EP2205899A2

EP2205899A2 - Method for the real-time determination of the filling level of a cryogenic tank

Info

Publication number: EP2205899A2
Application number: EP08840893A
Authority: EP
Inventors: Fouad Ammouri; Florence Boutemy; Jonathan Macron; Alain Donzel
Original assignee: Air Liquide SA; LAir Liquide SA pour lEtude et lExploitation des Procedes Georges Claude
Current assignee: Air Liquide SA; LAir Liquide SA pour lEtude et lExploitation des Procedes Georges Claude
Priority date: 2007-10-26
Filing date: 2008-10-16
Publication date: 2010-07-14
Also published as: US8370088B2; FR2922992A1; FR2922992B1; US20100241371A1; WO2009053648A3; WO2009053648A2

Abstract

The invention relates to a method for the real-time determination of the filling level of a cryogenic tank (1) intended to house a two-phase liquid/gas mixture, in which at least one of the following variables is calculated for the liquid and optionally for the gas at each time step (t, t+ ?t...), namely: the level, volume or mass contained in the tank (1), whereby, at each time step, the method includes the measurement of the pressure differential (DP=PB-PH) (in Pa) between the upper and lower parts of the tank and at least one of the pressures (PH, PI) of said differential. The invention is characterised in that the method includes the following steps: use of a thermal model at each time step (t, t+ ?t...) to calculate the average temperatures of the liquid (Tl) and the gas (Tg) in the tank (1) on the basis of the measured pressure differential (PB-PH) and at least one of the pressures (PH, PI) of said differential; calculation of the change over time (t, t+ ?t...) in at least the density of the liquid (pl) (in kg/m3) on the basis of the average temperature of the liquid (Tl) and the pressures (PH) (PB) in the tank; calculation of the liquid level (hl) (in m) in the tank (1) by applying the general law of hydrostatics to the liquid, of type dP=- pl.g.dhl, on the basis of the calculated liquid density (pl) (wherein dP is the liquid pressure variation, pl is the density of the liquid, g is ground acceleration and dhl is the variation in the height of the liquid).

Description

Method for real-time determination of the filling level of a cryogenic tank

The present invention relates to a method for determining in real time the filling level of a cryogenic tank. The invention also relates to a method for determining in real time the quantity of fluid available at each moment.

This process requires knowing the parameters (geometry) of the tank. These parameters can be known to the system or estimated according to an estimation method (radius, height ...) independent.

The invention relates more particularly to a method of determining in real time the filling level of a cryogenic tank intended to contain a two-phase liquid-gas mixture in which is calculated at each time step for the liquid and possibly for the gas at least one of: the level, the volume or the mass contained in the tank, the method measuring at each time step the pressure differential between the high and low parts of the tank and at least one of the pressures of said differential.

The invention thus relates to the improvement of level measurement in cryogenic tanks in order to improve the efficiency of the liquid supply logistics chain of these tanks. The reservoirs concerned comprise an internal reservoir for storing the fluid (or inner casing) disposed in an external reservoir (or outer casing) with a vacuum between these reservoirs. The tanks store cryogenic liquids such as oxygen, argon, nitrogen with capacities of 100 liters to 100000 liters for example. Storage pressures can be between 3 bar and 35 bar.

In general, deliveries of cryogenic liquid by truck are based on two pieces of information: the time of delivery and the quantity available. The delivery time is based on the liquid crossing of a fixed threshold (delivery threshold usually 30% of the tank capacity). This threshold incorporates measurement uncertainty to prevent the user from drying out. By making reliable the liquid level measurement in the tank it is possible to lower this trigger threshold and thus reduce the delivery frequency and therefore the associated costs. The knowledge of the quantity of fluid available in each tank makes it possible to determine the routes of the delivery trucks. The more the expected quantity of delivery will be close to that actually delivered, the more the tour plan will be respected thus making it possible to fully exploit the potential benefits generated by the many improvements made on the logistics part.

This knowledge of the current filling level of the tanks is obtained by measurements and calculations of a representative physical quantity, for example the volume (generally used in France) or the mass (generally used in Germany).

The known techniques for estimating these quantities (volume or mass) are generally satisfactory but do not allow for sufficient precision or repeatability, especially for high-pressure storage tanks, which greatly reduces the efficiency of the corresponding supply chain.

Whatever type of measurement is used, it is necessary to know the state of the liquid in the tank to improve the accuracy of the measurement. Indeed, the volume measurement is determined using in general an average liquid density for each range of pressure tanks. In practice, this density depends on the evolution of the internal pressures and the temperature. As a result, the higher the pressure in the tank, the greater the volume measurement error.

The total mass measurement depends less on the density, hence a better measurement. However, this measure is not sufficient to determine the mass capacity of a tank at the time of delivery (it would be necessary to know the density of the fluid as for the calculation of the volume).

A known technique for measuring the level of fluid in a cryogenic tank is to determine a liquid level using the principle of the pressure difference on the height of the tank.

According to this technique the volume measurement (% V) is simply obtained from the measurement of a pressure differential (DP) as follows:

Vol% = K.DeltaP The factor "K" physically depends on the density k ₀ of the fluid and the geometry of the reservoir k (K = k / ko). In practice, this factor is determined and used in the configuration so as to have 100% of the volume occupied by the liquid during the overflow by the overflow (at the time of calibration of the tank).

