METHOD AND DEVICE FOR FILLING OR WITHDRAWING FROM A PRESSURIZED GAS TANK

Abstract

A method for filling or withdrawing from a pressurized gas tank. The tank having a wall having a cylindrical overall shape with dimensions and thermophysical properties that are given and known. The method including the regulation of the flow rate of the introduced or withdrawn gas, and/or of the temperature of the introduced gas, to avoid a situation in which the tank reaches a given high temperature threshold or a given low temperature threshold. The method including a step of estimating, by calculating in real time, at least one tank temperature from: the average temperature of the tank wall, the maximum temperature reached by the tank wall, the minimum temperature reached by the tank wall, and in that the flowrate of gas or the temperature of the gas is regulated depending on the calculated tank temperature.

Claims

1-14. (canceled)

15. A method for filling or bleeding off a pressurized gas tank, the tank being delimited by a wall of cylindrical general shape having a longitudinal axis and determined and known dimensions and thermo-physical properties and comprising a liner, comprising a gas, wherein the gas comprises an inlet flow rate, an inlet temperature, and a bleed off flow rate, the method comprising; regulating inlet flow rate, the bleed off flow rate, and/or of the inlet temperature, thereby preventing the pressurized tank from reaching a determined high temperature threshold or a determined low temperature threshold, calculating, in real time at least one temperature of the tank selected from the group consisting of: an average temperature of the wall of the tank T.sub.wall,average(r,t) as a function of time (t) and r being a radius coordinate starting from a longitudinal axis of the tank, a maximum temperature reached by the wall of the tank T.sub.wall,max(t) as a function of time, a minimum temperature reached by the wall of the tank T.sub.wall, min(t) as a function of time, wherein the regulation of the inlet flow rate, the bleed off flow rate and/or the inlet temperature is carried out as a function of said calculated temperature of the tank.

16. The method of claim 15, wherein, during filling, when the calculated temperature of the tank reaches a determined high threshold (HT), the inlet flow rate is decreased and/or the inlet temperature is decreased by thermal exchange with a source of cold.

17. The method of claim 15, wherein, during filling, when the calculated temperature of the tank is less than a high threshold (HT) by a determined value, the inlet flow rate is increased and/or the inlet temperature and/or of the temperature of the tank is increased by thermal exchange with a source of heat.

18. The method of claim 15, further comprising; calculating a Richardson Number (Ri) for the gas in the tank as a function of time, comparing the Richardson Number (Ri) calculated with a determined reference value (Vr) lying between 0.05 and 1.5 and, when the Richardson Number (Ri) calculated is less than determined reference value (Vr) the temperature of the gas in the tank is considered to be homogeneous, wherein the maximum temperature reached by the wall of the tank T.sub.wall, max(t) as a function of time is equal to the average temperature of the wall of the tank T.sub.wall,average(r,t) in contact with the gas as a function of time (t): T.sub.wall,max(t)=T.sub.wall,average(r=r.sub._.sub.liner,t).

19. The method of claim 18, wherein, during filling, when the Richardson Number (Ri) is greater than the reference value (Vr), the inlet flow rate is increased.

20. The method of claim 18, further comprising regulating the inlet flow rate, wherein when the Richardson Number number (Ri) calculated is greater than determined reference value (Vr), the temperature of the gas in the tank is considered to be heterogeneous wherein the maximum temperature reached by the wall of the tank T.sub.wall,max(t) as a function of time is not equal to the average temperature of the wall of the tank in contact with the gas as a function of time (t) wherein at the liner, T.sub.wall,average(r=radius of the liner of the tank, t), the method comprises a step of increasing the inlet flow rate thereby decreasing the value of the Richardson Number (Ri) calculated below the determined reference value (Vr) and thus render the gas homogeneous in temperature.

21. The method of claim 18, further comprising, before filling, a step of determining or detecting, by sensor(s), an initial temperature T(0) of the gas in the tank, an initial pressure P(0) of the gas in the tank, an initial average temperature of the wall of the tank T.sub.w, average(0) and a step of determining an initial mass of gas in the tank m(0) and then, during filling when the Richardson Number (Ri) calculated is less than determined reference value (Vr) the temperature of the gas in the tank (1) is considered to be homogeneous, and under these conditions, the method comprises, in the course of filling, a step of calculating an average temperature T.sub.gas,average(t) Of the gas in the tank in real time as a function of time and the average temperature of the wall T.sub.wall,average(r,t) in real time as a function of time (t) on the basis of a mass and enthalpy balance applied to the gas in the tank and on the basis also of an energy balance in the wall of the tank, of the equation of state of the gas, and of a balance of the thermal exchanges between the gas and the wall, and between the wall of the tank is the exterior, and/or when the Richardson Number (Ri) calculated is greater than determined reference value (Vr) the temperature of the gas in the tank is considered to be heterogeneous, and under these conditions, the method comprises, in the course of filling, a step of calculating the average temperature T.sub.gas,average(t) Of the gas in the tank in real time as a function of time (t) and the average temperature of the wall T.sub.wall,average(r,t) in real time as a function of time on the basis of a mass and enthalpy balance applied to the gas in the tank and of an energy balance in the wall of the tank, of the equation of state of the gas, and of a balance of the thermal exchanges between the wall of the tank is the exterior, method comprising a step of calculating the maximum temperature reached by the wall of the tank T.sub.wall,max(t) as a function of time, this maximum temperature reached by the wall of the tank T.sub.wall,max(t) as a function of time being obtained by correlation on the basis of the average temperature T.sub.gas,average(t) of the gas in the tank calculated in real time as a function of time and as a function of the average temperature of the wall T.sub.wall,average(r,t) in real time as a function of time (t).

