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Marco Mazzotti - One of the best experts on this subject based on the ideXlab platform.

  • Equilibrium Theory analysis of liquid chromatography with non-constant velocity.
    Journal of chromatography. A, 2014
    Co-Authors: Franziska Ortner, Lisa Joss, Marco Mazzotti
    Abstract:

    In liquid chromatography, adsorption and desorption lead to velocity variations within the column if the adsorbing compounds make up a high volumetric ratio of the mobile phase and if there is a substantial difference in the adsorption capacities. An Equilibrium Theory model for binary systems accounting for these velocity changes is derived and solved analytically for competitive Langmuir isotherms. Characteristic properties of concentration and velocity profiles predicted by the derived model are illustrated by two exemplary systems. Applicability of the model equations for the estimation of isotherm parameters from experimental data is investigated, and accurate results are obtained for systems with one adsorbing and one inert compound, as well as for systems with two adsorbing compounds.

  • Equilibrium Theory based analysis of nonlinear waves in separation processes
    Annual Review of Chemical and Biomolecular Engineering, 2013
    Co-Authors: Marco Mazzotti, Arvind Rajendran
    Abstract:

    Different areas of engineering, particularly separation process technology, deal with one-dimensional, nonstationary processes that under reasonable assumptions, namely negligible dispersion effects and transport resistances, are described by mathematical models consisting of systems of first-order partial differential equations. Their behavior is characterized by continuous or discontinuous composition (or thermal) fronts that propagate along the separation unit. The Equilibrium Theory (i.e., the approach discussed here to determine the solution to these model equations) predicts this with remarkable accuracy, despite the simplifications and assumptions. Interesting applications are in adsorption, chromatography and ion-exchange, distillation, gas injection, heat storage, sedimentation, precipitation, and dissolution waves. We show how mathematics can enlighten the engineering aspects, and we guide the researcher not only to reach a synthetic understanding of properties of fundamental and applicative interest but also to discover new, unexpected, and fascinating phenomena. The tools presented here are useful to teachers, researchers, and practitioners alike.

  • Local Equilibrium Theory for the Binary Chromatography of Species Subject to a Generalized Langmuir Isotherm. 2. Wave Interactions and Chromatographic Cycle
    Industrial & Engineering Chemistry Research, 2011
    Co-Authors: Arvind Rajendran, Marco Mazzotti
    Abstract:

    The generalized Langmuir isotherm model was recently developed to describe the competitive adsorption equilibria of a binary mixture [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This formalism captures the competitive effect of solutes that show either Langmuirian or anti-Langmuirian behavior. This results in four isotherm types that show markedly different chromatographic behavior. The Equilibrium Theory of chromatography was developed in a previous work to study Riemann problems (saturation, elution, and the chromatographic cycle) that are of practical relevance [Mazzotti, M. Ind. Eng. Chem. Res. 2006, 45, 5332−5350]. This work focuses on the development of the Equilibrium Theory to account for wave interactions and is divided into two parts. In the first part, the Theory of wave interactions is developed on the basis of the method of characteristics. It is shown that the rules developed for competitive Langmuir isotherms can be extended to describe possible wave interactions in the case of ...

  • Equilibrium Theory based design of simulated moving bed processes for a generalized Langmuir isotherm
    Journal of Chromatography A, 2006
    Co-Authors: Marco Mazzotti
    Abstract:

    In the frame of the local Equilibrium Theory of chromatography, design criteria for complete separation of binary mixtures in simulated moving bed (SMB) separations are developed, presented and discussed. These apply to systems, whose retention behavior is characterized by a generalized Langmuir isotherm. By allowing for negative terms in the denominator of the classical Langmuir isotherm, this newly introduced adsorption model captures a broad class of competitive or synergistic adsorption, including anti-Langmuir behavior for both adsorbates, and mixed cases where one species behaves in a Lagmuirian and the other in an anti-Langmuirian manner. By extending classical Equilibrium Theory results for the binary Langmuir isotherm, and by generalizing the approach followed earlier to derive SMB design criteria for the binary and multi-component Langmuir isotherm, exact algebraic equations for the boundary of the complete separation region in the operating parameter space are derived for all possible generalized Langmuir isotherm. The effect of changing feed composition on the shape of the complete separation region and on the position of the optimal operating point is analyzed and discussed.

