Process Engineering Design Pressure Vessel

First the total volume of gas that is to be stored needs to be calculated. From the mass balance it is known that 30.92 kmol of methane can be expected every hour. This correlates to 742.0 kmol/day. The ideal gas law will be used, with a compressibility factor, Z, to account for departure for un-idealality. An operating temperature of 50 will be assumed, as this is the highest feasible ambient temperature that can be expected. Also assume that the pump or compressor used to transport the methane from the flash vessel will not cause the methane to rise above this design temperature.
The expected surge pressure from of the 15 atm storage pressure is 16.5 atm. This will be taken as the operating pressure throughout the design. As the actual pressure inside the vessel will be

is 0.979 from SOURCE.
The total volume of the daily quantity of methane at the specified conditions is calculated below.

However the vessels must not fall below 0 gauge pressure inside, there must be at least one atm absolute pressure inside each vessel otherwise they will fail due to the difference in pressure. So total amount of storage needs to account for this. Assuming a linear relationship exists between pressure and volume at constant temperature 1 atm would correlate to one fifteenth of the volume, such that total volume required.

Allowances for extra volume in=case of train delays etc will be made later in the design.
CHOICE OF END CAP
To avoid designing a shell and then having to make adjustments such that it fit a specific end cap the end cap was chosen first and the shell designed around it.
Sem-Ellipsoidal end caps were chosen as the operating pressure exceeds 15 bar (p28). Hot pressed caps will be used to save on costs. Whilst a greater range and larger sizes are available in the hot spun method of manufacturing it is not worth the higher cost.
The largest available semi ellipsoidal available by hot pressed manufacturing from Australia Pressure Vessel Heads catalogue has an internal diameter of 2731 mm. This is approaching the largest size that can be easily transported by conventional means. It will need to be manufactured to order but this is unavoidable as the largest stock size is 300mm smaller.
SHELL MATERIAL, THICKNESS AND CLASS
AS 1548 7-490R,N,T was selected from table 3.3.1(A) (pg 18) as the material to be used for the shell of the tank. It was selected as it is a carbon-manganese steel alloy, has no thickness restrictions, is part of the A2 steel group which should alloy versatility in vessel classing and exhibits a superior tensile strength at the design temperature.

Under design temperature this alloy has a tensile strength, f, of 123 MPa.
For economic reasons double butt welds will be used. If the vessel falls into class 3 the joint efficiency, , will be 0.7, as specified by table 1.6 AS 1210 (pg 23). Applying the minimum shell thickness equation at the design pressure:

So as a class 3 vessel the minimum thickness of the shell wall is 26.78 mm. This fails the criteria outlined by table 1.7, AS 1210 (pg 23) as Note that as well, justifying choice of an A2 material. An A1 grade material would have provided no benefit.

If it is class 2B, still using a double butt weld, the weld efficiency is increased to 0.8. Re applying the minimum thickness equation yields

For the vessels to fall under class three the diameter would need to be more than halved. This would result in either very long, uneconomic vessels or many smaller vessels. In either scenario it is not worth the savings made from leaner design restrictions and safety checks.

a corrosive substance to steel, so a minimal corrosion scenario is assumed. Assume 0.1 mm of corrosion per year (Coulson and Richardson V6). Designing for a tank life of 20 years gives a corrosion allowance of 2 mm. Total shell wall thickness given by mm
However steel sheets only available in either 25 mm or 28 mm. 28 mm would be overdesigning for no real benefit, so 25 mm sheet will is to be used. This reduces the corrosion allowance to 1.6 mm, which is still acceptable.

This is still below 32 mm, so vessel is still classed as 2B.

Cap Thickness
Firstly the same material as the shell will be used for the end caps, so the tensile strength will be the same, 123MPa. Table 1.6 AS 1210 (pg 24) shows the joint efficiency for double butt welds for circular welds is 0.8.
Minimum thickness for a semi-ellipsoidal end cap is given by

K is a factor dependant on the ratio between the diameter of the cap and its height. The height of the cap is given in Australian Pressure Vessel Heads data sheet and for the selected cap is given as 682 mm. The diameter, D, used is the internal diameter of the shell and end cap.
And applying the minimum end cap thickness equation gives
Internal corrosion for the end cap will be the same as that for the shell, so apply corrosion allowance of 1.6 mm.

However from the Australian Pressure Vessel Heads data sheet it can be seen it is only available in 25 mm or 32 mm thickness. The 25 mm thick variant will be used. It will decrease the corrosion factor to 1.57 mm, however this is still acceptable.
And to prevent buckling (pg 35, AS1210)

is fine. And as the shell and end caps have same internal diameter and thickness a strong weld will be easy.

Shell Aspect Ratio and Volume
The diameter was determined by the end cap as 2731 mm. Initially let

This is the middle of the recommended range for pressurised vessels (page 27) and close to the optimal of 3. This gives a shell length of 9558.50 mm. However steel sheets only available in 200mm increments and cutting to size would be wasteful and provide no benefits. Better to just have slightly larger tanks. So adjust shell length, L, to 9600 mm. Gives a new aspect ratio of

This is still within the recommended range.
Volume
Total volume of pressure vessel given by

Volume of endcap is specified in data sheet as 2661 litres and the volume of the shell is easily calculated.

