J. S. KIM and R. J. HAINES, Covestro, Baytown, Texas; and J. P. LOPEZ, Bechtel, Houston, Texas
Storage tanks that experience sudden heavy rain on what was a hot sunny day can be damaged due to inadequate venting devices. Due to the heavy rainfall, the storage tank vapor space is cooled and the tank pressure decreases. Many low-pressure storage tanks are operated at atmospheric conditions and are located outdoors without insulation. Therefore, venting devices must be designed properly to prevent serious damage to storage tanks. The American Petroleum Institute Standard 2000 (API 2000) is widely used as a standard for calculating storage tank thermal inbreathing rates to protect the tanks from under-pressure (vacuum). However, this standard method is overly simplified for ease of calculation, which may result in undersized or significantly oversized venting devices. API 2000 is particularly overly conservative for small, insulated tanks.
API 2000 Annex G introduced detailed thermodynamic results without providing detailed information. The detailed thermodynamic results are approximated by use of the API 2000 general method with C=5. The detailed results are still conservative for small tanks. This article provides a simplified dynamic approach for storage tank thermal inbreathing rates that are based on the specific site conditions and tank designs. This simplified dynamic approach was presented at the API 2022 Fall Subcommittee on Pressure-Relieving Systems (SCPRS) meeting.1 The thermal inbreathing rates generally lie between the API 2000 general method (C=5) and the API 2000 Annex A method. For an accurate calculation of thermal inbreathing, the simplified dynamic approach uses rain intensity, tank plate mass and vapor space mass in the tank.
Assumptions. The specific assumptions used in the simplified dynamic approach for storage tank inbreathing rates are based on available API 2000 guidelines: 2
Governing equations for dynamic approach. The amount of rain for 1 min is determined using Eq. 1.4 The rain angle is 60° vertically based on 10 m/sec wind velocity. Using the amount of rain will accurately reflect the rain intensity:
where:
Mrain = the amount of rain for 1 min, lb
Rain intensity = the rain flow density, lb/ft2/hr
D = the diameter of the tank, ft
H = the height of the tank, ft
= the rain angle with respect to vertical, 60°.
A few calculations are performed to compute the temperature change of the vapor space at 1-min time steps until the maximum rate of temperature change is identified using Eqs. 2–5. The tank plate’s mass should be based on the roof plate’s thickness, resulting in a conservative design. Generally, 15 min is adequate to identify the peak temperature change rate of vapor space. Rearranging those equations is necessary to obtain the calculation results without iterations.
Eq. 2 is used to calculate the average temperature of the tank plate and rain in thermal equilibrium for each step. In the first step, the starting temperature of the tank plate is 131°F:
Ave.Tplate + rain = the average temperature of the tank plate and rain in thermal equilibrium, °F
Mplate = the tank plate’s mass (shell and roof), lb
Cpplate = the heat capacity of the tank plate, Btu/lb/°F
Start Tplate = the starting temperature of the tank plate, °F
Cprain = the heat capacity of rain, Btu/lb/°F
Train = the rain temperature, 59°F.
The average temperature of the tank plate and rain from Eq. 2 is further cooled by ambient air. The tank plate’s final temperature for each step is determined using Eq. 3:
Final Tplate = the final temperature of the tank plate, °F
h = the ambient air heat transfer coefficient, 2.6415 Btu/hr/ft2/°F
Area = the total tank surface area (shell and roof), ft2
Tamb = the ambient temperature, 59°F.
The final vapor space temperature for each step is determined using Eqs. 4 and 5. In the first step, the vapor space’s starting temperature is 131°F:
Final Tvapor = the vapor space’s final temperature, °F
Start Tvapor = the vapor space’s starting temperature, °F
– • dT / dt = the temperature change rate of the tank’s vapor space, °F/hr
hi = the vapor space’s heat transfer coefficient, 0.8805 Btu/hr/ft2/°F
Mvapor = the vapor space’s mass, lb
Cpvapor = the vapor space’s heat capacity, Btu/lb/°F.
Once the maximum temperature change rate of the vapor space is determined, the tank thermal inbreathing rate is obtained using Eq. 6:
VIT = the maximum thermal inbreathing rate, sft3/hr of air
Vtk = the tank volume, ft3
Start Tat (–• dT / dt )max = the vapor space’s starting temperature at (– • dT / dt )max , °R
(– • dT / dt )max = the vapor space’s peak temperature change rate, °F/hr.
