Two Heated Tanks

As our next fairly simple system let us consider a process in which two energy balances are needed to model the system. The flow rate f of oil passing through two perfectly mixed tanks in series is constant at 90 ft min. The density p of the oil is constant at 40 and its heat capacity Cp is 0.6 Btu/lb °F. The volume 

There is one energy balance for each tank, and each will be similar to Eq. (2.26) except there is no reaction involved in this process. 

Since the throughput is constant Fq= Fi= Fi = F. Since volumes, densities, and heat capacities are all constant, Eqs. (3.10) and (3.11) can be simplified. 

Let s check the degrees of freedom of this system. The parameter values that are known are p, C, V, Vz, and F. The heat input to the first tank would be set hy the position of the control valve in the steam line. In later chapters we will use diis example and have a temperature controller send a signal to the steam valve to position it. Thus we are left with two dependent variables, and T2, and we We two equations. So the system is correctly specified. 

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Ammonium nitrate is made at Fisons Ltd and stored in solution in two heated tanks to prevent ciystalization. One tank holds 3,100 tonnes and the other 6,200 tonnes of 92% aqueous ammonium nitrate solution. Trains laden with oil refinery products from the Mobil and Shell refineries pass the factory on a near embankment. A derailment could spill and ignite hydrocarbons from a rail tank car to explode an ammonium nitrate storage tank. Suggestions were made to mitigate or prevent such a domino effect... 

Example 9.7. The two-heated-tank example modeled in Sec. 3.4 was described by two linear ODEs ... 

Figure 10.1b shows a specific example the two-heated-tank process discussed in Example 9.7. The load variable is the inlet temperature To. The manipulated variable is the heat input to the first tank Qi- The two transfer functions G, y and were derived in Chap. 9. 

The dynamics of this openloop system depend on the roots of the openloop characteristic equation, i.e., on the roots of the polynomials in the denominators of the openloop transfer functions. These are the poles of the openloop transfer functions. If all the roots lie in the left half of the s plane, the system is openloop stable. For the two-heated-tank example shown in Fig. 10.16, the poles of the openloop transfer function are 5 = 1 and s = — j, so the system is openloop stable. 

Note that the transfer function for the two-heated-tank process has a steadystate gain that has units of °F/°F. The Gm, ) transfer function has a steady-state gain that has units of °F/Btu/min. 

Figure 10.2h gives a sketch of the feedback control system and a block diagram for the two-heated-tank process with a controller. Let us use an analog electronic system with 4 to 20 mA control signals. The temperature sensor has a range of 100°F, so the Gj transfer function (neglecting any dynamics in the temperature measurement) is... 

Design a feedforward controller for the two-heated-tank process considered in Example 10.1. The load disturbance is inlet feed temperature 7. ... 

As a specific numerical example, consider the two-heated tank process from Example 10.1 with the openloop transfer function... 

Example 19.11. As our last example, let s consider the second-order two-heated tank process studied in Example 19.5. 

Figure 6.3 Two heated tanks in series with recycle.

We begin with the analysis of a basic system consisting of two heated tanks interconnected via a material recycle stream, which acts as an energy carrier, as in Figure 6.3. Let F be the molar feed flow rate to the first tank (with molar enthalpy ho), R the molar recycle flow rate, hi and ft-2 the molar enthalpies, and Qi and Q[Pg.152]

For the two-heated-tank process of Example 7.7, the two transfer functions were given in Eq. (7.92). The steady-state gain between the inlet temperature Tg and the output T2 is found to be 1°F/°F when s is set equal to zero. This says that a 1° change in the inlet temperature raises the outlet temperature by 1°, which seems reasonable. The steady-state gain between Tj and the heat input Q is 1/2160 °F/Btu/min. You should be careful about the units of gains. Sometimes they have engineering units, as in this example. At other times dimensionless gains are used. We discuss this in more detail in Chapter 8. 