As previously shown of tank space is required to store a day’s methane. So to calculate the required number of tanks

To allow for downtime, maintenance and late trains 20 tanks shall be used.
Inlet Nozzle
The pressure vessel requires an inlet nozzle, outlet nozzle, pressure relief valve and drain pipe.
Table 3 from AS 4343 (pg 9) specifies that extremely flammable gases are rated as Very Harmful Gas (VHG). Methane falls into this category.
From table 1.4 AS 4041 (pg 8) unless design pressure exceeds 2 MPa class 3 piping is acceptable.

Class 3 piping acceptable.

To calculate the size of inlet nozzle required the volumetric flowrate of methane is to be calculated. Note that for the following calculations to make literal sense a constant methane pressure of 1.67 MPa ( must be assumed through the inlet nozzle, ie the driving force from the pump. per day, therefore the volumetric flowrate, Q, is

A target gas velocity of is chosen as it sits in the middle of the optimum range. Using this velocity the cross sectional area of the pipe, , can be calculated

And the diameter can easily be calculated from the area
Note that this is the internal diameter.
PIPE MATERIAL
BS 806 BS 3601 430 ERW was chosen for all piping. Design conditions are neither unusually high or low, and this choice of material reflects that. From Table D2 AS 4041 (pg 59) it can be seen that at the design temperature this material exhibits a tensile strength, f, of 183 MPa.
From table 3.12.3 AS 4041 the design factor, M, for class 3 piping is 0.7. As it is piping seamless welds are to be used which have a weld joint factor, e, of 1.
The pressure design minimum pipe thickness, , can be calculated using the internal diameter based equation

The contribution of pressure to the necessary design thickness is very small. The total minimum pipe thickness is a function of the pressure design term and the corrosion allowance can be calculated by

As the material is a carbon alloy and methane being relatively un-corrosive a corrosion allowance of 2 mm will be used. Rearranging the formulae yields

And so the theoretical outer diameter

So a theoretical inner diameter of 46.50 mm and outer diameter of 49.13 mm. DN 40 schedule 40 (BlueScope Pipe catalogue, page 21), with an outer diameter of 48.3 mm and a thickness of 3.68 mm, fits the theoretical requirements the closest. Re checking the gas velocity:

This is still in the acceptable velocity range for gasses, and so this piping is fine.
OUTLET NOZZLE
In designing the outlet nozzle the amount of time desired to evacuate all the methane onto the train needs to be considered and 2 scenarios will be evaluated. In the first all of the methane is pumped from the storage vessels through a single pipeline, so tanks are evacuated one at a time. In scenario B there are 2 lines of pipe from the pressurised tanks to the train and 2 pumps, so that 2 tanks can be evacuated at once, effectively halving the volume needed to be pumped. Scenario A will require less length of pipe of a greater diameter to handle the higher volumetric flowrates. Scenario B will utilise more length of pipe of smaller diameter. Scenario B will also require a second pump. Assume in both scenarios it takes 2.8 hours to empty the storage tanks into the trains and the gas travels at 7.5 m/s. Note that pumps are required as, assuming the methane is also transported at 15 atm gauge pressure, the pressure difference across the trains tanks and the storage tanks will not be enough to transfer the gas across. The pressures would eventually equalise and a sizeable quantity of methane would be left in the storage tanks.
Calculations used are same as demonstrated for the inlet nozzle. A corrosion allowance of 2 mm is used and a gas velocity of 7.5 m/s is targeted.
SCENARIO A

Best fit is DN 125 schedule 40.
SCENARIO B

Best fit is DN 90 schedule 40.
So scenario A requires pipe of only 2 sizes higher than B. So whilst B is smaller pipe, and therefore cheaper, the cost of the extra lengths required and the extra pump, it is obvious that scenario A is the cheaper option.
Velocity Check Outer diameter of DN 90 Thickness of DN 90 Schedule 40
This velocity is well inside the acceptable range.
LENGTH: The nozzle will be 400 mm in length. This will leave plenty of room to attach the flange without extruding too far.
PLACEMENT AND REINFORCMENT: As seen on the diagram the outlet nozzle will be placed in the middle of the endcap
Flange
As the design pressure does not exceed 2 MPa a class 150 flange will be acceptable. A bolted full face style is chosen as it is proven and reliable. DN 90 will be required as to fit the outlet nozzle.
Pressure relief and drainage nozzles.
In the case of critical over pressurization a pressure relief valve is required to avoid vessel failure. To account for a worst case scenario where over pressurisation has occurred and methane is still being pumped into the tank at full capacity the pressure relief nozzle will be of the same design as the inlet nozzle so that gas can escape at the same rate as it enters. The relief valve will be spring automated and set at the vessels design pressure of 16.5 atm. It will be placed on the top, as seen in the engineering diagram, with the same reinforcing as the inlet nozzle.
In the event of a build-up of liquid within the vessel, such as from the hydrostatic pressure test of water condensation, a drainage valve is required. It will not be operated whilst the vessel is pressurised, so specific design is not of great importance. To simplify the design it will be identical to the design of the inlet and pressure relief nozzles. It will be placed on the underside of the vessel such that liquid build-up will be removed by gravity alone. Details of its placement can be found on diagram A. The will receive the same reinforcing as the other nozzles of the same design.