The tank’s outside heat transfer coefficient. A few detailed methods use the tank outside heat transfer coefficient; however, there is no consensus on the tank outside heat transfer coefficient, as shown in TABLE 1.
Due to the lack of consensus, the authors have developed an estimation for the tank outside heat transfer coefficient. The tank outside heat transfer coefficient can be back-calculated using Eqs. 7 and 8. Rain intensity has a significant impact on the tank’s outside heat transfer coefficient. Davies’ values are reasonable and relatively in good agreement with the results of Eq. 8. Higher tank outside heat transfer coefficients than the results of Eq. 8 are impractical because of the known limited cooling capacity of the rain intensity. Eq. 8 is based on an effective direct cooling method with the rain intensity specified. Note: The tank outside heat transfer coefficient is based on the total tank surface area (shell and roof). The local tank outside heat transfer coefficient on the roof’s surface area is much higher than the average tank outside heat transfer coefficient:
Q = the heat transfer rate from ambient during sudden rain to tank plate, Btu/hr
ho = the tank outside heat transfer coefficient, Btu/hr/ft2/°F.
The tank plate’s final temperature—based on the tank outside heat transfer coefficient—can be calculated using Eq. 9.
Eq. 3 can be replaced with Eq. 9 if the tank’s outside heat transfer coefficient is available. Both Eqs. 3 and 9 provide identical results:
Thermal inbreathing with insulation. The thermal inbreathing rate is significantly reduced if storage tanks are insulated because the tank insulation dominates the heat transfer rate during sudden weather changes. Generally, rain intensity does not affect the thermal inbreathing rate; however, the API 2000 general method (Eq. 10) does not follow the general heat transfer principle. The API 2000 general method represents the thermal inbreathing rate with insulation on the inside of the tank (FIG. 1).
The tank plate is assumed to be cooled down to ambient temperature immediately. Because of this, the thermal inbreathing rate is overly conservative for small tanks. The tank plate does not cool down quickly if the tank’s outside is insulated. If storage tanks are insulated, there is also no concern about condensation. The thermal inbreathing rate for condensing vapors is less than the thermal inbreathing rate for non-condensable vapors because tank insulation limits the heat transfer rate, and condensation requires a significant cooling capacity. For insulated tanks, assuming dry air in the tank vapor space is the worst-case scenario:
C = the factor that depends on vapor pressure, average storage temperature and latitude
Ri = the reduction factor for insulation, as provided by API 2000.
Most storage tanks are typically constructed as shown in FIG. 2. The temperature change rate of vapor space follows Eq. 11. The API 2000 Annex A method has similar results to those found in Eq. 11. As a general sizing method, using Eq. 12 is more reasonable for insulated tanks:
Annex A Method = the thermal inbreathing rate as given in Eqs. 14 or 15, sft3/hr of air
T = the vapor space’s temperature, °F
Twall = the tank wall (plate) temperature, 59°F
Rin = the reduction factor for a fully insulated tank, as provided by API 2000.
For a partially insulated tank (insulation on the shell surface area only), using Eq. 13 is a conservative general sizing option:
General Method = the thermal inbreathing rate, with Ri = 1, as provided in Eq. 10, sft3/hr of air
Shell Area = the shell’s surface area, ft2
Roof Area = the roof’s surface area, ft2.
The thermal inbreathing rate with the API 2000 Annex A method can be calculated using Eqs. 14 or 15. For tanks with a capacity of more than 180,000 bbl, the thermal inbreathing requirements can be based on 0.5 sft3/hr of air for each barrel of tank capacity.
For Vcap ≤ 20,000 bbl:
For 20,000 bbl < Vcap ≤ 180,000 bbl:
Vcap = the tank capacity, bbl
a = 2.04244E-21
b = -1.11941E-15
c = 2.37483E-10
d = -2.46783E-5
e = 1.66101
f = -5246.1.
Constant calculation time interval. This section explains why 1 min was chosen as the constant time interval for the proposed dynamic approach. Using the simplified dynamic approach, FIG. 3 plots the tank’s outside heat transfer coefficient with 225 kg/m2/hr rain intensity vs. calculation time intervals from 5 sec–120 sec. Literature has indicated that a steady rainwater film would not be formed within 60 sec. A 1-min selection could minimize the variation of the tank’s outside heat transfer coefficient by around +/- 20%. A 1-min interval also provides an adequate residence time for the thermal equilibrium between rainwater and the tank plate.
