Mass transfer through the deposited asbestos diaphragm in chlor-alkali cells

Hine, Fumio; Yasuda, M.; Tanaka, Toshio

doi:10.1016/0013-4686(77)85097-4

Cited by 11 publications

(15 citation statements)

References 4 publications

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“…[24], their dimensionless parameter U6/D, can be shown to be equal to A,t of Eq. [13], [14], and [16]. In addition, their equation for C,(x) is not complete because it depends on the concentration of OH-in the catholyte, which also depends on other variables in their expression for CoH-(x).…”

Section: Comparison Of Diaphragm Model To Existing Modelsmentioning

confidence: 99%

“…The weighting of the dependent variables in the LS objective function in this fashion gives the "best values" of the parameters for Eq. [16] and [21] and the data (27). These estimated variances are shown in cases A and B of Table I.…”

Section: Parameter Estimationmentioning

confidence: 99%

“…Of the simple models of the diaphragm that have been proposed (6)(7)(8)(9)(10), only Koh (9,10) and Mukaibo (7) included diaphragm characterizing properties, but neither recognized that NM can be measured directly from relatively simple experiments. Koh (9, 10) used a diaphragm characterizing parameter which was obtained from an assumed value for 9 or the product z and a presumably measured value for e. Mukaibo (7) [see also Hine (14,16,17)] used the ratio of the diaphragm area to the area of the dia-, Throughout this paper, the phrase "simple model of the diaphragm" is used to indicate a model with a linear potential gradient that can be solved by analytical integration of the governing differential equations. phragm pores, which is not measurable directly, and, hence, this ratio was an assumed quantity when the model was compared with experimental data (16).…”

Section: ] Pomentioning

confidence: 99%

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Using Parameter Estimation Techniques with a Simple Model of a Diaphragm‐Type Electrolyzer to Predict the Electrical Energy Cost for NaOH Production

Zee

White

1985

J. Electrochem. Soc.

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Predictions of the electrical energy cost for NaOH production are determined as a function of the independent operating variables and diaphragm characterizing properties. The predictions are based on data from a statistically designed experiment, a simple model of a diaphragm-type electrolyzer, a simple model of the cell voltage losses, and parameter estimation techniques. The data were obtained over a sufficiently large range of operating conditions so that the resulting design equation may be industrially useful. The simple model of the diaphragm is based on the mass transport of the hydroxyl ion, a linear potential gradient, and is presented in terms of measurable diaphragm properties.These properties are the thickness of the diaphragm (t) and a resistivityratio, P/Po, where p is the resistivity of the diaphragm filled with electrolyte and po is the resistivity of the electrolyte (this ratio may come to be known as the MacMullin number, NM). It is shown that, according to the model of the cell, the caustic yield or current efficiency of the diaphragm cell depends on the product of NM and t and not on each separately. The simple model of the cell voltage considers the diaphragm voltage drop, anode and cathode kinetics, and the bubble-filled brine-gap voltage drop. Parameter estimation techniques are used to determine the best values of the diffusion coefficient, average specific conductivity, exchange current densities, and transfer coefficients; these parameters and the simple models provide a design equation for the electrical energy cost of NaOH production using a diaphragm cell. The design equation is used to predict a

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Section: Comparison Of Diaphragm Model To Existing Modelsmentioning

confidence: 99%

Section: Parameter Estimationmentioning

confidence: 99%

Section: ] Pomentioning

confidence: 99%

See 1 more Smart Citation

Using Parameter Estimation Techniques with a Simple Model of a Diaphragm‐Type Electrolyzer to Predict the Electrical Energy Cost for NaOH Production

Zee

White

1985

J. Electrochem. Soc.

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“…This ratio denoted here as Nm, has been referred to by others as the formation factor (7) and the labyrinth factor (8). Other diaphragm properties have also been proposed (9)(10)(11)(12)(13)(14)(15), but none of these is measurable directly, even though they have been shown to be equivalent to the product NML (3,4,16). Simple steady-state models of the diaphragm-type cell for chlor-alkali cells have been presented and reviewed recently (3,4).…”

Section: Literaturementioning

confidence: 99%

“…[12]-[14] yields the following dimensionless initial and boundary conditions at t = 0 0,(~:, t) = 0~(~, O) ---C~*(X)…”

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confidence: 99%

Simple Models for Diaphragm‐Type Chlorine/Caustic Cells: I . Dynamic Behavior

Zee

White

Watson

1986

J. Electrochem. Soc.

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A simple model of the dynamic behavior of a diaphragm-type chlorine/caustic cell is presented. The model is based upon measurable diaphragm properties and the mass transfer of hydroxyl ion through the diaphragm. The anolyte is modeled simply as a region in which the OH-ion concentration is fixed, the diaphragm is modeled as a plug-flow reactor with an electrochemical reaction occurring at the catholyte/diaphragm interface where the cathode is placed, and the catholyte is modeled as a completely stirred flow reactor. Analytical integration of the governing equations for these models yields two mathematical expressions: one for the concentration distribution of hydroxyl ion within the diaphragm and one for the effluent concentration. Both of these expressions are functions of time, independent operating variables, diaphragm properties, and physical constants. They are used to show how the concentration distribution of OH-within the diaphragm and the cell effluent change when subjected to a step change in the current density. Also presented is a numerical method of solution for the model equations to predict the required change of the cell head subject to an arbitrary time-dependent change in the current density at a fixed cell effluent concentration.Diaphragm-type cells are used extensively in the United States to produce chlorine and caustic (1). The diaphragm is the key to efficient cell operation, because the diaphragm properties affect the voltage loss, the yield, and the effluent caustic concentration. Recently (2, 3, 4), measurable diaphragm properties have been proposed and used to predict the performance of these cells under steady-state conditions. A simple model ~ of the cell is presented here to predict the effect of these diaphragm properties on the dynamic behavior of the caustic yield.The time-dependent or dynamic behavior of diaphragm-type cells is of interest during start-up and in situations where a differential cost structure for electricity provides an opportunity to reduce the cost of production by operating the cells accordingly. This may mean a high production rate during the night and a low production rate during the day, for example. The model presented in this paper can be used to predict the changes in the operating conditions (e.g., current density and differential head) which would be required to maintain a fixed caustic effluent concentration or a fixed caustic yield.In a diaphragm-type chlorine/caustic cell (see Fig. 1), hydroxyl ions are produced at the cathode according to the following electrochemical reaction H20 + e--~ OH-+ 1/2 H2[1]The buoyancy of the hydrogen gas causes stirring in the catholyte and this compartment is consequently assumed to be completely mixed. A similar statement could be made concerning the anolyte and the chlorine gas generated at the anode. This is, however, not necessary here since the anolyte is modeled simply as a region in which the OH-ion concentration is fixed at a known value that depends on the fixed anolyte pH. As shown in Fig. 1, a diffe...

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