  • Local Equilibrium Theory for the Binary Chromatography of Species Subject to a Generalized Langmuir Isotherm
    Industrial & Engineering Chemistry Research, 2006
    Co-Authors: Marco Mazzotti
    Abstract:

    The local Equilibrium Theory of chromatography is applied to binary systems subject to the generalized Langmuir isotherm. This newly introduced adsorption isotherm allows describing a variety of competitive and synergistic adsorption behaviors, by letting each of the two components be Langmuir-like or anti-Langmuir-like. It is shown that all four possible types of isotherms (one of which is the classical competitive Langmuir isotherm) share the key property that characteristics in the composition plane are straight lineshence, the application of the method of characteristics leads to explicit expressionsand the solution of Riemann problems, e.g., elution of a saturated column or adsorption on an initially clean column, boils down to the use of simple algebraic relationships. Similarities and differences among the four different cases are presented, analyzed, and discussed, including their physical legitimacy and thermodynamic consistency, particularly for the case where the first eluting component is anti...

Achim Kienle - One of the best experts on this subject based on the ideXlab platform.

  • Equilibrium Theory of ion exchange chromatography with variable solution normality and steric hindrance
    Chemical Engineering Science, 2019
    Co-Authors: Marcus Fechtner, Achim Kienle
    Abstract:

    Abstract The paper extends Equilibrium Theory of ion exchange chromatography to account for variable solution normality and steric hindrance. Both effects are crucial for many separations including the separation of proteins. Analytical solutions are given for a full chromatographic cycle consisting of the loading of an empty bed equilibrated at different salt concentrations followed by a regeneration step. Special emphasis is on selectivity reversals. It is shown that additional reversals may occur due to a change in solution normality. Results are illustrated step by step and relation to ion exchange chromatography with constant solution normality and/or mass action Equilibrium without steric hindrance is discussed. Theoretical findings are validated by comparison with numerical simulation.

  • efficient simulation and Equilibrium Theory for adsorption processes with implicit adsorption isotherms ideal adsorbed solution Theory
    Chemical Engineering Science, 2018
    Co-Authors: Marcus Fechtner, Achim Kienle
    Abstract:

    Abstract Recently an efficient method for the simulation of packed bed adsorbers with implicit adsorption isotherms was presented. It uses a method of lines approach and exploits standard software for the simultaneous solution of the resulting differential algebraic equations (DAEs). Application was demonstrated for stoichiometric ion exchange. In the present paper, the approach is extended to systems described by the adsorbed solution Theory. For that purpose, the relation between the differential index of the DAE system and the spectral properties of the underlying adsorption Equilibrium is established. In particular, it is shown that real and positive eigenvalues of the Jacobian of the underlying conservation equations will lead to a differential index of one. It is further shown that real and positive eigenvalues of the Jacobian related to the IAST can be guaranteed for binary mixtures with any type of pure component adsorption isotherm or for multicomponent mixtures with certain restricted types of pure component isotherms. The new method is illustrated for different explicit and implicit pure component adsorption isotherms belonging to this class. It is compared with alternative solution approaches using the modified FastIAS method by Do and Myers and semi-analytical solutions from Equilibrium Theory.

  • efficient simulation and Equilibrium Theory for adsorption processes with implicit adsorption isotherms mass action equilibria
    Chemical Engineering Science, 2017
    Co-Authors: Marcus Fechtner, Achim Kienle
    Abstract:

    Abstract An efficient method for the simulation of packed bed adsorbers is presented. It is based on Equilibrium models and can be applied to any implicit adsorption isotherm. It uses a method of lines approach, avoids explicit differentiation of the adsorption isotherm, and exploits standard numerics for the simultaneous solution of the resulting ordinary differential and implicit algebraic equations. Application is illustrated for stoichiometric ion exchange, which also admits an analytical approach using Equilibrium Theory. Classical theoretical results from Equilibrium Theory are summarized, further extended and compared to the numerical calculations for different scenarios. Focus is on selectivity reversals and their influence on process operation. It is shown that the selectivity reversal may introduce multiple solutions.

