A previous post talked about venting through a gooseneck, where I just assumed the amount of venting had already been figured out. This time I want to go into more details of the API-2000 method for venting, the assumptions, and the models.

(The following deals with the 2014 edition of the code)

API 2000 breaks down venting into two broad categories: normal venting and emergency venting. Normal venting is, as you would expect, the venting required during normal operation of the tank. Emergency venting is commonly the fire case, that is when the tank is on fire, everything is on fire, omg fire.

### Normal Venting -- Filling and Emptying

When the tank is being emptied, the outflowing fluid draws a vacuum. As a first approximation you can assume the volume of fluid removed must be filled with an equivalent volume of air. Much like when pulling a piston out of a syringe. The syringe draws in air to replace the volume previously filled by the piston.

In API 2000 the assumption is that the amount of air needed, in Nm^{3}/h, is equal to the max out-flow, in m^{3}/h.

When a tank is being filled the same logic applies, but with the added wrinkle that if the fluid is hot it can be adding vapour to the tank as well as displacing air. API-2000 has a simple: the normal venting rate is, in Nm^{3}/h, is equal to the max in-flow, in m^{3}/h. However if the vapour pressure of the fluid at the max operating temperature is greater than 5kPa then double that.

### Normal Venting -- Thermal Breathing

Thermal breathing is a result of the environment around the tank, in a hot environment the fluid inside the tank will expand and in a cold environment the fluid inside the tank will contract. How much depends upon both the environment and the fluid inside the tank.

For the sake of thermal out-breathing, the hot-environment tank, a series of models were development with the following general characteristics:

- tank is full of air (ideal gas)
- heat flux only from the roof and tank walls, with no insulation
- natural convection inside the tank, $ h = 2 \frac{W}{m*K} $
- natural convection outside the tank, $ h = 2 \frac{W}{m*K} $
- max insolation, with emissivity $ \epsilon = 0.6 $

The tanks start at a uniform 15C and heat to a uniform ambient temperature. Tanks of various sizes were modeled and the the results correlated to give the formula: $$ \dot{V}_{OT} = Y \cdot R_{i} \cdot V_{tk}^{0.9} $$

With thermal in-breathing, the cold-environment tank, the models are very similar:

- tank is full of air (ideal gas)
- heat flux only from the roof and tank walls, with no insulation
- natural convection inside the tank, $ h = 2 \frac{W}{m*K} $
- natural convection and rain outside the tank, $ h = 5000 \frac{W}{m*K} $
- thermal radiation, with emissivity $ \epsilon = 0.6 $

The tanks start at a uniform 55C and cool to a uniform ambient temperature of 15C. The resulting correlation to the tank volume is: $$ \dot{V}_{OT} = C \cdot R_{i} \cdot V_{tk}^{0.7} $$

Having the tanks full of air is a good "worst-case" thermal expansion of gases is far greater than liquids, typically (similarly an ideal gas model for air adds to the worst-case).

The parameters *C* and *Y* are correction factors to correct for location. The degree of insolation and the average ambient temperature are dependent upon latitude, and these factors correct for the actual latitude of the tank relative to the models. This is reasonable, however there is a lot of variation in ambient temperature and insolation at given latitudes, the climate is just more complicated than that. The *C* parameter also corrects for vapourization if the fluid is similar to hexane but kinda not-really.

The factor *R _{i}* corrects for the presence of insulation and other changes to the heat transfer parameters.

### Emergency Venting

Emergency venting is typically calculated assuming a pool fire of flame height 9.14m (30 ft).

First step is to calculate the wetted surface area. This is the area of the tank with fluid on the inside and fire on the outside. Usually the floor is neglected since tanks tend to rest directly on foundations or the ground, and since the fire only goes up 9.14m the wetted surface area is the part of the shell that is less than 9.14m from the ground. Assuming the tank is vertical which is most of what I have looked at. If the tank is horizontal, well, do some geometry I guess.

A series of models and other things were done to figure out the heat flux into the tank for a given wetted surface area. These are tabulated in a big table in API-2000.

The model tank was determined based upon a tank full of hexane, at its bubble point, subjected to the heat from the fire. The hexane boils and the vapour then must escape. The vapour is assumed to be an ideal gas.

The final equation corrects for *not hexane* by using the actual bubble temperature, molar mass, and latent heat.

$$ q = 906.6 \cdot \frac{Q \cdot F}{L} \sqrt{\frac{T}{M}} $$

Where *Q* is the heat flux into the tank due to the fire, *F* is a correction factor based on other fire protection accessories such as fire resistant insulation, *L* is the latent heat of the fluid.

### Final remarks

The code models of tanks are just that, models. They are based on worst-case scenarios and assuming the fluid inside is a hydrocarbon somewhat like hexane. This is pretty reasonable for fluids like gasoline, but not necessarily for fluids like, say, water, mine tailings, molten sulfur or any of the other myriad things people store in tanks.

Places with severe weather, either hot or cold, also may not be addressed all that well by the averaged out latitude corrections. The British isles are the same latitude as most of Canada, however the *climate* is very different. The winter in Winnipeg (latitude 49.899 deg N) can get as low as -45C, whereas the winter in London (latitude 51.529 deg N) only gets to -14C, at worst. Winter in Winnipeg is an arctic hell-hole compared to winter in London, and yet London is further north than Winnipeg.