The density of the liquid k ₀ is in fact not constant. It varies over time depending on the internal pressure and the temperature of the liquid when it is not saturated, or when filling with a subcooled liquid. Therefore, the volume result given by the known technique is not always relevant (0-10% error approximately). This phenomenon is especially felt for high pressure (HP) tanks, that is to say greater than 10 bar and especially greater than 15 bar.

In addition, two additional phenomena lead to large measurement dispersions at high pressure. In this case, the density of the liquid is very close to that of the gas, but the known measuring and estimating apparatus do not distinguish between the liquid and the gas. In addition, the volume of gas becomes greater than that of the liquid when the delivery is triggered. On the other hand, at low pressure, the density of the gas is negligible, which is why the known techniques give better results at relatively low pressures (a few bar for example).

Liquid level estimates are usually based on regular measurements of the pressure differential (eg every hour), pressure, and reservoir geometry (diameter, height, and maximum level).

The estimation errors are therefore mainly due to: a poor conversion of a pressure differential measured in the corresponding liquid level, to the difference between the measured pressure differential and the real pressure differential (effects of the measuring conduits connecting tank sensors), calibration errors (density of the liquid). In the case where the mass of the liquid that is to be measured (estimated), the measurement of the pressure differential DP is the image of a mass, one thus obtains measurements independent of the evolution of the density. Nevertheless, two masses must be distinguished: the total mass before filling (gas + liquid) and the mass capacity (mass of liquid after filling). The first can be easily obtained by measuring the differential pressure DP.

The second, however, requires knowing the characteristics and quantity of the product remaining in the tank in order to estimate the quantity of liquid actually deliverable by a truck.

As the density varies, even when working in bulk, it is impossible to relate a physical level to a geometric level.

On the other hand, it is possible, for example, to define a filling level at 100% that corresponding to the maximum mass that can be placed in the reservoir. This mass corresponds of course to a complete filling of the tank with the sub-cooled liquid. With such a calibration of 100%, we will be sure to never exceed 100%. However, we will never know what is the value corresponding to a full filling, this will depend on the conditions at the time of filling. Therefore we join the constraints of using the value of the volume.

Thus, whether working in bulk or in volume, the single level of liquid or the mass of liquid is not sufficient to meet both issues: trigger threshold of a delivery and quantity deliverable.

There are other principles of measures to obtain a level of liquid listed below with their disadvantages:

- Measurement by a float: its implementation is however delicate and the precision is weak with big risks of hysteresis (friction, blocking by the frost),

- Measurement via a submerged diver: this system is simple but there is possibility of hysteresis and the measurement depends on the density,

- Measurement by differential hydrostatic pressure: it is however necessary to know the density,

- Measurement by bubbling technique: however the measuring rod can clog, and an excessive gas flow leads to an error. Moreover, the measure depends on the liquid height above the lower orifice of the cane and the density and is therefore not very precise.

- Measurement via a resistive gauge: however, there is considerable dissipation of heat and derives resistance values over time,

Measurement by superconducting gauge: this technique is expensive and requires a significant response time to reach the equilibrium state,

- Measurement by conductimetric sensor: it is however sensitive to the conductivity of the liquid,

- Measurement by capacitive probe: this technique is however sensitive to the deposit in the tank, to the dielectric constant, requires a heavy calibration and constraining in terms of instrumentation,

- Measurement by tube of Taconis: there is however significant evaporation of liquid, and this works only for liquid helium (moreover there is no transmissible signal)

- Ultrasonic measurement: here the result depends on the surface of the liquid (agitated, or foam), the pressure, the temperature, the nature of the gas, dust, condensate ...

- Measure by the peson technique: there is in this case need to take into account the reactions of the pipes, moreover this technique is very expensive,

- Radar measurement: this method is robust and precise, but expensive,

- Gamma radiation measurement: this measurement, however, is sensitive to the density of the product crossed and is constraining in terms of safety (radioactive source).

In summary, either the method is accurate but very expensive (and difficult to implement), or it is simple, inexpensive but too sensitive to the environment of the reservoir to be reliably reliable.

An object of the present invention is to overcome all or part of the disadvantages of the prior art noted above.

To this end, the method according to the invention, moreover in conformity with the generic definition given in the preamble above, is essentially characterized in that it calculates: by a thermal model at each time step the average temperatures of the liquid and the gas in the tank from the measured pressure differential and at least one of the pressures of said differential,

the evolution over time at least the density of the liquid from the average temperature of the liquid and the pressures in the reservoir,

the level of liquid in the tank by applying the general law of the hydrostatic fluid to the liquid of the type: dP = - pl.g.dhl from the calculated density of liquid (with dP the variation of pressure of the liquid, pi the density of the liquid, g the terrestrial acceleration, and dhl the variation in the height of the liquid).