22. The method of claim 21, further comprising calculating the enthalpy hin(t) of the gas entering or exiting the tank as a function of time, measuring or calculating the mass of gas m(t) introduced or bled off from the tank as a function of time or, respectively, determining the pressure P(t) in the tank as a function of time, determining the average temperature of the gas T.sub.gas,average(t) at the instant tin the tank in degrees K, this average temperature T.sub.gas,average(t) being expressed as a first-degree function of the average temperature of the gas T(t1) at the previous instant (t1) and of a coefficient of convective heat exchange between the gas and the internal wall of the tank at the instant (t1) in W.Math.m.sup.2.Math.K-1 in which the heat exchange coefficient k.sub.g(t1) is given by the relation k.sub.g=(g/Dint).Math.Nuint in which g is the thermal conductivity of the gas in the tank in W.Math.m.sup.1.Math.K-1 Dint is the internal diameter of the tank in meters and NuDint the Nusselt number of the gas in the tank (dimensionless), and in which the Nusselt number of the gas is expressed as a function of the Reynolds number (Redin) (dimensionless) relating to the forced convection in the tank and of the Rayleigh number (RaDint) (dimensionless) relating to the internal natural convection in the tank according to a formula NuDint=a.Math.RaDint.sup.b+c,Redin.sup.d in which a and c are dimensionless coefficients dependent on the ratio (Lint/Dint) between the internal length of the tank Lint in meters and the internal diameter of the tank Dint in meters and on the ratio (Dint/di) between the internal diameter of the tank Dint in meters and the diameter of the injector di in meters, a, b, c and d being dimensionless positive real numbers, a lying between 0 and 1, b lying between 0.2 and 0.5, c lying between 0 and 1 and d lying between 0.5 and 0.9.

23. The method of claim 21, further comprising estimating the maximum temperature reached in the thickness of the tank T.sub.wall,max(t) as a function of time, or respectively the minimum temperature reached in the thickness of the tank T.sub.wall,min(t) as a function of time, on the basis of the average temperature T.sub.gas,average(t) of the gas in the tank calculated in real time as a function of time (t), said maximum or minimum temperature being obtained on the basis of a correspondence chart(s) obtained by experiment, and/or on the basis of calculation and/or of simulations so that to an average temperature T.sub.gas,average(t) of the gas in the tank calculated in real time as a function of time (t) there corresponds, according to the known conditions of gas flowrate, of the diameter of an injector of gas into the tank and of the dimensions and characteristics of the tank, a maximum or, respectively minimum, temperature in the thickness of the tank as a function of time.

24. The method of claim 18, wherein the Richardson Number (Ri) for the gas in the tank as a function of time is calculated on the basis of the Grashoff number (Gr) for the gas and of the Reynolds number (Re) for the gas at the time (t) according to the following formula: Ri=Gr/Re.sup.2, in which the Grashof (Gr) and Reynolds (Re) numbers are data which are known or calculated on the basis of the measured value of pressure of the gas or of the mass of gas in the tank and of the average gas temperature T.sub.gas,average(t) of the gas in the tank.

25. The method of claim 15, wherein, during bleed-off, when the calculated temperature of the tank reaches a determined low threshold (LT), the outlet flow is decreased.

26. The method of claim 15, further comprising a step of continuous measurement or calculation of a property selected from the group consisting of; the pressure P.sub.in(t) at the time (t) of the gas introduced into or bled off from the tank, the temperature T.sub.in(t) at the time (t) of the gas introduced into or bled off from the tank, the pressure P(t) in the tank at the time (t), the ambient temperature T.sub.amb(t) at the time (t), and the mass of gas m(t) in the tank at the time (t).

27. The method of claim 15, further comprising implementing by a station for filling hydrogen gas tanks comprising at least one high-pressure hydrogen source, at least one gas transfer pipe selectively linking the source to a tank, and an electronic facility for data acquisition, storage and processing such as a computer or microprocessor, said facility piloting the transfer of gas between the source and the tank, wherein the electronic logic is programmed to calculate in real time at least one temperature of the tank from among: the average temperature of the wall of the tank T.sub.wall,average(r,t) as a function of time (t), the maximum temperature reached in the thickness of the tank T.sub.wall,max(t) as a function of time, the minimum temperature reached in the thickness of the tank T.sub.wall,min(t) as a function of time and to regulate the flowrate of the gas flow and/or of the temperature of said gas as a function of said calculated temperature of the tank.

28. A device for filling or bleeding off gas from a tank comprising a transfer pipe comprising a valve and connectable to a tank, the device comprising an electronic facility for data acquisition, storage and processing such as a computer or microprocessor, said facility piloting the transfer of gas between the source and the tank, wherein at the electronic logic is programmed to calculate at least one temperature of the tank from among: the average temperature of the wall of the tank T.sub.wall,average(r,t) according to its thickness (radius r) and as a function of time (t), the maximum temperature reached in the thickness of the tank T.sub.wall,max(t) as a function of time, the minimum temperature reached in the thickness of the tank T.sub.wall,min(t) as a function of time and to regulate the flowrate of the gas flow as a function of said calculated current temperature of the tank.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0075] Other features and advantages will become apparent on reading the description hereinafter, given with reference to the figures in which:

[0076] FIG. 1 represents a schematic and partial view illustrating an exemplary tank filling installation able to implement the invention,

[0077] FIGS. 2 to 6 illustrate in a schematic and partial manner various logic diagrams illustrating examples of steps able to be implemented by the method according to the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0078] FIG. 1 schematically illustrates a filling (or bleed-off) station for a pressurized gas tank 1, in particular for fuel such as gaseous hydrogen.

