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Chapter 3: Problem 50

The chemical reactor shown below has a cover that is held in place by a series of bolts. The cover is made of stainless steel ( \(\mathrm{SG}=8.0\) ), is 3 inches thick, has a diameter of 24 inches, and covers and seals an opening 20 inches in diameter. During turnaround, when the reactor is taken out of service for cleaning and repair, the cover was removed by an operator who thought the reactor had been depressurized using a standard venting procedure. However, the pressure gauge had been damaged in an earlier process upset (the reactor pressure had exceeded the upper limit of the gauge), and instead of being depressurized completely, the vessel was under a gauge pressure of 30 psi. (a) What force ( \(\left(\mathrm{b}_{\mathrm{f}}\right)\) were the bolts exerting on the cover before they were removed? (Hint: Don't forget that a pressure is exerted on the top of the cover by the atmosphere.) What happened when the last bolt was removed by the operator? Justify your prediction by estimating the initial acceleration of the cover upon removal of the last bolt. (b) Propose an alteration in the turnaround procedure to prevent recurrence of an incident of this kind.

Short Answer

Expert verified
The force exerted by the bolts was 86,155 N. If the last bolt was removed, the cover would fly off rapidly with an initial acceleration of about 6333 m/s^2. To prevent this incident, verify the pressure inside the reactor using a secondary, separate gauge before dismounting the cover.

Step by step solution

01

Calculate the force exerted by the bolts

Use the formula \( F = P \cdot A \) to calculate the force exerted on the cover. Here, \( P \) is the pressure (30 psi) plus atmospheric pressure (14.7 psi), and \( A \) is the area covered by the bolts, which is the area of the circle with diameter 20 inches. Convert the psi to \( N/m^2 \) before calculation. Make sure you calculate the area in \( m^2 \).
02

Predict what would happen if the last bolt was removed

The force of pressure inside the reactor would make the cover fly off rapidly. We will need to calculate the net force, which is the force from the pressure minus the weight of the cover. The weight of the cover can be calculated by \( W = \text{Volume} \cdot \text{Density} \cdot g \), where the density is \( 8000 \times 1000 \, kg/m^3 \). The acceleration is then given by \( a = F_{\text{net}}/m \), with \( m \) the mass of the cover.
03

Propose a preventative measure

Implementing a safety measure that includes verifying the pressure inside the reactor with an additional, separate gauge before dismounting the cover could prevent recurrence of this incident in the future.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Force Calculation in Chemical Engineering
Force calculation is a critical aspect of chemical engineering that ensures the stability and integrity of various apparatuses, including chemical reactors. In the context of the exercise, the force the bolts were exerting to keep the cover in place amidst the internal pressure can be found utilizing the formula for force, which is the product of pressure and area, namely, \( F = P \cdot A \).

To calculate this correctly, the pressure included is the sum of the internal pressure in the reactor and the atmospheric pressure, while the area is the surface area of the cover that the bolts are securing. Careful unit conversion is necessary to ensure accuracy in these calculations. Pressure, commonly measured in pounds per square inch (psi), should be converted to pascals (Pa) in SI units for consistency, while inches must be converted to meters for the area calculation. In practice, these force calculations are used to design covers and bolts that can withstand expected internal pressures, including safety factors to prevent failures.
Reactor Depressurization Procedures
Reactor depressurization is a critical operation performed to ensure safe access to the internals for maintenance, inspection, or cleaning as in the case of turnaround. The procedure typically involves lowering the internal pressure to atmospheric levels systematically to avoid abrupt pressure changes that could endanger the maintenance crew or damage equipment.

In the exercise scenario, a damaged pressure gauge resulted in an inaccurate reading, misleading the operator into thinking the system was fully depressurized. To improve upon this, the procedure should include using redundant pressure gauges to confirm depressurization, and installing safety protocols such as lockout-tagout (LOTO) systems to prevent premature access. Additionally, training operators to recognize the signs of improper depressurization, such as listening for ongoing release of pressure, can significantly enhance safety.
Pressure and Force Relationship
Understanding the relationship between pressure and force is fundamental in chemical engineering and fluid mechanics. Pressure is the force exerted by a fluid per unit area and is expressed as \( P = \frac{F}{A} \), where \( P \) is pressure, \( F \) is force, and \( A \) is the area over which the force is applied. Conversely, to find the force from a known pressure, we rearrange the equation to \( F = P \cdot A \).

In the given exercise, the internal pressure within the reactor exerts a force on the cover, which is counteracted by the bolts. When the pressure inside the reactor is greater than the atmospheric pressure outside, there is a net outward force. If this force exceeds the holding capacity of the bolts, the cover may detach suddenly, as would have occurred when the last bolt was removed. The effective safety design of reactors, such as bolt strength and cover material, relies heavily on accurate calculations based on this relationship.

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Most popular questions from this chapter

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