Simulated solutions

This method [24,26,30] is specifically suited for simulating solutions. A great deal of the more interesting properties of solutions are essentially determined by the solute-solvent and solvent-solvent interactions close the solute. This fact suggests that the convergence of many solution properties can be accelerated by mainly sampling in the vicinity of the solute in contrast with the Metropolis method that samples among all the solvent molecules with identical probability. 

Only digital simulation solutions for ordinary differential equations are presented. To present anything more than a very superficial treatment of simulation techniques for partial differential equations would require more space than is available in this book. This subject is covered in severd texts. In many practical problems, distributed systems are often broken up into a number of lumps which can then be handled by ordinary differential equations. 

Analog Simulation Solution of Field Problems, McGraw-Hill, NY(1958) 13)F,L. 

Simulated solutions of Russian waste and INL (Idaho National Laboratory, USA) waste were used as feed solutions. Extraction of cesium was 98.4%, and of strontium, 98.1%. A problem with low solubility of the crown ethers (<180 mg/L for all type of solutions) was shown in the tests. The authors pointed out the main positive features of the proposed flowsheet a salt-free strip product with very low nitric acid concentration (<0.1 M), possibility to extract both cesium and strontium, and low losses of extractants. A last step in the modification of this solvent was the addition of polyalkylphosphonitrilic acid to the mixture of crown ethers.65 Positive results were obtained for extraction of not only Cs and Sr, but also MAs from simulated HLW. 

Alternatively, suppose you want to determine which heteroatom in a molecule is protonated first as pH is lowered. Or conversely, you may want to know which is the most acidic proton in a compound (even if it is a hydrocarbon, for example). In such cases, you can obtain optimized geometries for the parent molecule Z and its conjugate acid ZH+ (or conjugate base Z ) for each site of proton attachment or removal. Simply take the differences in total energy (obtained quantum mechanically), E(ZH+)-E(Z) [or E(Z ) E(Z)], and you have a theoretical assessment of the relative gas-phase acidity (basicity). (The electronic energy of a proton is zero because it has no electron.) Of course, these energy differences do not account for solvation, but if the two protonation (or deprotonation) sites are very similar, the vacuum results may suffice. Alternatively, you can turn on implicit (continuum) solvation in your calculation and obtain energies of the simulated solution species. 

To model the behavior of a solute in a membrane environment, 15 cells simulating solute molecules at a concentration of 0.01 were positioned randomly near the lower edge of the membrane surface. These cells were endowed with rules making them hydrophilic. As the dynamics proceeded, it was... 

Formic Acid Denitrations. Simulated solutions were subjected to laboratory formic acid denitrations (Figures 2 and 3). The most usable free acid concentration for the simulated solutions was obtained when a formic acid to free acid ratio of about 1.6 to 1.9 was used. This ratio yielded a final free acidity of about 0.6 to 0.8M. As a result of Al3+ hydrolysis, it was possible to drive the A1-Am-Cm solution to about pH 10. However, acid concentrations less than 0.2M had to be avoided to prevent hydrolysis and precipitation of the actinides. 

Precipitation of Simulated Solutions. For the Am-Cm-NaN03 solutions, acceptable losses (<1%) of transplutonium elements could be achieved using 0.3M in the final slurry with a... 

As the result of oxalate ion complexing of Al3+, precipitation of Am-Cm-A1(N03)3 solutions was not straightforward. Using Dy as a stand-in for Am-Cm, simulated solutions were prepared where the ratio of A1(N03>3 to Dy (1 03)3, KF, NaN03, and Hg(1 03)2 was held constant as would result in actual process solutions. However, the total ratio of these species to free nitric acid was varied in the stock solutions. Precipitation conditions were simulated by additions of either a half-equal or an equal volume of either an 0.9M or a saturated ( 2M) potassium oxalate... 

The volume of precipitate and settling rate were also determined by precipitation of 2 L of simulated solution, adjusted to 0.5M Al3+ and 0.25M HNO3 by the addition of 4 L of 0.9M H2C2O1. When the precipitation was carried out at room temperature, less than 10% of the precipitate had settled after a 60-hour settling period. When the oxalic acid was added to a 60°C solution and then held at 40-45°C for an additional 2 hours, the settling rate and final volume of precipitate were very similar to the Am-Cm material containing NaN03-... 

Proceeding as we have done before with complex systems, we calculate theoretical data to deal with these systems. Since straightforward analytical solutions are not available, even for such simple cases as Eqn. 9.44, numerical methods are used to simulate solutions of the equilibria. 

Another example of electrodialysis applied to the nuclear industry [27] is the recovery of NaOH and H2SO4 from the secondary liquid waste created by the regeneration of ion-exchange columns installed in LWRs. This application has been successfully demonstrated at a plant scale facility using simulated solutions. Long-term life tests on the ion-exchange membranes indicate a shorter life for anionic membranes than cationic membranes. 

The polarization of the electrosorption membranes was carried out at a potential difference of 5 V and 10 V. Electrosorption tests were carried using a simulated solution of an industrial nickel effluent and a mine water source. The chemical composition of both solutions is given in Table 40.3. 

It is beyond the scope of this short review to list every available molecular mechanics program. Only a selected few programs are mentioned here, without descriptive details of the potential functions, minimization algorithms, or comparative evaluations. Both the CHARMM and AMBER force fields use harmonic potential functions to calculate protein structures. They were developed in the laboratories of Karplus and Kollman, respectively, and work remarkably well. The CFF and force fields use more complex potential functions. Both force fields were developed in commercial settings and based extensively or exclusively on results obtained from quantum mechanics. Unlike the other molecular mechanics methods, the OPLS force field was parameterized by Jorgensen to simulate solution phase phenomena. 

To prevent during the denitration step the formation of precipitates on which Pu and Am were partially and irreversibly adsorbed, denitration and oxalate precipitation were carried out in a single step by addition of the waste solution to the formic and oxalic acid mixture, the latter acid acting as a metal complexant during the denitration step. By experimental tests performed on simulated HAW according to this modified process scheme, separation yields of about 99.5% for Pu and 99.8% for Am were measured. A further reduction of the actinide content was reached by flowing the clarified HAW solution through a Dowex 50 resin column. The oxalate precipitation experiments on fully active HAW solutions have practically been completed. The results obtained from five runs (Table IV) confirmed the previous results obtained on simulated solutions. 

A new model that explicitly accounts for multiple sources of nonequilibrium influencing solute transport in porous media was presented by Brusseau et al. (1989c, 1990b). The multiprocess nonequilibrium (MPNE) model was designed to simulate solute transport in porous media where both transport-related and sorption-related nonequilibrium processes contribute to the observed nonequilibrium. The sorption dynamics of such systems was represented by two serially arranged bicontinuums coupled in parallel. A schematic of the model conceptualization is shown in Fig. 11-6, taken from Brusseau et al. (1989c). This conceptualization results in discretization of the porous medium into four sorption domains, where instantaneous sorption occurs in the first domain and rate-limited sorption occurs in the other three. 

Recent particle tracking simulations in soil network models indicate that solute dispersion is more sensitive to the water retention curve than to the particular combination of pore-size distribution and topology that determine its shape (Vogel, 2000). Numerical particle tracking techniques have also been used to simulate solute dispersion in fractured media. Examples for two-dimensional randomly intersecting fracture networks include the models developed by Hull et al. (1987), Smith and Schwartz (1984), Robinson and Gale (1990), and Clemo and Smith (1997). Recently Nordqvist et al. (1996) and Margolin et al. (1998) have extended this approach to three-dimensional fracture networks. 

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