Unless otherwise stated, physical quantities are expressed in units SI (m for distances, m ³ for volumes, kg for masses, kg / m ³ for densities, Pa for pressures or pressure differentials, etc.). Furthermore, embodiments of the invention may include one or more of the following features:

the method calculates the density of the gas at each instant from a part of the average temperature of the gas obtained and estimated at the previous instant and, secondly, from the pressure differential and from at least one of the measured pressures of said differential.

the thermal model calculates, at each time step, the average temperatures of the liquid and the gas in the tank from a part of the measured pressure differential and at least one of the pressures of said differential and from the liquid and gas temperatures known from the previous moment,

the model uses as initial value for the temperature of the liquid and the gas, the initial temperature values obtained during a complete filling of the tank, the level of the liquid at this known instant of complete filling being the known level of the weir of the tank,

- the model uses the following calculation approximation: the gas after complete filling is at equilibrium liquid-vapor at the pressure of the tank,

the model uses the following calculation approximation: the liquid and the gas are constantly isothermal, each in its respective volume, but at respective temperatures which may be different, the model calculates at each time step the mean temperatures of the liquid and the gas in the tank from the mass and energy balances modeled and applied separately to the liquid and the gas contained in the reservoir,

the mass and energy balances modeled and applied separately to the liquid and the gas contained in the reservoir are made at a given instant on the basis of the density values and the volume of liquid and gas calculated from an estimate of the the instant and the model iterates the calculation of the average liquid and gas temperatures in the reservoir until the average liquid and a predetermined value towards the temperatures estimated at the preceding instant and in that after convergence the process resumes the steps of calculating the density and liquid level temperatures for the following instant,

- mass and energy budgets modeled and applied to gas use the enthalpy equation according to which the variation of the enthalpy of the gas corresponds to the thermal and mass exchanges applied to the gas, that is to say in taking into account at least one of the following exchanges: the exchange of heat between the liquid and the gas, the heat exchange between the outside of the tank and the gas, the heat exchange provided by a possible vaporization heater located usually below the tank, the vaporization of liquid in the tank,

the mass and energy balances modeled and applied to the liquid use the enthalpy equation according to which the variation of the enthalpy of the liquid corresponds to the heat and mass exchanges applied to the gases, that is to say in taking into account at least one of the following exchanges: the exchange of heat between the outside and the liquid, the heat exchange between the gas and the liquid, the heat exchange provided by a possible vaporization heater located in general below the tank, the vaporization of liquid in the tank, the consumption of liquid withdrawn by a user of the tank,

the method comprises measuring the temperature in the vicinity of the tank, to calculate the heat exchange between the outside and the tank,

the measurement of the pressure differential between the high and low parts of the reservoir is carried out by at least one remote pressure sensor connected to the high and low parts of the tank via respective measuring pipes, characterized in that the method corrects the calculated liquid level (hl) and / or the pressure differential measured taking into account an additional pressure difference value created by the gas present in the measuring pipes, the differential pressure measured remotely between the upper and lower parts of the tank being connected to the pressure differential called "real" between the high and low parts of the tank according to the formula: DP = PB -PH = DPreal-DPpipe,

the tank being of the jacketed type with inter-wall volume under vacuum, characterized in that the additional pressure difference value is calculated by adding or subtracting the gas and liquid levels in the measuring pipes by taking into account the calculated liquid level and neglecting the pressure influence of the pipe portions located in the inter-wall space,

- when the upper pressure measuring pipe connected to the upper part of the tank is situated outside the tank, the additional pressure difference value is calculated according to a formula of the type:

DPpipe = pg_pipe.g. (2len_w + total_length) where pg_pipe is the density of the gas at room temperature (outside the tank), g is the Earth's acceleration in m / s ² , len_w is the thickness of the tank wall and totaljength the total height of the inner tank and in that, when the upper pipe is located inside the tank in the inter-wall space, the additional pressure difference value (DPpipe) is calculated according to a formula of the type: DPpipe = DPside_gas + DPsideJiq;

DPside_gas being the pressure difference in the portion of the pipe connected to the upper part of the tank and facing the gas in the tank, DPsideJiq being the pressure difference in the part of the upper pipe and facing the liquid in the tank ; DPside_gas being obtained according to the formula _S = p DPside_gas ide_ _g as g hg wherein p _S ide_ _g as is the density of the gas calculated in the pipe to a temperature representative of the pipe, g being the gravitational acceleration and the height of hg gas in the tank; DPsideJiq being obtained according to the formula DPsideJiq = p _S ide_ii _q g hl where Psidejiq is the density of the gas in the upper pipe facing the liquid in the reservoir calculated at a temperature representative of the pipe, g being the earth's acceleration and hl the height of the liquid in the tank,

the method for dynamically determining the filling level of a cryogenic tank is intended to contain a diphasic liquid-gas mixture, according to any one of the preceding claims, comprising a step of measuring a pressure differential between levels situated respectively at the low and high ends of the tank, characterized in that it comprises a calculation of a volume and / or a mass of liquid in the tank from the pressure differential measured, the known or estimated geometry of the reservoir and at least one density of liquid in the tank, the method further comprising the steps of calculating the following quantities for a moment (t + Δt):

a first step of calculating a density of the liquid in the reservoir from the pressure measurements at the level of the low and high ends of the reservoir respectively, and the value estimated at the preceding instant of a temperature Tl of the liquid in the tank, a second stage of calculating the level of liquid in the tank by applying the law in hydrostatic fluid type: dP = - pl.g.dhl from the density of the liquid calculated in the previous step a third step of calculating the pressure level at the interface between the liquid phase and the gas phase in the reservoir from the calculated liquid level in the reservoir,

a fourth step of calculating the volume of liquid and gas in the reservoir from the level of liquid calculated in the second step,

a fifth step of calculating the energy balance applied to the gas of the reservoir from the gas enthalpy variation equation and taking into account at least one of the following heat exchanges: heat exchange between the liquid and the gas, the heat exchange between the outside of the tank and the gas, the heat exchange provided by a possible vaporization heater located in the tank, the vaporization of liquid in the tank, a sixth step of calculating the energy balance applied to the liquid of the reservoir from the equation of variation of the enthalpy of the liquid and taking into account at least one of the following exchanges: the exchange of heat between the outside and the liquid, the heat exchange between the gas and the liquid, the heat exchange provided by a possible vaporization heater located in the tank, the vaporization of liquid in the tank,

