Problem 30-4E. The "spinning disk" reactor is often used to carry out chemical reactions under controlled hydrodynamic conditions. Consider the highly-simplified process shown in Figure 30-4E, where one spinning disk is mounted within a chamber equipped a single gas inlet and outlet stream. The surface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneous reaction where gaseous reactant A goes to gaseous product B (A →B on the surface). Since the reaction is presumed instantaneous, the rate process is mass transfer limited, and the concentration of A at the catalyst surface is essentially zero (CAS≈ 0). As the disk spins, a hydrodynamic boundary layer is created between the surface and the bulk gas, and the spinning motion also mixes the bulk gas to create a well-mixed environment within the chamber. The process is carried out at 600 K and 2.0 atm, where 20 cm³/sec of feed gas (also at conditions of 600 K and 2.0 atm) containing 5.0 mole % of reactant A and 95 mole% of inert carrier gas C are delivered to the chamber. The diameter of the disk is 10 cm, and the volume of the chamber is 2000 cm³. Potentially relevant properties for A, B, and C are provided below: Selected properties of gaseous species A, B, and C at T = 600 K and P = 2.0 atm. molecular diffusion coefficient DAC = 0.300 cm²/sec kinematic viscosity VA = 0.520 cm²/sec DBC = 0.235 cm²/sec VB = 0.300 cm2²/sec DAB=0.219 cm²/sec Vc = 0.520 cm²/sec (a) A mass transfer coefficient of ke = 1.345 cm/sec for reactant A in the gas mixture is desired. What is the required spinning disk rotation rate, oo, in units of rev/sec? Is the mass-transfer process for reactant A within the boundary layer best described as a dilute unimolecular diffusion process (UMD) process, or an equimolar counter-diffusion (EMCD) process? Justify your reasoning. (b) Develop a steady-state process material balance model, in fully algebraic form (no numbers), to predict the outlet concentration, CA. (c) Determine the outlet concentration, CA, based on kc = 1.345 cm/sec. If the natation of the dial in i which of the fallami

Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
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**Problem 30-4E: The Spinning Disk Reactor**

The "spinning disk" reactor is often utilized for conducting chemical reactions under controlled hydrodynamic conditions. Consider the highly-simplified process shown in **Figure 30-4E** (not provided here). This process involves one spinning disk mounted within a chamber equipped with a single gas inlet and outlet stream. The surface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneous reaction where gaseous reactant **A** is converted into gaseous product **B** (**A → B** on the surface). Given the reaction's presumed instantaneous nature, the reaction rate process is mass transfer limited, and the concentration of **A** at the catalyst surface is essentially zero (**C_AS ≈ 0**). During disk spinning, a hydrodynamic boundary layer forms between the surface and bulk gas, while the spinning motion also creates a well-mixed environment within the chamber. The process is carried out at **600 K** and **2.0 atm**, involving 20 cm³/sec of feed gas (20 cm³/sec at 600 K and 2.0 atm), of which 5.0 mole% is reactant **A** and 95 mole% is inert carrier gas **C** delivered into the chamber. The diameter of the disk is **10 cm**, and the chamber has a volume of 2000 cm³. Potentially relevant properties of gaseous species **A**, **B**, and **C** are provided below:

**Selected properties of gaseous species A, B, and C at T = 600 K and P = 2.0 atm.**
| Property                        |    A                    |  B                       |  C                  |
|---------------------------------|-------------------------|--------------------------|---------------------|
| molecular diffusion coefficient | D_AC = 0.300 cm²/sec    | D_BC = 0.235 cm²/sec     | D_AB = 0.219 cm²/sec |
| kinematic viscosity             | ν_A = 0.520 cm²/sec     | ν_B = 0.300 cm²/sec      | ν_C = 0.520 cm²/sec  |

### Questions:

(a) **Mass Transfer Coefficient Calculation:**

Determine the required spinning disk rotation rate, ω, in units of rev/sec, to achieve a mass transfer coefficient of **k_c = 1
Transcribed Image Text:**Problem 30-4E: The Spinning Disk Reactor** The "spinning disk" reactor is often utilized for conducting chemical reactions under controlled hydrodynamic conditions. Consider the highly-simplified process shown in **Figure 30-4E** (not provided here). This process involves one spinning disk mounted within a chamber equipped with a single gas inlet and outlet stream. The surface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneous reaction where gaseous reactant **A** is converted into gaseous product **B** (**A → B** on the surface). Given the reaction's presumed instantaneous nature, the reaction rate process is mass transfer limited, and the concentration of **A** at the catalyst surface is essentially zero (**C_AS ≈ 0**). During disk spinning, a hydrodynamic boundary layer forms between the surface and bulk gas, while the spinning motion also creates a well-mixed environment within the chamber. The process is carried out at **600 K** and **2.0 atm**, involving 20 cm³/sec of feed gas (20 cm³/sec at 600 K and 2.0 atm), of which 5.0 mole% is reactant **A** and 95 mole% is inert carrier gas **C** delivered into the chamber. The diameter of the disk is **10 cm**, and the chamber has a volume of 2000 cm³. Potentially relevant properties of gaseous species **A**, **B**, and **C** are provided below: **Selected properties of gaseous species A, B, and C at T = 600 K and P = 2.0 atm.** | Property | A | B | C | |---------------------------------|-------------------------|--------------------------|---------------------| | molecular diffusion coefficient | D_AC = 0.300 cm²/sec | D_BC = 0.235 cm²/sec | D_AB = 0.219 cm²/sec | | kinematic viscosity | ν_A = 0.520 cm²/sec | ν_B = 0.300 cm²/sec | ν_C = 0.520 cm²/sec | ### Questions: (a) **Mass Transfer Coefficient Calculation:** Determine the required spinning disk rotation rate, ω, in units of rev/sec, to achieve a mass transfer coefficient of **k_c = 1
## Spinning Disk Reactor

