Optimum exit temperature

The only variable in Eq. (55) is the temperature of the cooling water leaving the condenser. The optimum cooling-water rate occurs when the total annual cost is a minimum. Thus, the corresponding optimum exit temperature can be found by differentiating Eq. (55) with respect to t2 (or, more simply, with respect to t - t2) and setting the result equal to zero. When this is done, the following equation is obtained ... 

Derive an expression similar to Eq. (56) for finding the optimum exit temperature of cooling water from a heat exchanger when the temperature of the material being cooled is not constant. Designate the true temperature-difference driving force by... 

In converter passes downstream of the first pass, exit temperatures are limited by thermodynamic equiUbrium to around 500°C or less. To obtain optimum conversion, the heats of reaction from succeeding converter passes are removed by superheaters or air dilution. The temperature rise of the process gas is almost direcdy proportional to the SO2 converted in each pass, even though SO2 and O2 concentrations can vary widely. 

Rice [15] made a comprehensive study of the reheated gas turbine eombined plant. He first analysed the higher (gas turbine) plant with reheat, obtaining (t o)h> turbine exit temperature, and power turbine expansion ratio, all as funetions of plant overall pressure ratio and firing temperatures in the main and reheat burners. (The optimum power turbine expansion ratio is little different from the square root of the overall pressure ratio.) He then pre-seleeted the steam eyele eonditions rather than undertaking a full optimisation. 

Several techniques are available in the literature for evaluation of the flame temperature, exit temperature, equilibrium composition of combustion products, and performance parameters of energetic composites [11-13]. The optimum combination of the composite ingredients is determined by thermodynamic means, so as to arrive at a composition having maximum performance... 

The variability of the process parameters with flow causes variability in load response, as shown in Fig. 8-50. The PID controller was tuned for optimum (minimum-IAE) load response at 50 percent flow. Each curve represents the response of exit temperature to a 10 percent step in liquid flow, culminating at the stated flow. The 60 percent curve is overdamped and the 40 percent curve is underdamped. The differences in gain are reflected in the amplitude of the deviation, and the differences in dynamics are reflected in the period of oscillation. 

The optimum steady-state economic design was determined with these new kinetic parameters, and the parameters are given in Table 7.4. The FS2 flowsheet is used with a ratio (2p,/2totai = 0.1. The impact of the kinetic parameters on the optimum design is striking. The hotter reaction requires a much larger recycle flowrate and a higher reactor inlet temperature for the same reactor exit temperature 7 ollt = 500 K. These lead... 

Example 4.1 Optimum Cooling-Water Exit Temperature ... 

Frequently, an approximate value of the optimum exit-water ten Derature is all that is required, and a rule-of-thumb will be satisfactory. Table 4.4 hsts the approach tenperature difference, which is the difference between the two terminal temperatures of two passing streams, for several heat exchangers. Several approach temperature differences were taken from Uhich [8], For refrigerants, Ulrich s range of 10 to 50°C is on the high side. Frank [7] recommends a range of 3 to 5°C whereas Walas [3] recommends a value of 5.6 C or less. 

New tube materials allow the design for much higher exit temperatures and heat fluxes, in particular when applying a side wall fired reformer furnace to ensure better control of the maximum tube wall temperature and optimum use of the high alloy material. Thinner tube walls made possible by the use of the new materials reduce the risk for creep due to faster relaxation of stresses at start and stop of the reformer (14). 

The second condition in Eq. (11.5.d-6) is satisfied only when 5r/5T the partial derivative of the rate with respect to the temperature is partly positive and partly negative. Substituting into this partial derivative the relation between x and T along an adiabatic reaction path starting from F, (condition Eq. 11.5.d-5) turns 5p/5T, = /i(x, r,) into a function dp/dTi = /2(T,). The root of this equation is easily found by a one-dimensional search procedure and is the optimum inlet temperature leading to the exit conditions represented by the point chosen on Fi. This procedure is repeated for a certain number of points on F, to obtain the locus of optimum inlet conditions for bed 1, represented by F, in Fig. 11.5.d-l. It follows from Eq. 11.5.d-6 that F, and F, intersect on F , not on F. ... 

A module has a power rating of 170 MW(th) at 950°C helium outlet temperature for process heat applications, while for electricity production or coproduction of electricity and process steam or district heating a rating of 200 MW(th) at an exit temperature of 700 °C is achieved. For reasons of economics and demand, plant sizes of 8 units appear to be an upper limit. Additionally the modular HTR as a small and inherent safe reactor system fullfil the criterion for the design of an autarc barge-mounted energy station in an optimum way. 

Longer tubes provide a longer co-current heat transfer path in the reformer, and thereby reduce the flue gas exit temperature, which conserves fuel. Longer tubes also reduce the number of tubes. However, the pressure drop is higher. The optimum tube length is typically 40 to 45 feet. 

---