapid increase in the early morning hours. Because a high discharge QWin reduces the change of the wastewater temperature in the conduit, DTW ¼ TWout TWin,rec, regular diurnal variations of QWin can also be used to improve the strategy of variable heat recovery.
6.
Conclusions
The technique of heat recovery from wastewater in sewers by means of a heat exchanger and a heat pump is wellestablished, and hundreds of facilities have successfully operated based on this technique for many years. However, successful planning and operation require that the specific conditions of a given situation be analyzed beforehand. These conditions include the properties of the sewer system, the diurnal and seasonal variations of the wastewater discharge and temperature, legal restrictions imposed on the downstream wastewater temperature, and the demand and available supply of energy for heating or cooling. Based on this
558
w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
information, it is possible to decide whether heat recovery at a given site is feasible and, if it is possible, to determine the optimal location and the extractable amount of heat energy. Part of the planning process is the establishment of a quantitative relation between the change of the sewer wastewater temperature and the amount of heat recovered. The relation between the temperature change at the site of extraction and the heat recovered can readily be estimated, but the change of the wastewater temperature between the extraction site and the end of the sewer can only be calculated by means of mathematical modeling and simulations. The presented pseudo two-dimensional mathematical model can calculate the changes of the wastewater temperature in a sewer conduit along the flow direction and over time. The model was implemented in the simulation program TEMPEST (temperature estimation) and was used to evaluate field data taken from the sewer of Ru¨mlang, Switzerland. The calibration and validation with these data confirmed that the model is able to adequately reproduce the spatial profiles and dynamics of the wastewater temperature and to predict the effect of heat recovery on the wastewater temperature in the sewer conduit examined. Since the model equations were mostly based on physical principles, the model should be applicable under different conditions as well, but further applications are needed to prove general validity. Lateral inflows that are not negligibly small may limit practical applicability of the model because it usually is not feasible to acquire data of every single inflow. The analysis of the simulations performed with the calibrated model revealed that the temperature of the undisturbed soil, the thermal conductivity of the soil and the distance between the sewer pipe and undisturbed soil are the most sensitive model parameters in steady state situations. The most dominant transfer process is the direct exchange of heat between wastewater and the pipe wall, but evaporation and convection at the water surface can also be relevant depending upon the environmental conditions. In dynamic situations, the storage of heat in and subsequent release from the pipe wall have a significant effect on the dynamics of the wastewater temperature. If the influent temperature of a WWTP falls below the required minimum of 10 C due to heat extraction, the model can be used to determine the maximum extractable amount of heat, to analyze whether more heat can be gained if the extraction is varied during the day, or to switch from the heat pump to a conventional heater in bivalent facilities if necessary.
references
Abdel-Aal, M., Schellart, A., Mohamed, M., Tait, S., 2012. Modelling heat transfer processes for buried pipes. In: 9th International Conference on Urban Drainage Modelling, Belgrade. AWEL, 2010. Heating and Cooling with Wastewater (Heizen und Ku¨hlen mit Abwasser, Leitfaden fu¨r die Planung, Bewilligung und Realisierung von Anlagen zur Abwasserenergienutzung).
Baudirektion Kanton Zu¨rich, Amt fu¨r Abfall, Wasser, Energie und Luft, Zu¨rich. URL: http://www.ara.zh.ch/abwaerme [May 20, 2013]. Bischofsberger, W., Seyfried, C.F., 1984. Heat Extraction from Wastewater (Wa¨rmeentnahme aus Abwasser). In: Schriftenreihe des Lehrstuhls fu¨r Wassergu¨tewirtschaft und Gesundheitsingenieurwesen der Technischen Universita¨t Mu¨nchen, vol. 56. Cunge, J.A., Holly, F.M., Verwey, A., 1980. Practical Aspects of Computational River Hydraulics. Pitman, Boston. DIN, 2000. DIN EN 12524:2000, Building Materials and Products e Hygrothermal Properties e Tabulated Design Values. Du¨rrenmatt, D.J., Wanner, O., 2008. Simulation of the wastewater temperature in sewers with TEMPEST. Water Sci. Technol. 57 (11), 1809e1815. Du¨rrenmatt, D.J., Wanner, O., 2013. TEMPEST e Computer Program for the Simulation of the Wastewater Temperature in Sewers, Version 1.02. Available at: http://www.tempest. eawag.ch. Edwini-Bonsu, S., Steffler, P.M., 2004. Airflow in sanitary sewer conduits due to wastewater drag: a computational fluid dynamics approach. J. Environ. Eng. Sci. 3 (5), 331e342. EWZ, 2008. The Schlieren Energy Network. URL: http://www. stadt-zuerich.ch/content/dam/stzh/ewz/Deutsch/Ueber% 20ewz/Publikationen%20und%20Broschueren/EDL_Schlieren_ E.pdf [May 20, 2013]. Fischer, H.B., List, E.J., Koh, R.C.Y., Imberger, J., Brooks, N.H., 1979. Mixing in Inland and Coastal Waters. Academic Press, New York. Flamink, C., Langeveld, J., Clemens, F., 2005. Aerobic transformations in sewer systems: are they relevant? Water Sci. Technol. 52 (3), 163e170. Ghafghazi, S., Sowlati, T., Sokhansanj, S., Melin, S., 2010. Technoeconomic analysis of renewable energy source options for a district heating project. Int. J. Energy Res. 34 (12), 1109e1120. Hager, W.H., 2010. Wastewater Hydraulics: Theory and Practice. Springer, Berlin Heidelberg. Huisman, J.L., Gasser, T., Gienal, C., Ku¨hni, M., Krebs, P., Gujer, W., 2004. Quantification of oxygen fluxes in a long gravity sewer. Water Res. 38 (5), 1237e1247. Incropera, F.P., DeWitt, D.P., 2002. Fundamentals of Heat and Mass Transfer. John Wiley and Sons Inc., New York. Olsson, G., 2012. Water and Energy. IWA Publishing, London. Press, W.H., 2005. Numerical Recipes in Cþþ: the Art of Scientific Computing. Cambridge University Press, Cambridge. Schmid, F., 2008. Sewage water: interesting heat source for heat pumps and chillers. In: International Energy Agency Heat Pump Centre, Conference Proceedings, vol. 5(22). URL: http:// www.bfe.admin.ch/php/modules/publikationen/stream.php? extlang¼en&name¼en_508290240.pdf [May 20, 2013]. Unsworth, M.H., Monteith, J.L., 1990. Principles of Environmental Physics. Butterworth-Heinemann, Oxford. Wanner, O., 2004. Heat Recovery from Sewers (Wa¨rmeru¨ckgewinnung aus Abwasser). Bundesamt fu¨r Energie, Bern. URL: http://www.bfe.admin.ch/dokumentation/ energieforschung/index.html?lang¼de&publication¼8156 [May 20, 2013]. Wanner, O., Panagiotidis, V., Siegrist, H., 2004. Heat recovery from sewers: effect on the wastewater temperature (Wa¨rmeentnahme aus der Kanalisation e Einfluss auf die Abwassertemperatur). Korrespondenz Abwasser 51 (5), 489e495. Wanner, O., Panagiotidis, V., Clavadetscher, P., Siegrist, H., 2005. Effect of heat recovery from raw wastewater on nitrification and nitrogen removal in activated sludge plants. Water Res. 39 (19), 4725e4734.
