Unsteady-state measurement methods

Unsteady-state measurement methods are based upon the fact, that the sorption process proceeds according to the first-order time law, whereby ki,a represents the time constant of the process  

The semi-logarithmic plot of the relative concentration of oxygen c/cs or (Cj - c)/ 

---

The Measurement of There are two main methods for measuring the unsteady-state method, and the steady-state method. In the... 

Unsteady reaction data are often an excellent means for estimating physical parameters that would be difficult or impossible to elucidate from steady-state measurements. However, the associated problems in nonlinear optimization can be formidable. A recent review and comparison of methods is given by... 

Steady-state periodic heating and unsteady-state methods can be applied to measure the thermal conductivity and diffusivity of coal. Methods such as the compound bar method and calorimetry have been replaced by transient hot-wire/line heat source, and transient hot plate methods that allow very rapid and independent measurements of a and X. In fact, such methods offer the additional advantage of measuring these properties not only for monolithic samples but also for coal aggregates and powders under conditions similar to those encountered in coal utilization systems. 

The most widely used unsteady state method for determining diffusivities in porous solids involves measuring the rate of adsorption or desorption when the sample is subjected to a well defined change in the concentration or pressure of sorbate. The experimental methods differ mainly in the choice of the initial and boundary conditions and the means by which progress towards the new position of equilibrium is followed. The diffusivities are found by matching the experimental transient sorption curve to the solution of Fick s second law. Detailed presentations of the relevant formulae may be found in the literature [1, 2, 12, 15-17]. For spherical particles of radius R, for example, the fractional uptake after a pressure step obeys the relation... 

In many practical applications, gas-liquid mass transfer plays a significant role in the overall chemical reaction rate. It is, therefore, necessary to know the values of effective interfacial area (aL) and the volumetric or intrinsic gas-liquid mass transfer coefficients such as kLah, kL, ktaL, kg, etc. As shown in Section IX, the effective interfacial area is measured by either physical e.g., photography, light reflection, or light scattering) or chemical methods. The liquid-side or gas-side mass-transfer coefficients are also measured by either physical (e.g., absorption or desorption of gas under unsteady-state conditions) or chemical methods. A summary of some of the experimental details and the correlations for aL and kLaL reported in the literature are given by Joshi et al. (1982). In most practical situations, kgaL does not play an important role. 

What constitutes an advance in any field will always be subjective. However, the combination of the inherent ability of MR methods to probe the internal structure and transport processes from the A- to cm-scale phenomena non-invasively, quantitatively and with chemical resolution, and with the ability to acquire these data sufficiently fast so that unsteady state processes can be studied is undoubtedly going to open up new avenues of research and allow us to investigate many phenomena for the first time. This section summarises five recent developments in the field of MR in chemical engineering. The first four sub-sections (Sections III.A-III.D) report developments of fast MR measurement pulse sequences, which have recently been implemented for application in chemical engineering research. The final sub-section (Section III.E) addresses a new and different field of research, that of gas-phase imaging. 

Unsteady-state methods are experimentally easier to do, whereby a shot of tracer is added followed by the measurement downstream of the time variation of tracer concentration. This technique was used in bubble columns by Seher and Schumacher... 

Judat [249] evaluated comparatively 12 publications in the area of coalescing systems. The measurements were carried out both under unsteady-state (nine publications) and also under steady-state (hydrazine method three publications) test conditions, in which the geometric parameters were varied within extraordinarily wide boundaries d = 0.05-3.1 m D = 0.15-12.2 m H = 0.15-6.1 m the volume... 

Very few studies have been conducted so far to determine the transient drop size distributions used to elucidate the dynamic processes related with breakage and coalescence of the dispersed phase. Bajpai et al. [92] proposed a method for the measurement of the unsteady-state drop size distributions by... 

A quasi steady-state solution for the tracer distribution in a soilpolutnn has been developed for the inlet boundary concentration being a constant plus a Sinusoidal component. Then an unsteady state solution for tracer distribution a soil column was developed for the same inlet boundary condition as above. The unsteady-state tracer concentration distribution applies to the section of a soil column that still remembers the initial condition. The two solutions may be applicable to those planning experiments to measure parameters such as the dispersion coefficient from tracer tests. A sinusoidal loading of tracer at the inlet boundary may enable one to obtain repeated data traces at the column outlet as part of an extended experiment. Continued collection of tracer concentration vs. time data at the column outlet over a number of periods would enable one to collect data from repeated experiments, for each period of the sine wave would represent another experiment. This should enable one to obtain more replicates of data to improve statistical estimates of the dispersion coefficient than could be obtained by experimental methods that use a slug loading or a step change of concentration at the column inleL"... 

Numerical solutions. Numerical solution was obtained by the Implicit alternating method for the above shown equations. As the strain amplitudes are not known a priori, solutions were obtained with several combinations of e. and e and the solution which would match the measured temperatures best was selected as the final solution (2). Equations (A-2) - (A-4) represent unsteady state changes In temperature. By allowing sufficient number of time steps, the steady state solution could be obtained. 

The chief drawback of this method is the uncertainty associated with parameter estimation. To overcome this problem, the reaction can be carried out in a chromatographic reactor packed with beads of the immobilized enzyme and the amounts of the enantiomers eluted directly measured. An unsteady-state analysis of such a reaction leads to the following simple expression (Wu, 1998) ... 

Transient-state or unsteady-state methods make nse of either a line source of heat or plane sources of heat. In both cases, the usual procedure is to apply a steady heat flux to the specimen, which mnst be initially in thermal eqnUibrinm, and to measnre the tanperatnre rise at some point in the specimen, resnlting from this applied flux [83]. The Fitch method is one of the most common transient methods for measuring the thermal conductivity of poor conductors. This method was developed in 1935 and was described in the National Bureau of Standards Research Report No. 561. Experimental apparatus is commercially available. 

The methods of experimental measurement of heat and mass transfer coefficients are summarized in Table 4.8, and resulted mainly from heat and mass transfer investigations in packed beds. Heat transfer techniques are either steady or unsteady state. In steady-state methods, the heat flow is... 

MEASUREMENT OF THERMAL CONDUCTIVITIES OF ORGANIC ALIPHATIC LIQUIDS BY AN ABSOLUTE UNSTEADY-STATE METHOD. 

---