Equipment Sizing Based on Heuristics

Equipment Sizing

Size does matter James Cameron An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

An order-of-magnitude estimate is usually sufficient for preliminary design calculations.

This estimate has an error of 25-40%

We will consider equipment sizing heuristics for the following:

Vessels

Heat Transfer Equipment

Distillation and Absorption Columns Compressors, Pumps and Refrigeration

All these calculations require flow rate, temperatures, pressures and heat duties from the flowsheet and energy balance.

Vessel Sizing

Vessels include flash drums, storage tanks, decanters and some reactors. Unless specified otherwise by particular unit requirements, these will be sized by the following criteria:

Select vessel volume V based on a five-minute liquid holdup time with an equal volume added for vapor flow:

V = 2 [\frac{F_{L}τ}{ρ_{L}} ]

F_{L} liquid flow rate leaving the vessel
ρ_{L} density of liquid
τ residence time (5 minutes)

Vessels include flash drums, storage tanks, decanters and some reactors. Unless specified otherwise by particular unit requirements, these will be sized by the following criteria:

Select vessel volume V based on a five-minute liquid holdup time with an equal volume added for vapor flow:

V = 2 [\frac{F_{L}τ}{ρ_{L}} ]

F_{L} liquid flow rate leaving the vessel
ρ_{L} density of liquid
τ residence time (5 minutes)

Vessels include flash drums, storage tanks, decanters and some reactors. Unless specified otherwise by particular unit requirements, these will be sized by the following criteria:

Select vessel volume V based on a five-minute liquid holdup time with an equal volume added for vapor flow:

V = 2 [\frac{F_{L}τ}{ρ_{L}} ]

F_{L} liquid flow rate leaving the vessel
ρ_{L} density of liquid
τ residence time (5 minutes)

Vessels include flash drums, storage tanks, decanters and some reactors. Unless specified otherwise by particular unit requirements, these will be sized by the following criteria:

Select vessel volume V based on a five-minute liquid holdup time with an equal volume added for vapor flow:

V = 2 [\frac{F_{L}τ}{ρ_{L}} ]

F_{L} liquid flow rate leaving the vessel
ρ_{L} density of liquid
τ residence time (5 minutes)

Specification of the residence time is dictated by maintaining a liquid buffer for on/off switching times for pumps.

The aspect ratio \frac{L}{D} = 4.

This ratio is optimal if bottom and top heads are 4 times as expensive as sides.

If D > 4 ft size the unit as a horizontal vessel. This requires more space but costs less for structural support.

As a safety factor, choose the vessel (gauge) pressure to be 50% higher than the actual pressure from the material and energy balance.

For desired temperature range, consider the required material of construction.

Equipment Sizing Based on Heuristics – p.5/12

The aspect ratio \frac{L}{D} = 4.

This ratio is optimal if bottom and top heads are 4 times as expensive as sides.

If D > 4 ft size the unit as a horizontal vessel. This requires more space but costs less for structural support.

As a safety factor, choose the vessel (gauge) pressure to be 50% higher than the actual pressure from the material and energy balance.

For desired temperature range, consider the required material of construction.

Equipment Sizing Based on Heuristics – p.5/12

The aspect ratio \frac{L}{D} = 4.

This ratio is optimal if bottom and top heads are 4 times as expensive as sides.

If D > 4 ft size the unit as a horizontal vessel. This requires more space but costs less for structural support.

As a safety factor, choose the vessel (gauge) pressure to be 50% higher than the actual pressure from the material and energy balance.

For desired temperature range, consider the required material of construction.

Equipment Sizing Based on Heuristics – p.5/12

The aspect ratio \frac{L}{D} = 4.

This ratio is optimal if bottom and top heads are 4 times as expensive as sides.

If D > 4 ft size the unit as a horizontal vessel. This requires more space but costs less for structural support.

As a safety factor, choose the vessel (gauge) pressure to be 50% higher than the actual pressure from the material and energy balance.

For desired temperature range, consider the required material of construction.