Available online at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/watres
A mathematical model to predict the effect of heat recovery on the wastewater temperature in sewers David J. Du¨rrenmatt*, Oskar Wanner Swiss Federal Institute of Aquatic Science and Technology, Eawag, 8600 Du¨bendorf, Switzerland
article info
abstract
Article history:
Raw wastewater contains considerable amounts of energy that can be recovered by means
Received 5 August 2013
of a heat pump and a heat exchanger installed in the sewer. The technique is well
Received in revised form
established, and there are approximately 50 facilities in Switzerland, many of which have
29 September 2013
been successfully using this technique for years. The planning of new facilities requires
Accepted 4 October 2013
predictions of the effect of heat recovery on the wastewater temperature in the sewer
Available online 17 October 2013
because altered wastewater temperatures may cause problems for the biological processes used in wastewater treatment plants and receiving waters. A mathematical model is
Keywords:
presented that calculates the discharge in a sewer conduit and the spatial profiles and
Sewer
dynamics of the temperature in the wastewater, sewer headspace, pipe, and surrounding
Modeling
soil. The model was implemented in the simulation program TEMPEST and was used to
Wastewater temperature
evaluate measured time series of discharge and temperatures. It was found that the model
Heat transfer
adequately reproduces the measured data and that the temperature and thermal con-
Heat recovery
ductivity of the soil and the distance between the sewer pipe and undisturbed soil are the most sensitive model parameters. The temporary storage of heat in the pipe wall and the exchange of heat between wastewater and the pipe wall are the most important processes for heat transfer. The model can be used as a tool to determine the optimal site for heat recovery and the maximal amount of extractable heat. ª 2013 Elsevier Ltd. All rights reserved.
1.
Introduction
Wastewater released into the sewer from showers, sinks and washers is an attractive source of energy. It is permanently available almost everywhere, has temperatures of 10e20 C throughout the year and contains considerable amounts of energy. If 1 m3 of water is cooled down by 1 C, 1.16 kWh of heat energy can be gained. If in the city of Zurich, Switzerland, the dry weather wastewater discharge of 230,000 m3/s were continuously cooled down by 1 C, the heat energy theoretically gained would correspond to a continuous delivery of 10 MW. At present, approximately 50 facilities are operating in
Switzerland, extracting heat from the wastewater by means of heat pumps and heat exchangers installed in the sewer; among these are three facilities in Zurich that produce a total power of 5 MW (EWZ, 2008). One of these facilities heats 800 apartments, and another heats and cools the largest building in Switzerland. There is a facility in Norway that heats and cools an entire district of the city of Oslo (Schmid, 2008). Basically, there are two techniques to recover heat from the sewer. The conventional technique is to install a heat exchanger at the bottom of the sewer pipe. This technique is simple and well established, but the efficiency of the heat exchanger will be reduced drastically if its surface is covered
* Corresponding author. Tel.: þ41 58 765 5297. E-mail address: [email protected] (D.J. Du¨rrenmatt). 0043-1354/$ e see front matter ª 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.watres.2013.10.017
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w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
Fig. 1 e Top view of a section of the sewer between the villages of Ru¨mlang and Oberglatt in the Canton of Zurich, Switzerland.
by sediments or biofilms or is not completely submerged. An alternative and newer technique is to pump the wastewater through a heat exchanger installed outside the sewer. This technique makes it easier to control fouling of the heat exchanger, but it requires that the wastewater be filtered and leads to higher installation and pumping costs.
From an ecological point of view, it is logical to close energy cycles by bringing the energy back to the original user to reuse the energy disposed with the wastewater a second time instead of warming the environment (Olsson, 2012). The economic competitiveness of heat extraction from wastewater depends on the price of oil and gas, on the distance between the recovery site and the user of the energy and on the availability of alternative ambient energy sources (Ghafghazi et al., 2010). Facilities using wastewater for both heating and cooling are usually very economical. However, there are legal constraints in most countries on the permitted temperature changes for influents of wastewater treatment plants and receiving waters (AWEL, 2010; Wanner et al., 2005). Therefore, successful planning and operation of heat recovery facilities require that their effect on the wastewater temperature be quantifiable. In this paper, a model is presented to calculate the dynamics and spatial profiles of wastewater temperature in a sewer pipe as a function of wastewater discharge, airflow in the sewer and heat transfer between the sewer, soil and atmosphere. The model is implemented in the simulation program TEMPEST (temperature estimation) and is calibrated and
Table 1 e Overview of the information required to model the wastewater temperature in a sewer. Parameter Sewer pipe Length Nominal diameter Friction coefficientb,h Slope Wall thickness Wall thermal conductivityb, h Wall thermal diffusivityb, h Soil Undisturbed temperaturee, h Penetration depthh Thermal conductivityf, h Thermal diffusivityf Wastewater Discharge at influentc Temperature at influentc COD degradation rated, h Fouling factorh Densityg Thermal conductivityg Specific heat capacityg Air Ambient temperaturec Ambient pressurec Ambient relative humidityc Density Thermal conductivity Specific heat capacity a
Symbol
Value
Unit
Source a
L D kst S0 s lP aP
1845 0.9 70 0.0091 0.1 2.3 1,106
m m m1/3 s1 e m W/(mK) m2/s
IP IP L IP IP IP/L IP/L
TS,inf dS lS aS
5.5 0.1 1.1 0.2,106
C m W/(mK) m2/s
M/E E IP/L IP/L
QWin TWin rCOD f rW lW cp,W
0.03 12 2.8 200 998.2 0.60 4181
m3/s C mgCOD/(m3 s) W/(m2 K) kg/m3 W/(mK) J/(kg K)
M M E L L L L
TA pA 4A rL lL cp,L
8.3 966 0.75 1.19 0.0257 1007
W W W L L L
C mbar e kg/m3 J/(kg K) J/(kg K)
Key: IP ¼ implementation plan, E ¼ estimate, L ¼ literature, M ¼ field measurement and W ¼ weather station. Typical parameter for concrete reinforced with 1% steel (e.g., Hager (2010) for friction coefficient and DIN (2000) for thermal properties) selected according to the implementation plan. c Average during calibration period. d Based on studies by Huisman et al. (2004) and Flamink et al. (2005). e Estimate based on measurements with temperature probes buried in the soil. f Typical parameter for clay (Unsworth and Monteith, 1990), which is prevalent according to the implementation plan. g Physical properties of wastewater approximated by clean water values at 10 C. h Parameter subject to calibration. b
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validated with data obtained from a field study in the sewer of Ru¨mlang, Switzerland. The model is then used to identify the processes and environmental conditions that primarily determine the wastewater temperature in the sewer, to predict the effect of heat recovery on the downstream wastewater temperature and to discuss various scenarios for the recovery of heat energy.
