Relating Storage Tank Stock Temperature to Meteorological Data

Transcription

1 Relating Storage Tank Stock Temperature to Meteorological Data September 11, 2008 Prepared by: Robert L. Ferry J. Randolph Kissell The TGB Partnership Prepared for: American Petroleum Institute 1220 L Street, NW Washington, D.C.

2 1. INTRODUCTION API 19.1 [1] and 19.2 [2] provide a relationship between a storage tank s bulk temperature and the ambient temperature. These relationships depend solely on tank paint color and condition. Because evaporative loss is very sensitive to temperature, a more accurate model of the relationship between stock temperature and meteorological data could improve the accuracy of storage tank emission estimates. Data were collected from two tanks for 14 months to investigate the effect of tank construction on this relationship. 2. TANK PARAMETERS The bulk temperature, ambient temperature, and product level were recorded for 14 months at 3 hour increments for two storage tanks at Dhahran, Saudi Arabia. The tanks had the same diameter, height, paint color, peripheral pontoon external-floating roof, and product, but one tank also had a fixed aluminum dome roof. The tank parameters were: Table 1: Tank Parameters tank number tank type external floating roof tank (EFRT) domed EFRT (DEFRT) diameter height maximum fill height minimum fill height average fill height stock June, July, Aug, Sept, Oct Mar, Apr, May Nov, Dec, Jan, Feb gasoline, RVP (psi) summer: 9.0 intermediate: 10.0 winter: 11.5 gasoline, RVP (psi) summer: 9.0 intermediate: 10.0 winter: 11.5 shell color aluminum aluminum floating roof peripheral pontoon external floating roof fixed roof none aluminum dome peripheral pontoon external floating roof The floating roof peripheral pontoons had an inside radius of 66-5, so the portion of the tank s horizontal area with a pontoon compartment above the liquid is π( )/( π75 2 ) = 0.20 Relating Storage Tank Stock Temperature to Meteorological Data 2

3 Figure 1: Aerial View of Tanks Before Aluminum Dome Installation Temperature probes were located at the following elevations above the tank bottom (at approximately 8.2 ft increments in height), and 80 cm (31 in.) from the shell: Sensor No. Elevation (m) Elevation (ft) The bulk temperature reported was the average of the temperatures at the elevations below the product level. The tanks were filled and emptied approximately every 3 days. The roof of the domed tank had 4 skylights of approximately 35 ft 2 each, for a total of 140 ft 2 of skylights, or 0.8% of the horizontal projected area of the roof. The dome had open vents consisting of a 20 diameter center vent and continuous venting around the periphery. Relating Storage Tank Stock Temperature to Meteorological Data 3

4 3. DATA ANALYSIS Data were manually recorded, scanned, and transmitted to TGB in pdf files. Temperatures were reported to the nearest 0.1 o C, and product heights were reported to the nearest m. Several issues were noted regarding the data: a) Missing data: From April 1, 2007 to May 31, 2008, there were 3,416 3 hour intervals (427 days with 8 intervals per day). Of these intervals, the following portions of the data were missing: Table 2: Missing Data Ambient Tank 800 Temperature (EFRT) Bulk Temperature 8.8% 4.6% 4.9% Tank 810 (DEFRT) Bulk Temperature No data were reported from April 14, 2008 through April 30, 2008; this period comprises most of the missing data. b) Outliers: From a graph of the data, some apparent outliers can be noted. For example, at noon on August 14, the Tank 810 bulk temperature was reported as 43.6 o C, but no other Tank 810 bulk temperatures were above 37.8 o C. c) Inconsistent data: During the periods from 5/1/07 to 5/6/07 and 5/13/07 to 5/18/07, bulk temperatures for both tanks varied much more widely than at any other times during the year. In fact, the bulk temperatures for both tanks were often reported to reach nearly 40 o C during May, hotter than at almost any other time of the year. Furthermore, the liquid levels for Tank 810 were reported to drop from m to m in the 3 hr interval from May 6 at 21:00 to May 7 at 0:00. It appears that at least portions of the April and May 2007 data are inconsistent with the other 12 months of data. To address the above issues, bulk temperatures for each tank were reviewed and the following data were discarded: a) Where data were not available for ambient, Tank 800 bulk, and Tank 810 bulk temperatures for a given time, none of the data for that time were used. For example, on 5/30/07 at 15:00 hr ambient and Tank 800 bulk temperatures were recorded, but Tank 810 bulk temperature was not available. Therefore, none of the data for 5/30/07 at 15:00 hr was used in the analysis. b) Where a bulk temperature varied by more than two standard deviations from the average of the temperatures 3 hours before and 3 hours after that temperature was taken, the bulk temperature was not used. The standard deviation was determined from the entire data set, and was 0.48 o C (0.86 o F) for Tank 810 and 0.74 o C (1.33 o F) for Tank 800, indicating there were greater fluctuations in the EFRT bulk temperatures. c) We also discarded all data from April and May While most of the April data met the above criteria, data from 5/1/07 to 5/6/07 and 5/13/07 to 5/18/07 did not. Each of these time intervals correspond to a single sheet of data, and the data entered on these sheets do not appear to be consistent with data on other sheets. Of the 3416 time intervals, then, 2549 intervals had usable data, or about 75%. Of the 2928 time intervals from June 1, 2007 to May 31, 2008 (366 days x 8 intervals/day), the 2549 intervals of usable data represent 87% of the time intervals. The usable data are graphed in Figure 2. Relating Storage Tank Stock Temperature to Meteorological Data 4