  • Equilibrium Theory and nonlinear waves for reactive distillation columns and chromatographic reactors
    Chemical Engineering Science, 2004
    Co-Authors: S Gruner, Achim Kienle
    Abstract:

    A general framework for analyzing and understanding the dynamics of reactive separation processes is developed. The Theory is based on the assumption of simultaneous phase and reaction Equilibrium. It makes use of transformed concentration variables, which were first introduced by Doherty and co-workers for the steady state design of reactive distillation processes (Proc. Roy. Soc. London A 413 (1987a) 459). It is shown that these transformed variables can be directly generalized to the dynamic problem considered here. Further, they can also be applied to other reactive separation processes like fixed bed as well as countercurrent chromatographic reactors, for example. They provide profound insight into the dynamic behavior of these processes and reveal bounds of feasible operation caused by reactive azeotropy. It is shown that reactive azeotropy, which is a well-known phenomenon in reactive distillation (Proc. Roy. Soc. London A 413 (1987b) 443) may also rise under very similar conditions in other reactive separation processes like chromatographic reactors for example.

James A. Ritter - One of the best experts on this subject based on the ideXlab platform.

  • Equilibrium Theory for solvent vapor recovery by pressure swing adsorption analytic solution with velocity variation and gas phase capacity
    Chemical Engineering Science, 1999
    Co-Authors: Dharmashankar Subramanian, James A. Ritter, Yujun Liu
    Abstract:

    Equilibrium Theory has been used to analyze the effect of velocity variation and gas-phase capacity on the performance of a pressure swing adsorption-solvent vapor recovery (PSA-SVR) process. An analytic expression for the wave interaction that transpires between the inlet feed conditions and the initial column conditions is developed. The periodic state is formulated by forcing repetition of characteristic conditions to obtain a polynomial equation. It is found that both velocity variation and gas-phase capacity have significant effects on the depth of wave penetration. For systems with relatively low feed concentrations, gas-phase capacity has a larger effect than velocity variation and vice versa for systems with relatively high feed concentrations. The analysis also reveals some remarkable insight into the subtleties associated with nominal purge-to-feed ratios of less than unity.

  • Equilibrium Theory for binary solvent vapor recovery by pressure swing adsorption conceptual process design for separation of the lighter component
    Chemical Engineering Science, 1998
    Co-Authors: Dharmashankar Subramanian, James A. Ritter
    Abstract:

    A simple Equilibrium Theory has been formulated soley in terms of wave interactions for binary pressure swing adsorption-solvent vapor recovery (PSA-SVR). An analytic resolution of all the ensuing wave interactions, including shock wave interactions with compressive simple waves, has been obtained for the case of the separation of the lighter impurity, i.e. the case of recovering the lighter impurity during the feed step, while obtaining a stream enriched in the heavier impurity during the purge step. Analytic expressions have also been obtained for all the key process performance indices. Two conceptual process designs have been carried out that demonstrate the utility of these simple expressions for rapid elucidation of binary PSA-SVR separation process heuristics, performance and feasibility.

  • Equilibrium Theory for solvent vapor recovery by pressure swing adsorption analytical solution for process performance
    Chemical Engineering Science, 1997
    Co-Authors: Dharmashankar Subramanian, James A. Ritter
    Abstract:

    Abstract A simple, analytic, Equilibrium Theory model based on wave interactions that occur in adsorption columns, has been formulated to predict directly the periodic state and to analyze the application of pressure swing adsorption (PSA) for solvent vapor recovery (SVR). The analysis of this cyclic process has been carried out using a fully convex, Langmuirian isotherm, with and without breakthrough of the solvent vapor into the light (inert) product. The analytic structure of this model shows the infeasibility of a periodic state with complete containment of solvent vapor, when the purge-to-feed ratio is less than unity. Analytic expressions have also been derived in terms of the key process performance indices: heavy component enrichment and recovery, and light product impurity. Results obtained from these expressions, when studying the effects of the purge-to-feed ratio, pressure level, pressure ratio, feed flow rate, feed mole fraction, cycle time, and bed length-to-diameter ratio, compare qualitatively with results obtained from a more rigorous numerical model. The comparison with a more rigorous model also exposes subtleties about the effect of model approximations on the predicted process performance, in that the cancellation of the effects of certain simplifying assumptions results in near quantitative agreement with the more rigorous model, in some cases.

Piero Gottardi - One of the best experts on this subject based on the ideXlab platform.