2.
Experimental
2.1.
Site description
The investigated sewer line is 1845 m in length; lies parallel to the river Glatt; and has a circular cross-section, uniform geometrical and material properties, and no tributaries (cf. Fig. 1). A manhole, consisting of a cover with a small opening, was built approximately every 60 m. The surrounding soil is homogenous along the sewer line; however, the groundwater table varies with time. Upstream of the considered section, at a distance of 75 m, there is a combined sewer overflow, while downstream, at a distance of 120 m, there is an inverted siphon; both allow for free air exchange with the atmosphere.
2.2. Field measurements of wastewater discharge and temperature A data acquisition campaign was carried out from February 14 to March 22, 2008, during which the wastewater discharge was measured with two Nivus PCM 3 ultrasonic flow meters in the upstream manhole (RS 4943) and in the downstream manhole (RS 3096). Temperature was logged using Onset TMC6-HD temperature probes mounted in both manholes. To obtain a good estimate for the soil temperature, another temperature logger was buried at a depth of 1.2 m and a distance of 2 m from the sewer at manhole RS 4943.
2.3.
Sewer properties and ambient conditions
Modeling of the spatial profiles and dynamics of the wastewater temperature in a sewer conduit requires information on the sewer pipe properties, soil properties and influent and ambient conditions.
Information on the geometry, thermal properties and friction coefficient of the sewer pipe and on the properties of the surrounding soil can be extracted from implementation plans or from the literature. Ambient data were taken from a meteorological station located nearby. Table 1 gives an overview of the values of the parameters and ambient conditions used for modeling of the wastewater temperature in the sewer of Ru¨mlang.
3.
Modeling
A pseudo two-dimensional mathematical model of a sewer conduit is designed in which the compartments “wastewater”, “sewer headspace”, “pipe” and “surrounding soil” are distinguished (Fig. 2). The model contains one-dimensional balance equations that describe the changes in flow direction and in time of discharge, water temperature, air temperature and water vapor, and it contains one-dimensional balance equations that describe the radial profiles and changes in time of the temperature in the pipe wall and soil. The processes considered in the model are the flow of water and air, the heat flux between wastewater and soil and between sewer headspace and soil, the latent and convective heat exchange at the water surface and at the pipe wall, the latent and sensible heat transfer in the sewer headspace, and the heat production by biochemical reactions in the water body. The conduit is assumed to be a prismatic pipe with a circular cross-section and with no discontinuities.
3.1.
Wastewater
The wastewater discharge QW in the sewer conduit is modeled by the well-known de St. Venant equations (Cunge et al., 1980) as 2 vQW v QW vh ¼ gAW þ gAW S0 Sf vx AW vx vt
(1)
and rW
vAW vQW ¼ rW jeW P vt vx
(2)
where AW is the wetted cross-sectional area, h is the water depth, g is the gravitational force, S0 is the sewer slope, rW is the wastewater density, P is the water level width, t is time, x is the spatial coordinate in the longitudinal direction, and Sf is the friction slope, which can be expressed as Sf ¼
QW jQW j 2 2 4=3 AW kst RW;hy
(3)
where kst is the Strickler friction coefficient, RW,hy ¼ AW/UW is the hydraulic radius and UW is the wetted perimeter (Cunge et al., 1980). The specific mass flux of evaporation or condensation at the water surface, jeW, is modeled as jeW ¼ aeW psat ðTW Þ pL hfg Fig. 2 e Compartments, processes and state variables considered in the model of wastewater temperature dynamics and spatial profiles in a sewer conduit.
(4)
where pL and psat are the water vapor partial pressure in the headspace and saturation partial pressure at the water surface, respectively; TW is the wastewater temperature; and
w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
hfg ¼ 2.453 106 J/kg (Incropera and DeWitt, 2002) is the enthalpy, which is approximated by the evaporation enthalpy. The partial pressure is calculated as pL ¼ 4Lpsat(TL) using the relative humidity 4L and temperature TL of the air in the sewer, and the saturation partial pressure at temperature T is calculated as psat ðTÞ ¼ pso e
Tso T
(5)
where pso ¼ 1.73 109 mbar and Tso ¼ 5311 K (Bischofsberger and Seyfried, 1984). The transfer coefficient aeW has units of W/m2/mbar and can be modeled by the equation of Trabert (Bischofsberger and Seyfried, 1984) as pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aeW ¼ 8:75 juL uW j
(6)
where uL and uW are the velocities of the sewer air and wastewater, respectively, which must have the units m/s when used in Eq. (6). The solution of Eqs. (1) and (2) requires initial and boundary conditions for QW and AW. In the case of sub-critical flow, a downstream and an upstream boundary condition are required, whereas in the case of super-critical flow, two upstream boundary conditions must be provided (Cunge et al., 1980). If pressurized flow can occur in the sewer, an additional assumption such as the Preissmann slot (Cunge et al., 1980) must be introduced to solve Eqs. (1) and (2).
paper are functions of uL. According to Fischer et al. (1979), uW,c of a circular conduit is uW;c ¼ uW þ
uW 3 2h0 þ 2:30log k 2 D
Airflow
uW ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gRW;hy S0
vAL vQL ¼ vt vx
(7)
where AL is the cross-sectional area of the headspace. Because AL ¼ A AW, where A is the cross-sectional area of the sewer pipe, substitution for AL in Eq. (7) followed by integration yields QL ðt; xÞ ¼ 0
vAW ðt; xÞ dx þ QL0 vt
(8)
where k z 0.4 is the von Karman constant, D is the nominal diameter of the sewer pipe, and h0 ¼ h if h D/2 or h0 ¼ D h if h > D/2. Eq. (8) is based on the assumption that the airflow only depends on the geometric and hydraulic quantities of the conduit considered, i.e., it is independent of the airflow in the upstream and downstream conduits and external forces. This assumption is fulfilled if the upstream and downstream ends of the conduit are chosen at locations where differences of the airflow in subsequent conduits are equilibrated by free exchange of air between the sewer and the atmosphere.
