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Impact of liquid phase volume changes on estimating reaction rate parameters: the homogeneously catalyzed hydrolysis of methyl formate Hong Duc Ta, and Andreas Seidel-Morgenstern Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01343 • Publication Date (Web): 31 May 2017 Downloaded from http://pubs.acs.org on June 12, 2017
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Industrial & Engineering Chemistry Research
Impact of liquid phase volume changes on estimating reaction rate parameters: the homogeneously catalyzed hydrolysis of methyl formate Hong Duc Ta a ,b, Andreas Seidel Morgenstern a ,c* a Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany b Hanoi University of Science and Technology, No. 1 Dai Co Viet str., Hai Ba Trung, Hanoi, Vietnam c Max-Planck-Institut für Dynamik komplexer Technischer Systeme, Sandtorstr.1, D-39106 Magdeburg, Germany
KEYWORDS: liquid phase reactions, batch reactors, excess volumes, reaction kinetics, methyl formate hydrolysis
Abstract
The homogeneously catalysed hydrolysis of methyl formate was studied experimentally in a batch reactor. The kinetics of this reversible liquid phase reaction were quantified analysing measured concentration transients in two different ways: i) neglecting temporal changes of the volume of the reaction mixture, and ii) considering volume changes caused by the reaction and/or by mixing. Assuming the same structure of the kinetic expression, for both cases reaction rate constants were estimated. Consistent usage of the obtained constants within the corresponding models provided relative small differences in the predicted concentration transients. Even the most simplified approach, i.e. neglecting volume changes completely, was found to be capable to describe well concentration transients observed in a batch reactor. However, for the specific reaction investigated, the absolute values of the reaction rate constant varied up to 9.4% for the different volume effect scenarios considered. ACS Paragon Plus Environment
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1 INTRODUCTION
Liquid phase reactions are often performed in conventional batch reactors. This type of reactor is also frequently used to perform experiments in a laboratory scale in order to identify kinetic models and to estimate corresponding parameters. Due to the incompressibility of liquid phases, constant reaction volumes are typically assumed in analysing observed concentration transients. The rates of reactions taking place in liquid phase are a function of the activities of the species involved [1,2]. Related concentrations depend on the volume of the reacting system. Changes in the total liquid phase volume are typically neglected in quantifying reaction kinetics by analysing batch reactor experiments. However, this neglect might cause errors which are difficult to quantify. Even for reactions in ideal liquid phases, volume changes are unavoidable due to the composition changes caused by the chemical reactions and the differences in the molar volumes of the components involved. Further, it is well-known that mixing of liquids can cause volume changes [3-5]. In general, volume changes occur if the liquid phases behave in a non-ideal manner. It is the goal of this paper to study for a specific simple model reaction the mentioned volume effects both experimentally and theoretically. For this purpose the reversible water hydrolysis of methyl formate to methanol and formic acid was chosen: HCOOCH3 (MF) + H2O (W) ↔ CH3OH (M) + HCOOH (F)
(1)
Several studies regarding the kinetics of the MF hydrolysis have been already carried out and kinetic models and parameters were reported [6-8]. However, no systematic study was performed, which quantifies effects of volume changes on the precision of the analysis of the reaction kinetics. Our study intends clarifying, to which extent volume changes due to mixing, reaction and non-idealities must be incorporated into a reliable reactor model, and how strong do estimated values of reaction rate constants depend on the approach taken to evaluate the volume effects. First, we will provide the mass balance equations of a batch reactor for different assumptions regarding the reaction volume. Then we will describe the model reaction considered, the simplified reaction rate model used and the experiments carried out. Subsequently, the values of the reaction rate constants obtained using volume related sub-models of different complexity will be presented and discussed along with their specific potential to describe the observed concentration transients. Finally, some conclusions will be drawn regarding the need of quantifying volume changes within an the analysis of liquid phase reactions. ACS Paragon Plus Environment
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2 THEORY 2.1 Mass balances of perfectly mixed isothermal batch reactors Considering a single reaction proceeding with a volume specific reaction rate r in a homogeneous liquid phase present in a perfectly mixed (ideal) batch reactor, the following material balance holds for each component i:
= r V i = 1, N
(2)
Hereby, the ni are the numbers of the moles of N components involved in the reaction, the are the stoichiometric coefficients, and V is the total volume of the reaction mixture. To solve this system of ODE, the initial molar amounts have to be provided: t = 0: n = n i = 1, N
(3)
For the specific reaction considered holds ∑ = 0
(4)
and thus for this particular case of batch operation n (t) = ∑ n (t) = n = ∑ n
(5)
To complete the model expressions for the reaction rate r and the reaction volume V are needed. Concerning the time dependence of the reaction volume there exists three well defined scenarios, which are described below.
