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# Criterial equations for calculating mass transfer from the surface of gasoline in vertical cylindrical tanks

UDK: 622.692.4
DOI: 10.24887/0028-2448-2020-12-131-133
Key words: prediction of losses of gasoline from evaporation, mass transfer dynamics, criterion equations of mass transfer, rule of limiting transition, operational calculation of concentration change, vapor concentration at the beginning of a technological operation
Authors: An.A. Korshak (Pipeline Transport Institute LLC, RF, Moscow), A.A. Korshak (Pipeline Transport Institute LLC, RF, Moscow)

To predict gasoline losses fr om evaporation from tanks that are not equipped with means to reduce them, it is necessary to have reliable methods for assessing mass transfer from its surface. By now, many such methods are known, starting with simplified empirical formulas or graphs and ending with criterion equations. The use of simplified empirical formulas can significantly simplify the calculations. However, this is achieved at the cost of a high calculation error. When predicting the concentration of hydrocarbons in the gas space of reservoirs at the time of the beginning of "exhalation" for several decades, graphs of the increase in the relative concentration of gasoline vapors over time are also used. The curves on them have the form of a parabola and differ only in the value of its exponent. However, the monotonic nature of the increase in the relative concentration over several tens of hours contradicts the foundations of the theory of losses from "small breaths", according to which the concentration of hydrocarbons in the HZ reservoirs is minimal in the morning, then increases with sunrise, reaches a maximum in the afternoon, after which, again at according to the behavior of the sun, decreases. The use of criterion equations is most preferable since mass transfer from the surface of gasoline in tanks is a thermodynamic process, the rate of which is determined by many factors: temperature, pressure of saturated vapors, concentration of hydrocarbons above the surface of an evaporating liquid, intensity of its mixing, speed of air flow around the surface of gasoline, etc. In the known criterion equations, these factors are taken into account in the form of dimensionless similarity criteria of Sherwood, Schmidt, Reynolds, Prandtl and Grashof. However, they have a number of disadvantages, including insufficient consideration of the real conditions of these processes (filling level of tanks, intensity of mixing gasoline, etc.), inconsistency with the requirement of the lim it transition at low rates of filling and emptying tanks, etc. In addition, when calculating the similarity criteria, the value of the average concentration of hydrocarbons above the surface of gasoline is used, this makes the calculation of mass transfer iterative. The article presents the criterion equations for mass transfer, which allow performing calculations without numerous iterations.

References

1. Rybakov Yu.N., Volgin S.N., Larionov S.V. et al., Predicting of the kinetics of fuel losses in polymer tank storage (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation,, 2018, no. 2, pp. 142–146.

2. Bazhaykin S.G., Mukhametzyanov R.R., Stepanyugin A.V., Oil product losses rationing in the airport fuel supply system (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation,, 2018, no. 2, pp. 142–146.

3. Korshak A.A., Korshak An.A., Method for predicting breathing losses of oil and oil products for a long period (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation,, 2018, no. 5, pp. 79–87.

4. Korshak A.A., Leont'ev S.A., Fominykh O.V., Snizhenie poter' uglevodorodov v sistemakh sbora i podgotovki skvazhinnoy produktsii (Reduction of losses of hydrocarbons in systems of gathering and preparation of well products), Tyumen': Publ. of TIU, 2019, 95 p.

5. Abuzova F.F., Skovorodnikova T.K., A simplified method for calculating the loss of oil products from large breaths from above-ground metal tanks (In Russ.), Transport i khranenie nefti i nefteproduktov, 1967, no. 2, pp. 22–24.

6. Abuzova F.F., Issledovanie poter' nefti i nefteproduktov i effektivnosti sredstv sokrashcheniya ikh v rezervuarakh (Study of losses of oil and oil products and the effectiveness of means to reduce them in tanks): thesis of doctor of technical science, Ufa, 1977.

7. Mukhamed'yarova R.A., Abuzova F.F., Mass transfer from the evaporating surface during saturation of the gas space of the reservoir (In Russ.), Transport i khranenie nefti i nefteproduktov, 1981, no. 4, pp. 27–29.

8. Molchanova R.A., Issledovaniya po vyboru tipov rezervuarov dlya khraneniya legkoisparyayushchikhsya nefteproduktov (Research on the selection of types of tanks for the storage of volatile oil products): thesis of candidate of technical science, Ufa, 1981.

9. Martyashova V.A., Khabibullina S.S., Mass transfer when filling the tank with "hot" gasoline (In Russ.), Transport i khranenie nefteproduktov i uglevodorodnogo syr'ya, 1977, no. 11, pp. 1–3.

10. Korshak S.A., Sovershenstvovanie metodov rascheta poter' benzinov ot ispareniya iz rezervuarov tipov RVS i RVSP (Improving methods for calculating the loss of gasoline from evaporation from tanks of the VST and VSTP types): thesis of candidate of technical science, Ufa, 2003.

11. Tugunov P.I. et al., Tipovye raschety pri proektirovanii i ekspluatatsiy neftebaz i nefteprovodov (Typical calculations in the design and operation of tank farms and oil pipelines), Ufa: Dizain-PoligrafServis Publ., 2002, 658 p.