a seventh step of calculating the temperature Tg of the gas from the energy balance of the fifth and sixth steps, and an eighth step of comparing the temperature T (t + Δt) calculated for the following moment at the seventh step; with and the temperature T (t) estimated for the preceding instant, and when the difference between the temperature T (t + Δt) calculated for the following instant at the seventh stage and the temperature T (t) estimated for the moment preceding is greater than a determined threshold: a step of returning to the second step and of iteration until convergence, when the difference between the temperature T (t + Δt) calculated for the following instant in the seventh step and the temperature T (t) estimated for the previous instant is less than a threshold (convergence): reiteration of the above steps for the moment (t + 2Δt) with the pressure values measured for this moment.

Other particularities and advantages will appear on reading the following description, made with reference to the figures in which:

FIG. 1 represents a schematic view illustrating a first example of a cryogenic reservoir for implementing the invention (conduits external to the walls of the tank),

FIG. 2 represents a schematic view illustrating a second example of a cryogenic reservoir for implementing the invention (conduits internal to the walls of the tank),

FIG. 3 is a simplified and partial representation of the steps implemented by the method according to the invention,

FIG. 4 is a simplified and partial representation of the initialization steps implemented by the method according to the invention. The estimation method that will be described below may be implemented by a computer of a tank control system (local or remote). This method includes a pressure measurement (differential DP), an estimate and may include a remote transmission. The pressures are measured via conduits 11, 12 which may be in the inter-wall space of the reservoir (FIG. 2) or outside 11 (FIG. 1).

The tank 1 comprises a pressurizing device such as a vaporizer heater 3 able to take liquid to vaporize and reinject it into the tank. This heater 3 conventionally regulates the pressure within the tank 1.

For the sake of simplicity, the inner tank which stores the fluid will be hereinafter referred to only by the term "tank".

The liquid brought by truck when filling may also be considered in the steady state (temperature range of ⁰ 10 K around the balance, for example from 77.2 to 87.9 ° K for nitrogen) . The pressure of the liquid in the truck is chosen, according to the pressure of the tank, between 1 and 2 bar. The liquid is introduced into the tank by pumping.

When transferring liquid from a truck into the tank, relatively cooler liquid is added to the relatively hotter liquid in the tank. When liquid comes out of overflow, the tank is filled. After filling the vaporizer heater 3 changes the pressure if necessary. Thus, during the filling part of the liquid is consumed to increase and stabilize the pressure (of the order of 4kg for a tank of 10000 liters).

Between two fillings the tank 1 is subjected to the following phenomena:

the quantity of liquid decreases (consumption of the user) and the corresponding pressure drop is corrected by the heater 3,

- heat enters the tank (conduction, radiation).

After a certain period of equilibrium, liquid vaporizes in the reservoir which contributes to a loss of liquid. In addition, the density of the liquid changes and the liquid level is higher than if it had kept its delivery temperature. According to an advantageous feature, gas and liquid-specific temperatures are considered in the tank but without these temperatures being a function of the location in the tank. That is, in the following the gas temperatures Tg and liquid T1 are average temperatures.

According to an advantageous feature, the pressure at the interface between the liquid phase and the gaseous phase, taken as the average of the pressures at the bottom and at the top (PB and PH), is considered.

Preferably, the energy balance equations are applied separately to the gas and liquid phases of the reservoir.

The method does not directly measure the level of liquid in the tank but estimates it on the basis of a differential measurement DP = PB-PH of pressure between the high parts PH and low PB of the tank 1 and a pressure ( PB or PH).

The estimated liquid level is based on the pressure differential measured DP = PB-PH between the low and high ends of the tank.

According to the current method, the calculated liquid height hl1 (in m) is calculated according to the formula (equation 1):

DP {enPa) hll = p / 1. boy Wut

With fold a density value of constant calibration liquid in kg / m ³ (but modifiable by an operator); g being the acceleration of earth gravity in m / s ² .

Because the reservoir is not a geometrically perfect cylinder (elliptical ends, see Figures 1 and 2), the volume VU of liquid uses two equations depending on whether the liquid is at or below the elliptical F part (equations 2):

If hl1 is in the elliptical F zone

then VlX = Ti R ² M - -

otherwise - hlif

R being the radius of the tank (at its cylindrical portion). The maximum volume Vlmax of liquid in the tank 1 is calculated by replacing the height value of liquid hl1 in equation 2 by the maximum liquid height Hmax (equation 3):

, ι F Vl max = π R \ Hmax

The percentage of total liquid% VI in the reservoir is calculated using the following equation (equation 4):

% n = 1000 FZl

Vlmax

The mass of liquid contained in the millet reservoir is deduced using the density of the liquid fold (equationδ):

Ι / l = p / 1 VJl

Using the equations 1, 2 and 5 above the mass of millet liquid can be expressed as a function of the pressure differential measured DP = PB-PH (in Pa).