Equipment Sizing Based on Heuristics – p.5/12

The aspect ratio \frac{L}{D} = 4.

This ratio is optimal if bottom and top heads are 4 times as expensive as sides.

If D > 4 ft size the unit as a horizontal vessel. This requires more space but costs less for structural support.

As a safety factor, choose the vessel (gauge) pressure to be 50% higher than the actual pressure from the material and energy balance.

For desired temperature range, consider the required material of construction.

Equipment Sizing Based on Heuristics – p.5/12

Heat Transfer Equipment

Consider a counter-current shell-and-tube heat exchanger.

Heat transfer area can be found from:

Q = UAΔT_{lm}

where

ΔT_{lm} = \frac{(T_{1} − t_{2}) − (T_{2} − t_{1})}{ln [\frac{T_{1} − t_{2}}{T_{2} − t_{1}} ]}

The overall heat transfer coefficient, U, can be estimated from heuristics or from standard references (e.g. Perry’s Handbook)

Equipment Sizing Based on Heuristics – p.6/12

Consider a counter-current shell-and-tube heat exchanger.

Heat transfer area can be found from:

Q = UAΔT_{lm}

where

ΔT_{lm} = \frac{(T_{1} − t_{2}) − (T_{2} − t_{1})}{ln [\frac{T_{1} − t_{2}}{T_{2} − t_{1}} ]}

The overall heat transfer coefficient, U, can be estimated from heuristics or from standard references (e.g. Perry’s Handbook)

Equipment Sizing Based on Heuristics – p.6/12

Consider a counter-current shell-and-tube heat exchanger.

Heat transfer area can be found from:

Q = UAΔT_{lm}

where

ΔT_{lm} = \frac{(T_{1} − t_{2}) − (T_{2} − t_{1})}{ln [\frac{T_{1} − t_{2}}{T_{2} − t_{1}} ]}

The overall heat transfer coefficient, U, can be estimated from heuristics or from standard references (e.g. Perry’s Handbook)

Equipment Sizing Based on Heuristics – p.6/12

Consider a counter-current shell-and-tube heat exchanger.

Heat transfer area can be found from:

Q = UAΔT_{lm}

where

ΔT_{lm} = \frac{(T_{1} − t_{2}) − (T_{2} − t_{1})}{ln [\frac{T_{1} − t_{2}}{T_{2} − t_{1}} ]}

The overall heat transfer coefficient, U, can be estimated from heuristics or from standard references (e.g. Perry’s Handbook)

Equipment Sizing Based on Heuristics – p.6/12

If there is a phase change, the overall heat transfer coefficient, U, changes.

This case is modeled as two heat exchangers in series, each with a different U and A.

A_{vap} = \frac{Q_{vap}}{U_{vap}ΔT_{lm}^{a}}

where ΔT_{lm}^{a} = \frac{(T_{1} − t_{2}) − (T_{c} − t_{3})}{ln [\frac{T_{1} − t_{2}}{T_{c} − t_{3}} ]}

A_{con} = \frac{Q_{con}}{U_{con}ΔT_{lm}^{b}}

where ΔT_{lm}^{b} = \frac{(T_{c} − t_{3}) − (T_{2} − t_{1})}{ln [\frac{T_{c} − t_{3}}{T_{2} − t_{1}} ]}

We choose 10, 000 sq. ft. as the maximum exchanger area. If more area is required, multiple heat exchangers in parallel are used.

Equipment Sizing Based on Heuristics – p.7/12

If there is a phase change, the overall heat transfer coefficient, U, changes.

This case is modeled as two heat exchangers in series, each with a different U and A.

A_{vap} = \frac{Q_{vap}}{U_{vap}ΔT_{lm}^{a}}

where ΔT_{lm}^{a} = \frac{(T_{1} − t_{2}) − (T_{c} − t_{3})}{ln [\frac{T_{1} − t_{2}}{T_{c} − t_{3}} ]}

A_{con} = \frac{Q_{con}}{U_{con}ΔT_{lm}^{b}}

where ΔT_{lm}^{b} = \frac{(T_{c} − t_{3}) − (T_{2} − t_{1})}{ln [\frac{T_{c} − t_{3}}{T_{2} − t_{1}} ]}

We choose 10, 000 sq. ft. as the maximum exchanger area. If more area is required, multiple heat exchangers in parallel are used.