3.3.
Temperature and humidity
Models of temperature and humidity are based on mass balance equations for the water vapor X in the sewer headspace, which is defined as the loading of water per unit mass of dry air,
0:856 L
(12)
vðAW TW Þ vðQW TW Þ 1 ¼ þ q_ UW q_ WL P q_ eW P vt vx cp;W rW PW 0 þ q_ COD AW ;
(13)
for the air temperature TL in the sewer headspace vðAL TL Þ vðQL TL Þ 1 ¼ þ q_ UL þ q_ WL P þ q_ 0cL AL vt vx cp;L rL PL
(14)
for the temperature TP in the pipe wall vTP 1v vTP r ¼ aP r vr vt vr
(15)
and for the temperature TS in the surrounding soil
The effect of changes of the water depth on the airflow is modeled by the first term on the right-hand side of Eq. (8). In a steady state situation, this term is zero, and QL(x) ¼ QL0 throughout the conduit. To determine QL0, the model of steady airflow suggested by Edwini-Bonsu and Steffler (2004) is used in a modified version in which the airflow in a sewer conduit with a backwater curve can be calculated as QL0 ¼
(11)
and the heat balances for the wastewater temperature TW
Assuming that the air is incompressible, the mass balance of the airflow QL in the headspace of a sewer conduit is
Zx
(10)
with
vðAL XÞ vðQL XÞ 1 ¼ þ jeW P jcP UL j0cL AL ; vt vx rL
3.2.
551
ZL AL 0
P uW;c dx UL þ P
(9)
where L is the length of the sewer conduit, UL is the headspace perimeter and uW,c is the wastewater velocity at the water surface. According to this model, uL ¼ QL0/AL is determined by the friction at the pipe wall and at the moving water surface and usually has a value of approximately 0.5$uW,c. This factor is relevant because several transfer functions used in this
vTS 1v vTS r ¼ aS r vr vt vr
(16)
where j and q_ are mass and heat fluxes per unit area, respectively; j0 and q_ 0 are mass and heat fluxes per unit volume, respectively; r are densities; cp are heat capacities; a are thermal diffusivities; and r is the radial distance from the sewer pipe center. Longitudinal dispersion in the wastewater and headspace was found to be small compared to advective transport. The transfer rates used to model the exchange of mass and heat between the various compartments were taken from the literature. The condensation rate q_ cP at the pipe wall in the sewer headspace is q_ cP ¼ 0 if pL ðTL Þ < psat ðTPL Þ q_ cP ¼ acP pL psat ðTPL Þ if pL ðTL Þ psat ðTPL Þ
(17)
552
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where TPL is the pipe temperature at the interface between the sewer pipe and headspace, and the heat transfer coefficient acP is modeled as pffiffiffiffiffiffiffiffi acP ¼ 8:75 juL j
(18)
and has the units W/m2/mbar if uL has the units m/s (Bischofsberger and Seyfried, 1984). Mass and heat transfer are proportional because they depend on the same boundary layer properties (Incropera and DeWitt, 2002). Thus, the condensate mass flux of water vapor at this interface, jcP, can be modeled by jcP ¼ q_ cP =hfg
(19)
It is assumed that the condensate flows back into the wastewater, but this flux is very small compared to the discharge and can therefore be neglected in Eq. (2). The proportionality between mass and heat transfer is also used to model condensation and evaporation at the water surface analogous to Eqs. (4) and (19) as q_ eW ¼ aeW psat ðTW Þ pL
(20)
Condensation in the air of the sewer headspace occurs if the water loading of the air, X, is equal to or greater than the saturation value Xsat. This process is modeled by an empirical function j0 cL, which is zero if X < Xsat or is given a value such that v(ALX)/vt in Eq. (12) is equal to zero if X Xsat. The heat transfer associated with this process is modeled as q_ 0cL ¼ 0 if XðTL Þ < Xsat ðTL Þ q_ 0cL ¼ hfg j0cL if XðTL Þ Xsat ðTL Þ
(21)
The water vapor loading is related to the relative humidity
4L psat ðTL Þ pL 4L psat ðTL Þ
(22)
where psat is given by Eq. (5) and pL is the air pressure (Wanner et al., 2004). For 4L ¼ 1, Eq. (22) yields the water vapor saturation value Xsat. The convective heat transfer rate q_ WL between wastewater and sewer air is modeled as q_ WL ¼ aWL ðTW TL Þ
(23)
with the heat transfer coefficient aWL
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 5:85 juL uW j
aPW ¼
1=3 0:023Re4=5 W PrW lW RW;hy
(27)
where lW is the thermal conductivity as given in Table 1. The heat flux q_ PL between the pipe wall and the sewer air is modeled as q_ PL ¼ aPL ðTPL TL Þ
(28)
where the heat transfer coefficient aPL can be calculated using Eq. (27) by substituting the values for air for all parameters instead of those for water, i.e., aPL ¼
1=3 0:023Re4=5 L PrL lL : RL;hy
(29)
Heat produced by biochemical reactions in the nutrient rich wastewater is modeled by the heat production rate q_ 0COD ¼ eCOD rCOD
(30) 6
where eCOD ¼ 14 10 J/kgCOD is the reaction enthalpy (Wanner et al., 2005) and rCOD is the degradation rate, which has values of the order of 106 kgCOD/m3/s (Huisman et al., 2004). The solution of Eqs. (12)e(16) requires initial values TW ðt ¼ 0; xÞ; TL ðt ¼ 0; xÞ; TP ðt ¼ 0; rÞ; TS ðt ¼ 0; rÞ and Xðt ¼ 0; xÞ; upstream boundary conditions TW ðt; x ¼ 0Þ ¼ TWin ; TL ðt; x ¼ 0Þ ¼ TLin and Xðt; x ¼ 0Þ ¼ Xin ; continuity conditions for the temperature and heat flux between the wastewater and the pipe wall,
by XðTL Þ ¼ 0:622
turbulent flow, with Reynolds numbers ReW 10000 and Prantl numbers in the range 0.7 PrW 160 (Incropera and DeWitt, 2002) is modeled as
TP ðt; r ¼ D=2Þ ¼ TPW and lP
vTPW ¼ q_ PW ; vr D=2
between the headspace and the pipe wall, TP ðt; r ¼ D=2Þ ¼ TPL and lP
vTPL ¼ q_ PL q_ cP ; vr D=2
(32)
and between the pipe wall and the soil, TP ðt; r ¼ D=2 þ sÞ ¼ TPS and lP
(24)
(31)
vTPS ¼ q_ PS ; vr D=2þs
(33)
which has the units W/m /K if uL and uW have the units m/s (Bischofsberger and Seyfried, 1984). The heat flux q_ PW between the pipe wall and the wastewater is modeled as
where lP is the heat conductivity of the pipe; s is the wall thickness; and TPS is the pipe temperature at the interface between pipe and soil; and a boundary condition at the interface between the disturbed and undisturbed soil
q_ PW ¼ kPW ðTPW TW Þ
TS ðt; r ¼ D=2 þ s þ dS Þ ¼ TS;inf
2
(25)
where TPW is the pipe temperature at the interface between the pipe wall and the wastewater, and the heat transmission coefficient kPW is calculated as 1 1 1 ¼ þ kPW aPW f
(26)
where f is a fouling factor whose reciprocal value can be interpreted as a heat transfer resistance caused by biofilm growth on the pipe wall. The heat transfer coefficient aPW for