[0079] The tank 1, for example a composite tank of type IV, is delimited by a wall 1 of cylindrical general shape having determined and known dimensions and thermo-physical properties.

[0080] The station can comprise at least one high-pressure hydrogen source 10, at least one transfer pipe 2 selectively linking the source 1 to the tank 1 and an electronic facility 4 for data acquisition, storage and processing such as a computer or microprocessor.

[0081] The electronic facility 4 pilots the transfer of gas between the source 10 and the tank 1 and can be programmed to calculate in real time at least one temperature of the tank (1) from among: the average temperature of the wall of the tank Twall,average(r,t) as a function of time (t), the maximum temperature reached in the thickness of the tank Twall,max(t) as a function of time, the minimum temperature reached in the thickness of the tank Twall,min(t) as a function of time and to regulate the flowrate of the gas flow and/or of the temperature of said gas as a function of said calculated temperature of the tank (cf. FIG. 3).

[0082] Of course, conventionally, in addition to the control of the extreme temperature (minimum and/or maximum) reached by the wall of the tank, the mass of gas in the tank is preferably controlled also (or any other parameter reflecting the quantity of gas in the tank). This mass of gas can be calculated conventionally on the basis of the calculated temperature of the gas and of the measured pressure of the gas.

[0083] The known input parameters for this or these calculations of estimations comprise for example: [0084] the thermodynamic properties of the gas (of the tank in particular of its liner and of composite structure), the geometry GE of the tank (length, diameter, etc.). These data are known constants. [0085] the known conditions of Pressure P(0), temperature T(0) and temperature of the wall Twall(0) at the initial instant t=0. These conditions can be measured or determined or approximated, [0086] the conditions in real time of Pressure of the incoming gas at the time t Pin(t), of temperature of the incoming gas Tin(t) at the time t, the pressure of the gas in the tank P(t) at the time t (measured for example in the pipe linked to the inlet/outlet of the tank 1), the ambient temperature Tamb(t) at the time t. [0087] heat exchange and correlation coefficients a, b, c, d (explained hereinafter).

[0088] The coefficients a, b, c, d can be obtained by experimental trials for each type of tank on the basis of tests of pressure rise and fall in the tank. These coefficients can if appropriate be correlated with dimensions or ratios of dimensions of the tank.

[0089] On the basis of these known input data, the electronic facility 4 can be configured to calculate in real time the following output data: [0090] the average temperature of the gas in the tank T(t)=Tgas,average(t) at the time t as a function of time t, [0091] the mass m(t) of gas in the tank at the time, [0092] the average temperature of the wall of the tank Twall,average(r,t) as a function of time t, r being the radius coordinate from the longitudinal axis of the tank, [0093] the maximum temperature reached by the wall of the tank Twall,max(t) as a function of time, [0094] the Richardson number Ri(t) for the gas in the tank at the time t (cf. hereinafter).

[0095] The average temperature of the wall of the tank Twall,average(r,t) represents the average in two dimensions (2D), that is to say that it represents the temperature of the wall layer at the coordinate r taken from the longitudinal axis of the tank. This temperature is homogeneous in two dimensions but can vary according to the radius r. This average temperature is calculated by solving for example the heat equation in the wall.

[0096] The maximum (respectively minimum) temperature reached by the wall of the tank Twall,max(t) as a function of time can be the temperature of the wall at the time t at the level of the interface between the gas and the wall.

[0097] An exemplary use of such a model for a filling station will be described hereinafter.

[0098] Let us assume a filling carried out at a constant inlet gas temperature. At each time interval the model (implemented by the electronic facility 4 which pilots the filling/bleed-off) estimates in real time the maximum temperature reached by the wall of the tank Twall,max(t) as a function of time.

[0099] If this maximum temperature becomes close to the allowable limit (85 C. for example), in this case the control facility 4 can reduce the pressure rise by acting for example on the control valve 3. This decrease in the pressure ramp (increase in pressure per unit time) reduces or eliminates the increase in the temperature. If the maximum temperature is below the allowable value, the rate of pressure increase can be increased.

[0100] This therefore entails a method of controlling the filling flowrate as a function of the estimated/calculated maximum temperature of the wall of the tank.

[0101] An exemplary application is illustrated schematically in FIG. 5. Thus, on the basis of the input parameters (steps 11, 12, 13, 14, 15) the average temperatures of the gas Tgas,average(t) as a function of time t and the maximum temperature reached by the wall of the tank Twall,max(t) as a function of time are calculated (step 16). On this basis, the state of charge SOC is calculated (step 17) and then this state of charge is compared with the target state of charge (100%). If the target state of charge is reached, filling is interrupted (step 19) otherwise it is continued and the maximum temperature of the tank Twall,max(t) is compared with the limit threshold 85 C. (less a safety factor TS) cf. step 20. If this temperature remains in the allowable limits (step 21) the filling rate can be maintained or increased and the process returns to the step of measuring the pressure of (step 15). If this temperature is not in the allowable limits (step 22) the filling rate can be reduced and the process returns to the step of measuring the pressure P(t) of (step 15).