  • a general Equilibrium Theory of banks capital structure
    Journal of Economic Theory, 2020
    Co-Authors: Douglas Gale, Piero Gottardi
    Abstract:

    Abstract We develop a general Equilibrium Theory of the capital structures of banks and firms. The liquidity services of bank deposits make deposits a “cheaper” source of funding than equity. In Equilibrium, banks pass on part of this funding advantage in the form of lower interest rates to firms that borrow from them. Firms and banks choose their capital structures to balance the benefits of debt financing against the risk of costly default. An increase in the equity of a firm makes its debt less risky and that in turn reduces the risk of the banks who lend to the firm. Hence there is some substitutability between firm and bank equity. We find that firms have a comparative advantage in providing a buffer against systemic shocks, whereas banks have a comparative advantage in providing a buffer against idiosyncratic shocks.

  • Equilibrium Theory of banks capital structure
    Social Science Research Network, 2017
    Co-Authors: Douglas Gale, Piero Gottardi
    Abstract:

    We study an environment where the capital structure of banks and firms are jointly determined in Equilibrium, so as to balance the benefits of the provision of liquidity services by bank deposits with the costs of bankruptcy. The risk in the assets held by firms and banks is determined by the technology choices by firms and the portfolio diversification choices by banks. We show competitive equilibria are efficient and the Equilibrium level of leverage in banks and firms depend on the nature of the shocks affecting firm productivities. When these shocks are co-monotonic, banks optimally choose a zero level of equity. Thus all equity should be in firms, where it does “double duty”. Protecting both firms and banks from default. On the other hand, if productivity shocks have an idiosyncratic component, portfolio diversification by banks may be a more effective buffer against these shocks and, in these cases, it may be optimal for banks, as well as firms, to issue equity.

Renato Rota - One of the best experts on this subject based on the ideXlab platform.

  • optimal design of dual reflux pressure swing adsorption units via Equilibrium Theory process configurations employing heavy gas for pressure swing
    Chemical Engineering Journal, 2017
    Co-Authors: Tushar S Bhatt, Giuseppe Storti, Joeri F M Denayer, Renato Rota
    Abstract:

    Abstract Dual-reflux pressure swing adsorption process is theoretically capable of completely separating binary feed gas mixtures into two pure species. The pressure of bed to which the binary gas mixture is fed and the type of gas utilized for pressure swing, results in different process cycle configurations, even if the majority of the previous studies of DR-PSA are restricted to two cycle configurations: that employ heavy gas for pressure swing and deliver feed to the bed operated at either high or low pressure. However, the comparative assessment and the optimal operating pressure ratio of these two process cycle configurations are not well-established. We previously reported an optimal design strategy (that identified a triangular operating zone, inside which, complete separation of binary gas mixtures can be achieved) for one such DR-PSA process cycle configuration. In this work, we report an optimal design strategy for another DR-PSA process cycle configuration: feed to low pressure bed and pressure swing using heavy gas. With respect to previous literature, the Equilibrium Theory based comprehensive tracking of the characteristic curves and shock transitions during constant and non-constant pressure steps of this specific cyclic process revealed distinct constraints, design parameter values and boundary conditions of the triangular operating zone. Additionally, an in-depth comparative assessment of the impact of process variables (adsorbent selectivity, feed gas composition and, operating pressure ratio) on the design parameters (optimal feed injection position and ratio of pure light reflux to feed rate) and a novel selection criterion is discussed for both of these cycle configurations in order to (i) facilitate the choice of appropriate cycle configuration and (ii) identify the optimal high to low operating pressure ratio range.

  • optimal design of dual reflux pressure swing adsorption units via Equilibrium Theory
    Chemical Engineering Science, 2013
    Co-Authors: Tushar S Bhatt, Giuseppe Storti, Renato Rota
    Abstract:

    An optimal design strategy for dual-reflux pressure swing adsorption units targeted at achieving the separation of binary gas mixtures into two pure components (complete separation) is presented. Based on the Equilibrium Theory, detailed study of a specific configuration (feed to high pressure bed and pressure swing using heavy gas) reveals that feed location along the adsorption column, capacity ratio of the purge step (ratio between amount of feed to be processed and amount of adsorbent) and light recycle ratio (ratio of pure light reflux to feed rate) are the three most relevant design parameters. With respect to previous literature, two major achievements can be mentioned: (i) the development of an expression to evaluate optimum feed location and (ii) the identification of an operating region inside which complete separation at cyclic steady-state conditions can be established. In the plane defined by the two quantities feed position-capacity ratio of the purge step, such region has triangular shape and optimal conditions correspond to a vertex.