Dual-water model

The dual-water model (Clavier et al., 1977, 1984) is based on the concept of two types of water in a shaly sand ... 

Clavier, C., Coates, G., Dumanoir, J., 1977. The theoretical and experimental bases for the dual water model for the interpretation of shaly sands. Society Petroleum EngineCTS (SPE) 52nd Armual Meeting Denver preprint 16, p., SPE Paper No. 6859. 

This work was done with a Waters Model 244 liquid chromatograph having two Du Pont Blmodal IIS columns (29,000 plates/meter) and a Linear dual-pen recorder. Also used was a Waters Model 440 UV absorbance detector. Samples were run at 0.1% (w/v) using an Injection volume of 25-pL and a flow rate of 1 mL/mln. The system was calibrated with polystyrene standards from Pressure Chemical Co. according to the universal callbaratlon procedure. Data collection and computation were done with an Intel 80/30 microprocessor. 

Liquid chromatographic separations were performed on a Waters Model ALC/GPC 204 liquid chromatograph equipped with two model 6000 pumps, a model 660 solvent programmer, and a model 440 dual UV absorbance detector. 

The sorption isotherm for many substances in polymers in the glassy state, as well as water in cellulose, can be described by two processes that are independent of one another (dual sorption model) ... 

Pederson described a specific HPLC method for the determination of dipyridamole in serum [74]. The HPLC system used was a Waters model 600 liquid chromatograph equipped with a U6K injector, a pBondapak Ci8 column (30 cm x 39 mm) (10 pm), and a model 440 dual channel filter absorbance detector in conjunction with a Tarkan W + W 600 recorder. The mobile phase was a 75 25 mixture of methanol and a 0.02 M solution of sodium acetate (adjusted to pH 4 with acetic acid). The solvent flow rate of 2 mL/min was produced by an applied pressure of approximately 2000 p.s.i. Detection of the analyte was made at the UV absorption maximum of 280 nm. 

Predicting fast and slow rates of sorption and desorption in natural solids is a subject of much research and debate. Often times fast sorption and desorption are approximated by assuming equilibrium portioning between the solid and the pore water, and slow sorption and desorption are approximated with a diffusion equation. Such models are often referred to as dual-mode models and several different variants are possible [35-39]. Other times two diffusion equations were used to approximate fast and slow rates of sorption and desorption [31,36]. For example, foraVOCWerth and Reinhard [31] used the pore diffusion model to predict fast desorption, and a separate diffusion equation to fit slow desorption. Fast and slow rates of sorption and desorption have also been modeled using one or more distributions of diffusion rates (i.e., a superposition of solutions from many diffusion equations, each with a different diffusion coefficient) [40-42]. 

Gerke, H.H. and van Genuchten, M.Th. (1993) A dual porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resources Research 29 305-319. 

Recently, dual-head pumps with a special piston movement designed so that the Sum of the flow-rates delivered by the two heads is constant, have become commercially available. The principle of operation is shown in Fig. 9c for the Waters Model 6000 and 6000A pumps. During the period when one piston moves forwards at constant speed, the other moves backwards for re-filling. During the intermediary period, the second piston is uniformly accelerated forwards while the first is uniformly decelerated forwards at the same acceleration rate. 

Fig. 9. Waters Model 660 solvent programmer, a, a = solvent reservoirs, b, b = dual-head pumps, c, c = pressure sensors, d = solvent programming manifold, e = high-pressure noise filter, f = to column.

Dual-sorption models are based on the premise that whilst some penetrant molecules diffuse normally in the polymer matrix, others will be affected by polymer-penetrant interactions or micro-void filling. Carter and Kibler (1978) addressed this problem in terms of the probability that a water molecule may react with a polymer molecule. Their model is based on the theory that moisture in a polymer network can be either bound or free. The probability that a free water molecule becomes bound is y and the probability that a bound water molecule is... 

The skeletal LN procedure is a dual timestep scheme, At, Atm, of two practical tasks (a) constructing the Hessian H in system (17) every Atm interval, and (b) solving system (17), where R is given by eq. (3), at the timestep At by procedure (23) outlined for LIN above. When a force-splitting procedure is also applied to LN, a value At > Atm is used to update the slow forces less often than the linearized model. A suitable frequency for the linearization is 1-3 fs (the smaller value is used for water systems), and the appropriate inner timestep is 0.5 fs, as in LIN. This inner timestep parallels the update frequency of the fast motions in force splitting approaches, and the linearization frequency Atm) is analogous to the medium timestep used in such three-class schemes (see below). 

The reaction is reversible and therefore the products should be removed from the reaction zone to improve conversion. The process was catalyzed by a commercially available poly(styrene-divinyl benzene) support, which played the dual role of catalyst and selective sorbent. The affinity of this resin was the highest for water, followed by ethanol, acetic acid, and finally ethyl acetate. The mathematical analysis was based on an equilibrium dispersive model where mass transfer resistances were neglected. Although many experiments were performed at different fed compositions, we will focus here on the one exhibiting the most complex behavior see Fig. 5. 

The principal solar water-splitting models predict dual-band gap photoelectrolysis efficiencies of 16% [40], and 10-18% [41]. 

Photoinduced electron transfer from eosin and ethyl eosin to Fe(CN)g in AOT/heptane-RMs was studied and the Hfe time of the redox products in reverse micellar system was found to increase by about 300-fold compared to conventional photosystem [335]. The authors have presented a kinetic model for overall photochemical process. Kang et al. [336] reported photoinduced electron transfer from (alkoxyphenyl) triphenylporphyrines to water pool in RMs. Sarkar et al. [337] demonstrated the intramolecular excited state proton transfer and dual luminescence behavior of 3-hydroxyflavone in RMs. In combination with chemiluminescence, RMs were employed to determine gold in aqueous solutions of industrial samples containing silver alloy [338, 339]. Xie et al. [340] studied the a-naphthyl acetic acid sensitized room temperature phosphorescence of biacetyl in AOT-RMs. The intensity of phosphorescence was observed to be about 13 times higher than that seen in aqueous SDS micelles. 

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