Models adsorption coefficients

Almost all models can simulate organic, inorganic and metal fate, assuming that a careful calibration via an adsorption coefficient may alter the model output to predict measured/monitored values. However, not all models have by design increased chemistry capabilities (e.g., cation exchange capacity complexation), therefore, the most representative capabilities are indicated. 

Model selection, application and validation are issues of major concern in mathematical soil and groundwater quality modeling. For the model selection, issues of importance are the features (physics, chemistry) of the model its temporal (steady state, dynamic) and spatial (e.g., compartmental approach resolution) the model input data requirements the mathematical techniques employed (finite difference, analytic) monitoring data availability and cost (professional time, computer time). For the model application, issues of importance are the availability of realistic input data (e.g., field hydraulic conductivity, adsorption coefficient) and the existence of monitoring data to verify model predictions. Some of these issues are briefly discussed below. 

Before an in-depth discussion of mass transfer models and coefficients we need to be explicitly clear that all mass transfer models are approximations that allow us to solve the partial differential equations (pde) describing an adsorption problem. There are a great many sources that derive and present the partial differential equations that describe adsorption of gases appropriate for column separations. The Design Manual For Octane Improvement, Book I [7] was among the earlier works to show them. The forms as presented by Ruthven [2] are shown here owing to the consistent and compact nomenclature that he has employed. There are a wider array of forms to choose from in the literature including [6, 7]... 

The model followed single-site, nondissociative, Langmuir-Hinshelwood poisoning. This resulted in the same adsorption coefficients for deactivation and start-of-cycle kinetics. 

For some models adsorption or storage is important. For example, oxygen storage is important in a 3-way catalysis, a catalyst may contain a hydrocarbon storage component for improved low-temperature performance, and ammonia storage is important for ammonia SCR (selective catalytic reduction). Clearly, this sort of behaviour needs to be included in the final model. The nature of the measurements depends on the exact system being studied and will be discussed in more detail later. Suffice to say, from measurements at steady state, the heats of adsorption and coefficients of... 

Thus, the passage from an adsorption isotherm of a pure substance to the corresponding adsorption isotherm of a mixture is very easy, supposing that the model of a nonuniform surface is applicable and adsorption coefficients are proportional. If, for instance, adsorption of pure gas A is described by the Freundlich isotherm (135), then for adsorption of A from mixture... 

A2 is also a known function of T and space velocity since the rate constant K2 is known from the steady state results (eq. 1). The parameters Ai and Af are not known independently however, the ratio Aj/Af equals the adsorption coefficient Kpr of propylene oxide which is a known function of T obtained from the steady state measurements (eq. 1). Since the steady state kinetics indicate that the surface reaction is the rate limiting step it can be concluded that Ai is larger than A2. It was assumed that propylene oxide adsorption is nonactivated and Aj was arbitrarily set equal to be two times larger than A2 at 400°C,for Y =. 002 then Aj was calculated from Af = Ai/Kpro Yp. The numerical simulations indicated that the model predictions are rather insensitive to Aj but are sensitive to the unknown parameters A3 and 0 c Since the Heat of Polymerization of Propylene Oxide is 18 Kcal/mol the parameter 0 was set equal to 0 exp(-18000/RT). 

Hore importantly, the response curves are noticeably affected where one or both of the components is adsorbable, even at low tracer concentrations. The interpretation of data is then much more complex and requires analysis using the non-isobaric model. Figs 7 and 8 show how adsorption of influences the fluxes observed for He (the tracer), despite the fact that it is the non-adsorbable component. The role played by the induced pressure gradient, in association with the concentration profiles, can be clearly seen. It is notable that the greatest sensitivity is exhibited for small values of the adsorption coefficient, which is often the case with many common porous solids used as catalyst supports. This suggests that routine determination of effective diffusion coefficients will require considerable checks for consistency and emphasizes the need for using the Wicke-Kallenbach cell in conjunction with permeability measurements. 

In the above equations the symbols A, B, C, D designate phenol, hydrogen, cyclohexanone and cyclohexanol. Table 5.7 presents the model parameters at 423 K and 1 atm. The model takes into account the effect of the products on the reaction rate in the region of higher conversion. This feature is particularly useful for describing the product distribution in consecutive catalytic-type reactions. Note that the adsorption coefficients are different in the two reactions. Following the authors, this assumption, physically unlikely, was considered only to increase the accuracy of modeling. 