where D/2 þ s þ ds is the radius from the pipe’s center, at which the soil is assumed to have the undisturbed soil temperature TS,inf. If TW and TL change along the flow direction (x), the radial profiles of TP and TS also change along the flow direction. Changes of the soil temperature during a simulation period usually are small. If this is the case, TS can be modeled by radial steady state profiles that depend on the actual TPS and TS,inf; for vTS/vt ¼ 0, there is an analytical solution to Eq. (16):
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TS ðrÞ ¼ TPS þ TS;inf
r ln D=2þs
; TPS S ln D=2þsþd D=2þs
(34)
q_ PS ¼ lS
dTS lS TPS TS;inf
: ¼ dr D=2þs D=2 þ s ln D=2þs
The simulation program TEMPEST
The presented model was implemented in an interactive simulation program for temperature estimation in sewers, TEMPEST (Du¨rrenmatt and Wanner, 2008), which was developed to facilitate the application of the model and which was used for all simulations presented in this paper. The program can be obtained from the authors free of charge (Du¨rrenmatt and Wanner, 2013). In TEMPEST, the balance equations are integrated by the two-step LaxeWendroff algorithm (Press, 2005). Discretization in space can be specified by the user, who defines the number of spatial grid points in the flow direction and in the radial direction in the pipe wall. Integration over time is controlled by the program, which continuously optimizes the length of the integration time step according to the CouranteFriedrichseLevy criterion (Press, 2005). The heat exchange between sewer and soil is calculated separately for the wastewater and the headspace according to the actual water depth, which is limited to 0 < h hmax ¼ 0.95*D. The necessary input data include the wastewater discharge and temperature at the upstream end of the sewer, which are QWin and TWin, respectively; the ambient temperature TA, which is used to approximate TLin; and the ambient humidity and pressure, 4A and pA, which are used to approximate Xin by Eq. (22). To provide the initial conditions needed, a steady state solution is calculated by TEMPEST, and the thermal properties of various soil types and sewer pipe materials can be found in a small database. For the simulations presented in this paper, the discretization in space was gradually refined until its effect on the results became negligible. This was the case with a discretization along the flow axis of 50 m, and a pipe wall with five radial layers.
5.
Results and discussion
5.1.
Model calibration
To test the ability of the model to adequately reproduce the temperature profiles in the Ru¨mlang sewer, a simulation was performed, and the measured and calculated time series of discharge and wastewater temperature were compared. The quality criteria employed were the rootmean-squared error
RMSD ¼
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi uP u ðTm;t Ts;t Þ2 t t n
P
(37)
t
(35)
D=2þsþdS
4.
and the NasheSutcliffe coefficient of efficiency ðTm;t Ts;t Þ2 t E¼1P 2 Tm;t Tm
which can be used to calculate q_ PS as
553
(36)
where Tm,t and Ts,t denote the measured and simulated temperatures at time t, respectively; Tm is the mean of the measured temperature; and n denotes the number of data pairs. The NasheSutcliffe coefficient has an optimum value of E ¼ 1, whereas E < 0 indicates that the approximation of the measured series Tm,t by Ts,t is worse than the approximation by Tm . The parameters TS,inf, lS, dS, lP, aP, kst, rCOD and f were chosen for model calibration and will later on be examined by a sensitivity analysis. These parameters were selected according to the following criteria: parameters that have a dominant effect on the result, are difficult to measure, or can vary with time and space were included, whereas parameters that are readily available and have reliable values, such as sewer material properties and geometry, were not included to keep the number of fitted parameters as low as possible. Influent and effluent discharge and wastewater temperature data measured on February 26 and 27, 2008, were used for the calibration. A comparison of the measured and calibrated discharges, QWout and QWout, calib, reveals that a satisfactory correspondence can be reached (Fig. 3, top). A comparison of the effluent wastewater temperature TWout, apriori, which was simulated with the a priori parameter values of Table 1, and the temperature TWout, calib, which was simulated with the
Fig. 3 e Influent and effluent discharge and wastewater temperature time-series measured in the sewer conduit and effluent discharge and wastewater temperature calculated with a priori and calibrated values of the model parameters.
554
w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
calibrated parameter values, shows that the pattern of the measured effluent temperature TWout is adequately reproduced by both simulations (Fig. 3, bottom). However, the values of the quality criteria from the calibration, RMSD ¼ 0.14 C and E ¼ 0.97, were significantly better than those of the a priori simulation, RMSD ¼ 0.35 C and E ¼ 0.79. For the model parameters, the calibration yielded TS,inf ¼ 5.2 C, lS ¼ 0.65 W/m/K, dS ¼ 0.11 m, lP ¼ 2.3 W/m/K, aP ¼ 0.6*106 m2/s, kst ¼ 70 m1/3/s, rCOD ¼ 2.8 mgCOD/m3/s and f ¼ 200 W/m2/K. These values differ between 0 and 41% from the values of the a priori model parameters of Table 1. By a local sensitivity analysis the quantitative effect of the model parameters on the wastewater temperature was assessed. The analysis was performed for a steady state situation and included the calibrated model parameters, except for aP, since the thermal diffusivity is related to changes of the amount of stored heat and does not affect TW in a steady state situation (Eq. (15)). The most sensitive parameters are the temperature of the undisturbed soil, TS,inf; the thermal conductivity lS of the soil; and the soil penetration depth dS, which represents the distance at which the soil temperature can be assumed to be independent of the heat exchange with the sewer (Fig. 4). Thus, the processes and conditions in the soil surrounding the sewer are of primary importance when modeling the heat exchange between sewer and soil and will be discussed in detail in a subsequent section. The thermal diffusivity of the soil, aS, was not included in the calibration or the sensitivity analysis because these were performed using Eq. (35). The COD degradation rate rCOD and the fouling factor f do not have a significant effect on TW; therefore, it is usually not worthwhile to determine their values with high accuracy. However, these parameters vary with time, and f can change by more than 10% if sediments and biofilms that developed during long dry weather periods are suddenly washed off by a storm event (Wanner, 2004).