12. Korshak A.A., Korshak S.A., A universal method for calculating the total losses from the "breaths" of tanks (In Russ.), Izvestiya vuzov “Neft' i gaz”, 1999, no. 4, pp. 85–87.

To predict gasoline losses fr om evaporation from tanks that are not equipped with means to reduce them, it is necessary to have reliable methods for assessing mass transfer from its surface. By now, many such methods are known, starting with simplified empirical formulas or graphs and ending with criterion equations. The use of simplified empirical formulas can significantly simplify the calculations. However, this is achieved at the cost of a high calculation error. When predicting the concentration of hydrocarbons in the gas space of reservoirs at the time of the beginning of "exhalation" for several decades, graphs of the increase in the relative concentration of gasoline vapors over time are also used. The curves on them have the form of a parabola and differ only in the value of its exponent. However, the monotonic nature of the increase in the relative concentration over several tens of hours contradicts the foundations of the theory of losses from "small breaths", according to which the concentration of hydrocarbons in the HZ reservoirs is minimal in the morning, then increases with sunrise, reaches a maximum in the afternoon, after which, again at according to the behavior of the sun, decreases. The use of criterion equations is most preferable since mass transfer from the surface of gasoline in tanks is a thermodynamic process, the rate of which is determined by many factors: temperature, pressure of saturated vapors, concentration of hydrocarbons above the surface of an evaporating liquid, intensity of its mixing, speed of air flow around the surface of gasoline, etc. In the known criterion equations, these factors are taken into account in the form of dimensionless similarity criteria of Sherwood, Schmidt, Reynolds, Prandtl and Grashof. However, they have a number of disadvantages, including insufficient consideration of the real conditions of these processes (filling level of tanks, intensity of mixing gasoline, etc.), inconsistency with the requirement of the lim it transition at low rates of filling and emptying tanks, etc. In addition, when calculating the similarity criteria, the value of the average concentration of hydrocarbons above the surface of gasoline is used, this makes the calculation of mass transfer iterative. The article presents the criterion equations for mass transfer, which allow performing calculations without numerous iterations.

References

1. Rybakov Yu.N., Volgin S.N., Larionov S.V. et al., Predicting of the kinetics of fuel losses in polymer tank storage (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation,, 2018, no. 2, pp. 142–146.

2. Bazhaykin S.G., Mukhametzyanov R.R., Stepanyugin A.V., Oil product losses rationing in the airport fuel supply system (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation,, 2018, no. 2, pp. 142–146.

3. Korshak A.A., Korshak An.A., Method for predicting breathing losses of oil and oil products for a long period (In Russ.), Nauka i tehnologii truboprovodnogo transporta nefti i nefteproduktov = Science & Technologies: Oil and Oil Products Pipeline Transportation,, 2018, no. 5, pp. 79–87.

4. Korshak A.A., Leont'ev S.A., Fominykh O.V., Snizhenie poter' uglevodorodov v sistemakh sbora i podgotovki skvazhinnoy produktsii (Reduction of losses of hydrocarbons in systems of gathering and preparation of well products), Tyumen': Publ. of TIU, 2019, 95 p.

5. Abuzova F.F., Skovorodnikova T.K., A simplified method for calculating the loss of oil products from large breaths from above-ground metal tanks (In Russ.), Transport i khranenie nefti i nefteproduktov, 1967, no. 2, pp. 22–24.

6. Abuzova F.F., Issledovanie poter' nefti i nefteproduktov i effektivnosti sredstv sokrashcheniya ikh v rezervuarakh (Study of losses of oil and oil products and the effectiveness of means to reduce them in tanks): thesis of doctor of technical science, Ufa, 1977.

7. Mukhamed'yarova R.A., Abuzova F.F., Mass transfer from the evaporating surface during saturation of the gas space of the reservoir (In Russ.), Transport i khranenie nefti i nefteproduktov, 1981, no. 4, pp. 27–29.

8. Molchanova R.A., Issledovaniya po vyboru tipov rezervuarov dlya khraneniya legkoisparyayushchikhsya nefteproduktov (Research on the selection of types of tanks for the storage of volatile oil products): thesis of candidate of technical science, Ufa, 1981.

9. Martyashova V.A., Khabibullina S.S., Mass transfer when filling the tank with "hot" gasoline (In Russ.), Transport i khranenie nefteproduktov i uglevodorodnogo syr'ya, 1977, no. 11, pp. 1–3.

10. Korshak S.A., Sovershenstvovanie metodov rascheta poter' benzinov ot ispareniya iz rezervuarov tipov RVS i RVSP (Improving methods for calculating the loss of gasoline from evaporation from tanks of the VST and VSTP types): thesis of candidate of technical science, Ufa, 2003.

11. Tugunov P.I. et al., Tipovye raschety pri proektirovanii i ekspluatatsiy neftebaz i nefteprovodov (Typical calculations in the design and operation of tank farms and oil pipelines), Ufa: Dizain-PoligrafServis Publ., 2002, 658 p.

12. Korshak A.A., Korshak S.A., A universal method for calculating the total losses from the "breaths" of tanks (In Russ.), Izvestiya vuzov “Neft' i gaz”, 1999, no. 4, pp. 85–87.

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