Method for estimating the volume of a pressurized gas tank
AssigneeL'Air Liquide, Societe Anonyme pour l'Etude et l’Exploitation des Procedes Georges Claude
InventorsRemi GONIN, Fouad AMMOURI, David VEMPAIRE
Life of this patent
Estimating the term…
Abstract
Method for estimating the volume of a pressurized gas tank, the method comprising an injecting step and a step of calculating the volume of the tank depending on: i) the initial pressure (p0) of the gas in the tank, ii) the initial temperature (T0) of the gas in the tank, iii) an amount (Δm) of gas flow injected into the tank, iv) the temperature (T_inj) of injection of the gas flow into the tank, v) the variation (Δp) in the pressure of the gas in the tank, wherein the calculating step also uses the duration (Δt) of the injecting step, said duration (Δt) being defined between a time (t1) marking the end of the injecting step and a time (t0) marking the beginning of the injecting step.
Claims11
A method for estimating the volume of a pressurized gas tank, the method comprising the following steps:
- a) determining an initial pressure of the gas in the tank;
- b) determining an initial temperature of the gas in the tank;
- c) injecting a pressurized gas flow into the tank;
- d) determining a temperature of injection of the gas flow into the tank;
- e) determining the mass of the gas flow injected into the tank during the injecting step;
- f) determining the variation in the pressure of the gas in the tank, between a final pressure determined at the end of the injecting step and the initial pressure determined at the beginning of the injecting step;
- and
- g) calculating the volume of the tank depending on:
- i. the initial pressure of the gas in the tank,
- ii. the initial temperature of the gas in the tank,
- iii, the temperature of injection of the gas flow into the tank,
- iv. the mass of the gas flow injected into the tank,
- V. the variation in the pressure of the gas in the tank;
- wherein the calculating step also uses the duration (Δt) of the injecting step, said duration (Δt) being defined between a time (t1) marking the end of the injecting step and a time (t0) marking the beginning of the injecting step.
The method according to claim, wherein the calculating step also uses a predetermined parameter (Λ) taking into account both the geometry and the material of the tank.
The method according to claim, wherein the predetermined parameter (Λ) is the product of a characteristic length (lc) of the tank multiplied by a coefficient (kg) of heat transfer between the pressurized gas and an inner wall of the tank.
The method according to claim, wherein the characteristic length (lc) has a value between a lower bound associated with a first reference tank of spherical shape, and an upper bound associated with a second reference tank of cylindrical shape.
The method according to claim, wherein the lower bound of the characteristic length (lc) is equal to one third of a first internal radius (Rint) of the first reference tank of spherical shape,
- i
- .
- e
- .
- l
- c
- =
- R
- i
-
- n
-
- t
- 3
- ,
- the upper bound of the characteristic length (lc) being equal to half a second internal radius (Rint) of the second reference tank of cylindrical shape,
- i
- .
- e
- .
- l
- c
- =
- R
- i
-
- n
-
- t
- 2
- .
The method according to claim, wherein the coefficient of heat transfer (kg) has a value between a predetermined lower bound equal to 150 W/m2/K, and a predetermined upper bound equal to 10,000 W/m2/K.
The method according to claim, wherein the step of determining the temperature (Tinj) of injection of the gas into the tank is carried out using a temperature sensor placed in a refuelling station to which the tank is connected.
The method according to claim, wherein the initial temperature (T0) is estimated to be equal to the ambient temperature in a region surrounding the tank.
The method according to claim, wherein the calculating step uses a mathematical function or formula (V) obtained from a mass and energy conservation balance of the gas injected into the tank.
The method according to claim, wherein the calculating step also uses a predetermined parameter (Λ) taking into account both the geometry and the material of the tank, wherein the function (V) is expressed as follows:
- V
- =
- 1
- t
- 1
- -
- t
- 0
-
- ∫
- t
- 0
- t
- 1
- [
- 1
- -
- ∂
- ρ
- ∂
- T
- |
- p
- [
- (
- h
-
- (
- p
- ,
- T
- inj
- )
- -
- h
-
- (
- p
- ,
- T
- )
- ρ
-
- c
- p
- +
- Λ
-
- (
- t
- -
- t
- 1
- )
- ]
- ]
- [
- ∂
- ρ
- ∂
- p
- |
- T
- +
- ∂
- ρ
- ∂
- T
- |
- p
- [
- β
-
- T
- ρ
-
- c
- p
- +
- Λ
-
- (
- t
- -
- t
- 1
- )
- ]
- ]
-
- dt
-
- dm
- dp
- with
- ρ [kg/m3] the density of the gas,
- [K] the temperature of the gas,
- p [bar] the pressure of the gas,
- t [s] time,
- cp [J/K/kg] the heat capacity of the gas,
- β [1/K] the isobaric expansion coefficient of the gas,
- h [J/kg] the enthalpy of the gas,
- Tinj [K] the temperature of the injected gas,
- Λ [W/m3/K] a parameter taking into account the geometry and material of the tank.
The method according to claim, wherein the function (V) takes one of the following two forms (Vadia) and (Viso) depending on the filling duration (Δt):
- when the filling duration (Δt) tends towards zero, the function (V) takes the following form (Vadia):
- V
- adia
- =
- [
- 1
- -
- ∂
- ρ
- ∂
- T
- |
- p
- [
- (
- h
-
- (
- p
- ,
- T
- inj
- )
- -
- h
-
- (
- p
- ,
- T
- )
- )
- ρ
-
- c
- p
- ]
- ]
- [
- ∂
- ρ
- ∂
- p
- |
- T
- +
- ∂
- ρ
- ∂
- T
- |
- p
- [
- β
-
- T
- ρ
-
- c
- p
- ]
- ]
-
- Δ
-
- m
- Δ
-
- p
- when the filling duration (Δt) tends towards infinity, the function (V) takes the following form (Viso):
- V
- iso
- =
- 1
- [
- ∂
- ρ
- ∂
- p
- |
- T
- ]
-
- Δ
-
- m
- Δ
-
- p
Dependencies are inferred from the claim text.