Comparison of Cooling Lake Mathematical Models for Mount Storm Lake

Abstract

Mt. Storm Lake is an impoundment of the Stony River that provides cooling for the three-unit electric generating station which is owned by Virginia Power. The lake is relatively deep and narrow with a submerged intake and a surface discharge. Although the temperature structure in a cooling lake is usually three dimensional, it is often possible to use reduced dimension calculations to make sufficiently accurate predictions by dividing the lake into zones. MITEMP is a time-dependent temperature model for cooling lakes consisting of a 1-D (longitudinal) surface layer overlying a 1-D (vertical) variable-area hypolimnion. This model was adapted to Mt. Storm Lake using available field data for calibration and verification. The initial model predictions, using data from Sept. 1986 - Aug. 1987 and made prior to our calibration, were quite good with average errors ranging from -0.1 to -1.10�C depending on location within the lake. Model calibration consisted of adjustments to the net solar radiation, as well as the entrance dilution coefficient and the surface layer longitudinal dispersion coefficient. The average errors after calibration were reduced to about 0-0.50 C with a standard deviation of 1-1.40 �C. The residual time series of model errors after calibration was shown to be correlated to station generation, indicating that better model performance could be achieved by an improved representation of the heat rejection. As part of a related study, a O-D water and energy balance model was developed to assess water availability at Mount Storm Lake under several different scenarios. This model is very efficient, requiring less than five minutes of CPU time to do over 1000 years of simulation in comparison with about 3 minutes for a 1-year simulation with MITEMP. (Both are for a MicroVax II.) The temperature predictions of the 0-D model were evaluated to assess its accuracy as a screening model. Although the model is steady-state, it was shown theoretically and empirically to have similar thermal inertia to a transient model if 30-day (monthly averaged) data were used as input. Results show that the 0-D model predicts the lake temperature fairly accurately. The mean error varies between 0.35 �C for different averaging intervals between 10 and 40 days, and the standard deviation is 2.50� C using 30-day averaged data. A preliminary comparison was also made between MITEMP and a 2-D (longitudinal and vertical transient model), NARES, to see what changes in thermal structure result from an improved description of the flow field.. There was not time to complete this part of the study, but initial model predictions show reasonable agreement between observed and predicted longitudinal variation in hypolimnetic temperature. However, because the maximum observed longitudinal variation is only about 2.00 �C, the added detail is not critical especially since the 2-D model is quite time consuming to run (about 14 hours of MicroVax II CPU time for an annual simulation). This is two-and-one-half orders of magnitude more expensive than MITEMP. However, there is the potential for this model to provide useful information if a new generating facility were to be added at a different location on the lake. However, it would require more calibration and validation effort.