BASIC CRYOGENICS

That Even I Can Understand

THIS MONTH WE REVIEW DENSITY AS IT RELATES TO CRYOGENS
Keith Hall

Density is a measure of mass per unit of volume. A dense object, such as a brick of lead, weighs much more than an equal-sized brick of a less dense substance, like styrofoam. To determine the density, you simply divide an object’s weight by its volume. This formula is expressed as ρ= m / V, where ρ is the object’s density; m is the object’s total mass); and V is the object’s total volume.

THE EFFECTS OF THERMAL EXPANSION & CONTRACTION ON DENSITY

Sidewalks are constructed with expansion joints because they expand in the heat of the summer and contract in the colder months of winter. This expansion and contraction affects density. To understand this, let’s compare the weight and size of a cold concrete block to a warm one.

A section of concrete from a sidewalk in Alaska, at - 40°, measures 12.0 inches tall by 12.0 inches across by 12.0 inches thick. The block weighs 100 pounds. Thus the density of this cold concrete block is 100 lbs/ft3.

If we re-measure the same block down to our warm laboratory in Houston, it now measures 12.1 inches tall by 12.1 inches across by 12.1 inches thick. If we resize the block, taking off an additional 1/10th of an inch from the three perpendicular sides (sawing it to its original Alaskan dimensions), we discover it now weighs only 95 pounds. The density of the warm concrete block is only 95 lbs/ft3.

DENSITY OF CRYOGENIC LIQUIDS

Cryogenic liquids also expand when hot and contract when cold. As heat leaks into a cryogenic vessel, the cryogen expands and the molecules become more active, bouncing around with more energy, causing them to move farther apart from each other. Hence, a warmer cryogen is less dense than a cooler cryogen. In contrast, as a cryogen looses heat, its molecules move more slowly and do not move very far apart, increasing density.

DENSITY, EXPANSION AND PRODUCT LOSS

In our industry, understanding these principles of density and thermal expansion are important to managing product.

Two cryogenic terms are used in this discussion. “Ullage” (or Head Space) is the vapor space above the liquid in a vessel. It is the portion of a vessel that is left unfilled with liquid to allow for thermal expansion of the liquid, and for vapor pressure control. A Trycock is a small liquid line that extends into the inner vessel of a cryogenic tank at a predetermined height. It is used to verify the proper fill level. The height of the trycock in the inner vessel varies by gas service and working pressure.

The trycock allows the operator to know when the vessel is full. As the liquid level rises during a fill, it eventually reaches and spews out the open trycock valve, signaling that the fill should be terminated. When liquid is no longer seen venting from the trycock valve, the proper ullage space is achieved and the trycock may be closed.

Given the maximum allowable working pressure (MAWP) of a vessel, the cryogenic design engineer calculates the proper trycock elevation in the tank. The height of the trycock in a tank is different for different gas species, as cryogens expand at different rates and vessels are designed to operate at different MAWPs. The trycock is located so that when filled to this level with cold liquid (e.g 0 psi), there will still be sufficient ullage space to accommodate the expansion of the liquid as it warms (if the product is left unused). Depending upon its volume capacity, the trycock height for a tank used to transport cryogens over the road, may be set lower than the height calculated to accommodate thermal expansion of the liquid. In this case the operator will know when to terminate the fill operation to keep the overall weight of the loaded vehicle under the legal road weight limit.

If the product is not used and the safety relief valve has not opened, the number of gas molecules in a vessel remains constant over time. However, the product will expand as it warms and the pressure in the vessel increases. Thus, a vessel filled with 100 gallons of cold liquid, can be drained of 105 gallons two weeks later (at the now higher pressure) because the liquid has expanded. For this reason a temperature probe is used in concert with a flow meter when delivering product. A totalizer records the flow volume and then compensates for the density of the liquid based on temperature, enabling a distributor to accurately invoice customers for the actual quantity of molecules delivered.

The properties of density and thermal expansion require that a cryogenic vessel never be over-filled. In a vessel completely full of liquid, the liquid expands as it warms and the pressure rises. This causes the safety relief valve to open and creates waste. These valves are designed to vent excess gas pressure. Unexpected venting liquid is not safe to be around and can damage the outside of the cryogenic vessel, by exposing it to cryogenic temperatures.

Keith Hall is the Customer Technical Support Manager at Cryogenic Vessel Alternatives, headquartered in Mont Belvieu, TX. He can be reached at khall@cvatanks.com, www.cvatanks.com, or by phone at 281-385-1204.