To:Matthew Memmott
From:Engineering Group
Date:27 September 2018
Subject:Proposal to characterize the new heating system on the stirred tank.
Introduction
The heating system on one of our stirred, short-term storage tanks was recently replaced. The previous system used an externally-mounted heat exchanger to maintain the temperature of the fluid in the tank at the desired value prior to delivery into the reactor. The new system uses a steam coil installed directly inside the tank. The heat transfer properties of this new system need to be characterized in order to develop the control system for the process. This document describes the approach proposed to create the needed heat transfer model.
Theory
Analysis of the heat transfer characteristics in the tank begins with an energy balance. Taking the system to be the fluid in the tank, the following assumptions are made:
- The system is stationary.
- No mass flows into or out of the system because the tank is used for storage.
- The shaft work done on the fluid by the stirrer is negligible.
The resulting energy balance is
/ (1)where is the total internal energy of system, is time, and is the heat flowing into the system. The heat transfer rate can be expressed by
/ (2)where is the overall heat transfer coefficient between the steam and the fluid in the tank, is the surface area available for heat transfer, is the temperature of the steam, and is the temperature of the fluid in the tank.
Assuming the fluid is incompressible,
/ (3)where is the density of the fluid, is the volume of the fluid, and is the constant pressure heat capacity of the fluid. Substituting Equations 2 and 3 into Equation 1 gives
/ (4)The initial condition of the system is at , where is the temperature of the fluid before steam is introduced into the coil. Assuming the contents of the tank are well mixed so that the temperature inside the tank is uniform and that the properties of the fluid are constant with respect to temperature, integration of Equation 4 yields
/ (5)Equation 5 is the design equation that can be used to model the heat transfer characteristics of the system. The unknown of interest in Equation 5 is. Experiments will be done to calculate for the fluid stored in the tank. Once known, Equation 5 can be used to control the system within desired temperature ranges.
Methods
Apparatus
Figure 1shows a schematic of the experimental apparatus. The actual storage tank and stirrer that will be installed in the plant will be used in the experiments. The tank is 66 inches tall and the inside diameter is 39 inches which gives a total capacity of 341.3 gallons. The heating coil is made of ¾-in, Schedule 40, galvanized iron pipe (O.D. 1.05 in, I.D. 0.824 in) and is 33 ft in length. The entrance of the coil is 55 inches from the bottom of the tank so that the entire coil is submerged when the tank is filled with 300 gallons of reagents—the amount currently used in the process.
Figure 1 Storage tank with heating coil.
The height of the liquid in the tank can be read on the side of the tank. Two, type K thermocouples, obtained from the Omega company, have been installed inside of the tank to measure the temperature of the liquid. The in-house steam plant supplies the heating coil with saturated steam. The pressure of the saturated steam is regulated using a manual control valve and is measured using a pressure transducer from Data Instruments Inc. (Model # 9300101). A stirrer ensures the contents of the tank are well mixed. The entire system is controlled with Labview software which records the temperature measurements as a function of time.
Experimental Design
In order to determine the overall heat transfer coefficient for the process, experiments will be performed to measure the temperature rise of the fluid as a function of time when steam is introduced into the coil. The tank will be filled with 300 gallons of culinary water, and it is assumed that the properties of water are the same as those of the aqueous reagents used in the plant. After the initial temperature of the water is recorded, the steam will then be turned on and temperature vs. time data will be collected. These data will be fit to Equation 5 to produce values of . The density and heat capacity of the waterwill be obtained from the DIPPR database. Steam pressures of 1, 2, 3, and 4 psig will be tested. At least 5 replicates at each pressure will be done to ensure statistical significance.
Expected Outcomes
The transfer of heat from the steam to the fluid can be modeled as a series of thermal resistances. Heat is transferred by condensation on the steam side of the coil to the inner wall of the coil. This heat is then transferred by conduction through the wall and then from the outside wall of the coil to the fluid by forced convection. The convective heat transfer resistance by condensation, and the conduction resistance through the iron pipe, are likely small compared to theforced convection resistance on the outside of the pipe. As such, stream pressure will likely have little influence on, and the value of will shouldbe on the order of the convective heat transfer coefficient, , on the outside of the coil.
Assuming W m-2 K-1, an initial water temperature of 50 °F, and a final water temperature of 50 °F, a sample calculation was done to determine the system behavior that should be observed during the experiments. Figure 2 shows these calculations. The apparatus physical dimensions and compound properties are defined at the top of the figure. These are followed by the specification of hypothetical values for theunknown variables. The bottom of the figure shows the temperature vs. time graphobtained from Equation 5 and the hypothetical values given above. As predicted from Equation 5, the temperature increases logarithmically with time until it reaches steady state at approximately 8 minutes. Note, as mentioned in the Theory section, the exact value of will be obtained by performing experiments to obtain real temperature vs. time data that will be fit Equation 5.
Figure 2 Sample calculations showing expected temperature vs. time plot using estimates of the heat transfer coefficient.