Constant volume scenario (“Const”) In many studies of liquid-phase reactions it is assumed that the volume of the reaction mixture remains constant. Thus, for this classical reference case denoted below as “Const” holds: V = const. = V
or
#
=0
(6)
The volume of the initial feed mixture introduced, Vinit, which is in this case assumed to remain un-
changed, can be calculated using the specific initial molar amounts, , and the molar volumes at the operation temperature, $%&'( , for all components j supplied to the batch reactor: *+,-
t =0: V = V = ∑ n v
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(7)
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In general, the volume of a reacting liquid mixture will not be constant. As already mentioned above, the volume will change due to temporal composition changes and due to non-ideal mixing. This gives rise to the following two more realistic descriptions of the evolution of the reaction mixture volume.
Volume changes due to composition changes and molar volume differences (“Ideal”) In ideal solutions (“Ideal”), the partial molar volume of a component j in solution is equal to the mo-
lar volume of the pure component, i.e. $%&'( [9]. Thus, the total volume of the reaction mixture can be expressed in each moment based on the molar amounts of all components currently present, (.): *+,-
V(t) = V = ∑ n (t)v
(8)
Taking the time derivatives of both sides of this equation and considering eq. (2)one obtains: #
*+,-
= rV(t) ∑ μ v
(9)
Thus, the ODE system which represents the component material balances of the batch reactor constitutes now of eqs. (2) and (9). Eq. 7 provides again the initial volume.
Incorporating real phase behaviour (“Real”) In real solutions the actual molar volumes have to be computed as the sum of the ideal values and the molar excess volumes valid for the specific temperature, pressure and composition [9].Thus, extending eq. 8, the time dependence of the total volume, V(t), needs to be rewritten as %&'( 3 (.) 0(.) = ∑1 + 0(1) (.)$
(10)
3 where 0(1) (t) is the time dependent total excess volume of the N components in the mixture. Taking
again time derivatives of both sides of the equation and considering eq. (2) provides: 45 4
%&'( = 6 0(.) ( ∑1 ) + $
8 45(7)
4
(11)
Thus, in this third and most realistic case the material balances are given by eqs. (2) and (11). As an initial condition we can consider for simplicity, that the pure reactants areperfectly mixed prior 3, to the beginning of the reaction. Thus, an established initial total excess volumes 0(1) is respected: 3, %&'( t = 0: 0 = 0 ,'(9: = ∑1 $ + 0(1)
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(12)
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Below we will consider and compare the three approaches (“Const”, “Ideal”, “Real”) in an analysis of batch reactor data acquired experimentally in order to estimate reaction kinetic parameters. We will evaluate the impact of the selection of these three reaction volume sub-models on the results of analysing identical concentration transients observed for the methyl formate hydrolysis. The specific systems of ODE belonging to the three approaches were solved using the solver “ode45” available in MATLAB [16].
2.2 Extents of reaction, concentrations and activities In order to analyse the course of a single reaction it is expedient to condense the information of the various transients in the component specific molar amounts, ni(t), into a single transient of the extent of reaction,;(.), defined as: ;(.) =
< ()=