Results of the best MLR are presented in figure 2, which compares experimental and computed eneigies. The best MLR corresponds to the maximum coefficient of determination which was 0.833 on the working data set and 0.879 on the testing data set. This means that more than 83% of the variability in the data may be explained with the linear model. Adsorption energies are then predicted with a precision around +/-10%. Following the stepwise procedure, 3 explicative variables were discriminated ... 

Different charge-compensating cations in zeolite L have been tested for their promotional effect in n-hexane aromatization. Apparently, high basicity of the alkaline and alkaline earth promoter favors n-hexane aromatization. Basicity and selectivity both increase from Li and Cs 331) and from Mg to Ba (22,25). Bezouhanova et al. studied the FTIR bands of linearly adsorbed CO in the range of 2060-2075 cm . One band at 2075 cm", which is also found on unsupported Pt, is attributed to extrazeolite Pt particles, a second band shifts from 2060 cm" for Li to lower wavenumbers with K and Rb 331). Another criterion, used by Larsen and Haller, is the measured rate of competitive hydrogenation of benzene and toluene, which has been found to correlate with the zeolite basicity (25). As described in a previous section, this method had previously been used by Tri el al. to probe for the electron deficiency of Pt particles in acidic zeolites 332). The rate data are analyzed in terms of a Langmuir-Hinshelwood model and the ratio of the adsorption coefficients of toluene and benzene, A, /b, is determined. It was found to decrease from 8.6 for Pt/Si02, and 5.4 for Pt/MgL, to 4.4 for Pt/BaL. As direct electron transfer from the cations to neutral Pt particles is unlikely, an interaction of Pt with the zeolite framework or with... 

Fig. 3 shows the comparison of experimental data and of model curves at the specific temperature T = 473 K for four different relative water concentrations from 0.6 to 1.0 according to eq. (5). The whole set of data includes additional measurements at selected hydrothermal conditions at 453 K and 433 K, and treatment times t, in order to guess the temperature dependency of the reaction coefficient kjfT) and of the adsorption coefficient k CT). ... 

Approximation of the linear form is not necessary for the Langmuir isotherm, and the first plot of the adsorption data will determine whether or not the model is applicable, and also will allow calculation of the adsorption coefficients. Usually a single model will not be satisfactory for a wide range of adsorbate concentrations but will only serve in narrow range of concentration. At low concentrations, C/C 1, the BET model reduces to a Langmuir model. 

Aquatic fate If released to water, 2-heptanone is expected to rapidly volatalize to the atmosphere. The half-life for volatilization from a model river Im deep, flowing at Ims with a wind speed of 3ms is 8.4 h. The calculated bioconcentration factors ranging from 5.5 to 19 indicate that 2-heptanone is not expected to bioconcentrate in fish and aquatic organisms. The calculated soil adsorption coefficients ranging from 44 to 285 indicate that adsorption to sediment and suspended organic matter is not an environmentally important process. Screening... 

Figure 6. The reduced value of the adsorption coefficient, T, as the function of reduced temperature, T for the RPM model with a bulk volume fraction, rji = 0.00785 near to uncharged hard wall. The solid curve gives theoretical prediction [24] while the symbols correspond to Monte Carlo data [51,52].

The parameters were defined by choosing y = 1 for a model pair of substrates A = 2-methyl-3-butene-2-ol, B = 1-hexene, with methanol (standard solvent and 5% Pt/silica gel as the standard catalyst, similarly (69) to the definition of the parameter t. The values of the parameters r and are given in Table III. The adsorption coefficients of 2-methyl-3-butene-2-ol, 2-propene-l-ol, and cyclohexene related to 1-hexene and determined by Cerveny et al. (70) could be correlated neither with the t(t ) parameters of... 

Adsorption. The solution used to evaluate the pesticide transport equation, Equation 4a, assumes a linear adsorption isotherm that is constant with depth. However, linearity may not be the case for some pesticides and the adsorption coefficient will almost never be constant with depth. The rationale for using a linear model is initially based on the Freundlich isotherm... 

Adsorption Coefficients of Explosive Contaminants in Natural and Model Systems... 

Biodegradation of RDX, HMX, and CL-20 by Microorganisms Adsorption Coefficients of Explosive Contaminants in Natural and Model... 

A detailed computational model was developed for several different iimovative designs for the preferential carbon monoxide (CO) oxidation reactor using a kinetic mechanism and reaction sequence derived from a micro-kinetic model and literature data for the specific adsorption coefficients and kinetic parameters for a platinum-based catalyst. 

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