[0102] Alternatively to or cumulatively with the control of the flowrate, the temperature of the gas can be controlled (the gas is cooled or its cooling is increased if the maximum temperature approaches the allowable limit). Such an example is illustrated in FIG. 6. The process of FIG. 6 is distinguished from that of FIG. 5 solely in that, on completion of step 17 of calculating the state of charge SOC, the process comprises a step 27 during which the Richardson number Ri of the gas is compared with a reference value Vr (here Vr=1). If the Richardson number R1 exceeds the reference value (Y, step 21) the filling rate can be maintained or increased and the process returns to step 16 of calculating the average temperature of the gas Tgas,average as a function of time t and the maximum temperature reached by the wall of the tank Twall,max(t) as a function of time. If the Richardson number Ri is less than the reference value (N, step 21) the maximum temperature of the tank Twall,max(t) is compared with the limit threshold (less a safety factor TS) cf. step 20. Depending on whether this maximum temperature of the tank Twall,max(t) reaches the limit threshold (less a safety factor TS (Y step 122)), a new gas inlet temperature is calculated (that is to say that the temperature of the filling gas is lowered). The process returns to step 11 in which the model is supplied with the temperature of the gas Tin(t).

[0103] If on the other hand this maximum temperature of the tank Twall,max(t) remains below the limit threshold (less a safety factor TS (Y step 121)), a new gas inlet temperature is calculated (that is to say that the temperature of the filling gas is increased). The process returns to step 11 in which the model is supplied with the temperature of the incoming gas Tin(t).

[0104] As illustrated schematically in FIG. 2, during filling, when the calculated temperature of the tank (1) reaches a determined high threshold (HT), the flow and in particular the flowrate of gas is decreased and/or the temperature of the gas supplied to the tank (1) is decreased by thermal exchange with a source of cold. Likewise, during bleed-off, when the calculated temperature of the tank reaches a determined low threshold (LT), the gas flow can be decreased.

[0105] FIG. 4 illustrates in greater detail a possible taking into account of the Richardson number Ri.

[0106] The Richardson number Ri for the gas in the tank 1 as a function of time is calculated. The method comprises a step 27 of comparing the Richardson number number Ri calculated with a determined reference value Vr lying between 0.05 and 1.5 and preferably between 0.05 and 0.15 and in particular equal to 0.1. When Richardson Number number Ri calculated is less than determined reference value Vr (step 127), the temperature of the gas in the tank 1 is considered to be homogeneous that is to say that the maximum temperature reached by the wall of the tank Twall,max(t) as a function of time is considered to be equal to the average temperature of the wall of the tank Twall,average(r,t) in contact with the gas as a function of time (t): Twall,max(t)=Twall,average(r,t), r being the radius starting from the longitudinal axis of symmetry of the cylindrical tank. At the level of the interface in contact with the gas (that is to say r=radius at the level of what constitutes the liner of the tank), r=radius of the liner.

[0107] When the Richardson Number number Ri calculated is greater than determined reference value Vr, the temperature of the gas in the tank 1 is considered to be heterogeneous that is to say that the maximum temperature reached by the wall of the tank Twall,max(t) as a function of time is not equal to the average temperature of the wall of the tank Twall,average(r=radius of the liner,t) in contact with the gas as a function of time (t), and under these conditions, the method can comprise a step of increasing the flowrate supplied to the tank 1 so as to decrease the value of the Richardson Number (Ri) calculated below the determined reference value Vr (step 227 FIG. 4).

[0108] A nonlimiting exemplary model for calculating the average temperature of the gas in the tank Tgas,average(t) and the extreme temperature Twall,max(t) (maximum or minimum) of the wall of the tank will now be described.

[0109] Said model can be based on: [0110] a mass and energy balance for the gas in the tank 1, [0111] an equation of state of the gas, [0112] correlations with dimensionless coefficients modeling the heat exchanges between the gas and the wall of the tank, and between the wall of the tank and the exterior environment [0113] a one-dimensional heat equation in the wall of the tank, [0114] a correlation between the maximum temperature of the wall of the tank as a function of time and the average temperature of the gas and of the wall in contact with the gas as a function of time. This correlation can be obtained by trials and/or simulations.

[0115] It will be possible to refer for example to document WO2013014346A1 (or the article Evaluating the temperature inside a tank during a filling with highly-pressurized gas, published in 2014, authors: Thomas Bourgeois and al. Seoul (Korea): Proceedings of the 20th World Hydrogen Energy Conference, 2014.

[0116] Calculational details of said model will be described hereinbelow. For the sake of simplification, the tank is considered to be filled with gas. However, the adaptation of the model to the case of a bleed-off or of a stabilization (neither filling nor bleed-off) will be described afterwards.

[0117] The model combines the mass and energy balances of the gas and of the equation of state of the gas.

[0118] For a filling, the temperature and the pressure of the gas in the tank are considered to be homogeneous. The gas entering the tank 1 possesses an enthalpy h.sub.in and the gas in the tank is considered to exchange heat with the wall via a thermal exchange coefficient k.sub.g. The mass of gas in the tank is considered to vary directly according to the incoming gas flowrate.

