Extraction model

In order to design an extraction unit, the rate-limiting step in the extraction process has to be determined. As explained in Section 14.4 and Fig. 14.3, the film model can be used to describe extraction in the three-phase system. The overall mass transfer flux of monomer in this extraction process is given by Eq. (14) 

By calculating the time constant of each resistance, the largest resistance for mass transfer can be determined. For this purpose, the partition coefficients rrii and m2, the mass transfer coefficients kpon and kcOj- well as the interfacial surface areas Apopw and ATjyco2 have been determined in various ways as discussed below. For a more detailed description we refer to eleven [48]. 

---

The seminal work on these materials began at American Cyanamid Co. in the 1960s (4,23), though these workers did not author the ion-insertion/extraction model that has become widely accepted (5). Numerous patents were granted to American Cyanamid Co. as a result of its display-oriented work. Much of what others have written in the open Hterature either confirms or adds to what these teach. Important papers (16) about... 

In the preceding solvent extraction models, it was assumed that the phase flow rates L and G remained constant, which is consistent with a low degree of solute transfer relative to the total phase flow rate. For the case of gas absorption, normally the liquid flow is fairly constant and Lq is approximately equal to Li but often the gas flow can change quite substantially, such that Gq no longer equals Gj. For highly concentrated gas phase systems, it is therefore often preferable to define flow rates, L and G, on a solute-free mass basis and to express concentrations X and Y as mass ratio concentrations. This system of concentration units is used in the simulation example AMMONAB. 

In solubility limited extractions the rate is reduced at the beginning of the extraction. Models for SFE predict that these extractions should be carried out at as high a temperature and pressure as possible. However, the polymer will eventually soften and melt, and the particles will coalesce. 

The material covered in the appendices is provided as a supplement for readers interested in more detail than could be provided in the main text. Appendix A discusses the derivation of the spectral relaxation (SR) model starting from the scalar spectral transport equation. The SR model is introduced in Chapter 4 as a non-equilibrium model for the scalar dissipation rate. The material in Appendix A is an attempt to connect the model to a more fundamental description based on two-point spectral transport. This connection can be exploited to extract model parameters from direct-numerical simulation data of homogeneous turbulent scalar mixing (Fox and Yeung 1999). 

Nicolas, A. (1986). A melt extraction model based on structural studies in mantle peridotites. J. Petrol., 27, 999-1022. 

The interface extraction model assumes that HA reacts with B at the interface. Thus... 

Keywords. Downstream processing. Reverse micelles, Protein/enzyme extraction. Modeling, Recent developments... 

A simplified equilibrium extraction model (Fig. 6) was presented by Dordick and colleagues [188] to explain the resolution behavior of glycoproteins in affinity based reverse micellar extraction and separation (ARMES). Their system for the study includes soybean peroxidase (SBP, MW 37 KDa, pi 4.1) and aj-acid glycoprotein (AGP, MW 43 KDa, pi 3.7) as glycoprotein solutes, concanavalin A (ConA) as the affinity ligand in AOT/isooctane RMs. The separation factor (a) for the separation of SBP from AGP can be given by... 

Fig. 6. Equilibrium extraction model involved in the ARMES process. (Reproduced from [188] with permission of AIChE)...

Bruel, D. 1995. Heat extraction modeling from forced fluid flow through stimulated fractures rock masses Applications to the Rosemanowes hot-dry rock reservoir. Geothermics, 24, 361-374. 

By using experimentally obtained data for 1 mM salicylic acid, a plot of reciprocal analytical signal versus reciprocal a, yielded a linear relationship for the pH range 1.65-3.01. This result supported the solvent extraction model. The corresponding estimate of capacity ratio and distribution coefficient using this treatment was 8.5. 

Analytical separation of several organics from water by PVC polymer is feasible. A solvent extraction model describes the separation dynamics and pH dependence. Selectivity via pH control of the extraction step and preconcentration of analyte can be accomplished. These results suggest that other polymer solvent extraction schemes can be developed by using this approach. The flow-through amperometric technique provides a well-suited detector component for the technique. 

Sonicator for samples extraction (model YC 100) from Vibracell Sonics and Materials. 

