Bilan thermique sous climat tempéré des lagunes aérées et naturelles Thermal balance of aerated lagoons and waste stabilization ponds in temperate climates

Résumé

Un modèle décrivant la température d'équilibre des lagunes a été développé, tenant compte des différents flux de chaleur que celles-ci échangent avec l'air et le sol environnant. Six composantes différentes ont été inclues dans le calcul de ce bilan thermique: radiation solaire, évaporation, convection, rayonnement atmosphérique, rayonnement de la surface du plan d'eau, échange via les parois en contact avec le sol.

Le modèle ainsi obtenu a été testé avec efficacité sur deux lagunes aérées et une lagune naturelle situées sous climat tempéré ; sa précision sur l'estimation des températures d'équilibre étant de l'ordre de 0.7 °C. Des simulations en continu ont également pu être effectuées au moyen d'une variante dynamique, tenant compte de l'inertie thermique qu'entraîne le volume des bassins.

Quelle que soit la saison envisagée, la principale forme d'apport de chaleur est représentée par la radiation solaire tandis que la dissipation d'énergie se partage entre les flux d'évaporation et la balance des deux flux de rayonnement. Les bassins échangeraient en moyenne plus de 250 W/m² ; le maximum de transfert de chaleur correspondant au printemps et à la période estivale.

Enfin, l'analyse de sensibilité du modèle nous a permis de mettre en évidence la contribution de chacun des termes intervenant dans le calcul de ce bilan thermique et de révéler sa dépendance vis-à-vis principalement de la température d'entrée, du rayonnement solaire et de la température de l'air.

Mots-clés:

• Lagunage aéré,
• lagunage naturel,
• bilan thermique,
• température d'équilibre,
• transfert de chaleur

Abstract

Very few studies have ever focused on the thermal balance of a wastewater treatment process, despite its major impact on various aspects of sanitary engineering, such as biological growth, oxygen transfer and, most importantly, purification kinetics. This lack of knowledge is particularly worrying for the design of aerated lagoons and waste stabilization ponds, since these two extensive treatment technologies are extremely dependent on climatic conditions and subject to high thermal variations. In temperate regions, a pond annual temperature range can even exceed 20 °C, while a 10 °C variation will induce a more than 60% drop or increase in its removal yield. Our paper intends to present a comprehensive temperature prediction model which accounts for the main heat loss and gain terms exchanged through the pond surface and walls.

Our approach includes six different energy inputs and outputs, namely: solar radiation, air-water surface convection, atmospheric radiation, back surface radiation, evaporation and ground-water-walls convection. Each of these components was described extensively by means of a literature review of all previous efforts made to predict equilibrium temperature in lakes, rivers, salt-gradient solar ponds, cooling tanks, even outdoor pools. The best aspects of each prediction model were then incorporated into a new computer model developed as two different but complementary variants: one for steady-state conditions and the other for continuous and therefore also transient simulations. The main difference between these two approaches is that the first one neglects enthalpy variation while the second one takes the form of a differential equation, with basin temperatures being estimated by an iterative calculation procedure and a numerical integration method, respectively.

Two hypotheses were necessary to develop this model. The first one posits that pond hydrodynamics correspond to completely mixed conditions. Such hydraulic behavior is extremely frequent in aerated lagoons and waste stabilization ponds in temperate climates, but less so in tropical or Mediterranean regions, where thermal balances appear much more complex since stabilization ponds are often thermally stratified. The second hypothesis is that all radiation fluxes received by the ponds are completely absorbed by the pond's contents and are never reflected, even partially, by their bottoms or walls.

This model, which is in fact the thermal balance of the basins, relies mainly on meteorological factors and pond characteristics. Only two out of the six estimated fluxes - evaporation rates and solar radiation - are measured directly in situ. It seemed too difficult to estimate them, since predictive equations found in literature constantly gave unsatisfactory results.

To establish the validity of this model, experimental data were collected at a wastewater treatment plant located in the southern part of Belgium. This plant consists of a series of two aerated lagoons and four waste stabilization ponds, designed for a nominal capacity of 7,500 inhabitant-equivalents. Five rounds of measurements, each lasting from five to twenty days, were conducted at different periods of the year. Meteorological factors were continuously monitored by a data acquisition unit while the pond water temperatures and hydraulic flows were measured hourly. Evaporation rates were determined daily with several floating evaporation pans set at the pond surfaces. Vertical temperature and illumination profiles were also measured in order to verify the strict applicability of the two previous hypotheses.

Ninety-three experimental data sets were collected on this particular facility. Predicted temperatures were compared with measured temperatures as well as with the results of three other models previously developed for waste stabilization ponds. Our new model systematically proved more reliable and accurate than previous approaches, since equilibrium temperatures were predicted with a mean absolute error of only 0.7 °C. More than 52% of the deviations between calculated and observed temperatures were even below 0.5 °C, which indicates their relatively low dispersion.

Continuous simulations were also conducted during a one-day period to demonstrate the importance of the ponds' large thermal capacities. The steady-state approach, which does not account for this latter phenomenon, failed to give consistent results, unlike our dynamic heat balance approach, which yielded extremely good fits with experimental data.

A sensitivity analysis allowed us to show the influence of the various meteorological factors on the basins' equilibrium temperatures. In decreasing order, the fits seemed particularly sensitive to inlet temperature, solar radiation, air temperature and evaporation. Surprisingly, wind speed made only a small contribution to the total heat balance. However, this must be seen as a direct consequence of the fact that in our model this latter parameter is no longer used to calculate the predominant evaporation rates but only to estimate the much smaller convection term.

Whatever the season considered, more than 90% of the ponds' energy inputs come from solar radiation while the dominating loss mechanisms are represented by the balance of the two infrared radiation fluxes (46%) and evaporation (42%). The sign of the air-water convection term varies according to the period of the year but never accounts for more than 10% of the total heat balance. Heat losses or gains from basin walls always remain insignificant and could therefore easily be neglected in order to simplify our approach to basin equilibrium temperatures.

Keywords:

• Aerated lagoon,
• waste stabilization pond,
• thermal balance,
• equilibrium temperature,
• heat transfer