[0119] In this case,

[00001]$\frac{\mathrm{dm}}{\mathrm{dt}}={\stackrel{.}{m}}_{\mathrm{in}}$

[0120] Hereinafter, the mass variation as a function of time will be called

[00002]$\frac{\mathrm{dm}}{\mathrm{dt}}={\stackrel{.}{m}}_{\mathrm{in}}=\stackrel{.}{m}.$

[0121] The first energy equation of the model and the enthalpy balance are applied to the open system of the interior of the tank 1. The kinetic energy and the variations of gravitational energy are neglected. Knowing the volume V of the tank, the internal surface area S.sub.int of the tank and the specific enthalpy of the gas, we have the expression:

[00003]$\begin{array}{cc}m.Math.\frac{\mathrm{dh}}{\mathrm{dt}}=V.Math.\frac{\mathrm{dP}}{\mathrm{dt}}+k_g.Math.S_{\mathrm{int}}\left(T_{\mathrm{wi}}-T\right)+\stackrel{.}{m}\left(h_{\mathrm{in}}-h\right)& \left(\mathrm{expression}.Math..Math.1\right)\end{array}$

[0122] With these assumptions, the enthalpy variations are due to three factors: the compression of the gas, the incoming enthalpy, and the heat exchanges with the wall. The second energy equation is the definition of the enthalpy variation of a real gas:

[00004]$\begin{array}{cc}\mathrm{dh}=c_p.Math.\mathrm{dT}+\left(1-.Math..Math.T\right).Math.\frac{\mathrm{dP}}{}& \left(\mathrm{expression}.Math..Math.2\right)\end{array}$

[0123] By combining expressions 1 and 2 we obtain an equation describing the evolution of the temperature of the gas in the tank as a function of the pressure increase, of the temperature of the wall, of the gas flowrate and of the enthalpy of the incoming gas.

[00005]$\begin{array}{cc}m.Math..Math.c_p.Math.\frac{\mathrm{dT}}{\mathrm{dt}}=V.Math..Math..Math..Math.T.Math.\frac{\mathrm{dP}}{\mathrm{dt}}+k_g.Math.S_i\left(T_{\mathrm{wi}}-T\right)+\stackrel{.}{m}\left(h_e-h\right)& \left(\mathrm{expression}.Math..Math.3\right)\end{array}$

[0124] To complete the model, the following equation of state of a real gas can be used:

PV=nRZ(T,P)T(expression 4)

To estimate the evolution of the temperature of the gas the system of equations can be discretized by considering that certain derivatives can be calculated as variations and that certain variables at the instant t are close to the values at the previous instant (t1).

[0125] Thermodynamic parameters Cp, , h and Z can be estimated for each pressure and temperature by using the tables of the NIST standard.

[0126] At this juncture two discretizations can be undertaken according to the choice of the input parameters: mass flowrate Q(t), or pressure of the gas P(t). The term input parameter designates a variable is known either by its measurement (example the pressure measured in the filling/bleed-off duct) or known because it is provided in the model (for example a pressure increase of 0.2 bar per second).

[0127] The following paragraphs relate to the discretization of the equations in the case of the mass flowrate or pressure input datum.

[0128] Combining and discretizing expressions 3 and 4 we obtain:

[00006]$T_t=T_{t-1}.Math.\frac{1-\frac{m_{t-1}}{m_t}.Math.A_{t-1}}{1-A_{t-1}}+\frac{.Math..Math.{\mathrm{tk}}_{g_{t-1}}.Math.s_{\mathrm{int}}\left(T_{{\mathrm{wi}}_{t-1}}-T_{t-1}\right)+\left(m_t-m_{t-1}\right).Math.\left(h_{{\mathrm{int}}_{t-1}}-h_{t-1}\right)}{m_t.Math.c_{p_{t-1}}\left(1-A_{t-1}\right)}$$.Math.\mathrm{with},m_t=m_{t-1}+Q_t.Math..Math..Math.t$$.Math.\mathrm{with},A_{t-1}=\frac{{}_{t-1}.Math.T_{t-1}.Math.\mathrm{RZ}\left(T_{t-1},P_{t-1}\right)}{c_{p_{t-1}}.Math.M}$

[0129] On the basis of these equations, knowing the state at the previous time (t1), in addition to the flowrate signal Q(t) at the time t, it is possible to determine the temperature of the gas at the time t.

[0130] On the basis of the equation of state of the gas, knowing the pressure P at the time (t1) the temperature of the gas T at the time t and the mass m(t) at the time t, the pressure P(t) at the time t can be calculated.

[0131] With the following notation:

[00007]$A=\frac{V.Math..Math.{}_{t-1}.Math.T_{t-1}\left(P_t-P_{t-1}\right)}{.Math..Math.t}+k_{g_{t-1}}.Math.S_{\mathrm{int}}\left(T_{{\mathrm{wi}}_{t-1}}-T_{t-1}\right)-\frac{m_{t-1}}{.Math..Math.t}.Math.\left(h_{{\mathrm{int}}_{t-1}}-h_{t-1}\right)$$.Math.\mathrm{and}$$.Math.B=\frac{P_t.Math.\mathrm{VM}}{\mathrm{RZ}\left(T_{t-1},P_t\right).Math..Math..Math.t}$

[0132] It is possible to discretize the previous equations to obtain the expression for the temperature T at the instant t.