Figure 20-9 shows the negative effect of uninsulated heating elements on corrosion protection. In a 250-liter tank, an electric tube heating element with a 0.05-m surface area was screwed into the upper third without electrical separation, and in the lower third a tinned copper tube heat exchanger with a 0.61 -m surface area was built in. The Cu heat exchanger was short-circuited for measurements, as required. For cathodic protection, a potential-controlled protection system with impressed current anodes was installed between the two heating elements. The measurements were carried out with two different samples of water with different conductivities. 

Liquefied ammonia is delivered in rail tankcars to Fisons Limited for storage in a 1,900 tonnes spherical tank at -6° C. Several hundred tonnes of liquefied ammonia could be released on land if either of the two storage tanks, at Shell UK Oil and at Fisons Limited failed. The consequences of f lilure of the Shell tank would be minimal, because a high concrete wall to contain the contents and limit the heat transfer and consequently the rate of evaporation of the liquid. Such protection has not been provided. Because of the storage under pressure there are numerous ways the tank could fail from material defect to missile. The spillage of 50 to 100 tonnes, could kill people if noi [imrnp( , evacuation. 

At 5 45 A.M., a flash fire resulted. The vapor cloud is assumed to have penetrated houses, which were subsequently destroyed by internal explosions. A violent explosion, probably involving the BLEVE of several storage tanks, occurred 1 minute after the flash fire. It resulted in a fireball and the propulsion of one or two cylindrical tanks. Heat and fragments resulted in additional BLEVEs. 

Application of a divided cell containing one pair of electrodes (Pt-coated Ti anode 316 type stainless steel cathode) with an effective area of 100 cm2. Nafion-324 was used as the membrane. Two 81 tanks contained anolyte (feed) and catholyte (caustic). A coil-type heat exchanger was used to maintain the heat... 

Properties and handling. At ambient temperatures, phthalic anhydride is a white crystalline solid. It is slightly soluble in water. It is commercially available in two grades—pure (99.5%) and technical (99%). It is shipped in drums and bags in the solid form. Liquid phthalic anhydride is shipped in heated tank cars and trucks. It is not classified as a hazardous material because it is not corrosive or flammable. 

Stabilized nitroglycerine in the form of an aqueous emulsion flows into storage tank (1). If every batch of nitroglycerine is subjected to heat-test two storage tanks should be provided. 

Hazardous properties and handling procedures are summarised [1], Conditions under which it may explode by detonation, heat or shock were determined. It was concluded that it is potentially very explosive and precautions are necessary to prevent its exposure to severe shock or high temperatures in use [2], Later work, following two rail tank explosions, showed that shock caused by sudden application of gas pressure, or sudden forced flow through restrictions, could detonate the liquid. The stability and... 

Two nonconducting tanks of negligible heat capacity and of equal volume initially contain eq quantities of the same ideal gas at the same T and P. Tank A discharges to the atmosphere throu a small turbine in which the gas expands isentropically tank B discharges to the atmosphere throu a porous plug. Both devices operate until discharge ceases. 

The system under study includes one cogeneration unit (a Stirhng Engine) and a backup boiler, both fueled by natural gas. The system supphes heat to two heat storage tanks one for the heating system, the other for the domestic hot water (dhw). The temperature in the heat distribution system (radiator system) is controlled by a 3-way valve and the temperature set point is determined as a function of the ambient and room temperatures using a heat loss model and heat distribution model. 

First, the monomers found most useful for nylon RIM systems are E-caprolactam and lauryl lactam. Unlike the liquid polyol and isocyanate materials in common use in urethane RIM, these materials have melting points of 158°F and 320°F respectively, making them solids at room temperature. Thus, nylon RIM equipment must have heated tanks, pumps, lines and molds. In commercial practice, this is accomplished by jacketing the equipment with circulating hot oil or water systems, by enclosing the hardware in temperature-controlled ovens or by electrically tracing the equipment with resistance heating hands and tapes. The first two methods are preferred because of their uniformity of control and lack of hot spots. 

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