Depending on whether the liquid level hl1 is in the elliptical F zone (see case (a) below) or below (see case (b) below), the equation becomes (equation 6):

DP p li F case (a) ml 1 = π R ² g case (b)

DP mi l = - p / lπ EN ² - π p / lF - * g

Preferably according to a possible advantageous characteristic of the invention, the calculated liquid level hl1 is corrected taking into account an additional pressure difference value DPpipe created by the gas present in the measuring pipes 11, 12, both when the pipes 11 are located in the tank (Figure 2) or out of the tank (Figure 1). That is, the pressure sensors 4 are deported and "read" fluid-influenced pressures in the conduits 11, 12 connecting them to the upper and lower parts of the reservoir.

The differential pressure DP = PB-PH measured remotely between the upper and lower parts of the tank being connected to the so-called "real" pressure differential DPreal between the upper and lower parts of the tank according to the formula: PB-PH = DPreal- DPpipe

Case where the ducts are outside the tank wall (Figure 1): In this case, the relationship between the "real" pressures PHr, PBr, the real pressure differential DPreal = PBr-PHr and the measured differential DP = PB-PH is (equation 7): (see Figure 5)

PH = PHr - DPwall + DPtot - length PB = PBr + DPwall - DPamb

DPtot _ length = pg _ pipe. g (len_w + total _leng th - hl 1) with i DPamb = pg _ pipe .g (hl 1 + len_w) thιck_w

DPwall = g j pg (T (x), P) dx

DPwall is the pressure differential between the two ends of the vertical duct crossing the inter-wall (top or bottom).

DPtotJength being the pressure difference due to the gas pressure in the pipe portion 11 connecting the highest point to the measuring member 4 (sensor) remote.

DPamb is the pressure difference due to the gas pressure in the pipe portion 11 connecting the lowest point to the remote sensor member 4 (sensor). pg pipe being the density of the gas in the conduit thick_w being the thickness of the wall of the tank, T (x) being the temperature at point x and P the pressure. In this equation 7 the pressure differential DPwall between the two ends of the vertical duct passing through the inter-wall (top or bottom) can be considered substantially identical to the upper and lower parts (only the fact of gas in the duct). Considering the shape of the lower duct 12 in the inter-wall: the duct extends near the outer casing to "capture" the calories outside the tank and completely vaporize the fluid in the conduit 12 measurement. Between the upper and lower ends of this portion, the pressure is substantially the same (differential of 0.5 bar maximum).

In equation 7, pg_pipe is the density of gas at asbestos temperature (the outer conduits 11, 12 are preferably not isolated).

The real pressure differential DPreal = PBr-PHr can be deduced from the measured differential pressure DP = PB-PH according to the formula:

DP = PB - PH

D Pr eal = DP - 2 DPwall + pg_ pipe. g (2len _ w + total _ length)

len_w being the thickness of the walls of the tank and totaljength being the total height of the tank forming the storage volume.

Where the ducts are in the inter-wall (Figure 2):

Since the upper duct 11 is close to the outer casing, it can not be considered that it contains only gas at ambient temperature. Two temperatures are to be considered:

Tside-gas = the temperature of the gas in the upper part of the duct 11 (adjacent to the gas phase),

Tsidejiq = the temperature of the gas in the lower part of the duct 11 (adjacent to the liquid phase of the tank).

To estimate these temperatures, we assume a linear temperature profile between the ambient and the cryogenic liquid of the tank. Since the temperature of the cryogenic liquid T1 is colder than the temperature of the gas Tg, the temperature profile in the conduit near the liquid is different from the temperature of the cryogenic liquid T1. temperature profile adjacent to the gas. We obtain the following approximation (equation 9):

I TsiMae gas = I Tg

I TsiMae l / i'q = a Jpi-peIl ^{Tamb ~ Tl} I +, 1 T1 / len w

dpipe being the distance (spacing) between the upper duct 11 and the wall of the inner tank.

In addition, even when the duct 11 is located outside, there is a pressure drop due to the ambient temperature gas DPamb.

There are therefore three corrective terms for the pressure measured in the upper part, each of these three corrective terms (I, II, III) corresponding to a different gas density (equation 10, see Figure 2):

\ PH = PHr + DPside _ gas + DPside _ Uq - DPamb

[PB = PBr + DPwall - DPamb with

DPside _ gas = pside _ gas. g hg; pside _ gas = pg (Tside _ gas, P)

DPside _ Hq = pside _ Hq. g hl; pside _ Hq = pg (Tside _ Hq, P) hg = total length - hl

totaljength being the total height of the inner tank, hl and hg the actual heights of liquid and gas in that shell.

Thus, the relation between the real pressure differential DPreal = PBr-PHr and the measured pressure differential DP = PB-PH is (equation 11):

D Preal = DP + DPside gas + DPside Uq - DPwall

We can write the global formula (equation 12) DP = DVreal - DPpipe = (PB - PH) - DPpipe with: DPpipe =

[- 2 DPwall + pg_pipe, g il len_w + total _ lengtfi) (1 st case, figure 1) [DPside_gas + DPside_Hq - DPwall (2nd case, figure 2))

DPipe being the additional pressure difference value created by the gas present in the measuring pipes 11, 12.

As the thickness of the insulation of the inner tank (len_w) is a few centimeters, one can neglect the DPwall pressure differential between the two ends of the vertical duct passing through the inter-wall. Thus, equations 11 and 8 indicate that the measured pressure differential DP underestimates the real pressure differential DPreal. And since the liquid level in the internal reservoir and the real pressure differential DPreal are proportional, at low liquid levels this underestimation can be significant.

This underestimation is also greater for high-pressure tanks and for the case of measuring ducts 11 located in inter-island space.

