Isotherm conditions

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

If the experiment was now reversed, starling from A and increasing the pressure, the first drop of ethane liquid would appear at point C, the dew point of the gas. Remember that throughoufthis process, isothermal conditions are maintained. 

The initial condition for the dry gas is outside the two-phase envelope, and is to the right of the critical point, confirming that the fluid initially exists as a single phase gas. As the reservoir is produced, the pressure drops under isothermal conditions, as indicated by the vertical line. Since the initial temperature is higher than the maximum temperature of the two-phase envelope (the cricondotherm - typically less than 0°C for a dry gas) the reservoir conditions of temperature and pressure never fall inside the two phase region, indicating that the composition and phase of the fluid in the reservoir remains constant. 

Reservoir fluids (oil, water, gas) and the rock matrix are contained under high temperatures and pressures they are compressed relative to their densities at standard temperature and pressure. Any reduction in pressure on the fluids or rock will result in an increase in the volume, according to the definition of compressibility. As discussed in Section 5.2, isothermal conditions are assumed in the reservoir. Isothermal compressibility is defined as ... 

In isothermal conditions this can also be written in terms o the molar concentration c, since p = c RT. Thus we obtain... 

For a step change in sorbate concentration at the particle surface (r = R) at time 2ero, assuming isothermal conditions and diffusion control, the expression for the uptake curve maybe derived from the appropriate solution of this differential equation ... 

Heat pipes are used to perform several important heat-transfer roles ia the chemical and closely aUied iadustries. Examples iaclude heat recovery, the isothermaliziag of processes, and spot cooling ia the mol ding of plastics. In its simplest form the heat pipe possesses the property of extremely high thermal conductance, often several hundred times that of metals. As a result, the heat pipe can produce nearly isothermal conditions making an almost ideal heat-transfer element. In another form the heat pipe can provide positive, rapid, and precise control of temperature under conditions that vary with respect to time. 

The OLEFLEX process uses multiple side-by-side, radial flow, moving-bed reactors connected in series. The heat of reaction is suppHed by preheated feed and interstage heaters. The gas-phase reaction is carried out over a catalyst, platinum supported over alumina, under very near isothermal conditions. The first commercial installation of this technology, having an annual capacity of 100,000 t, was made in 1990 by the National Petrochemical Corporation in Thailand. A second unit, at 245,000 t capacity, has been built in South Korea by the ISU Chemical Company (70). 

Maintenance of isothermal conditions requires special care. Temperature differences should be minimised and heat-transfer coefficients and surface areas maximized. Electric heaters, steam jackets, or molten salt baths are often used for such purposes. Separate heating or cooling circuits and controls are used with inlet and oudet lines to minimize end effects. Pressure or thermal transients can result in longer Hved transients in the individual catalyst pellets, because concentration and temperature gradients within catalyst pores adjust slowly. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Under isothermal conditions where energy is not added or removed from the system, the second law of thermodynamics obtains, and... 

Table 6-6 gives characteristics of rounded-inlet circular jets and rounded-inlet infinitely wide slot jets (aspect ratio > 15). The information in the table is for a homogeneous, incompressible air system under isothermal conditions. The table uses the following nomenclature ... 

If the compression cycle approaches the isothermal condition, pV = constant, as is the case when several stages with intercoolers are used, a simple approximation of the power is obtained from the following formula ... 

The profiles of temperature and composition shown in Fig. 23-3 are not of homogeneous liqmd reactions, but are perhaps representative of all lands of reactions. Only in stirred tanks and some fluidized beds are nearly isothermal conditions practically attainable. 

An immobilized enzyme-carrier complex is a special case that can employ the methodology developed for evaluation of a heterogeneous cat ytic system. The enzyme complex also has external diffusional effects, pore diffusional effects, and an effectiveness factor. When carried out in aqueous solutions, heat transfer is usually good, and it is safe to assume that isothermal conditions prevail for an immobihzed enzyme complex. 

The thermos phon circulation rate can be as high as 10 to 15 times the coolant evaporation rate. This, in turn, eliminates any significant temperature difference, and the jacket is maintained under isothermal conditions. In this case, the constant wall temperature assumption is satisfied. During starting of the thermosiphon, the bottom can be 20-30°C hotter, and the start of circulation can be established by observing that the difference between the top and bottom jacket temperature is diminishing. Figure 2.2.5 (Berty 1983) shows the vapor pressure-temperature relationship for three coolants water, tetralin, and Dowtherm A. 

In previous studies, the main tool for process improvement was the tubular reactor. This small version of an industrial reactor tube had to be operated at less severe conditions than the industrial-size reactor. Even then, isothermal conditions could never be achieved and kinetic interpretation was ambiguous. Obviously, better tools and techniques were needed for every part of the project. In particular, a better experimental reactor had to be developed that could produce more precise results at well defined conditions. By that time many home-built recycle reactors (RRs), spinning basket reactors and other laboratory continuous stirred tank reactors (CSTRs) were in use and the subject of publications. Most of these served the original author and his reaction well but few could generate the mass velocities used in actual production units. 

Figure 8.14. Typical curve for viscosity against time of condensation of essentially trifunctional monomer systems under isothermal conditions...

The change in total energy or free energy, under isothermal conditions, is then given by... 

Most chemical reactions are greatly affected by temperature. The previous chapters discussed reactions at isothermal condition, however, industrial reactors often operate under non-isothermal condition. This is because chemical reactions strongly depend on temperature, either absorbing (i.e., endothermic) or generating (i.e., exothermic) a large amount of heat. 

Modeling of Chemioal Kinetios and Reaotor Design Since Tj = Tj (i.e., isothermal condition), then... 

In an idealized situation, the vessel and its jacket each operate continuously under isothermal conditions. Rearranging Equation 7-69 becomes ... 

Example 5.14 A power law fluid with constants i]q= 1.2 x lO Ns/m and n = 0.35 is injected through a centre gate into a disc cavity which has a depth of 2 mm and a diameter of 200 mm. If the injection rate is constant at 6 X 10 m /s, estimate the time taken to fill the cavity and the minimum injecdon pressure necessary at the gate for (a) Isothermal and (b) Non-isothermal conditions. 

Detailed experimental data were obtained by Sadovskaya on a physical model in isothermal conditions. She has found that the confined air jet has two critical cross-sections (Fig. 7.38). In the first cross-section, where the ratio of jet cross-sectional area to the area of ventilated space equals 0.24, the jet... 

Similar studies were conducted by Troyanovsky, who concluded that to maintain the airflow pattern in rooms with heated or cooled air supply as in isothermal conditions, it is necessary that the rise of horizontally supplied jet does not exceed Ay = 0.1 BH at the distance from the outlet X = 0.15K BH) -. From this assumption the following equation for the maximum air temperature difference was derived ... 

The velocity distribution in the reverse flow is assumed to be uniform in the case of isothermal conditions. In most practical cases, however, there is a... 

If the room is longer there will be rotating cells as indicated in Fig. 8.21 in isothermal conditions. 

FIGURE 8.21 Multiple rotadng cells in a long room Isothermal conditions... 

FIGURE 8.28 Horizoncal piston airflows are possible only in isothermal conditions... 

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