Piston flow model

Realistic examples of variable-property piston flow models, usually nonisother-mal, are given in... 

Observe that the axial dispersion model provides a lower and thus more conservative estimate of conversion than does the piston flow model given the same values for the input parameters. There is a more subtle possibility. The model may show that it is possible to operate with less conservative values for some parameters—e.g., higher values for Tin and T aii— without provoking adverse side reactions. 

The piston flow model in Example 9.6 showed a thermal runaway when... 

Axial Dispersion. Enthusiastic modelers sometimes add axial dispersion terms to their two-phase, piston flow models. The component balances are... 

The convolution integral and the Exponential Piston Flow Model (EPM) were used to relate measured tracer concentrations to historical tracer input. The tritium input function is based on tritium concentrations measured monthly since the 1960s near Wellington, New Zealand. CFC and SF6 input functions are based on measured and reconstructed data from southern hemisphere sites. The EPM was applied consistently in this study because statistical justification for selection of some other response function requires a substantial record of time-series tracer data which is not yet available for the majority of NGMP sites, and for those NGMP sites with the required time-series data, the EPM and other response functions yield similar results for groundwater age. 

PDE piston flow model with axial dispersion and mass exchange... 

A far more promising approach is represented by the so-called differential models, such as the axial dispersion model (ADM) (170) as well as the piston-flow model with axial dispersion and mass exchange (PDE) (171). Experimental studies (168) show that the ADM gives an appropriate description of the nonideal flow behavior of the liquid phase in catalytic packings (see Figure 31). Considering... 

The piston flow model in Example 9.6 showed a thermal runaway when T, = Twau =374. Will the axial dispersion model show a runaway (defined as d2Tjdz2 > 0) If so, at what value of Tin = Twalp. 

If the unsaturated zone is composed of relatively fine sediment (silt and fine sands) a quasi-uniform seepage flow can be assumed for the unsaturated zone in humid climate zones over long time spans. Therefore, the transport of infiltration water can be simulated in PHREEQC as a monotonous movement in accordance with the "piston flow model. A constant flow of infiltration water of 0.5 m per year is assumed for the following simulation. Furthermore, it is considered simplistically that the infiltrating precipitation has a tritium activity of 2000 TU (tritium units) over a period of 10 years. Then, it is assumed that the tritium activity decreases to zero again. 

According to the characteristics of the flow within the aquifer, two models may be contemplated. In the former case, the age of water is proportional to the covered distance (the piston flow model). The radiometric age corresponds to the actual mean age of water. In the latter where the various water streamlets are mixed as a result of different permeabilities [limit values recorded from test pumping 0.3 10 —8.1 10" m/s (S.C.G.A.L., 1972)], the flow is said to be exponential. Then the radiometric age is an apparent age (ta) related to the actual mean age ( r) by the following relation (Olive, 1970) ... 

Fix-bed reactor is a typical reactor in FTS process, which is firsdy applied in industrial FTS process. As early as 1979, Atwood and Bennett (Albal et al., 1984) have built a 0.25 bilHon c.f/d syngas management FT tubular reactor one-dimensional pseudo homogeneous piston flow model, based on dynamic model of molten iron catalysts as shown in Eqs. (9) and (10), in which dx is the occupancy of CO, dt is the diameter of the tank, r is the reaction rate, F is the inlet amount of the gas, Cp is the specific heat capacity of the system, hu, is the heat transfer coefficient, and 2 is the axial coordination of the tank. 

Modeling of mass transfer has been carried out in the field of chemical engineering and environmental engineering (e.g., Takamatsu et al. 1977). Models commonly used are (1) batch model, (2) perfectly mixing model (Fig. 3.7), (3) piston flow model (Fig. 3.8), and (4) tank model (multi-step model). 

Concentration in aqueous solution is homogeneous in perfectly mixing model. However, in fact, concentration varies in a system. According to piston flow model the variation in concentration is expressed as... 

The difference between these equations and those for the ideal piston-flow model is the inclusion of the first term on the left side in each of them. These terms represent the rate of accumulation of ammonia and heat in the bed element, due to mass dispersion and heat conduction, respectively. For small deviations from the ideal piston-flow model, these terms can be omitted in obtaining the second-order derivatives ... 

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