[00008]$T_t=\frac{c_{p_{t-1}}.Math.T_{t-1}+h_{{\mathrm{int}}_{t-1}}-h_{t-1}}{c_{p_{t-1}}-\frac{A}{B}}$

[0133] Here again, knowing the system at the previous time (t1) and the pressure value at the time t it is possible to calculate the temperature of the gas at the time t.

[0134] On the basis of the state equation, by knowing Tgas,average(t) and P(t) it is possible to calculate the mass of gas in the tank at the time t.

[0135] In the case of a bleed-off, the temperature of the gas in the tank can be calculated. The only difference with the previous equations resides in the fact that the enthalpy at the inlet is now the enthalpy at the outlet and is considered to be equal to that of the gas in the tank. Thus the term (h.sub.inh) of the expression is zero. The input datum in this case can be either the pressure in the tank or the outgoing mass flowrate.

[0136] The modeling of the heat exchanges is a significant parameter of the model. Unlike complex modelings via the Navier Stokes equations, the thermal exchanges between the gas and the wall can be modeled via correlations based on dimensionless numbers.

[0137] In the case of tank filling at high pressure 200 bar, 700 bar or 1000 bar, a correlation is advocated based on the Nusselt, Rayleigh and Prandtl numbers (NU.sub.Dint, Ra.sub.Dint and Re.sub.d.sub.in) for example according to the scheme described in document EP2824378A1.

[0138] The expression is for example:

NU.sub.Dint=aRa.sub.Dint.sup.b+cRe.sub.d.sub.in.sup.d

The Nusselt number (Nu.sub.Dint) is based on the internal diameter of the tank and represents the convective heat exchanges between the gas and the wall. The correlation is based on two terms. A first term represents the natural convection (based on the Rayleigh number) while the second term represents the exchanges by forced convection and depends on the Reynolds number.

[0139] The correlation coefficients a, b, c and d are assumed to be constant and depend solely on the geometry of the tank and the nature of the gas flow within it.

[0140] This model can determine this expression (and therefore the coefficients) by trials. They are therefore assumed to be known and fixed for various filling conditions.

[0141] In the case of a bleed-off the expression may be

NU.sub.Dint=aRa.sub.Dint.sup.b

[0142] that is to say that the heat exchanges are due solely to natural convection based on the Rayleigh number.

[0143] This type of correlation is well known in the literature.

[0144] When wind blows around the tank, the external exchanges of heat between the tank and its environment can be modeled with an equation of forced convection between the air and a cylinder according to a formula of the typo:

[00009]${\mathrm{Nu}}_a=\frac{k_a.Math.D_{\mathrm{ext}}}{{}_{\mathrm{air}}}=\left(\left(0.4.Math.{\mathrm{Re}}_{D_{\mathrm{ext}}}^{0,5}+0.06.Math.{\mathrm{Re}}_{D_{\mathrm{ext}}}^{\frac{2}{3}}\right).Math.{\mathrm{Pr}}_{\mathrm{air}}^{0.4}\right)$

[0145] If the wind is zero the Reynolds number can be considered to be zero. It is possible to choose a free convection correlation.

[0146] The modeling of the gas and of the heat exchanges between the gas and the wall have thus been explained, the principle of the model calculating the evolution of the temperature of the wall will now be described.

[0147] To solve the heat equation in the wall, the wall will be modeled as one-dimensional.

[0148] A heat balance is carried out in an elementary volume element dV lying between the portions of radius r and r+dr (with respect the longitudinal axis of the tank).

[0149] This elementary volume is an enclosed cylinder assumed to be homogeneous in temperature (T(r,t)). This elementary volume has a homogeneous thickness dr and an internal diameter r. Its internal length is L.sub.int+2(rr.sub.int) with L.sub.int and r.sub.int being respectively the internal length and the radius of an equivalent zero-dimensional cylinder (0D).

[0150] The heat exchanges with the elementary volume and through a heat flow j can be expressed according to Fourier's law {right arrow over (j)}={right arrow over (grad)}T(r, t).

[0151] The heat balance in the elementary volume can be expressed as follows:

[00010]${{.Math..Math.c_p.Math.\mathrm{dV}.Math.\frac{T}{t}=-{}_r.Math.\frac{T}{r}.Math.}_r.Math.S_r+{}_{r+\mathrm{dr}}.Math.\frac{T}{r}.Math.}_{r+\mathrm{dr}}.Math.S_{r+\mathrm{dr}}$

[0152] At the interface between the gas and the internal wall (liner) we consider continuity of the power at the time t+t Consequently:

[00011]$\begin{array}{c}P=k_g(t+.Math..Math.t.Math.).Math.A_{\mathrm{int}}\left(T_{\mathrm{gas}}\left(t+.Math..Math.t\right)-T\left(r_{\mathrm{liner}},t+.Math..Math.t\right)\right)=.Math.{}_{A_{\mathrm{int}}}^{}.Math.-\left(r_{\mathrm{liner}},t+.Math..Math.t\right)\\ .Math.\stackrel{\_}{\mathrm{grad}}.Math.T.Math.\stackrel{\_}{n}.Math.\mathrm{dA}\\ =.Math.{}_{A_{\mathrm{int}}}^{}.Math.-\left(r_{\mathrm{liner}},t+.Math..Math.t\right)\\ .Math.\frac{T}{r}.Math.\mathrm{dA}\end{array}$

[0153] At the level of the interface between the composite and the liner we consider equality of the flows (index w for the flow in one direction, for example west, and index e for the opposite direction).

