Water network modeling

Clegg, J. S. (1979). Metabolism and the intracellular environment The vicinal-water network model. In Cell-Associated Water (Drost-Hansen, W., Clegg, J.S., eds.), pp. 363 13, Academic Press, New York. 

Chen et al. [24] provide a good review of Al techniques used for modeling environmental systems. Pongracz et al. [25] presents the application of a fuzzy-rule based modeling technique to predict regional drought. Artificial neural networks model have been applied for mountainous water-resources management in Cyprus [26] and to forecast raw-water quality parameters for the North Saskatchewan River [27]. 

Iliadis LS, Maris E (2007) An artificial neural network model for mountainous water-resources management the case of Cyprus mountainous watersheds. Environ Modell Softw 22 1066-1072... 

Zhang Q, Stanley SJ (1997) Eorecasting raw-water quality parameters for the North Saskatchewan River by neural network modelling. Water Res 31 2340-2350... 

Waters KM, Shankaran H, Wiley HS, Resat H, Thrall BD. Integration of microarray and proteomics data for biological pathway analysis and network modeling of epidermal growth factor signaling in human mammary epithelial cells. Keystone Symposia, 2005. 

Table 4.4 is the summary of the mathematical model and the results obtained for the case study. The model for scenario 1 involves 637 constraints, 245 continuous and 42 binary variables. Seventy nodes were explored in the branch and bound algorithm. The model was solved in 1.61 CPU seconds, yielding an objective value (profit) of 1.61 million over the time horizon of interest, i.e. 6 h. This objective is concomitant with the production of 850 t of product and utilization of 210 t of freshwater. Ignoring any possibility for water reuse/recycle, whilst targeting the same product quantity would result in 390 t of freshwater utilization. Therefore, exploitation of water reuse/recycle opportunities results in more than 46% savings in freshwater utilization, in the absence of central reusable water storage. The water network to achieve the target is shown in Fig. 4.14. 

As shown in Table 4.4, the model for scenario 2, which is a nonconvex MINLP, consists of 1195 constraints, 352 continuous and 70 binary variables. An average of 151 nodes were explored in the branch and bound algorithm over the 3 major iterations between the MILP master problem and NLP subproblems. The problem was solved in 2.48 CPU seconds with an objective value of 1.67 million. Whilst the product quantity is the same as in scenario 1, i.e. 850 t, the water requirement is only 185 t, which corresponds to 52.56% reduction in freshwater requirement. The water network to achieve this target is shown in Fig. 4.15. 

Fig. 5.4 Water reuse/recycle network for minimum water use - model Ml (Majozi, 2006)...

Fig. 5.6 Water reuse/recycle network for minimum reusable water storage - model M2 (Majozi,... 

Ludwig s (2001) review discusses water clusters and water cluster models. One of the water clusters discussed by Ludwig is the icosahedral cluster developed by Chaplin (1999). A fluctuating network of water molecules, with local icosahedral symmetry, was proposed by Chaplin (1999) it contains, when complete, 280 fully hydrogen-bonded water molecules. This structure allows explanation of a number of the anomalous properties of water, including its temperature-density and pressure-viscosity behaviors, the radial distribution pattern, the change in water properties on supercooling, and the solvation properties of ions, hydrophobic molecules, carbohydrates, and macromolecules (Chaplin, 1999, 2001, 2004). 

A different test, one less satisfactory because the standard of comparison is simulated water not real water, is obtained by examining the functions hon(R) and dd(-R) predicted. The functions derived from the Narten model are shown in Fig. 54 they should be compared with those for simulated water, displayed in Figs. 27 and 28. Just as for the function hoo R), the curves for simulated water are narrower and higher than those in Fig. 54. In all other respects the agreement between the two sets of functions is excellent. It now remains to be shown that a full calculation, based on precisely the random network model proposed will reproduce the data as well as this (sensibly equivalent ) model. 

This oversimplified random network model proved to be rather useful for understanding water fluxes and proton transport properties of PEMs in fuel cells. - - - It helped rationalize the percolation transition in proton conductivity upon water uptake as a continuous reorganization of the cluster network due to swelling and merging of individual clusters and the emergence of new necks linking them. ... 

The earliest fully atomistic molecular dynamic (MD) studies of a simplified Nation model using polyelectrolyte analogs showed the formation of a percolating structure of water-filled channels, which is consistent with the basic ideas of the cluster-network model of Hsu and Gierke. The first MD... 

The effective conductivity of the membrane depends on its random heterogeneous morphology—namely, the size distribution and connectivity of fhe proton-bearing aqueous pafhways. On fhe basis of the cluster network model, a random network model of microporous PEMs was developed in Eikerling ef al. If included effecfs of varying connectivity of the pore network and of swelling of pores upon water uptake. The model was applied to exploring the dependence of membrane conductivity on water content and... 

An external gas pressure gradient applied between anode and cathode sides of the fuel cell may be superimposed on the internal gradient in liquid pressure. This provides a means to control the water distribution in PEMs under fuel cell operation. This picture forms the basis for the hydraulic permeation model of membrane operation that has been proposed by Eikerling et al. This basic structural approach can be rationalized on the basis of the cluster network model. It can also be adapted to include the pertinent structural pictures of Gebel et and Schmidt-Rohr et al. ... 

Notwithstanding the natural heterogeneity of the subsurface, we can usefully consider homogeneous (bulk, effective) descriptions for at least some problems, especially for water flow (but less so for contaminant migration see Sect. 10.1). Therefore, two basic approaches to modeling generally are used to describe and quantify flow and transport continuum-based models and pore-network models. We discuss each of these here. 

The dynamics of water flow therefore are a combination of those governing flow in the partially saturated zone (essentially vertical, downward flow) and flow in saturated zones (aquifers), which can be fnlly three-dimensional. In general, the modeling approaches mentioned in Sect. 9.1 are applicable here—continnnm models and pore-scale network models—althongh detailed qnantification of flow and transport in the CF has received only limited attention. 

Redman JA, Grant SB, Olson TM, Estes MK (2001) Pathogen filtration, heterogeneity, and the potable reuse of wastewater. Environ Sci Technol 35 1798-1805 Redman JA, Walker SL, Elimelech M (2004) Bacterial adhesion and transport in porous media Role of the secondary energy minimum. Environ Sci Technol 38 1777-1785 Reeves CP, CeUa MA (1996) A functional relationship between capillary pressure, saturation, and interfacial area as revealed by a pore-scale network model. Water Resour Res 32 2345-2358 Richards LA (1931) Capillary conduction of liquids through porous mediums. Physics 1 318-333... 

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