Equipment Sizing Based on Heuristics – p.7/12

If there is a phase change, the overall heat transfer coefficient, U, changes.

This case is modeled as two heat exchangers in series, each with a different U and A.

A_{vap} = \frac{Q_{vap}}{U_{vap}ΔT_{lm}^{a}}

where ΔT_{lm}^{a} = \frac{(T_{1} − t_{2}) − (T_{c} − t_{3})}{ln [\frac{T_{1} − t_{2}}{T_{c} − t_{3}} ]}

A_{con} = \frac{Q_{con}}{U_{con}ΔT_{lm}^{b}}

where ΔT_{lm}^{b} = \frac{(T_{c} − t_{3}) − (T_{2} − t_{1})}{ln [\frac{T_{c} − t_{3}}{T_{2} − t_{1}} ]}

We choose 10, 000 sq. ft. as the maximum exchanger area. If more area is required, multiple heat exchangers in parallel are used.

Equipment Sizing Based on Heuristics – p.7/12

If there is a phase change, the overall heat transfer coefficient, U, changes.

This case is modeled as two heat exchangers in series, each with a different U and A.

A_{vap} = \frac{Q_{vap}}{U_{vap}ΔT_{lm}^{a}}

where ΔT_{lm}^{a} = \frac{(T_{1} − t_{2}) − (T_{c} − t_{3})}{ln [\frac{T_{1} − t_{2}}{T_{c} − t_{3}} ]}

A_{con} = \frac{Q_{con}}{U_{con}ΔT_{lm}^{b}}

where ΔT_{lm}^{b} = \frac{(T_{c} − t_{3}) − (T_{2} − t_{1})}{ln [\frac{T_{c} − t_{3}}{T_{2} − t_{1}} ]}

We choose 10, 000 sq. ft. as the maximum exchanger area. If more area is required, multiple heat exchangers in parallel are used.

Equipment Sizing Based on Heuristics – p.7/12

If there is a phase change, the overall heat transfer coefficient, U, changes.

This case is modeled as two heat exchangers in series, each with a different U and A.

A_{vap} = \frac{Q_{vap}}{U_{vap}ΔT_{lm}^{a}}

where ΔT_{lm}^{a} = \frac{(T_{1} − t_{2}) − (T_{c} − t_{3})}{ln [\frac{T_{1} − t_{2}}{T_{c} − t_{3}} ]}

A_{con} = \frac{Q_{con}}{U_{con}ΔT_{lm}^{b}}

where ΔT_{lm}^{b} = \frac{(T_{c} − t_{3}) − (T_{2} − t_{1})}{ln [\frac{T_{c} − t_{3}}{T_{2} − t_{1}} ]}

We choose 10, 000 sq. ft. as the maximum exchanger area. If more area is required, multiple heat exchangers in parallel are used.

Equipment Sizing Based on Heuristics – p.7/12

Distillation Column

1. Determine actual number of trays and reflux ratio.

2. Calculate column diameter and height as follows:

To determine the diameter, design the column to run at 80% of the flooding velocity. At the flooding velocity, the vapor flow rate is so high that no net liquid flow occurs and entrainment begins.

1. Determine actual number of trays and reflux ratio.

2. Calculate column diameter and height as follows:

To determine the diameter, design the column to run at 80% of the flooding velocity. At the flooding velocity, the vapor flow rate is so high that no net liquid flow occurs and entrainment begins.

1. Determine actual number of trays and reflux ratio.

2. Calculate column diameter and height as follows:

To determine the diameter, design the column to run at 80% of the flooding velocity. At the flooding velocity, the vapor flow rate is so high that no net liquid flow occurs and entrainment begins.

