Sit beside a mountain stream
See her waters rise
Listen to the pretty sound of music as she flies

("Mother Nature's Son," by the Beatles, 1968)

 

THE PROCESS VARIABLE LEVEL

The obvious prerequisite to understanding how the PV Pressure interfaces with the PV Level is to be knowed-up on what is meant by the phrase "PV Level."

The PV Level applies to a liquid level ...

and sometimes even a solid level  ... for example ...

The HMI screen of a DCS control system shown below displays an FCC Reactor (right) and its Catalyst Regenerator (left).

The PV Level of the catalyst in each vessel is represented as a "dipstick" outlined in blue with variable white light area which the Control Board Operator can easily interpret with one glance to be a current PV Level indication of 75% in both vessels.

The point is that the PV Level does not apply to gases or vapors.

A gas or vapor would have to condense into its liquid form before the PV Level would apply.

And the above statement provides the perfect segue to begin focusing on the two relationships between the PV Pressure and the PV Level.

 

TWO IMPORTANT PV PRESSURE + PV LEVEL RELATIONSHIPS

The PV Pressure has two important relationships with the PV Flowrate and the same can be said with respect to the PV Level.

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order already learned in PTOA Segment #146 that the liquid stored in any container creates a hydrostatic head and a Pressure Profile which is minimum at the liquid's surface and maximum at the bottom of the container.

In the future PTOA PV Level Focus Study Area, PTOA Readers and Students will learn how the hydrostatic head Pressure of a contained liquid can be used to monitor the changing PV Level in a tank.

Sneak Preview:

The tank is calibrated so that the maximum hydrostatic head Pressure will be indicated as a 100% Level (right side of above graphic) which declines linearly to 0% Level as the hydrostatic head likewise declines (left side of the above graphic).

The remainder of this PTOA Segment #160 is dedicated to exploring the second important PV Pressure + PV Level relationship which is a bit more complex as it only occurs when a "saturated vapor" occupies the vapor space above its corresponding "saturated liquid."

 

QUICKIE REVIEW OF SATURATED LIQUIDS AND THEIR VAPORS

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order were first introduced to the classic example of a saturated liquid and its vapor while learning how Saturated Steam is generated from Boiler Feed Water (BFW) in a Package Boiler (featured in PTOA #26).

So PTOA Readers and Students already know that steam is none other than the vapor/gas that hovers above the surface of its liquid form ... which is known as Boiler Feed Water (BFW).

In the Steam Drum, the BFW water droplets at the surface of the BFW are just as likely to vaporize into steam as the steam particles above the BFW surface are likely to condense back into BFW ...

Hence .. the criteria to meet the fancy scientific phrase ... "a saturated liquid in equilibrium with its saturated vapor" have been met!

And logically ...

Since there is the same amount of vaporizing and condensing going on between the saturated liquid and the saturated vapor ...

The PV Level of the BFW in the Steam Drum does not change at all. Like, Duh!

Of course there is itty, bitty caveat:

Were it not for the BFW being added to the Steam Drum to balance the flow of the Saturated Steam product exiting the Steam Drum ...

The PV Level of the Steam Drum most certainly would decrease!

With that important caveat understood, the Steam Drum of a successfully operating Package Boiler still provides a go-to example of "a saturated liquid/vapor system that is in equilibrium between the two phases."

But what happens when the PV Pressure of the Boiler is increased or decreased?

Guess what?

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order already know the answer to that question!

 

THE RELATIONSHIP BETWEEN THE PV PRESSURE AND THE PV LEVEL

PTOA Readers and Students just recently learned in PTOA Segment #157 that an increase in the PV Pressure over a boiling pot of water will require a simultaneous increase in the PV Temperature if the goal is to keep the water boiling ... aka changing state into its corresponding vapor composition.

Thus, in the absence of a simultaneous increase in the PV Temperature ...

PTOA Readers and Students can conclude the same outcome for ANY saturated system of water and vapor:

An increase in the PV Pressure will make it harder for water droplets to vaporize into Saturated Steam.

Since less BFW can vaporize into the vapor state, the PV Level in the Steam Drum will increase.

Likewise ...

When a decrease in the PV Pressure of the Steam Drum occurs with no compensating decrease in the PV Temperature ...

the water droplets feel less pressure above them and are more able to vaporize into the Saturated Steam phase thus decreasing the PV Level in the Steam Drum.