5.2.
Model validation
To validate the model, a simulation was performed for another set of measured wastewater temperature data. This simulation was performed using the parameter values found by the calibration run and the values from Table 1 for any remaining parameters except for the ambient parameters, which had slightly different values of TS,inf ¼ 5.8 C, TA ¼ 7.2 C, pA ¼ 948 mbar and 4A ¼ 0.72 during the validation data’s time period of March 11 to March 13, 2008. Fig. 5 shows that the effluent temperature predicted by the calibrated model, TWval, corresponds quite well with the measured effluent temperature, TWout, except for the initial phase of the diagram. The values of the quality criteria found by the validation were RMSD ¼ 0.20 C and E ¼ 0.94. These values are almost as good as the values obtained by the calibration, which indicates that the model can indeed be used to predict the effluent wastewater temperatures of the sewer conduit.
5.3. Effect of heat transfer processes and environmental conditions on the wastewater temperature To assess the significance of the heat transfer processes considered in the model, steady-state simulations for typical situations with different environmental conditions were performed. These situations and the resulting model predictions are summarized in Table 2. On the left-hand side of the table, the examined environmental conditions are shown and are characterized by dS, lP, lS, f and daily averages of TWin and TS,inf. The columns in the center of the table show the difference between the calculated downstream and upstream values of wastewater temperature and heat flux, DTW ¼ TWout TWin and DQ_ W ¼ Q_ Wout Q_ Win , respectively, where the upstream and downstream wastewater heat fluxes are calculated according to Q_ W ¼ cp;W rW QW TW
(38)
The columns on the right-hand side of the table show the heat flux through the wetted perimeter (PW), the convection (WL), the evaporation (eW) and the biodegradation (COD), i.e., the processes by which heat is exchanged between the wastewater and the other compartments (cf. Fig. 1). The given
Fig. 4 e Sensitivity of the effluent wastewater temperature to the parameters used for the calibration of the model.
Fig. 5 e Influent and effluent wastewater temperatures measured in the sewer conduit and the effluent wastewater temperature predicted by the calibrated model.
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Table 2 e Change of the wastewater temperature and heat flux in the sewer of Ru¨mlang, Switzerland, for various situations and environmental conditions. Please note that negative values indicate a loss of heat from the wastewater. Situation
Calibrated model Winter (benchmark) High heat transport in pipe wall and soila Low heat transport in pipe wall and soilb Unsaturated aquifer, no groundwater flow Saturated aquifer, high groundwater velocity Wetted perimeter with biofilm Summer a b
Environmental conditions
Change in the sewer
Processes accounting for heat transfer into wastewater
TWin ( C)
TS.inf ( C)
dS (m)
lP (W/ m/K)
lS (W/ m/K)
f (W/ m2/K)
DTW ( C)
DQ_ W (kW)
PW (%)
WL (%)
eW (%)
COD (%)
12.0 11.0 11.0
5.2 5.0 5.0
0.11 0.11 0.11
2.3 2.3 2.5
0.65 0.65 2.2
200 200 200
0.63 0.55 0.98
79 77 123
75 75 86
11 12 7
20 20 11
þ6 þ7 þ4
11.0
5.0
0.11
0.17
0.25
200
0.16
20
51
26
47
þ24
11.0
5.0
1.0
2.3
0.65
200
0.19
24
50
25
44
þ19
11.0
5.0
0.01
2.3
0.65
200
1.24
155
89
5
9
þ3
11.0
5.0
0.11
2.3
0.65
20
0.46
57
70
14
24
þ8
18.7
12.5
0.11
2.3
0.65
200
0.62
77
69
10
27
þ6
Change of pipe type from 1% to 2% steel in reinforced concrete and soil type from sandy clay to saturated sand. Change of pipe type from concrete to PVC with a wall thickness of 0.079 m and soil type from sandy clay to gravel.
numbers represent the specific heat fluxes q_ integrated over the interfacial areas as percentages of DQ_ W . The environmental conditions in the first line of Table 2 are those determined by the calibration of the model with measured data from February 2008 and the a priori parameter values, as given in Table 1. In this situation, the model predicted a change of the wastewater temperature in the sewer of DTW ¼ 0.63 C and a rate of the heat loss from the wastewater of DQ_ W ¼ 79 kW. This loss is attributed 75% to the heat flux through the wetted perimeter of the sewer pipe to the surrounding soil, 20% to evaporation at the water surface and 11% to the convective heat flux across the water surface. The contribution of heat production due to the degradation of organic matter in the water is insignificant (6%). The rate of the heat loss DQ_ W in the sewer is approximately 5% of Q_ Win ¼ 1500 kW, as calculated by Eq. (38). To facilitate a discussion of the significance of the heat transfer processes and environmental conditions in the cold season, typical winter conditions are introduced and used as a benchmark. During wintertime, the wastewater temperature is usually between 10 and 20 C, depending upon the origin of the wastewater, sewer properties and ambient conditions. The model predictions based on a simulation with TWin ¼ 11.0 C and TS,inf ¼ 5.0 C were DTW ¼ 0.55 C and DQ_ W ¼ 77 kW. The predicted heat loss of the benchmark is slightly lower than that of the calibrated model, which can be explained by the smaller temperature gradient between wastewater and undisturbed soil. Because heat transfer between wastewater and the surrounding soil was found to be so important, the material properties of the sewer pipe and soil must have a significant influence on the wastewater temperature. Among the materials with the highest thermal conductivities are reinforced concrete (2% steel), with lP ¼ 2.5 W/m/K (DIN, 2000), and saturated sandy soil, with lS ¼ 2.2 W/m/K (Unsworth and Monteith, 1990). For these materials, the simulation yields DTW ¼ 0.98 C and DQ_ W ¼ 123 kW, and the dominant heat