1. Determine actual number of trays and reflux ratio.

2. Calculate column diameter and height as follows:

To determine the diameter, design the column to run at 80% of the flooding velocity. At the flooding velocity, the vapor flow rate is so high that no net liquid flow occurs and entrainment begins.

1. Determine actual number of trays and reflux ratio.

2. Calculate column diameter and height as follows:

To determine the diameter, design the column to run at 80% of the flooding velocity. At the flooding velocity, the vapor flow rate is so high that no net liquid flow occurs and entrainment begins.

1. Determine actual number of trays and reflux ratio.

2. Calculate column diameter and height as follows:

To determine the diameter, design the column to run at 80% of the flooding velocity. At the flooding velocity, the vapor flow rate is so high that no net liquid flow occurs and entrainment begins.

Calculate dimensionless flow parameter F_{lv}

F_{lv} = \frac{L′}{V′} (\frac{ρ_{g}}{ρ_{l}} )^{0.5}

where \frac{L′}{V′} is the liquid/gas mass ratio at the point of consideration and \frac{ρ_{g}}{ρ_{l}} is the gas/liquid density ratio.

Calculate capacity parameter C_{sb,f} from the chart below for a given tray spacing:

Calculate linear flooding velocity (ft/s) from

U_{nf} = C_{sb,f} (\frac{ρ_{l} − ρ_{g}}{ρ_{g}} )^{0.5} (\frac{20}{σ})

where ρ_{g} and ρ_{l} are the gas and liquid mass densities and σ is the liquid surface tension in dynes/cm.

Calculate area of cross-section from A = \frac{V′}{0.8U_{nf}ϵρ_{g}}

where ϵ is the fraction of area available for vapor flow (0.6 for bubble cap trays and 0.75 for sieve trays). Calculate column diameter from

D = \sqrt{\frac{4A}{π}}

U_{nf} = C_{sb,f} (\frac{ρ_{l} − ρ_{g}}{ρ_{g}} )^{0.5} (\frac{20}{σ})

where ρ_{g} and ρ_{l} are the gas and liquid mass densities and σ is the liquid surface tension in dynes/cm.

Calculate area of cross-section from A = \frac{V′}{0.8U_{nf}ϵρ_{g}}

where ϵ is the fraction of area available for vapor flow (0.6 for bubble cap trays and 0.75 for sieve trays). Calculate column diameter from

D = \sqrt{\frac{4A}{π}}

U_{nf} = C_{sb,f} (\frac{ρ_{l} − ρ_{g}}{ρ_{g}} )^{0.5} (\frac{20}{σ})

where ρ_{g} and ρ_{l} are the gas and liquid mass densities and σ is the liquid surface tension in dynes/cm.

Calculate area of cross-section from A = \frac{V′}{0.8U_{nf}ϵρ_{g}}

where ϵ is the fraction of area available for vapor flow (0.6 for bubble cap trays and 0.75 for sieve trays). Calculate column diameter from

D = \sqrt{\frac{4A}{π}}

U_{nf} = C_{sb,f} (\frac{ρ_{l} − ρ_{g}}{ρ_{g}} )^{0.5} (\frac{20}{σ})

where ρ_{g} and ρ_{l} are the gas and liquid mass densities and σ is the liquid surface tension in dynes/cm.

Calculate area of cross-section from A = \frac{V′}{0.8U_{nf}ϵρ_{g}}

where ϵ is the fraction of area available for vapor flow (0.6 for bubble cap trays and 0.75 for sieve trays). Calculate column diameter from

D = \sqrt{\frac{4A}{π}}

The number of actual trays is given by \frac{N_{T}}{η} where the efficiency is assumed to be 80%. Assume a tray spacing of 24′′ to calculate column height. Calculate heat duties for condenser and reboiler from energy balance.

The number of actual trays is given by \frac{N_{T}}{η} where the efficiency is assumed to be 80%. Assume a tray spacing of 24′′ to calculate column height. Calculate heat duties for condenser and reboiler from energy balance.