Module design

In order to determine the costs of the various components, they must first be designed. For this purpose, this section presents the various equations for calculating the component sizes for the methanol plant. The design is based on the equations and assumptions of BIEGLER et al. (1997, p. 111ff), since these allow a fast and solid determination of the required capacity or size parameters. For the calculation, various process variables must be known, which can be taken from the results of the process simulation in Aspen Plus. In the following sections, the equations for the calculation of the heat exchangers, the reactors and the separation vessels are presented.

Heat exchangers

Counter-current shell-and-tube heat exchangers are assumed, since they are used as a standard in the chemical industry (PETERS et al., 2003, p. 642). An important parameter for these heat exchangers is the heat transfer surface A, which can be calculated using equation 3.1 (BIEGLER et al., 1997, p. 113).

𝐴 = ^𝑄̇

𝑘⋅Δ𝑇_ln (3.1)

Here, 𝑄̇ is the heat flow and can be taken from the results of the process simulation.

k is the heat transfer coefficient, which is a proportionality factor for the heat transfer at an interface. It varies according to the transfer conditions, whereby liquid states provide particularly good conditions, which is expressed by high k values.

The values for different transmission conditions are shown in Table 3.1 and are taken from the VDI heat atlas (KIND et al., 2013, p. Cc 1). The upper k values of the respective category are chosen, since particularly suitable transmission conditions within the pipes are assumed. Δ𝑇_ln is the mean logarithmic temperature difference and is calculated using equation 3.2 (BIEGLER et al., 1997, p. 113).

Δ𝑇_ln =^{(𝑇1,in−𝑇2,out)−(𝑇2,in−𝑇1,out)}

𝑙𝑛(^𝑇_𝑇^{1,in−𝑇2,out}

2,in−𝑇1,out) (3.2)

Table 3.1: Typical heat transfer coefficients for shell-and-tube heat exchangers, condensers and evaporators depending on the type of transfer according to VDI heat atlas (KIND et al., 2013, p. Cc 1).

Construction design Transmission condition Estimated k-value (W/m²K) Shell-and-tube heat

exchanger

Gas-gas 5 to 35

Gas-liquid 15 to 70

Liquid-liquid 150 to 1200 Shell-and-tube condenser

Cooling water-organic

vapours 300 to 1200

Shell-and-tube evaporator Heating steam-thin liquids 600 to 1700

Here, Tin are the inlet temperatures and Tout the outlet temperatures of the two flows.

The temperature differences of the two media on both sides of the heat exchanger are put in proportion to each other. To illustrate this, the currents are shown in Figure 3.2 on a schematic diagram of a heat exchanger. The heat exchanger itself is displayed as a black box. The temperatures required for the calculation of the mean logarithmic temperature difference occur each at the inlet and outlet of both flows. Thereby, the two flows are not mixed in the heat exchanger, but indirect transfer takes place. One medium passes through the tubes in the heat exchanger, the other is fed into the casing through the heat exchanger, with the two media flowing in counter current. The heat is transferred via the lateral surface (Mantelfläche) of the pipes. The hot medium is cooled and the cold medium is heated. In this case, a minimum temperature difference of 10 K is applied to both sides of the heat exchanger (PETERS et al., 2003, p. 970).

Figure 3.2: Schematic diagram of a heat exchanger as black box with the two media 1 and 2.

Caption: own creation.

Using the results of the process simulation and the VDI heat atlas (KIND et al., 2013, p. Cc 1), the heat transfer surface A of the shell-and-tube heat exchangers can be calculated. Furthermore, this calculation can be used to calculate the condenser and reboiler of a column, since these are also heat exchangers. The usual heat transfer coefficients for these heat exchangers can also be found in Table 3.1.

In addition, the calculation of the heat transfer surface is required for the calculation

of the volume of a tube bundle reactor, since the principle of a heat exchanger is also effective there [46], which is described in more detail in the following section.

Reactor

For the calculation of the reactor, a standing tube bundle reactor is assumed analogous to the standard design of methanol reactors. This reactor is similar in its design to a shell-and-tube heat exchanger. It also consists of tubes which are placed in a casing and the heat transfer takes place between the fluids in the tubes and the housing. The difference to the shell-and-tube heat exchanger is that there are catalyst pellets inside the tubes, where the reaction takes place. The lateral surface is filled by a cooling medium that regulates the reaction temperature. In contrast to a normal tube bundle heat exchanger, the tubes have a larger diameter so that sufficient space for the catalyst pellets is available. In addition, the reactor is designed vertically and flows from bottom to top to prevent the catalyst pellets from being washed out. (OTT et al., 2012, p. 10f)

For the design of the reactor, the reactor volume must be determined. For a tube bundle reactor, the volume of the vessel VReactor,vessel, which is determined via the space velocity, and the volume of the tubes VTubes must also be determined, as described by OTTO (2015). Thus, the required total volume of the reactor VReactor,total can be determined via equation 3.3.

𝑉Reactor,total= 𝑉_Tubes+ 𝑉Reactor,vessel (3.3)

To calculate the pipe volume, the heat transfer surface A of the tubes is first determined using equation 3.1. This corresponds to the outer surface of the tubes.

Then, the volume of the tubes VTubes can be determined by means of the outside pipe diameter Da using equation 3.4.

𝑉Tubes=^𝐴⋅𝐷₄^a (3.4)

The volume of the vessel VReactor,vessel is determined by means of the catalyst volume VCat and the space velocity, which is the reciprocal of the retention time. The catalyst porosity ϵ is assumed to be 0.5, which gives equation 3.5 (BIEGLER et al., 1997, p. 118).

𝑉Reactor,vessel=^𝑉Cat

1−ϵ=^2⋅𝑛̇

𝑠⋅ρ (3.5)

Here, 𝑛̇ is the material flow and ρ the molar density under standard conditions. The values of material flow and density can be determined by means of the process simulation.

Separator vessels

For the design of the vertical vessels, their volumes VB are calculated using (BIEGLER et al., 1997, p. 112)

𝑉_B= 2 ⋅^𝑚̇_ρ^𝐿⋅τ

L , (3.6)

where 𝑚̇_𝐿 is the liquid mass flow at the container outlet, τ the retention time and ρL the liquid density. The values for the mass flow and its density can be taken from the results of the process simulation.