### Mass Transfer Performance
The performance of the spinning disk mass transfer is described by the Levich correlation, given by:

\[ Sh = 0.62 \text{Re}^{1/2} \text{Sc}^{1/3} \]

with \[ \text{Re} = \frac{\omega d^2}{\nu} \]

### Characteristic Length
The "characteristic length" for the spinning disk is its diameter, \( d \). The angular rotation rate \( \omega \) is defined as radians per unit of time. There are \( 2\pi \) radians in one revolution (rev).

### Apparatus and Operational Details

The diagram depicts a spinning disk reactor, which operates under the following conditions:
- Temperature: 600 K
- Pressure: 2.0 atm
- Gas is well mixed
- The system is equipped with a rotating disk

### Parameters
- **Inlet flow rate (\(v_0\))**: 20 cm\(^3\)/sec
- **Mole fractions at inlet**:
  - \( y_{A,0} = 0.05 \)
  - \( y_{B,0} = 0.0 \)
  - \( y_{C,0} = 0.95 \)
- Concentration at the inlet \([C_{A,0}]\)

The question (\( ? \)) marks the unknown concentration \([C_A]\) at a specific point in the reactor.

### Components and Phases
- **Rotating Disk**: The disk, with a diameter \( d = 10 \) cm, plays a crucial role in the mixing process.
- **Catalytic Surface**: This is where the reaction occurs. The concentration at the catalytic surface is \( C_{As} \approx 0 \), indicating a near-zero concentration due to the reaction consumption.
- **Boundary Layer**: Represented on the right side, it indicates a region where concentration changes from \( C_A \) at point B to \( C_{As} \approx 0 \) at the catalytic surface.

### Graphical Explanation
The diagram outlines the movement and reaction of gas on the spinning disk:
- With the reactant A concentration \(C_A\) entering the boundary layer at location A and reaching near zero at the catalytic surface.
- The angular velocity and rotation are depicted by the arrows
Transcribed Image Text:## Spinning Disk Reactor ### Mass Transfer Performance The performance of the spinning disk mass transfer is described by the Levich correlation, given by: \[ Sh = 0.62 \text{Re}^{1/2} \text{Sc}^{1/3} \] with \[ \text{Re} = \frac{\omega d^2}{\nu} \] ### Characteristic Length The "characteristic length" for the spinning disk is its diameter, \( d \). The angular rotation rate \( \omega \) is defined as radians per unit of time. There are \( 2\pi \) radians in one revolution (rev). ### Apparatus and Operational Details The diagram depicts a spinning disk reactor, which operates under the following conditions: - Temperature: 600 K - Pressure: 2.0 atm - Gas is well mixed - The system is equipped with a rotating disk ### Parameters - **Inlet flow rate (\(v_0\))**: 20 cm\(^3\)/sec - **Mole fractions at inlet**: - \( y_{A,0} = 0.05 \) - \( y_{B,0} = 0.0 \) - \( y_{C,0} = 0.95 \) - Concentration at the inlet \([C_{A,0}]\) The question (\( ? \)) marks the unknown concentration \([C_A]\) at a specific point in the reactor. ### Components and Phases - **Rotating Disk**: The disk, with a diameter \( d = 10 \) cm, plays a crucial role in the mixing process. - **Catalytic Surface**: This is where the reaction occurs. The concentration at the catalytic surface is \( C_{As} \approx 0 \), indicating a near-zero concentration due to the reaction consumption. - **Boundary Layer**: Represented on the right side, it indicates a region where concentration changes from \( C_A \) at point B to \( C_{As} \approx 0 \) at the catalytic surface. ### Graphical Explanation The diagram outlines the movement and reaction of gas on the spinning disk: - With the reactant A concentration \(C_A\) entering the boundary layer at location A and reaching near zero at the catalytic surface. - The angular velocity and rotation are depicted by the arrows
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