5 Figure 2: Ambient and Bulk Temperatures ( o C) vs. Time Table 3 summarizes the data, and Figure 3 illustrates it. Table 3: Temperature Data Summary ( o F) ambient temperature Tank 800 (EFRT) bulk temperature Tank 810 (DEFRT) bulk temperature minimum average maximum coefficient of variation 34.8% 25.4% 23.9% average daily maximum 87.8 average daily minimum 68.5 (average bulk temperature) (average ambient temperature) * * determined by converting the difference in metric temperatures, thus not exactly equal to From Figures 2 and 3 and Table 3, we observe: a) The ambient temperature varies much more widely than the bulk temperatures. b) The bulk temperature of the EFRT varies more than the bulk temperature of the domed tank. c) Bulk temperatures of both tanks rose when ambient temperature rose, and fell when ambient temperature fell. Relating Storage Tank Stock Temperature to Meteorological Data 5

6 Figure 3: Temperature Data Summary ( o F) 4. API RELATIONSHIP BETWEEN BULK AND AMBIENT TEMPERATURES For fixed roof tanks, API 19.1 equation 23 provides the relationship between bulk and ambient temperature as: T B = T A + (6α 1) where α = solar absorptance = 0.60 to 0.68 for diffuse type aluminum color paint depending on paint condition (good reflectivity or poor reflectivity). Assuming an average reflectivity, α = (API 19.1 Table 5) T B = bulk temperature ( o F) T A = average ambient temperature ( o F) T B = T A + (6α 1) = T AA + (6(0.64) 1) T B = T A For floating roof tanks (for a tank with aluminum paint), API 19.2 Table 16 provides the relationship as T B = T A API 19.2 will be revised to match API 19.1 soon, so the API 19.2 estimate is not considered further here. The tanks are compared API below. Table 4: Difference Between Bulk Temperatures and Ambient Temperature (Tank 800 (EFRT) measured bulk temperature) (ambient temperature) 2.6 o F (API estimated bulk temperature) (ambient temperature) 2.8 o F (Tank 810 (DEFRT) measured bulk temperature) (ambient temperature) 3.3 o F The temperature model in API 19.1 does not account for the amount of solar insolation occurring at the site or type of tank (for example, whether the tank is an external floating roof tank or internal floating roof tank). To investigate the effects of other factors such as solar insolation and tank type, TGB developed an expanded temperature model for storage tanks that accounts for these factors. The model is discussed next. Relating Storage Tank Stock Temperature to Meteorological Data 6

