Computer simulations fluid property calculations

Designing a column usually starts with heat and material balance calculations, preferably using a computer simulation program. These calculations determine the liquid and vapor flow rates and the number of equilibrium stages required to meet the design performance specifications (separation, recovery, etc.). Fluid properties, such as densities and viscosities, may also be generated by the computer program. 

The grand canonical ensemble is appropriate for adsorption systems, in which the adsorbed phase is in equilibrium with the gas at some specified temperature. The use of a computer simulation allows us to calculate average macroscopic properties directly without having to explicitly calculate the partition function. The grand canonical Monte Carlo (GCMC) method as applied in this work has been described in detail earlier (55). The aspects involving binary fluid mixtures have been described previously in our Xe-Ar work (30). 

The physical properties of the fluid model are then calculated through either classical computer simulation techniques, or by some adequate liquid-state theories. 

A key question about the use of any molecular theory or computer simulation is whether the intermolecular potential model is sufficiently accurate for the particular application of interest. For such simple fluids as argon or methane, we have accurate pair potentials with which we can calculate a wide variety of physical properties with good accuracy. For more complex polyatomic molecules, two approaches exist. The first is a full ab initio molecular orbital calculation based on a solution to the Schrddinger equation, and the second is the semiempirical method, in which a combination of approximate quantum mechanical results and experimental data (second virial coefficients, scattering, transport coefficients, solid properties, etc.) is used to arrive at an approximate and simple expression. 

The so-called product reactant Ornstein-Zernike approach (PROZA) for these systems was developed by Kalyuzhnyi, Stell, Blum, and others [46-54], The theory is based on Wertheim s multidensity Ornstein-Zernike (WOZ) integral equation formalism [55] and yields the monomer-monomer pair correlation functions, from which the thermodynamic properties of the model fluid can be obtained. Based on the MSA closure an analytical theory has been developed which yields good agreement with computer simulations for short polyelectrolyte chains [44, 56], The theory has been recently compared with experimental data for the osmotic pressure by Zhang and coworkers [57], In the present paper we also show some preliminary results for an extension of this model in which the solvent is now treated explicitly as a separate species. In this first calculation the solvent molecules are modelled as two fused charged hard spheres of unequal radii as shown in Fig. 1 [45],... 

In Chapter 2, we saw that the configuration integral is the key quantity to be calculated if one seeks to compute thermal properties of classical (confined) fluids. However, it is immediately apparent that this is a formidable task because it reejuires a calculation of Z, which turns out to involve a 3N-dimensional integration of a horrendously complex integrand, namely the Boltzmann factor exp [-C7 (r ) /k T] [ see Eq. (2.112)]. To evaluate Z we either need additional simplifjfing assumptions (such as, for example, mean-field approximations to be introduced in Chapter 4) or numerical approaches [such as, for instance, Monte Carlo computer simulations (see Chapters 5 and 6), or integral-equation techniques (see Chapter 7)]. 

Investigating column performance starts with heat and material balance calculations, which generate liquid and vapor flows and properties. The fluid foaming characteristics and corrosivity are also determined. Typically, the calculations are done on a computer simulator, which generates liquid and vapor flows as well as physical properties, such as densities, viscosities, and surface tension. 

A Comparison of Solid-Fluid Coexistence Properties for Hard Spheres Calculated via Various Theories with Results from Computer Simulation. Values of the Lindemann Parameter, L, for the Melting Solid are also Given... 

The computation of thermodynamic properties in computer simulation is based largely on generalised methods using PVT relationship. Let examine how we could calculate the variation of enthalpy of a fluid when going from (T, P,) to (Tj, P - As with any thermodynamic function the variation is independent of path. There are several possibilities (Fig. 5.7). A first one could be an isothermal compression at T followed by an isobaric heating at Pj (ACD) ... 

Tv and tg) that are chosen. When the lattice size and the fluid properties are given, the relaxation time is determined by the lattice speed of sound (c and c ). Figure 3 shows the effects of c on the LPM simulation results. The results show that the electric potential distribution is little influenced by c. The inset in Fig. 3 shows that the c values affect the calculated zeta potential on the surface. A larger c value leads to a value of the zeta potential which is closer to the prespecified value. However, when c is larger than 300, the deviation may be below 0.3 %. Calculations at a larger value of c need more computational time to reach stable results. One can obtain a balance between efficiency and accuracy according to the level of detail required. 

Two sets of methods for computer simulations of molecular fluids have been developed Monte Carlo (MC) and Molecular Dynamics (MD). In both cases the simulations are performed on a relatively small number of particles (atoms, ions, and/or molecules) of the order of 100simulation supercell. The interparticle interactions are represented by pair potentials, and it is generally assumed that the total potential energy of the system can be described as a sum of these pair interactions. Very large numbers of particle configurations are generated on a computer in both methods, and, with the help of statistical mechanics, many useful thermodynamic and structural properties of the fluid (pressure, temperature, internal energy, heat capacity, radial distribution functions, etc.) can then be directly calculated from this microscopic information about instantaneous atomic positions and velocities. 

On the other hand, the analysis of experimental shockwave data for water has shown (Ree 1982) that at the limit of high temperatures and pressures intermolecular interactions of water become simpler. In this case, it becomes even possible to use a spherically-symmetric model potential for the calculations of water properties either from computer simulations (Belonoshko and Saxena 1991, 1992) or from thermodynamic perturbation theory in a way similar to simple liquids (Hansen and McDonald 1986). However, such simplifications exclude the possibility of understanding many important and complex phenomena in aqueous fluids on a true molecular level, which is, actually, the strongest advantage and the main objective of molecular computer simulations. 

The classical DFTs have proven to be an excellent alternative approach to the simulation method. The gas confined in MOF materials physicaUy represents nothing but a highly inhomogeneous fluid system, in which the MOF materials exert external potential to the fluid system. As demonstrated above, statistical DFTs present the same level of accuracy with but superior efficiency than computer simulations for the predictions of the physicochemical properties of inhomogeneous fluid systems. Similar to classical simulation, the practical implementation of DFT calculations relies on a semiempirical force field that describes the gas-material interaction. 

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