transfer process through the wetted perimeter becomes even more important and accounts for 86% of the heat loss. Materials with low thermal conductivities are PVC-pipes, with lP ¼ 0.17 W/m/K (DIN, 2000), and unsaturated clay soil, with lS ¼ 0.25 W/m/K (Unsworth and Monteith, 1990). For this combination of materials, DTW ¼ 0.16 C and DQ_ W ¼ 20 kW, i.e., the relative importances of convection and evaporation at the water surface of 26% plus 47% exceed that of the heat loss through the wetted perimeter (51%). In addition to the material properties, the hydraulic conditions in the aquifer surrounding the sewer pipe also have a significant effect on the heat transfer between soil and sewer, which was clearly demonstrated in an experimental study by Abdel-Aal et al. (2012). In an unsaturated aquifer or a saturated aquifer with a very low groundwater flow velocity, the transport of heat in the soil is a slow process, and the soil temperature around the sewer pipe gradually adjusts to the wastewater temperature. This situation can be modeled by a large value of the penetration depth dS, i.e., the distance between the sewer pipe and the zone where the soil temperature is assumed to be undisturbed. A change of dS from 0.11 m to 1.0 m yields model predictions of DTW ¼ 0.19 C and DQ_ W ¼ 24 kW and also leads to a lower relative contribution of heat transfer through the wetted perimeter (50% vs. 25% plus 44%). If the groundwater flow velocity is high, the convective transport of heat results in a soil temperature in the vicinity of the sewer pipe that remains close to the undisturbed temperature. This situation can be accounted for by setting dS ¼ 0.01 m, which yields model predictions of DTW ¼ 1.24 C and DQ_ W ¼ 155 kW. In this situation, the heat flux through the wetted perimeter of the sewer pipe to the surrounding soil becomes absolutely dominant and is responsible for 89% of the heat loss from the wastewater. It is well-known that in nutrient-rich raw wastewater, a biofilm rapidly develops on the wetted perimeter of the sewer pipe and creates an additional resistance to heat transfer. This
556
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resistance is proportional to the inverse of the so-called biofouling factor f. In an experimental study of biofilm growth in a laboratory scale sewer conduit, values of f ¼ 20 W/ m2/K were observed (Wanner, 2004). A simulation with this value yielded DTW ¼ 0.46 C and DQ_ W ¼ 57 kW. A comparison with the benchmark shows that heat resistance caused by a biofilm considerably reduces the heat loss and lowers the relative contribution of heat loss through the wetted perimeter. It should be noted that inorganic sediments deposited on the bottom of the sewer pipe can form even higher heat transfer resistances, and the extent of biofilms is usually controlled by the shear of the flowing water (Wanner, 2004). In the summertime, the wastewater and soil temperatures are usually considerably higher than in the winter. In Ru¨mlang, typical summer temperatures are TWin ¼ 18.7 C and TS,inf ¼ 12.5 C (data not shown). A simulation with these temperatures yielded DTW ¼ 0.62 C and DQ_ W ¼ 77 kW. A comparison with the benchmark reveals that only the evaporation has a higher value in the summer, while the other heat fluxes have almost identical values. The explanation of this finding is that the gradients between TWin and TS,inf are practically equal due to the relatively high soil temperature. However, it must be noted that TS,inf can be considerably lower depending on how deep the sewer pipe is buried in the soil.
5.4. Prediction of the effect of heat recovery on the wastewater temperature
treatment plant (WWTP) must not be lowered below 10 C as a consequence of the total heat recovered from upstream sewers (AWEL, 2010). The reason for this regulatory constraint is that in Switzerland, most of the sewage is treated in nitrifying activated sludge plants, and nitrification is significantly reduced at low wastewater temperatures, or the nitrifying bacteria can even be washed out from the plant (Wanner et al., 2005). This constraint is not applied to sewer lines connecting WWTP effluents and receiving waters. However, there are other constraints based on ecological considerations that limit sudden temperature changes and warming of the receiving waters. These constraints are relevant because a heat pump can be used for heating and for cooling and because the latter is very attractive economically. The best site for heatproducing facilities is at the point of WWTP effluent because the amount of heat energy that can be extracted from the wastewater is usually a multiple of that which can be extracted from the sewer upstream of the WWTP. However, if there are no consumers near the site of extraction, the loss of heat during its transport may make this solution unfeasible. To determine the optimal site for a heat recovery facility and the amount of heat that can be extracted in a specific situation and under the constraints given, it is necessary to estimate the changes in wastewater temperature at the end of the sewer. These changes occur, on the one hand, directly at the site of heat extraction and, on the other hand, in the reach between the extraction site and the end of the sewer.
To ensure successful operation of a heat recovery plant, there are some technical aspects and legal constraints that must be addressed as early as the planning stage. The Swiss canton of Zurich, in which Ru¨mlang is located, requires that the daily average of the influent temperature of a wastewater
Fig. 6 e Time course of discharge QWin and wastewater temperature TWin measured at the upper end of the sewer and the wastewater temperature directly downstream of the extraction site, TWin,rec, calculated by Eq. (39) for an assumed amount of extracted heat of 250 kW.
Fig. 7 e Time course of wastewater temperatures directly downstream of the extraction site, TWin,rec, at the end of the sewer, TWout,rec and TWout,rec,var (top), and the heat transferred from the sewer headspace and pipe wall into the wastewater, Q_ TWrec , Q_ TWrec;var and the average of the latter, Q_ TWrec;avg (middle), predicted for two alternative time courses of the extracted heat, Q_ rec and Q_ rec;var (bottom).