7 5. TGB S BULK TEMPERATURE MODEL TGB s bulk temperature model predicts the difference between bulk temperature and ambient air temperature by equating the product s heat gain from solar insolation to the product s heat loss from conduction to the air and ground. The model assumes that the product is a well-mixed fluid so that the bulk temperature is uniform throughout the tank. Figure 4: Heat Flow for a Storage Tank solar insolation I vapor space temperature T V (fixed roof tanks) liquid surface temperature T L Q s liquid bulk temperature T B D Q r (heat flow thru the roof) ambient air temperature T A Q s (heat flow thru the shell) ground temperature T G Q b (heat flow thru the bottom) The tank parameters used for this model can be categorized as follows: Table 5: Tank Parameters Used for Bulk Temperature Calculation Tank construction: Environment: Operation: diameter ambient air temperature initial product height height ground temperature final product height solar absorptance of the roof solar insolation stock feed temperature solar absorptance of the shell day of year stock heat capacity roof emissivity latitude shell conductance altitude bottom conductance ground reflectivity roof conductance Solar insolation makes the bulk temperature greater than the ambient temperature, while stock feed temperature can make the bulk temperature greater than or less than ambient temperature (depending on whether the stock feed temperature is greater than or less than ambient temperature). Stock feed temperatures were not reported, but reviewing the data (for example, Tank 810 on April 2, 2007), the bulk temperature generally varies with ambient temperature and is independent of filling, so we assumed that the stock feed temperature is the same as the ambient temperature. Ground temperatures were not reported, but we assume that the ground temperature beneath the tank is the same as the ambient temperature, since solar insolation does not reach under the tank. Relating Storage Tank Stock Temperature to Meteorological Data 7

8 The roof conductance for both tanks is the conductance of the floating roof. This conductance is a function of whether there is an air space beneath the top surface of the floating roof and the wind speed on the top side of the floating roof: a) External floating roof: The conductance of the outside surface C O is a function of wind speed. The average wind speed at Dhahran is approximately 12 mph. The wind speed on an external floating roof is approximately 0.7 times the ambient wind speed (per API 19.2 equation 15), thus, the average wind speed on the floating roof is (0.7)(12 mph) = 8.4 mph. For a 7.5 mph wind speed, C O is 4 Btu/(hr o F ft 2 ) and for a 15 mph wind speed, C O is 6 Btu/(hr o F ft 2 ). Interpolating for the conductance at 8.4 mph gives C O = 4.2 Btu/(hr o F ft 2 ), which is a resistance of 1/4.2 = 0.24 (hr o F ft 2 )/Btu. The conductance of the inside surface depends on whether there is a vapor space between the top of the EFR and the liquid. A vapor space exists under the center deck if the liquid boils, at the rim space, and at peripheral pontoons. Where the steel rests on liquid, C I is large about 640 Btu/(hr o F ft 2 ), resulting in negligible resistance; if there is a vapor space, there are two still air surfaces each with a resistance of 0.61 (hr o F ft 2 )/Btu, for a total resistance of 2(0.61) = 1.22 (hr o F ft 2 )/Btu. If there is no vapor space under the center deck (recalling from Section 1 that the pontoon portion of the roof area is 0.20), the resistance is R = ( ) (0.20) (1 0.20) = 0.48 (hr o F ft 2 )/Btu, or a conductance of 1/0.48 = 2.1 Btu/(hr o F ft 2 ) If there is a vapor space under the full center deck, the resistance is R = ( ) = 1.46 (hr o F ft 2 )/Btu, or a conductance of 1/1.46 = 0.68 Btu/(hr o F ft 2 ) Using a conductance of 1.3 (approximately the average of these conductances) in the TGB calculator results in a calculated bulk temperature that matches the measured bulk temperature within 0.1 o F. b) Domed external floating roof: The wind speed is 0 on the top side of the roof (API 19.2 Section 5.2.2), so the resistance of the top side of the roof is The resistance of an enclosed space is 1.22, the same as for the EFRT. If there is no vapor space under the center deck, the resistance is R = ( ) (0.216) ( ) = 0.87, or a conductance of 1/0.87 = 1.1 Btu/(hr o F ft 2 ) If there is a vapor space under the center deck, the resistance is R = ( ) = 1.83, or a conductance of 1/1.83 = 0.55 Btu/(hr o F ft 2 ) Using a conductance of 0.7 in the TGB calculator results in a calculated bulk temperature that matches the measured bulk temperature within 0.2 o F. The shell conductance is determined by interpolating the conductances for 7.5 and 15 mph for an average wind speed of 12 mph, which gives a conductance of 5.2 Btu/(hr o F ft 2 ). The TGB model parameters are summarized below. Relating Storage Tank Stock Temperature to Meteorological Data 8