The developed cesium and potassium extraction model, based on extraction data obtained from simple aqueous media, was tested to ensure the validity of the prediction for the cesium extraction from actual waste.112 The predicted values agreed with the measured values for the simulants predicted values also agreed, with some exceptions, with measured values for the tank wastes. Discrepancies were attributed, in part, to the uncertainty in the cation/anion balance in the actual-waste composition, but likely more so to the uncertainty of the potassium concentration in the waste, given the demonstrated large competing effect of this metal on cesium extraction. It was demonstrated that the upper limit for the potassium concentration in the feed should not exceed 0.05 M, in order to maintain suitable cesium distribution ratios. 

Surface Inventories as Percentage of Starting Inventory Selective Extraction Model Prediction... 

The extraction of toluene and 1,2 dichlorobenzene from shallow packed beds of porous particles was studied both experimentally and theoretically at various operating conditions. Mathematical extraction models, based on the shrinking core concept, were developed for three different particle geometries. These models contain three adjustable parameters an effective diffusivity, a volumetric fluid-to-particle mass transfer coefficient, and an equilibrium solubility or partition coefficient. K as well as Kq were first determined from initial extraction rates. Then, by fitting experimental extraction data, values of the effective diffusivity were obtained. Model predictions compare well with experimental data and the respective value of the tortuosity factor around 2.5 is in excellent agreement with related literature data. 

In this work extraction models are developed for three different particle geometries using the shrinking core concept. Model calculations will be compared and fitted to extraction data of toluene and 1,2 dichlorobenzene (DCB) from shallow packed beds in order to obtain values of the efective diffusivity (De) and the tortuosity factor. 

In this work, some of the above mentioned features were investigated for a simple extraction model, using suitable complexing amphi-philes having different hydrophobicity. 

The results obtained with the reported extraction model showed that the separation of charged species is possible, provided a suitable ligand hydrophobicity. Further analytical developments of these multiphase extraction systems will require an accurate investigation of the equilibria and kinetic processes occurring at the interfaces, as well as the study of the micellar structure and properties of the host aggregates. 

Figure 4. Extraction model for sorption of 4-amino-3,5,6-trichloropicolinic acid...

Single-phase simulations in relatively small boxes (20 -30 sites) were performed after the determination of the surfactant/silica liquid crystal composition to generate model materials for adsorption simulation. The advantage of generating such materials is that they have truly periodic boundary conditions in the three directions. In contrast, extracted model materials obtained directly from the interfacial simulation will have periodic boundary conditions in two directions, but in the third direction (z-direction) there are two liquid-crystal/dilute phase interfaces. 

Enzymatic studies using selectively addressable fluorescent Rab proteins have elucidated the geranylgeranylation process (16). Structural studies on selectively prenylated Rab proteins have elucidated the exact interaction mechanism of Ras proteins with their transporter protein GDP dissociation inhibitor (GDI) and have led to a membrane extraction model for Rab proteins (58, 59). 

Figure 14 Normative spinel Iherzolite mineral abundances (wt.%) versus rock Mg for abyssal peridotite trends relative to calculated trends for polybaric, near-fractional melting. Three melt extraction models are shown over pressure ranges of 2.5-0.4 (short dashed line), 2.0-0.4 (long dashed line), and 1.5-0.4GPa (solid line). One percent melting occurs per 0.1 GPa of decompression, and 90% of the melt is extracted at each pressure. Starting mantle is fertile upper mantle (Table 1, 8).

Eased on two main lines of evidence, Niu et al. (1997) concluded that abyssal peridotites are the end products of melt extraction followed by variable amounts of olivine crystallization. First, in their set of reconstructed compositions they found that model fractional and batch melt extraction trends could not reproduce major and minor element variations in their data set. Most importantly, they found that melt extraction models failed to account for the strong positive correlation between FeO and MgO, as well as incompatible minor-element concentrations. Specifically, at a given Na20 or Ti02 content, abyssal peridotites are enriched in MgO relative to model melt extraction residues. Niu et al. (1997) showed that these compositional anomalies can be reconciled by a model of melt extraction followed by olivine crystallization, with more MgO-enriched samples having more accumulated olivine. If correct, this model has important implications for understanding melt extraction at oceanic ridges, and it has recently been the focus of re-evaluation. 

---