A commercial sulfonated copolymer of styrene and divinylbenzene in acid form resin (Ionic form: H⁺ R-SO₃-) was used with surface area and porosity 96 m²/gm and 0.67, respectively, mesh size 16 - 50 (0.3 - 1.2 mm) and Capacity min. (eq/l) 1.8.

Catalytic dehydration of methanol in the atmospheric gas phase in a fixed bed reactor has been achieved with the following details:

Dosing pump of maximum and minimum flow rate 2 and 0.02 liter/hr respectively was used to control methanol feeding, QAV tubular reactor with inside diameter 2.54 and 100 m length was used, this reactor is divided into two sections; evaporator and reaction section. The reaction has been conducted with a temperature range (90˚C - 120˚C) and 40 gm (i.e. 7 cm high) catalysts, methanol flow rates were 0.39 - 1.48 mole/hr or W/F = 27 - 100.2 (g hr/gm). The vent gases

were condensed with a condenser designed for this purpose, Samples of liquid and vapor were taken for analysis regularly. The apparatus of this examination is showing in Figure 3. More details about the experimental work are discussed in the literature [14]. The rate of methanol consumption, ethylene, and ether rate formation was calculated based on material balances.

Data were collected after an appropriate period (usually 1 h) for each set of experimental conditions to enable a steady state to be established. Testing was conducted by using a Gas Chromatography (Shimadzu-9A); an externally (3.17 mm) and 3 m long (Parapak Q)-treated steel section; The GLC segment was linked with warm TCD; hydrogen was used as a carrier gas. Column and TCD temperatures were 250˚C and 200˚C respectively, initial and injection temperatures were 175˚C and 200˚C.

In order to confirm that the process is kinetically controlled, the mass transport limitation and the internal diffusion limitation have to be discarded, i.e. the diffusion of the reactant from the outer surface of the porous catalyst to the reactive sites, external diffusion, i.e. the transport of reactants from the bulk to the outer surface of porous catalyst [5]. To confirm that, the procedure mentioned in the literature [24] has been followed.

Several mechanisms for catalytic dehydration of methanol to DME have been suggested by many researchers (some of these are mentioned in literature [27]). Thus, just two possible kinetic models have been evaluated for modeling reaction 1 over resin catalyst as shown below. Each model is based on the surface reaction as the rate-determining step.

L-H Model: assumes that the surface reaction takes place according to the Langmuir-Hinshelwood mechanism in which two chemisorbed adjacent alcohol molecules react to form the chemisorbed products. Sequence equations of the reaction for this model are depicted below:

2CH 3 OH → CH 3 OCH 3 + H 2 O (1)

2 A ⇔ W + E (2)

where:

A = Methyl alcohol

E = Ether

W = Water

A + S ⇌ k − A k A A . S (Step 1, chemisorption of methanol)

A . S + A . S ⇌ k − S k S W . S + E . S (Step 2, surface reaction)

W . S ⇌ k − D W k D W W + S (Step 3, desorption of water)

E . S ⇌ k − D E k D E E + S (Step 4, desorption of ether)

By assuming surface reaction is controlled step will get:

r S = κ K A 2 ( P A 2 − P E P W / K P ) ( 1 + K A P A + K W P W + K E P E + K I P I ) 2 (3)

REM model: It assumes that the surface reaction follows the Rideal-Eley mechanism in which one alcohol molecule in the gas phase reacts directly with another alcohol chemisorbed molecule in the presence of a vacant site adjacent to the chemisorbed product. The reaction sequence for this model is:

A + S ⇌ k − A k A A . S (Step 1, chemisorption of methanol)

A . S + A + S ⇌ k − S k S W . S + E . S (Step 2, surface reaction)

adsorbed ether and adsorbed water

W . S ⇌ k − D W k D W W + S (Step 3, desorption of water)

E . S ⇌ k − D E k D E E + S (Step 4, desorption of ether)

By assuming surface reaction is controlled step will get:

r S = κ K A ( P A 2 − P E P W / K P ) ( 1 + K A P A + K W P W + K E P E + K I P I ) 2 (4)

where r_S is a rate of reaction, κ is the reaction rate constant and K_i is materials adsorption equilibrium constant and P_i is the partial pressure of material where A, E, and W are Alcohol, ether, and water respectively.