9 Table 6: TGB s Tank Temperature Model Parameters Parameter Units Tank Tank Notes tank type EFRT DEFRT diameter ft height ft ground reflectivity desert sand solar absorptance of the roof API 19.1 Table 5: solar absorptance of the shell for mill finish aluminum in average condition, 0.64 for diffuse aluminum paint in average condition roof emissivity unpainted aluminum 0.1; unpainted steel 0.8 shell conductance Btu/(hr ft 2 o F) interpolated for 12 mph average annual wind speed bottom conductance Btu/(hr ft 2 o F) 2 2 see TGB Tank Temperature Study 1/4/05 section 3.3 roof conductance Btu/(hr ft 2 o F) average fill height ft from the data ambient air temperature o F from the data ground temperature o F assumed equal to ambient solar insolation Btu/( ft 2 day) annual average, Renewable Energy, Oct 2000 p. 129 day of year March 22, when sunlight is at its average angle latitude degrees Google Earth altitude ft Google Earth stock feed temperature o F assumed equal to ambient stock heat capacity Btu/(ft 3o F) see TGB Tank Temperature Study 1/4/05 section 3.5 measured bulk temperature o F from the tank data ambient temperature calculated bulk temperature ambient temperature o F from the TGB model 6. LIQUID SURFACE TEMPERATURE The liquid surface temperature may differ from the bulk temperature. Because evaporation takes place at the liquid surface, the liquid surface temperature should provide a more accurate measure of evaporation than bulk temperature. The liquid surface temperature could differ from the average temperature of the liquid (bulk temperature) when heat flows into or out of the product. The liquid surface temperature might also vary over the surface of the liquid, since different thermal conditions exist at the rim seal, the peripheral pontoons, and the center deck area. Recognizing this, an attempt was made to record liquid surface temperatures at these locations on each floating roof on each tank (the rim space, the peripheral pontoon, and the center deck). However, these data were not retrievable. Nonetheless, some observations regarding liquid surface temperature can be made. 6.1 External Floating Roof Tank Heat flow at the liquid surface is shown in Figure 5. Relating Storage Tank Stock Temperature to Meteorological Data 9

10 Figure 5: Heat Flow at the Liquid Surface (External Floating Roof) solar insolation I conductance of outside surface C O Q A (heat flow to the air) ambient air temperature T A steel temperature T S conductance of inside surface C I bulk temperature T B Q B (heat flow to the liquid) The equilibrium steel temperature is given by equating the steel s heat gain from solar insolation to the steel s heat loss to the air and the liquid: (T S T A )C O + (T S T B )C I = αi Solving for the steel temperature: T S = (T A C O + T B C I + αi)/(c O + C I ) Immediately beneath the steel, the liquid surface temperature is approximately equal to the steel temperature. The conductances of the outside and inside surfaces of the EFR were estimated in Section 5a above. The conductance of the outside surface was established as C O = 4.2 Btu/(hr o F ft 2 ). The conductance of the inside surface depends on whether there is a vapor space between the top of the EFR and the liquid. Where the steel rests on liquid, C I is about 640 Btu/(hr o F ft 2 ); where there is a vapor space, there are two still air surfaces each with a resistance of 0.61 (hr o F ft 2 )/Btu, for a total resistance of 2(0.61) = 1.22 (hr o F ft 2 )/Btu, or a conductance of (1/1.22) = 0.82 Btu/(hr o F ft 2 ). The effect of varying C I is shown in Table 7 by evaluating the steel temperature for C I much larger than C O and for C I much smaller than C O : Relating Storage Tank Stock Temperature to Meteorological Data 10