In other words, the PV Pressure + PV Level relationship of any saturated liquid/vapor system in equilibrium can be summarized:

WHEN PV PRESSURE ↑, THEN PV LEVEL ↑

WHEN PV PRESSURE ↓ , THEN THE PV LEVEL ↓

Spoiler Alert:

So ... who amongst the brilliant PTOA Readers and Students would be surprised to learn that the modern automatic control scheme on a Package Boiler:

• Controls the Steam Drum's PV Level.
• Also controls the BFW Flowrate into the Steam Drum.
• Monitors the (Mass!) Flowrate of the Saturated Steam that flows out of the Steam Drum. It is a Mass Flowrate instead of a Volumetric Flowrate because ... in English units ... the units of the PV Flowrate are in "pounds per hour."

 

THE RELATIONSHIP BETWEEN THE PV PRESSURE + PV LEVEL
APPLIES TO ANY LIQUID/VAPOR EQUILIBRIUM

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order have already learned what happens to a saturated vapor that is occupying the space above a saturated liquid when there is more than one component in the both phases.

In the very recent PTOA Segment #157, PTOA Readers and Students learned that a multi-component mixture of n-hexane and n-heptane could be physically separated from each other because of the variance between their Boiling Point Temperatures.

Therefore no PTOA Reader or Student will be surprised to learn that ...

In the absence of a corresponding increase in the PV Temperature applied to a multi-component saturated liquid/vapor system ...

An increase in the PV Pressure results in an increase in the PV Level because neither the n-hexane or the n-heptane can vaporize as easily as they could prior to the PV Pressure increase.

and vice versa ...

A decrease in the PV Pressure results in a decrease in the PV Level because both the n-hexane and n-heptane can vaporize more easily than they could prior to the PV Pressure decrease.

In summary ... the same rule applies for any multi component system that has a saturated liquid and its corresponding saturated vapor on the verge of vaporizing or condensing at equal rates ...

WHEN PV PRESSURE ↑, THEN PV LEVEL ↑

WHEN PV PRESSURE ↓ ,THEN PV LEVEL ↓

And that statement applies even when there are dozens and dozens of components in the liquid and vapor phases.

Control Board Operators Must Beware!

The change in the PV Level will not be instantaneous because it takes time for the liquid/vapor system to reach a new equilibrium.

 

Also ... since vapors/gases have much more space between particles ...

it takes a LOT of vapor/gas condensing to noticeably change the saturated liquid's level.

 

CONCLUSIONS OF THE PV PRESSURE + DIFFERENT PV FOCUS STUDIES

That's it!

PTOA Readers and Students have learned all about how the PV Pressure interacts with the PV Temperature, the PV Flowrate, and the PV Level ...

 

and are now ready to move on and learn about the process industry equipment that is purposely purchased and installed to create, maintain, or decrease the PV Pressure in an industrial complex.

 

PTOA Readers and Students who are reading the PTOA Segments in the intended sequential order are ready to move on because they possess a core competency with respect to the PV Pressure Fundamentals and understand the following PV Pressure relationships with:

• The PV Temperature. As the PV Pressure is increased so is the boiling point Temperature increased ... and vice versa.
• The PV (Volumetric) Flowrate:  Without a ΔP no flow can exist.
• The Fluid Velocity component of the PV (Volumetric) Flowrate: The PV Pressure ↔ PV Velocity Swap happens when the fluid flow area is restricted. The restriction causes an increase in a fluid Velocity and a corresponding decrease in the PV Pressure.
• The PV Level in a stored liquid: The hydrostatic head Pressure and Pressure Profile created by a stored liquid can be used to measure and monitor the PV Level.
• The PV Level in a Saturated Liquid/Vapor System: An increase in the PV Pressure results in an increase in the PV Level, and vice versa.

 

TAKE HOME MESSAGES: The phrase "PV Level" refers to a liquid ... and sometimes a granular solid ... but not to a gas or vapor.

There are two important PV Pressure + PV Level relationships.

#1. The hydrostatic head of a contained liquid creates a Pressure and Pressure Profile that can be used to measure and monitor the PV Level of the liquid that is contained.

#2. When a liquid/vapor system is in equilibrium:

• An increase in the PV Pressure will increase the PV Level and vice versa ...
• A decrease in the PV Pressure will decrease the PV Level.

PTOA Readers and Students can now predict how the PV Pressure will interact with the PV Temperature, PV Flowrate, and PV Level.

The next section in the PV Pressure Focus Study Area features the process industry equipment that is intentionally purchased and installed to increase, maintain, and decrease the PV Pressure in the processing complex.

©2017 PTOA Segment 0160
PTOA Process Variable Pressure Focus Study Area
PTOA PV Pressure Interrelationship with PV Level

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