According to the invention, the gas phase in the tank is taken into consideration. The real pressure differential DPreal is actually (equation 13):

DVr eal = [pg. kg. g + p / hl. boy Wut]

With hg and hl, the heights of gas and liquid in the tank.

Substituting this formula in formula 12 we obtain (equation 14):

DP = g.pl.hl + g.pg.hg -DPpipe.

(the last two members of this equation corresponding respectively to the effect of the gas in the tank and to the effect of the measuring ducts).

Using equations 1 and 14, the height of the calculated liquid h1 (measured according to the prior art) can be expressed as a function of the corrected actual liquid height h 1 (equation 15): _{hn =} PL _M _ DPpφe ₊ pg p / 1 p / .gp / 1

fold being the density of the liquid calibrated by default according to the procedure mentioned above. pg being the density of the gas.

The members A, B and C of equation 15 correspond respectively to the effects of the calibration, the effect of the measuring ducts 11, 12 and the effect of the gas in the tank.

Thus, the fact of opting for a fixed calibration density as in the prior art generates an error proportional to the difference between on the one hand the actual density of the liquid and on the other hand the constant density of liquid chosen during calibration.

Equation 15 shows that the error in the liquid level due to the effect of the gas in the tank partially offsets the error due to the effect of the measuring ducts.

By expressing the relative error on the liquid height the relation is written (equation 16):

hll - hl _ pi - fold DPpipe pg.hg hl ^~ fold DP pll hl

A B

The members A, B and C of equation 16 here also correspond respectively to the effects of the calibration, the effect of the measuring ducts and the effect of the gas in the tank.

From equation 4 the volume of liquid before filling VIa (equation 17) can be determined:

Therefore the delivered mass md is equal to (equation 18): md = (Vlmax-Vla) pll

This level estimate does not consider that the temperatures of the gas and the liquid are always at equilibrium (this would be false especially after filling). To follow the evolution of the temperature over time, two models can be developed (a model called "detailed" and a model called "constant flow").

Detailed model:

To describe the evolution of the liquid level and the mass it is necessary to know the densities of the liquid and the gas, which itself, depend on the pressure and the temperature. The thermodynamic model described below makes it possible to calculate these values.

By considering the gas and liquid temperatures as homogeneous in their respective volumes and constant insulation, the mass and energy balances modeled and applied separately to the liquid and the gas contained in the tank are carried out.

For an open volume, the mass and energy variation is the sum of the incoming masses minus the sum of the outgoing masses.

The tank can be divided into two working volumes: one for the gas phase and one for the liquid phase.

Applying the mass balance to the gaseous phase (mg = gaseous mass), we deduce the following equation (equation 19):

dm

, - = "m ^ι vap 4 ^~ -" m ^ι prc - 'm "g air

With ^m vap being the mass flow (in m / s) of incoming gas generated by the

vaporization of liquid, "* prc being the flow of incoming gas from

vaporizer; and ^m _g _air being the mass flow rate of gas exiting through the safety valve (vent). Concerning the energy of the gaseous phase, neglecting the kinetic and potential energies we obtain the following energy balance (equation 20):

d (m _g eg)

_Mc = m Hg _(pec T) + ήι _vap Hg (Teq) - ήt _{g ai} i _e rhG (Tg) + Q - W o Jt prc \ prc vap β ι - * * "is""ga

II IU

eg being the energy of the gas, Hg being the enthalpy of the gas.

In which Hg (T _prc ) is the enthalpy of the gas coming from the vaporizer, just

before going into the gas phase. Hg (Teq) equilibrium gas enthalpy (Teq)

equilibrium temperature) and Hg (Tg) is the enthalpy of the gas in the tank (at the temperature Tg of the gas).

According to the last equation, the variation of enthalpy is due to:

• ^m prc ** g (1 p _rc ) = the incoming energy due to the vaporizer.

• ^ ¹ _VUp Hg (TCq) = the incoming energy due to the vaporization of liquid.

m g_air ** g (* g) = the energy coming out when the venting valve is on.

• Q = the thermal power received by the gas phase is the sum of the contribution of the gas / liquid interface and the surface of the internal reservoir in contact with the gas phase.

• W = the mechanical power through the side surfaces of the gas phase.

Pg

By expressing the energy of the gas ^e g = Hg _j (Pg being the pressure of the gas

and pg being its density) the left part of the energy balance formula becomes (equation 21): eg ^dmg + mg ^ - - Vg ^ - + ^{MgPg dg> g} dt dt ^dg 9g

It is possible to find a relation expressing the variation of the dog-mass of the gas - - according to the formula (equation 22):

d ^m g. _{= Vg} * pg_ _{+ 9g} * ^v g dt dt dt

(Vg = volume of gas).

If the compressibility of the gas is taken into account, the only mechanical power W across the surface is produced by increasing or decreasing the liquid level (equation 23):

dVg

W = Pg dt

Finally, substituting equations 20, 21, 22 in equation 23, the enthalpy balance of the gas phase is written (equation 24):

mg ^ = fk _mc (Hg (T) - Hg (Tg)) + m (Hg (Teq) - Hg (Tg)) + Q ₊ Vg dPg dt dt

To simplify the model, we make the following approximations: - Cases where the ducts are intra-walled:

^T 8 ^{≈ τ} _prc the temperature of the gas from the vaporizer T _prc is substantially equal to the temperature (average) of the gas Tg in the tank (is verified if the return gas duct vaporized the inner tank). - Cases where the ducts are external to the walls:

Tamb ≈ T prc Thus, the flow ^m prc of incoming energy due to the vaporizer is relatively low. The gas passing through the vaporizer receives from the outside an energy estimated by H ¹ _PrC (Hg (TaItIb) -Hl (Tl)) and redistributes this energy by heat exchange against the reservoir towards the liquid and gaseous phases.

