Trace Systems

In accordance with our dassification the simplest stem to consider is an isothermal plug flow system in which a trace of an iad i ble species is adsorbed from an inert carrier under conditions such that mass transfer resistance is negligible. Although such systems are npt coniinon in practice, their analysis can provide useful insight into the betinvior of more complex systems. For such a system the differential fluid phase jitnaks balance for the adsorbable spedes [Eq. (8.1)] reduces to I 

Representing the equilibrium isotherm in general forin by and assuming mass transfer equilibrium  

This equation has the form of the kinematic wave equation. The velodty rith 

FIGURE 83 (a) Development of physically unrealistic overhanging concentration profile and corresponding shock profile for a favorable isotherm fi l.O). (6) Development of dispersive (proportionate-pattern) concentration profile for desorption of a uniformly saturated bed when the isotherm is favorable for adsorption, unfavorable for desorption 1.0 1.0) (after 

In most adsorption systems the isotherm is favorable for adsorption and therefore unfavorable for desorption. In desorption the mass transfer zone is therefore dispersive, leading to a continuously spreading concentration prOfife (proportionate-pattern behavior) while in adsorptioii the mass transfer zone is compressive, leading to constant-pattern behavior. For example, for a system which obeys the Langmuir isotherm (Eq. (8.6)] I 

---

Fluid Tracing Systems Steam tracing is the most common type of industrial pipe tracing. In 1960, over 95 percent of industrial tracing systems were steam traced. By 1995, improvements in electric... 

High reliability. Many things can go wrong with a steam tracing system but, very few of the potential problems lead to a heat tracing failure. Steam traps fail, but they usually fail in the open position. 

High in stalled co.sts. The incremental piping required for the steam supply system and the condensate return system must be installed, insulated, and, in the case of the supply system, additional steam traps are often required. The tracer itself is not expensive, but the labor required for installation is relatively high. Studies have shown that steam tracing svstems typically cost from 50 to 150 percent more than a comparable electric tracing system. 

Electric Tracing An electric tracing system (see Fig. 10-178) consists of an electric heater placed against the pipe under the thermal insulation, the supply of electricity to the tracer, and any control or monitoring system that may be used (optional). The supply of electricity to the tracer usually consists of an electrical panel and electrical conduit or cable trays. Depending on the size or the tracing system and the capacity of the existing electrical system, an additional transformer may be required. 

Temperature control. Even without a thermostat or any control system, an electric tracing system usually provides better temperature control than a steam tracing system. With thermostatic or electronic control, veiy accurate temperature control can be achieved. 

It is also possible to have a combined wave, which has both gradual and abrupt parts. The general rule for an isothermal, trace system is that in passing from the initial condition to the feed point in the isotherm plane, the slope of the path must not decrease, if it does, then a shock chord is taken for that part of the path. Referring to Fig. 16-19, for a transition from (0,0) to (1,1), the dashes indicate shock parts, which are connected by a simple wave part between points Pi and Pg. 

At the top end of the program monitoring scale is the use of online fluorescence tracing systems, whereby tracer dye polymers form part of the water treatment program and their concentration can be measured online at various locations throughout the boiler plant system. Much less expensive, handheld fluorometers are now available to conduct the same type of analysis at the laboratory bench or on the boiler house firing-floor. These tracer dye polymers can be used to determine ... 

Here K is the slope of the linear isotherm. Eor non-trace systems or for rather high loadings the true slope K may be replaced by the slope of the operating line or chord of the isotherm, which quantity is simply Aq/Ac. The equivalent expression in molar loadings and gas phase mole fractions is ... 

That this was known in industry at least 15 years earlier is one of the unfortunate discrepancies between academic research and commercial industrial research and development. Not all that is known is necessarily published. This realization subsequently lead to the development of both solid phase and gas phase linear driving force models that each provide very good representations of measured data without the excess labor involved with the diffusion-based models. For trace systems there are quite a few analytical solutions that are available and quite tractable for both design work and the analysis of adsorption column performance. 

---