Multi-component models model

The framework for constructing such multi-component equilibrium models is the Gibbs phase rule. This rule is valid for a system that has reached equilibrium and it states that... 

Different data interpretation models have been applied simple dissociation constants (Langford and Khan, 1975), discrete multi-component models (Lavigne et al., 1987 Plankey and Patterson, 1987 Sojo and de Haan, 1991 Langford and Gutzman, 1992), discrete kinetic spectra (Cabaniss, 1990), continuous kinetic spectra (Olson and Shuman, 1983 Nederlof et al., 1994) and log normal distribution (Rate et al., 1992 1993). It should be noted that for heterogeneous systems, analysis of rate constant distributions is a mathematically ill-posed problem and slight perturbations in the input experimental data can yield artefactual information (Stanley et al., 1994). 

Deeper insight into the consequences of counterion condensation is gained by an effective monomer-monomer and counterion-counterion potential, respectively. The idea is to reduce the multicomponent system (macromolecules + counterions) to effective one-component systems (macromolecules or counterions, respectively). We define the simplified model in such a way that the effective potential between the counterions or monomers, respectively, of the new system yields exactly the same correlation function (gcc, gmm) as found in the multicomponent case at the same density. Starting from the correlation function gcc -respectively gmm-of the multi-component model we calculate an effective direct correlation function cefy via the one-component Ornstein-Zernike equation. An effective potential is then obtained from the RLWC closures of the one- and multicomponent models [24]. For low and moderate densities the effective potential is well approximated by... 

A Multi-Component Model For Radiation Damage To DNA From Its Constituents... 

The second objective is to review the results of experimental studies on full DNA in the context of the computed and experimental results for single crystals. We conclude our chapter with a multi-component model for radiation damage to... 

Tezel, A. Horta su, A. Hortagsu, O. Multi-component models for seed and essential oil extraction. J. Supercrit. Fluids 2000, 79, 3-17. 

Isotherm models have to be divided into single-component and multi-component models. Because most of multi-component models are directly derived from singlecomponent models the latter will be presented first. 

Fitting data to multi-component isotherm model... 

Figure 6.29 shows a comparison between two different isotherm models (Fig. 6.21) used for validation agreement between theory and experiment is good using the modified multi-component Langmuir model (Fig. 6.21), while the symmetrical Langmuir isotherm leads to profiles shifted to earlier retention times. The structural... 

As a starting point for the tuning of our multi-component kinetic model we used kinetic data from closed-system non-isothermal pyrolysis experiments which describe the generation of oil and gas from a marine Type II source rock (Dieckmann et al. 1998). The frequency factors (A), activation energy ( ) distributions and hydrocarbon potentials of primary oil and gas generation of Dieckmann et al. (1998) were used as the framework for our model (Figure... 

Reservoir fluid compositions at each time step can be obtained for each reservoir in PetroMod. The reported fluid compositions were exported to PVTsim and the physical properties of the fluid calculated. The predicted physical properties were compared with those of the calibration data set and the individual compound kinetics of the multi-component kinetic model iteratively tuned until a good match was achieved (Fig. 4). Figure 6 and Table 4 show the tuned multi-component kinetic model for a marine Type II source rock developed by the method discussed previously. 

Mitsubishi Heavy Industries computer code CHAMPAGNE is a multi-phase, multi-component thermodynamics model originally created for the assessment of severe accidents in fast breeder nuclear power reactors. It was recently modified to also treat the formation and spreading of hydrogen gas clouds. CHAMPAGNE has been successfully applied both as a 2D and 3D version to the NASA LH2 spill tests from 1980 (Fig. 8-9) [30]. 

Scharfer et al. set up a multi-component transport model to describe the diffusion driven mass transport of water and methanol in PEM [170]. For a PEM in contact with liquid methanol and water on one side and conditioned air on the other, the corresponding differential equations and boundary conditions were derived taking into account the polymers three-dimensional swelling. Phase equilibrium parameters and unknown diffusion coefficients for Nafion 117 were obtained by comparing the simulation results to water and methanol concentration profiles measured with confocal Raman spectroscopy. The influence of methanol concentration, temperature and air flow rate was predicted by the model. Although there are indications for an influence of convective fluxes, the measured profiles are ascribed to a Fickean diffusion. Furthermore, the assumption to describe the thermodynamic phase equilibrium as liquid-type equilibrium also at the lower surface of the membrane, which is in contact with a gas phase, can be confirmed by their results. 

Zille, V. 2009. Multi component system modelling for complex maintenance strategies assessment. PhD Thesis, Technology University of Troyes. 

Zille, V, Berenguer, C., Grail, A., Despujols, A. 2008. Multi-component systems modelling for quantifying complex maintenance strategies. ESREL2008 proceedings conference, Valencia, September 2008. 

Perez-Ocon, R., Montoro-Cazoria, D. Ruiz-Castro, J.E. 2006. Transient analysis of a multi-component system modeled by a general Markov process. Asia Pacific Journal of Operational Research.VoX. 23, No.3, 311-327. 

M. M. Hussain, X. Li, and I. Dincer. Multi-component mathematical model of solid oxide fuel cell anode. Int. J. Energy Res., 29 1083-1101, 2005. 

Wang, W, Christer, A.H. (2003). Solution algorithms for a nonhomogeneous multi-component inspection model. Computers Operations Research 30 19-34. 

Due to the high pressures, Langmuir is used with fugacities determined from the virial equation of state. It was found that the predictions with the multi-component Langmuir model were better than with lAST for two binary gas mixtures (H2-CO and CO-CH4) at various temperatures, but lAST proved to be superior when modelling the systems CO-CO2 and CH4-CO2 and for aU the ternary and quaternary systems. However, overall both models proved to adequately predict the mixed gas data and the predictions from the two models were very similar. From a mathematical and computational point of view, the explicit Langmuir model is simpler, while lAST needs an iterative solution method ... 

HGSystem offers the most rigorous treatments of HF source-term and dispersion analysis a ailable for a public domain code. It provides modeling capabilities to other chemical species with complex thermodynamic behavior. It treats aerosols and multi-component mixtures, spillage of a liquid non-reactive compound from a pressurized vessel, efficient simulations of time-dependent... 

Crystallization-based separation of multi-component mixtures has widespread application. The technique consists of sequences of heating, cooling, evaporation, dilution, diluent addition and solid-liquid separation. Berry and Ng (1996, 1997), Cisternas and Rudd (1993), Dye and Ng (1995), Ng (1991) and Oyander etal. (1997) proposed various schemes based on the phase diagram. Cisternas (1999) presented an alternate network flow model for synthesizing crystallization-based separations for multi-component systems. The construction... 

Q. Han, J. D. Hunt. Numerical modelling of the growth of a cellular/dendritic array in multi-component alloys. Mater Sci Eng A 255 192, 1997. 

---