Method and system for tank refilling
Disclosed is an improved analytical method that can be utilized by hydrogen filling stations for directly and accurately calculating the end-of-fill temperature in a hydrogen tank that, in turn, allows for improvements in the fill quantity while tending to reduce refueling time. The calculations involve calculation of a composite heat capacity value, MC, from a set of thermodynamic parameters drawn from both the tank system receiving the gas and the station supplying the gas. These thermodynamic parameters are utilized in a series of simple analytical equations to define a multi-step process by which target fill times, final temperatures and final pressures can be determined. The parameters can be communicated to the station directly from the vehicle or retrieved from a database accessible by the station. Because the method is based on direct measurements of actual thermodynamic conditions and quantified thermodynamic behavior, significantly improved tank filling results can be achieved.
1. A method of filling a compressed gas tank, the method comprising:
calculating a hot soak initial temperature T HSinit for an initial mass of gas within the tank;
determining a projected fill time through T HSinit that is predicted to produce a gas final temperature T final no greater than a target temperature T;
calculating an initial cold soak initial temperature T CSinit for an initial mass of gas within the tank;
calculating for the tank a composite heat capacity value MC corresponding to heat transferred to the tank, a tank assembly, connection components and the initial mass of gas within the tank gas, while filling the tank;
determining a target pressure P target through T CSinit that is predicted to produce a target state of charge within the tank; and
delivering gas to the tank at a pressure ramp rate that will achieve P target at the projected fill time.
2. The method of filling a compressed gas tank according to claim 1 , wherein the calculating the MC comprises:
calculating a composite heat capacity value MC according to at least one of the equations
MC
(
U
,
t
)
=
C
+
Aln
(
U
adiabatic
U
initial
)
+
g
(
1
-
ⅇ
-
k
Δ
t
)
j
and
MC
(
U
,
t
)
=
C
+
A
(
U
adiabatic
U
initial
)
+
g
(
1
-
ⅇ
-
k
Δ
t
)
j
wherein C, A, g, k and j are constants specific to the tank, U initial represents the initial internal energy of the initial volume of gas and U adiabatic represents the adiabatic internal energy of a final mass of gas after filling the tank and U adiabatic incorporates an adjustment for heat added connection components, Q connector .
3. The method of filling a compressed gas tank according to claim 1 , wherein the determining the fill time comprises:
calculating an initial mass m init ;
calculating an additional mass m add necessary to achieve the state of charge of 100% within the tank;
calculating the initial internal energy U initial ;
estimating the average enthalpy h average to be delivered to the tank with the additional mass; and
calculating an adiabatic internal energy U adiabatic and an adiabatic temperature T adiabatic , and
wherein the calculating the MC comprises calculating a composite heat capacity value MC according to the equation
MC
=
C
+
A
U
adiabatic
U
init
+
g
(
1
-
ⅇ
-
k
Δ
t
)
j
wherein C, A, g, k and j are constants specific to the tank.
4. The method of filling a compressed gas tank according to claim 3 , comprising:
determining the values C, A, g, k and j for the tank.
5. The method of filling a compressed gas tank according to claim 1 , wherein calculating the MC comprises:
calculating a composite heat capacity value MC according to the equation
MC
=
C
+
A
U
adiabatic
U
init
+
g
(
1
-
ⅇ
-
k
Δ
t
)
j
wherein C, A, g, k and j are constants specific to the tank, U initial is the initial internal energy of the initial volume of gas and U adiabatic is the adiabatic internal energy of a final mass of gas after filling the tank to a state of charge of 100% and wherein U adiabatic incorporates an adjustment for heat added by connection components, Q connector .
6. The method of filling a compressed gas tank according to claim 1 , wherein determining the target pressure P target comprises
calculating a cold initial mass m initC ;
calculating an additional mass m add necessary to achieve the state of charge of 100% within the tank;
calculating the initial internal energy U initial ;
estimating the average enthalpy h average to be delivered to the tank with the additional mass; and
calculating an adiabatic internal energy U adiabatic , wherein U adiabatic incorporates an adjustment for heat added by connection components, Q connector ; and
calculating an adiabatic temperature T adiabatic ,
wherein the calculating the MC comprises calculating a composite heat capacity value MC according to the equation
MC
=
C
+
A
U
adiabatic
U
init
+
g
(
1
-
ⅇ
-
k
Δ
t
)
j
;
wherein C, A, g, k and j are constants specific to the tank.
7. The method of filling a compressed gas tank according to claim 4 , wherein determining the values C, A, g, k and j for the tank comprises
performing a plurality of test fills of the tank to a state of charge of 100% at a target fill time, wherein the test fills encompass a plurality of initial fill pressures and a plurality of pre-cooling temperatures;
calculating an end-of-fill MC for each test fill according to the equation
MC
=
m
2
(
u
adiabatic
-
u
final
)
(
T
final
-
T
initial
)
plotting MC against U adiabatic /U initial and performing a best fit to determine the constant, C, and coefficient, A of the resulting curve;
plotting ΔMC against Δt (time−target fill time) and performing a best fit model to the resulting curve to determine the coefficients g, k and j for the equation:
Δ MC=g (1− e −kΔt ) j .
8. The method of filling a compressed gas tank according to claim 7 , wherein:
a first initial pressure represents a state of charge of less than 10% within the tank; and
a first pre-cooling temperature is an ambient temperature.
9. The method of filling a compressed gas tank according to claim 8 , wherein:
a second initial pressure represents a state of charge of about 50% within the tank; and
a second pre-cooling temperature is less than 0° C.
10. The method of filling a compressed gas tank according to claim 7 , wherein:
a first initial pressure is 2 MPa and a second initial pressure represents a state of charge of at least about 50% within the tank; and
a first pre-cooling temperature is an ambient temperature and a second pre-cooling temperature is −20° C.
11. A method of refueling a hydrogen tank on a hydrogen powered vehicle, the method comprising:
calculating a hot soak initial temperature T HSinit for an initial mass of gas within the tank;
determining a projected fill time through T HSinit that is predicted to produce a final hydrogen temperature T final no greater than a target temperature T;
calculating a cold soak initial temperature T CSinit for an initial mass of gas within the tank;
calculating for the tank a composite heat capacity value MC corresponding to heat transferred to the tank, a tank assembly, connection components and the initial mass of gas within the tank gas, while filling the tank;
determining a target pressure P target through T CSinit that is predicted to produce a target state of charge; and
delivering gas to the tank at a pressure ramp rate that will achieve P target at the projected fill time.