w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
Estimates of the latter require simulations with a mathematical model, while the former can be calculated as TWin;rec ¼ TWin
Q_ rec cp;W rW QWin
(39)
and Q_ rec DTWin;rec ¼ TWin;rec TWin ¼ cp;W rW QWin
(40)
where Q_ rec is the amount of heat recovered from the wastewater per unit time; TWin and TWin,rec are the wastewater temperatures directly upstream and downstream of the site of heat extraction, respectively; and DTWin,rec is the decrease of the wastewater temperature at this site. According to Eq. (40), DTWin,rec is directly proportional to Q_ rec and inversely proportional to the wastewater discharge QWin. This mathematical relation is reflected in Fig. 6, which displays QWin and TWin measured from March 11 to 12, 2008, in Ru¨mlang and TWin,rec calculated by Eq. (39) for an assumed Q_ rec of 250 kW. For the large discharge on the right-hand side of the figure, the decrease in the wastewater temperature at the recovery site is almost null, whereas the small discharge on the left-hand side leads to a large decrease and to a low temperature TWin,rec of approximately 6 C. The smaller the ratio Q_ rec /QWin, the smaller the decrease of TWin at the site of extraction. In the early morning hours of March 12, TWin,rec also had a very low value, which was primarily due to the already low TWin. The smallest value of TWin,rec resulted from simultaneous low values of both QWin and TWin. These observations raise questions about the origin of the wastewater. Depending upon whether sewage is primarily municipal or industrial and whether it is groundwater or rain water sewage, the seasonal and diurnal variations and the average values of QWin and TWin will be different. Usually, QWin increases in the flow direction because of lateral inflows, and TWin decreases because of heat loss to the environment. Consequently, these two quantities, together with the availability of a consumer for the recovered heat, primarily determine where heat recovery from the wastewater is feasible and how much heat can be extracted. In addition to changes in the wastewater temperature resulting from the extraction of heat, there are also temperature changes due to the exchange of heat between the wastewater, sewer headspace and pipe wall in the sewer conduit. Fig. 7 displays the time course of the wastewater temperatures directly downstream of the extraction site and at the end of the sewer, TWin,rec and TWout,rec (top), respectively. The latter is the result of a simulation based on the calibrated model and parameters, and using TWin,rec and QWin, as displayed in Fig. 6, as input. As seen on the left-hand side of Fig. 7, the temperature TWin,rec decreases remarkably in the early morning hours, but TWout,rec is higher than TWin,rec, i.e., the wastewater is gaining heat in the sewer. This finding corresponds to the initially positive values of Q_ TWrec , which is the integral over the exchange area of the heat flux from the sewer headspace and pipe wall into the wastewater (middle). The explanation for this finding is that the heat stored in the pipe wall is released into the wastewater as long as TW is smaller than TP. If TWin,rec is low and then increases, Q_ TWrec is
557
negative, the wastewater is losing heat, and the pipe wall is accumulating heat. These phenomena are temporary; in a steady state situation, the direction of heat exchange is determined by the temperature difference between wastewater and the soil, TW TS,inf. If this difference has a high positive value, a large loss of heat occurs, while heat can be gained from the soil if it is negative. This gain requires a heat flux in the soil that is strong enough to maintain a stable value of TS,inf and a TWin,rec value that is constantly smaller than TS,inf. The former condition was discussed in Section 5.3, while the latter is usually feasible only if warmer lateral inflows downstream of the extraction site ensure that the daily average of the influent temperature of a downstream WWTP is above the required 10 C. For the data presented in Fig. 5, the daily average of TWout is 11.2 C; for the TWout,rec displayed in Fig. 7, it is 9.8 C. Thus, the value of the daily average of TWout,rec is critical, and the question is how the temperature can be increased above 10 C. The simplest possibility is to lower Q_ rec when the environmental conditions are critical. Usually, this can readily be achieved because almost all heat recovery facilities are bivalent, i.e., for safety reasons, they also have a conventional heater. Another possibility is to vary Q_ rec during the day according to a predefined pattern. The idea behind this strategy is to extract the heat at the time when it is abundant in the wastewater and to store it for later use. This strategy is successful if TWin follows a typical diurnal pattern, as is usually the case for municipal or industrial wastewater. Such a pattern can also be observed for the Ru¨mlang data, except on the afternoon of March 12, when a rain event led to a lower TWin (Figs. 3 and 6). To test this strategy, another simulation was performed in which Q_ rec;var was changed between a low value in the early morning hours and a high value during daytime such that the total daily amount of extracted heat remained the same as that of the constant Q_ rec case. As seen in Fig. 7, the effect of this strategy is that TWout,rec,var, which is simulated in the same way as TWout,rec, varies less and has a slightly higher daily average of 10.0 C; Q_ TWrec;var also varies less than Q_ TWrec . The wastewater discharge usually also exhibits a typical diurnal variation with low values during nighttime and a rapid increase in the early morning hours. Because a high discharge QWin reduces the change of the wastewater temperature in the conduit, DTW ¼ TWout TWin,rec, regular diurnal variations of QWin can also be used to improve the strategy of variable heat recovery.
6.
Conclusions
The technique of heat recovery from wastewater in sewers by means of a heat exchanger and a heat pump is wellestablished, and hundreds of facilities have successfully operated based on this technique for many years. However, successful planning and operation require that the specific conditions of a given situation be analyzed beforehand. These conditions include the properties of the sewer system, the diurnal and seasonal variations of the wastewater discharge and temperature, legal restrictions imposed on the downstream wastewater temperature, and the demand and available supply of energy for heating or cooling. Based on this
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w a t e r r e s e a r c h 4 8 ( 2 0 1 4 ) 5 4 8 e5 5 8
information, it is possible to decide whether heat recovery at a given site is feasible and, if it is possible, to determine the optimal location and the extractable amount of heat energy. Part of the planning process is the establishment of a quantitative relation between the change of the sewer wastewater temperature and the amount of heat recovered. The relation between the temperature change at the site of extraction and the heat recovered can readily be estimated, but the change of the wastewater temperature between the extraction site and the end of the sewer can only be calculated by means of mathematical modeling and simulations. The presented pseudo two-dimensional mathematical model can calculate the changes of the wastewater temperature in a sewer conduit along the flow direction and over time. The model was implemented in the simulation program TEMPEST (temperature estimation) and was used to evaluate field data taken from the sewer of Ru¨mlang, Switzerland. The calibration and validation with these data confirmed that the model is able to adequately reproduce the spatial profiles and dynamics of the wastewater temperature and to predict the effect of heat recovery on the wastewater temperature in the sewer conduit examined. Since the model equations were mostly based on physical principles, the model should be applicable under different conditions as well, but further applications are needed to prove general validity. Lateral inflows that are not negligibly small may limit practical applicability of the model because it usually is not feasible to acquire data of every single inflow. The analysis of the simulations performed with the calibrated model revealed that the temperature of the undisturbed soil, the thermal conductivity of the soil and the distance between the sewer pipe and undisturbed soil are the most sensitive model parameters in steady state situations. The most dominant transfer process is the direct exchange of heat between wastewater and the pipe wall, but evaporation and convection at the water surface can also be relevant depending upon the environmental conditions. In dynamic situations, the storage of heat in and subsequent release from the pipe wall have a significant effect on the dynamics of the wastewater temperature. If the influent temperature of a WWTP falls below the required minimum of 10 C due to heat extraction, the model can be used to determine the maximum extractable amount of heat, to analyze whether more heat can be gained if the extraction is varied during the day, or to switch from the heat pump to a conventional heater in bivalent facilities if necessary.
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