11 Table 7: External Floating Roof Average Temperature α = 0.64, I = (1830/24) Btu/(hr ft 2 ), T A = 80.3 o F, T B = 82.9 o F T S equation T S value Notes C I >> C O T B 82.9 o F minimum steel temperature C I = 0.8, C O = 4.2 (T A C O + T B C I + αi)/(c O + C I ) 90.5 o F full center deck vapor space C I << C O T A + αi/c O 91.9 o F maximum steel temperature The equations for the EFR temperature given above are a hypothesis to address the surface heating effect of solar insolation for average annual conditions. They are intended to establish these rational bounds: An upper bound on the EFR temperature, occurring when the EFR is fully insulated from the bulk liquid and thus all the solar heat gain is retained at the surface; A lower bound on the EFR temperature, occurring when there is no barrier to heat flow between the EFR and the bulk liquid and thus none of the solar heat gain is retained at the surface. The actual liquid surface temperature lies between these bounds, and depends on: The presence of a vapor space under the EFR s center deck; Stratification of the bulk liquid, by which the warmer liquid rises to the liquid surface. Table 7 shows that the estimated average temperature of the external floating roof is between 82.9 o F and 91.9 o F, and might be best estimated to be 90.5 o F. 6.2 Domed External Floating Roof Tank Using the liquid surface temperature for fixed roof tanks given in API 19.1 equation 24a and the 19.1 documentation file Section F5.3 as: T L = 0.437T A T B αI For T A = 80.3, T B = 83.7, I = 1830, and α = average absorptance of the roof and shell = ( )/2 = 0.38, T L = 87.7 o F The 87.7 o F estimated liquid surface temperature of the domed tank is 2.8 o F less than the 90.5 o F estimated liquid surface temperature of the EFRT. Conversely, the 83.7 o F average bulk temperature of the domed tank is 0.8 o F greater than the 82.9 o F average bulk temperature of the EFRT. So although the domed tank has a slightly greater bulk temperature than the EFRT, the domed tank is predicted to have a lower liquid surface temperature. Relating Storage Tank Stock Temperature to Meteorological Data 11

12 Figure 6: Liquid Surface and Bulk Temperatures ( o F) 7. SUMMARY This report: Analyzes bulk and ambient temperature data for two identical tanks at the same site (one with an aluminum dome roof and one without) for a one year period. The average measured bulk temperature was 3.3 o F greater than ambient temperature for the domed tank, and 2.6 o F greater for the EFRT. Compares measured bulk temperatures to predicted bulk temperatures from the current API estimating method. The API method predicts the bulk temperature for both tanks to be 2.8 o F greater than ambient. Compares measured bulk temperatures to estimates from TGB s bulk temperature model. The TGB model estimates the average bulk temperature to be 3.5 o F greater than ambient for the domed tank and 2.5 o F greater than ambient for the EFRT. Estimates liquid surface temperatures for both tanks. The EFRT s estimated liquid surface temperature is 10.2 o F above average ambient temperature; the domed tank s estimated liquid surface temperature is 7.4 o F above average ambient temperature. These findings are summarized in Figure 7. Relating Storage Tank Stock Temperature to Meteorological Data 12

13 Figure 7: Difference Between Ambient Temperature and Stock Temperature 8. REFERENCES 1. American Petroleum Institute, Manual of Petroleum Measurement Standards Chapter 19.1 Evaporative Loss from Fixed-Roof Tanks, 3 rd edition, March, American Petroleum Institute, Manual of Petroleum Measurement Standards Chapter 19.2 Evaporative Loss from Floating Roof Tanks, 2 nd edition, September, American Petroleum Institute, Manual of Petroleum Measurement Standards Chapter 19.4 Recommended Practice for Speciation of Evaporative Losses, 2 nd edition, September, APPENDIX 1 NOMENCLATURE Symbol Description A vapor pressure constant B vapor pressure constant C thermal conductance C I thermal conductance of EFR inside surface C O thermal conductance of EFR outside surface I solar insolation Q heat flow rate R thermal resistance T A ambient air temperature T B bulk temperature T G ground temperature T L liquid surface temperature T S EFR steel temperature T V vapor space temperature α solar absorptance Relating Storage Tank Stock Temperature to Meteorological Data 13