Modelling of Sewer Wastewater temperature Dynamics

By Himanshu Nagpal

Introduction

Wastewater in sewer systems is a promising alternative energy source for heating/cooling of buildings.  It is estimated that 6000 GWh of thermal energy is lost per year in sewers of Switzerland [1]. This accounts for 7% of total heating demand of Switzerland. According to a study, the sewer wastewater in Germany contains energy to heat 2 million homes [2]. The temperature of wastewater in sewer can range from C to C throughout the year depending upon external conditions [1].  The wastewater flow in sewer system is relatively large depending upon the number of inhabitants in the catchment. This significant amount of heat from the sewer system can be recovered and used to preheat cold water supply for hot water demands and space heating. The content of available energy in wastewater is calculates as

$$\dot{Q}= \dot{m}c_{p}\Delta T\,\,\,\,\,\,\,\,\,(1)$$

where $\dot{Q}$  is the recovered thermal power from wastewater, $m$ and $c_{p}$ are the mass flow rate and specific heat capacity of wastewater, and  is the temperature drop of wastewater due to heat recovery. A schematic diagram of wastewater heat recovery from sewer is shown in Figure 1. A heat exchanger is installed in sewer system which extract the heat from wastewater and a heat pump system is used to convert that low temperature heat to usable heating energy.

Figure 1 Heat recovery from wastewater in sewer [1]

Sewer wastewater temperature dynamics

As can be seen in equation (1) that the recovered heat content depends upon the temperature and flow rate of wastewater. The wastewater temperature in sewer system does not remain constant and changes across the longitudinal profile of sewer line because of heat losses and addition of lateral flows. So, it becomes vital to investigate the temperature dynamics of wastewater in sewer line in order to find the optimal location for installation of heat recovery system. One more important reason for this investigation is to analyse the impact of wastewater heat recovery on influent temperature of wastewater treatment plant (WWTP).  Since the reduction in wastewater influent temperature can cause reduced nitrification capacity of WWTP.  Modelling the thermal dynamics of wastewater can help the planners and engineers to determine the design of wastewater heat recovery system which complies with WWTP regulations.

Existing models

There are two main approaches to model the wastewater temperature dynamics,

1. Determining temperature change at certain point using limited measured data

2. Modelling the temperature dynamics along longitudinal profile of the sewer

Alligation alternate

Alligation alternate is a relatively simple method for modelling the wastewater temperature dynamics [3]. In this method, the temperature  of two fluid flows with discharge and temperature values of  and  is given by the following equation

$$(Q_1 + Q_2)\times T^* = Q_1\times T_1 + Q_2\times T_2\,\,\,\,\,\,\,\,\,\, (2)$$

This method does not consider the heat exchange processes with in-sewer air, surrounding soil and sewer pipe which is the main reason for the low-accuracy of the model.

TEMPEST-

TEMPEST is a computer simulation program, developed by Dürrenmatt and Wanner [4] at Swiss Federal Institute of Aquatic Science and Technology, Switzerland, which simulates dynamics of wastewater temperature in sewers. The program is based upon heat balance, mass conservation and momentum conservation equations in sewers and can calculate the dynamics and spatial longitudinal profile of wastewater temperature. This is the most detailed model available in the literature for wastewater temperature dynamics modelling; it considers many heat-transfer processes which can affect the wastewater temperature including interaction with surrounding soil of sewer and in-sewer air (Figure 2).

Model by Abdel aal et al.

The temperature evolution in this model is given by the equation (3). This model is simpler than the TEMPEST model and does not include all heat transfer processes [5].  

Table 1 - Description of parameters in equation (3)

$$T_{j+1} =T_j - \Big(\frac{\frac{1}{R_{wa}}\times (T_w-T_a) + \frac{1}{R_{ws}}\times (T_w-T_s)}{\dot{M}\times c_p}\Big)\,\,\,\,\,\,\,\,\,\,(3)$$

where

$$R_{wa} = \frac{1}{h_{wa}\times b\times n\times \nabla L}$$

$$R_{ws} = \frac{wt}{k_p\times wet.p\times n\times \nabla L} + \frac{d_s}{k_s\times wet.p\times n\times \nabla L}$$

Equation (3) is used sequentially to find the wastewater temperature at nodes $(T_{(j+1)},T_{(j+2)}…T_{(j+n)})$ along the sewer line starting from the upstream temperature . The parameters used in the equation (3) are presented in the Table 1

Opportunities and Future work

In the context of Dwr-Uisce, future work will be to perform a case study for wastewater temperature dynamics modelling in a sewer system. The test location has not been decided yet. The study will focus on measurements of temperature and flow in the sewer system of the test location. The finding will be verified against the TEMPEST model and model by Abdel aal et al. The best location will be identified based upon the models. The study will also present the design methodology for heat recovery system (heat exchanger and heat pump) based upon the measurements and estimate the energy savings and emissions reduction.  

References

[1] Schmid, Felix. "Sewage water: interesting heat source for heat pumps and chillers." In 9th International IEA Heat Pump Conference, Switzerland. Paper, no. 5.22, pp. 1-12. 2008.
[2] Mueller, E. A. "Heating and cooling with wastewater; Heizen und Kuehlen mit Abwasser." (2005).
[3] Leaflet, DWAM "114: Energy from wastewater - heat and location energy." (2009): 1