[00012]$-\left(r_w,t+.Math..Math.t\right).Math.{\left(\frac{T}{r}\right)}_w=-\left(r_e,t+.Math..Math.t\right).Math.{\left(\frac{T}{r}\right)}_e.Math.$

[0154] We consider a single temperature point for this interface between the composite and the liner, expressed by T(r.sub.LC,t).

[0155] At the level of the interface with the environment we have the expression:

[00013]$-\left(r_w,t+.Math..Math.t\right).Math.{\left(\frac{T}{r}\right)}_w=k_a\left(t+.Math..Math.t\right).Math.\left(T\left(D_{\mathrm{ext}},t+.Math..Math.t\right)-T_{\mathrm{amb}}\right)+\left({T\left(D_{\mathrm{ext}},t+.Math..Math.t\right)}^4-T_{\mathrm{amb}}^4\right)$

[0156] The left-hand term represents the flow into the tank while the right-hand term is the flow out of the tank, on the surface of the tank.

[0157] The discretization of the one-dimensional wall equations has been described previously with the zero-dimensional discretization of the mass of gas and the energy balance. Moreover the previously described correlation of the heat flows with the wall makes it possible to determine (calculate) the values of average temperature of the gas as a function of time Tgas,average(t) and of average temperature of the wall of the tank Twall,average(r,t).

[0158] On this basis, the device must determine the maximum temperature of the wall Twall,max(t).

[0159] Accordingly the method uses a correlation between the average temperature of the wall of the tank Twall,average(r,t) and the maximum temperature of the wall Twall,max(t).

[0160] The temperature heterogeneities in the tank and the wall are considered to depend essentially on the gas flowrates and speeds. A possible correlation has the following form:

[00014]$T_{\mathrm{wall},\max }\left(t\right)=f\left(T_{\mathrm{wall},\mathrm{avearge}}\left(r_{\mathrm{liner}},t\right),T_{\mathrm{gas},\mathrm{average}}\left(t\right),\frac{L}{D},\frac{D}{d},\stackrel{.}{m}\right)$

[0161] To determine this correlation (function f) experiments (fillings, bleed-offs) can be carried out by measuring the gas temperatures and the temperatures obtained at the level of the wall. Simulations in two or three dimensions can make it possible to calculate the hot/cold points during filling/bleed-off.

[0162] On the basis of experimental measurements it has been observed that the Richardson number is very useful for determining the homogeneity or heterogeneity conditions of the temperature in the tank.

[0163] The Richardson number is given by

[00015]$\mathrm{Ri}=\frac{\mathrm{Gr}}{{\mathrm{Re}}^2}$$\mathrm{With}.Math..Math.\mathrm{Gr}=\frac{g.Math..Math.{}_g.Math..Math.T_g-T_{\mathrm{wi}}.Math..Math.D_{\mathrm{int}}^3}{v_g^2}$

[0164] The Reynolds number can be written in the following manner

[00016]${\mathrm{Re}}_{d_{\mathrm{in}}}=\frac{{}_{\mathrm{in}}.Math.V_{\mathrm{in}}.Math.d_{\mathrm{in}}}{{}_g}$$\mathrm{With}.Math..Math.v_{\mathrm{in}}=\frac{4.Math.\stackrel{.}{m}}{.Math..Math..Math.d_{\mathrm{in}}}$$\mathrm{or}.Math..Math.\mathrm{else}.Math..Math.{\mathrm{Re}}_{D_{\mathrm{int}}}=\frac{{}_g.Math.V_{\mathrm{bottom}}.Math.D_{\mathrm{int}}}{{}_g}$$\mathrm{With}$$V_{\mathrm{bottom}}=6.2.Math.\frac{d_{\mathrm{in}}}{L_{\mathrm{int}}}.Math.v_{\mathrm{in}}$

[0165] This expression is dependent on the time t and can be calculated at each step by the model. The calculated Richardson number can be compared with a reference value Vr.

[0166] This makes it possible to indicate the homogeneity level during the filling/bleed-off process.

[0167] For tanks of cylindrical general shape with a ratio L/D (Length L over diameter D) of less than 4.5 (L/D<4.5), the reference value may be of the order of 1.

[0168] Ri<1 indicates homogeneity conditions and Ri>1 indicates non-homogeneous conditions.

[0169] During gas transfer the transfer conditions can be adapted to maintain the homogeneity conditions. Under these homogeneity conditions, the maximum temperature reached by the wall of the tank Twall,max(t) is the average temperature of the wall in contact with the gas. No correlation is necessary in this case between the average temperature of wall in contact with the gas and maximum wall temperature.

[0170] For tanks in which the ratio L/D>4.5 the heterogeneity conditions can be considered to still be present. A correlation is necessary in this case.

[0171] This method (calculation) can be applied during the transfer of gas in a filling/bleed-off station. Of course, these calculations may be carried out a priori for each type of tank so as to pre-establish the optimal gas transfer conditions.

[0172] Simulations may in particular be undertaken to determine different filling speeds and the temperature profiles obtained. In this manner, it is possible to determine the optimal filling conditions beforehand (speed, flowrate, cooling).

[0173] The invention applies equally well to filling in order to control the heating of the tank and to bleed-off in order to control the cooling of the tank.