As it is clearly shown, the kinetics of this reaction depends on the partial pressure of both products (water and DME), it is known [7] that DME concentration does not affect the reaction rate, most polar components (alcohol and water) are adsorbed considerably more than less polar components (ether), due to the marked difference in dielectric constants Linnekoski et al., 1997 [28]; Zhang and Datta, 1995 [29]. Therefore, ether contribution can be neglected in any kinetic equation, on the other hand, due to the absence of water in feed (i.e. pure methanol feed) its contributions can be neglected also [12] [30], therefore, Equations (3) and (4) could be reduced to:

r S = k K A 2 P 2 ( 1 + K A P A ) 2 (5)

r s = k K A P A 2 ( 1 + K A P A ) 2 (6)

To find which model better represents the kinetics of dehydration of methanol to DME, a series of experiments were done and listed in Table 3. Linear regression for the two rate expression Equations (5), (6) to find which one has the best fitting for the data was used. Regression showed that the L-H model (i.e. Equation (5)) has best fitting with the experimental data with excellent R² = 0.9997, the experimental results have been compared with those predicted by these models in Figure 4 with very well deviation (AD% = (Calc. − Predic./Predic) * 100). According to that, kinetic and adsorption parameters are calculated and listed in Table 4. The parameters of kinetic and adsorption with temperature dependence are shown in Figure 5 and Figure 6, The kinetic parameters were determined to be compatible with the Arrhenius Equation (7) with good straight-line plots, suggesting that the kinetic data were obtained during surface control and no major deactivation of the catalyst took place (Yue, 1984)

[31]. The value of activation energy E and pre-exponential factor A were calculated and it was 27.66 kJ/mole and 7.24 mol/kg.hr respectively. By comparing this value with the literature (Table 5), it was very low and that could be Attributed to the -SO₃H group network in polystyrene sulfonate which acts in methanol coordination as mentioned by Gates and co-workers [32] [33], Barbarossa [5] has also attributed the low activation energy to the ability of a propyl-sulfonic chain to be re-arranged around the methanol molecule.

k = A e − E R T (7)

where

A: Pre exponential factor

E: Activation energy

R: Gas constant

T: Rection temperature

A comprehensive numerical model of the entire reactor is now available with the obtained reaction rate function, According to Bird et al. [35] and the Packed Bed Tubler Reactor PBTR geometry shown in (Figure 7). The general mass balance equation can be presented in cylindrical coordination for z components as in (Equation (8)).

u s ∂ C i ∂ z − D r r ∂ ∂ r ( r ∂ C i ∂ r ) − D z ∂ 2 C i ∂ z 2 = − ρ B R i ( C , T ) (8)

where D_z and D_r denote the effective diffusivity in axial and radial directions respectively, ρ B and C i are catalyst density and material concentration respectively. Many assumptions to simplify this equation were given, according to Berčič [36] an adiabatic reactor can be well described as on dimensional model (i.e. no radial dispersion effect). However, this reactor could be assumed PFR (i.e. pseudo homogeneous reactor) according to Froment and Bischoff [37] and Rase [38] criteria for packed-bed reactors, these criteria ( L / d p > 50 and d t / d p > 10 where L, d_t and d_p are length of reactor, diameter of reactor tube and diameter of catalyst particle respectively) these confirm that reactor flow conditions are close to plug flow to achieve the isothermal reactor operation. In this investigation L / d p = 116.6 and d t / d p = 42.3 . By these assumptions we discard all transport resistance [22] and Equation (8) will be:

u s ∂ C i ∂ z = − ρ B R i ( C , T ) (9)

initial condition:

At z = 0 , C A = C A 0

Numerical method Runge-Kutta 4^th order model in MATLAB software was used to solve the first-order differential equation (Equation (9)) to obtain concentration profile in the reactor as shown in (Figure 8). The exit concentrations based on the solution of the numerical model (Equation (9)) of methanol were compared to those calculated experimentally and listed in (Table 6). The predicted and calculated results are in good agreement with a 0.32% average deviation.