The heat Q supplied to the gas phase can be evaluated as (equation 25):

hg hpSg (Tamb-Tg) + hlëSlëcri-Tg) + - _r zm (Hg (Tamd) -Hl (Tl)) total _ length

III

Q = for hp.Sg (Taml + Tg) + h \ gS \ g (Tl-Tg) + m (Hg (Tamfy-Hl (Tl))

¹ U III for ducts external to the walls with hp: the exchange coefficient between the ambient and the gas in the tank hlg: the coefficient of heat exchange between the gas and the liquid in the tank SIg = TlR ² = surface

The terms I, II and III respectively correspond to:

I = the heat coming from the outside environment towards the gas in the tank through the walls

II = the exchange of heat between the liquid and the gas at the interface and through the walls of the tank

111 = the power released by the gas passing through the vaporizer towards the inside of the tank in the gas phase (proportional to the height of the gas present in the tank for the intramural ducts)

Thus, by replacing equation 25 in equation 24, the enthalpy balance for the gas phase Hg is written (equation 26): mg- ^dH r ^g == hhppSSggTTaammbb-TTgg)) ++ h ItlIggSSlIgg ((TTll-TTgg)) + ₊ - ^ ^hg ; -m _prc (Hg (T amb) - Hl (Tl)) dt total length dPg

+ M _v v _m ap (Hg (Teq) - Hg (Tg)) dt + Vg-

The same relations as above applied to the liquid phase give the following equations 27 and 28 ("g" replaced by "I"): dml j. ^{~ ~ m} vap ^{~ m} prc ^{~ m} cons

Ml ^ _ m = Hl (Tl) - m _rec Hl (Tl) + Q d ^t ^ l ^{^} nm

In mass balance equation 27 above, members I, II and III define:

I = ^m vap mass flow out of vaporization

II = ^m prc the outgoing mass flow vaporized in the vaporizer

NI = ^m cons mass flow leaving consumption by the user of the tank.

With regard to the energy balance applied to the liquid phase, the terms I, II, IN of Equation 28 above have the following meanings:

I = m _prc Hl (Tl) = outgoing power when the vaporizer works

N = m _cons Hl (Tl) = outgoing power when liquid is consumed by the customer

NI = Q = internal thermal power

In equation 28 the mechanical work is neglected because the liquid is considered incompressible. The power related to the vaporization is not taken into account because this equation is used only in the case where there is precisely no vaporization (liquid temperature below equilibrium temperature 7) <T _eq ).

In contrast, when the liquid temperature is higher than the equilibrium temperature ^ i - T _eq power entering the system will not increase the liquid temperature but vaporize. Then there is the following relation (equation 29):

m _vap (Hg (Teq) -Hl (Tl)) = Q

As for the liquid phase, the total thermal power entering the liquid phase is composed of three terms I, II, III (equation 30):

hp.Sg (Tamb - Tl) ₊ h \ g S Ig (T - Tg) ₊ - ^ m _prc (Hg (Tamb) - Hl (Tl)) vv ^'v v' total length i π _^ - ° _v, m Q = \ for intra - wall ducts hp.Sg (Tamb - Tl) + h \ g S Ig (Tl - Tg)

T ÎΓ for external wall ducts

with hp: the exchange coefficient between the ambient and the gas in the tank hlg: the coefficient of heat exchange between the gas and the liquid in the tank.

S Ig = TIR ² = surface

The first term (I) represents the natural convection between the outside ambient and the liquid located inside the tank.

The second (II) represents the natural convection between the liquid and the gas at the interface and the third (III) represents the other part of energy released by the gas passing through the vaporizer 3 and which is not not taken into account in the gas equation. Using equations 27 to 30 above, the enthalpy balance for the liquid phase can be expressed as follows (equation 31):

a) if Tl <Teq IIgg ((TTgg - TTll)) ++ - - - - - m _prc (Hg (Tamb) - H1 (Tl)) b) if Tl ≥ Teq H1 = H1 (Teq) h1 hpSg (Tam - T1) + h1g S Ig (Tg - T1) + - - m _prc (H1 (Tamb) - H1 (T1)) total length

™ _vap =

(Hg (Teq) - Hl (Tl))

Constant flux model:

A simplified model of the thermodynamic behavior of the tank between two fillings can be established on the basis of the following conditions:

1) the rate of liquid consumption is constant

2) the gas is always at the liquid-gas equilibrium, both in the tank and in the ducts,

3) the specific heat of the liquid is constant C pi,

4) the vaporizer effect is negligible

5) all of the heat passing through the walls is absorbed by the liquid.