[0174] While the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications, and variations will be apparent to those skilled in the art in light of the foregoing description. Accordingly, it is intended to embrace all such alternatives, modifications, and variations as fall within the spirit and broad scope of the appended claims. The present invention may suitably comprise, consist or consist essentially of the elements disclosed and may be practiced in the absence of an element not disclosed. Furthermore, if there is language referring to order, such as first and second, it should be understood in an exemplary sense and not in a limiting sense. For example, it can be recognized by those skilled in the art that certain steps can be combined into a single step.

[0175] The singular forms a, an and the include plural referents, unless the context clearly dictates otherwise.

[0176] Comprising in a claim is an open transitional term which means the subsequently identified claim elements are a nonexclusive listing i.e. anything else may be additionally included and remain within the scope of comprising. Comprising is defined herein as necessarily encompassing the more limited transitional terms consisting essentially of and consisting of; comprising may therefore be replaced by consisting essentially of or consisting of and remain within the expressly defined scope of comprising.

[0177] Providing in a claim is defined to mean furnishing, supplying, making available, or preparing something. The step may be performed by any actor in the absence of express language in the claim to the contrary.

[0178] Optional or optionally means that the subsequently described event or circumstances may or may not occur. The description includes instances where the event or circumstance occurs and instances where it does not occur.

[0179] Ranges may be expressed herein as from about one particular value, and/or to about another particular value. When such a range is expressed, it is to be understood that another embodiment is from the one particular value and/or to the other particular value, along with all combinations within said range.

[0180] All references identified herein are each hereby incorporated by reference into this application in their entireties, as well as for the specific information for which each is cited.

Nomenclature and Units of the Terms Used

[0181] A surface area (m.sup.2) [0182] a Thermal conductivity (m.sup.2.Math.s.sup.1) [0183] c.sub.p Specific heat of the gas at constant pressure (J.Math.kg.sup.1.Math.K.sup.1) [0184] c.sub.v Specific heat of the gas at constant volume (J.Math.kg.sup.1.Math.K.sup.1) [0185] d Diameter of the injector of gas into the tank (m) [0186] D Diameter of the tank (m) [0187] e Thickness (m) [0188] g Acceleration due to gravity (m.Math.s.sup.2) [0189] h Specific enthalpy (J.Math.kg.sup.1) [0190] k Heat exchange coefficient (W.Math.m.sup.2.Math.K.sup.1) [0191] L Length of the tank (m) [0192] m Mass in the tank (kg) [0193] {dot over (m)} Mass flowrate into the tank (also Q) (kg.Math.s.sup.1) [0194] M Molar mass of the gas used (kg.Math.mol.sup.1) [0195] P Pressure of the gas (Pa) [0196] P.sub.0 Atmospheric pressure (Pa) [0197] q Heat flow (J.Math.s.sup.1.Math.m.sup.2) [0198] r Radius, coordinate in the wall of the tank starting from the longitudinal axis (m) [0199] R Ideal gas constant (J.Math.mol.sup.1.Math.K.sup.1) [0200] S Surface area of the tank (m.sup.2) [0201] t Time (s) [0202] T Temperature (K) [0203] T.sub.fe Temperature of the air in contact with the exterior wall of the tank (K) [0204] T.sub.fi Temperature of the gas in contact with the internal wall of the tank (K) [0205] T.sub.we Temperature of the wall in contact with the air (K) [0206] T.sub.wi Temperature of the wall in contact with the gas (K) [0207] V Volume of the tank (m.sup.3) [0208] V.sub.m Molar volume (m.sup.3.Math.mol.sup.1) [0209] Specific volume (m.sup.3.Math.kg.sup.1) [0210] Z Compressibility factor of the gas used in the real gas equation (dimensionless) [0211] Thermal expansion coefficient (K.sup.1) [0212] Ratio of specific heats c.sub.p/c.sub.v [0213] Emissivity of the external surface of the tank (dimensionless) [0214] Thermal conductivity (W.Math.m.sup.1.Math.K.sup.1) [0215] Dynamic viscosity (Pa.Math.s) [0216] .sub.JT Joule-Thomson coefficient of the gas (K.Math.Pa.sup.1) [0217] Density (kg.Math.m.sup.3) [0218] Speed of the gas (m.Math.s.sup.1)

Meaning of the Indices

[0219] air Air

[0220] amb Ambient

[0221] comp Property relating to the composite

[0222] ext External wall

[0223] f Final

[0224] g Gas

[0225] in Property or nature at the level of the inlet of the tank

[0226] int Internal

[0227] liner Property of the internal envelope (liner) of the tank

[0228] 0 Initial

[0229] w Property of the wall

[0230] Dimensionless Parameter

[0231] Nu.sub.g Nusselt Number of the gas,

[00017]${\mathrm{Nu}}_g=\frac{k_g.Math.D_{\mathrm{int}}}{}$

[0232] Nu.sub.air Nusselt Number of the air,

[00018]${\mathrm{Nu}}_{\mathrm{air}}=\frac{k_a.Math.D_{\mathrm{ext}}}{{}_{\mathrm{air}}}$

[0233] Ra.sub.Dint Rayleigh Number of the gas

[0234] Ra.sub.Dext Rayleigh Number of the ambient

[0235] Re.sub.d.sub.in Reynolds Number of the flow

[0236] Re.sub.D.sub.ext Reynolds Number of the air

[0237] Pr.sub.air Prandtl Number of the air,

[00019]${\mathrm{Pr}}_{\mathrm{air}}=\frac{{}_{\mathrm{air}}.Math.c_{p_{\mathrm{air}}}}{{}_{\mathrm{air}}}$