Validation of a simplified dynamic approach. One sample calculation from Davies’ presentation at the Design Institute for Emergency Relief Systems (DIERS) meeting was chosen to verify the simplified dynamic approach. The sample case provides the most detailed information for evaluation. Davies’ model is well accepted in industry. A simplified dynamic approach agrees with Davies’ results, as shown in TABLE 2.
The following are the details of sample calculations:
TABLE 3 provides the detailed calculations at each time step for 75 kg/m2/hr of rain intensity. The tank’s outside heat transfer coefficient was estimated at 53 W/m2/K, which is higher than 37 W/m2/K. The tank’s outside heat transfer coefficient for 225 kg/m2/hr is 117 W/m2/K.
Comparison of two sizing methods. Using API 2000, it could be assumed that all C factors are calculated using a tank vapor space temperature of 131°F. Several clarifications have important safety ramifications regarding the use of C factors. The relevant measurement is the vapor space temperature in a tank, not the liquid temperature. Vapor space temperatures can easily reach around 27°F–36°F above ambient temperatures due to solar radiation on an exposed, uninsulated tank. Shown in TABLE 4, each C factor has an implicit maximum vapor space temperature based on the API 2000 general method, using Eqs. 16 and 17. These implicit numbers are important to perceive because, if vapor space temperatures rise above the range assumed for each C factor, the vent device could be undersized.
The allowable vapor space temperature is tank specific and is ideally calculated on a uniquely designed tank with the general method. The simplified dynamic approach provides higher allowable temperatures than the general method mainly due to the inclusion of plate thickness in the heat transfer calculation. Ignoring the tank plate thickness makes the API 2000 general method conservative. The simplified dynamic approach with a negligible plate thickness will provide similar results to the API 2000 general method. The major difference between the two methods is whether tank plate mass is considered in the tank thermal inbreathing calculations. In addition, the simplified dynamic approach uses rain intensity (rain mass) in an energy balance on the tank plate to obtain an accurate calculation of thermal inbreathing:
T = the vapor space temperature, °F
T0 = the initial temperature of the vapor space, °R.
Takeaway. A sudden heavy rain on a hot sunny day can damage storage tanks due to inadequate venting devices. Therefore, venting devices must be designed properly. The API 2000 general method is overly simplified for ease of calculation. As an unexpected deficiency, some tank venting devices can be undersized for large tanks when C=2.5, C=3 or C=4 is applied for tanks with high vapor space temperatures. The vapor space temperature and rain intensity significantly affect thermal inbreathing rates. The API 2000 general method does not place a limitation on the maximum allowable operating temperatures of the tank vapor space. The API 2000 general method often significantly oversizes the venting devices for small tanks. For insulated tanks, the API 2000 general method is overly conservative. The API 2000 Annex A method, with a reduction factor for insulation, is more reasonable for insulated tanks. For non-insulated tanks, a simplified dynamic approach with conservative assumptions provides a rigorous thermal inbreathing estimation for specific site and tank design conditions. The results of the simplified dynamic approach are consistent for all sizes of tanks.
For non-condensable vapors, a simplified dynamic approach predicts the thermal inbreathing rate precisely for all different sized tanks. The simplified dynamic approach is applicable to most storage tanks that are generally superheated in the vapor space due to solar radiation; however, for condensing vapors, the simplified dynamic approach should be modified to consider condensation. API 2000 cautions the performance of the engineering analysis for heated, uninsulated tanks with vapor-space temperatures above 120°F. HP
LITERATURE CITED
JUNG SEOB KIM is a Principal Pressure Safety Engineer at Covestro and has more than 35 yr of experience in different roles within the petrochemical industry, including with ioMosaic, SK E&C USA, Bayer Technology Services, Samsung BP Chemicals and Samsung Engineering. He earned a BS degree in chemical engineering from the University of Seoul. He is a member of AIChE and is a registered professional engineer in the State of Texas.
JUAN P. LOPEZ is a Senior Process Safety Engineer at Bechtel. He has more than 10 yr of experience in process safety, including designing emergency relief systems and participating in process hazard analyses. Lopez earned a BS degree in chemical engineering from Texas A&M University and is a registered professional engineer in the State of Texas.
RYAN J. HAINES is a Process Safety Engineer at Covestro. He has 5 yr of experience in different roles, primarily focusing on reliability and process engineering. He earned a BS degree in chemical engineering from Texas A&M University.
