Comparison of finite element and finite difference methods in thermal discharge investigations

Abstract

Ultimately, the objective of scientific research into numerical methods must be to provide workers in the field with reliable credible tools which can be used to analyse complex problems. In the field of water resources, there is the further need to be able to assess potential environmental impacts before irreversible modifications are made to existing water systems. In addition, the analysis methodology must be credible, economical and achievable in a reasonable period of time. In this study, the use of numerical simulation models for analysing the impact of a proposed thermal-electric power plant on the proposed cooling reservoir are investigated. , The underlying objective of this present study is to provide an estimate of the thermal regime and subsequent evaporation for a cool-fired power plant with a potential for producing 1200 MW. However, the secondary objective was to determine whether existing finite element models or existing finite difference models could be used more effectively in meeting the stringent time frame imposed on completion of the study. It is this second objective which will be considered here. It is not the purpose of this present paper to make an assessment of the environmental implications of the proposed power plant. Rather, the proposed power plant system is to be the media to make a comparative study of the significance of existing, available, numerical models. An initial investigation of the reservoir, shown schematically in Fig. 1, indicated a potential for two possible hydrodynamic regimes. First, it was possible that the reservoir would stratify, resulting in a structure of layer homogeneity. Secondly, it was possible that, because of the relatively high persistent winds and the large thermal effluent, the reservoir would at any location in the reservoir be homogeneous throughout its depth. Therefore, two types of integrated models would be required to determine the expected hydrodynamic regime for the reservoir. Before continuing with the model exposition, it is necessary to review peripheral information with relevance to this study. The power plant at the reservoir is to begin operation in the early summer of 1979 at which time it is expected that the reservoir will finish filling for the first time. Hydrologic flows in the river are small and average approximately 12 500 acre-feet for the period of record from 1931 to 1976. Most of the runoff into the reservoir occurs in a relatively short period of time in the spring, thus resulting in a closed system for the remainder of the year. Water quality in the reservoir is generally good. However, due to the small inflows and due to plant treatment there is a potential for an accumulation of TDS in general and boron in particular. Based on the above, two conciosions can be drawn about the methodology required for the study. First, as there is no possibility of obtaining comparative data, every effort will have to be made to generate collaborating information. Second, because of the small external inflow and because of the small resergoir, errors in the temperature prediction will have a pronounced effect on the volume of water in the reservoir because of the increased evaporation. Also, as the surface of the reservoir begins to drop, the potential for short-circuiting in the reservoir will increase, resulting in a further elevation in temperature and an increase in evaporation. The period of record for the current study is 1931 to 1976. Simulation of the hydrodynamic regime for this extended period is economically unjustifiable and philosophically questionable. It was felt that simulating the steady state hydrodynamics of the reservoir under two unit (600 MW) plant operation with no hydrologic input would be representative of the questionable summer period. Consequently, the above philosophy Was adopted