Under these conditions, the correction of the measured differential pressure DP = PB-PH can be expressed in the two cases presented above in the following form (equation 32):

PH = PH + pg_pipe.g (H max + of _ len - M) PB = PB _B - pg pipe.gMl D Pr eal = DP + pg_ pipe. g (H max-H of _ len)

In this model, the density of liquid in the duct 9S-PΨ ^e is considered at room temperature in the first case (Figure 1) and at the equilibrium temperature in the second case (Figure 2). hp.Stot representing the power exchanged by degree of temperature difference can be calculated according to the mass flow rate of vaporized liquid and the latent heat of liquid oxygen at room temperature (298 ° K) according to the following equation 33:

•

AHlatent ⁰² atm. m I ₀ SsO ₂ hpStot = - ≈ - ² -

Tamb - Teq _a tm

Hlatent being the latent heat of vaporization of oxygen O ₂ under pressure

atmospheric, fttiossθ ₂ being the mass flow rate of oxygen loss characteristic of the reservoir, Tamb being the ambient temperature relative to the

measurement of tn iossθ _τ .

The evolution of the temperature of the liquid is given by the following equation 34:

mlCpl = hpStot (Tamb - Tl) - ^ → Tl <Teq dt

Tl = Teq - ?! → Tl ≥ Teq

With CpI = the specific heat of the liquid is constant.

From the first condition, the mass variation of the liquid can be deduced by the following formula:

ml = ^m init - ^consl cons ^t

With ml = mass of the liquid; m _in it = initial mass and ^m cons = mass flow rate consumed by the customer.

By substituting this in equations 33 and 34 and considering the constant Tamb ambient temperature, the following differential equation is obtained (equation 36): dTl _ d (Tamb - Tl) _ hpStot (Tamb - Tl) and dt (m _init - m _cons tt) Cpl

With Tl = liquid temperature

This is a separable differential equation whose solution can be obtained without difficulty by integration between the temperature T at the initial instant Tinit and the temperature at the instant T (t) (equation 37):

^{T (} f ^t) dd ((TTaammbb - TTll)) _ ff hpStotJt

Ti Jni _t ^((T Ta ^U m ^m h ^b - ^{~ Η} ^Tl)) J ^~ 0 ^{(~ tHinit} ^"1COH s *) Q> 1

The solution of equation 37 is given by equation 38 below:

T rli (st _* ) \ = T ramb u - I [Tramp u si> T rw, l, <T rpeq

Tl = Teq ^ → Tl ≥ Teq

Estimation of the temperature after filling:

Refilling with colder liquid causes a drop in temperature in the tank. In both models (constant flow model and detailed model) described above there is carried out a balance of the enthalpy between the fluid remaining in the reservoir and the delivered liquid. This makes it possible to estimate the temperature of the liquid after filling and the mass of liquid available.

During a filling there is a decrease in the mass of gas which can be related to two distinct effects.

The first effect is a condensation of the gas due to the cold liquid injected at the top. The second effect is a gas evacuation through the safety valve.

By filling at the top the first effect is privileged while the second effect is privileged when filling from below.

In the two estimation models considered below either the gas evacuated by the valve (model with condensation) is neglected, or it is estimated that all the mass of lost gas is evacuated by the valve (non-condensing model). Model with condensation:

By applying the enthalpy balance between the fluid remaining in the truck and the liquid of the truck, the resulting equation is written (equation 39):

Hl _ affermi _ after + Hg _ after.mg _ after = ml _ bef.Hl _ bef + ml _ deliv.Hl _ deliv + mg _ befilg _ bef

Hl_after being the enthalpy of liquid after delivery, ml_after being the mass of liquid after delivery, Hl_bef being the enthalpy of liquid before delivery, ml_bef being the mass of liquid before delivery, Hl deliv being the enthalpy of the liquid delivered, ml_deliv being the mass of liquid delivered, the same designations apply to the gas by replacing "I" by "g".

In this equation, the mass delivered in the reservoir WlI _ dellV is (equation 40): ml _ deliv = ml _ after + mg _ after - ml _ bef - mg _ bef

= Vl _ max. p / _ after + Vg _ after. pg _ after - ml _ bef - mg _ bef

To obtain an equation that depends solely on the temperature of the liquid T1 after filling, the working hypotheses are as follows: the filling is at 100%, that is to say that the liquid level is at most Hmax, the volumes of gas and liquid are known, the temperature of the gas is at equilibrium after filling With these two assumptions it is possible to determine the temperature after filling and the mass delivered during filling. Model without condensation:

In this model the gas is not considered, the resulting equations are (equation 41):

Hl _mix.ml _ after = ml _ bef.Hl _ bef + ml _ deliv. ## STR1 ## with ml, deliv = ml after ml, = max. p / _ after - ml _ bef

Hlmix being the enthalpy of the liquid mixture after filling. The same assumptions are maintained for calculating the temperature after filling and the mass available when filling. This first model underestimates the mass actually delivered during filling because it does not consider gas losses (venting through the valve). The second model (non-condensing) will overestimate the mass actually delivered because the reduction in mass during filling is only due to venting, so it will replace this mass with liquid from the delivery truck.

The numerical estimation can be conducted mathematically, we use: the letter u for the measured data used as input

(differential pressure measured DP and a measured pressure, for example PB), the letter x for the variables (temperature of the liquid and the gas (Tl

Tg), the letter p for the constant parameters

According to this method, the liquid mass ml and the mass of mg gas in the tank are calculated at each time step on the basis of the measured input data. After the measurement of the physical quantities, the calculation can comprise three phases:

1) initialization

2) simulation of the behavior of the tank between two fillings,

3) Reset when a fill is detected.

FIG. 3 schematically illustrates the process: after measuring the physical quantities (u = pressure differential step 100), an initialization process is performed (step 101, FIG. 3).

After initialization (101) the temperature and mass values are calculated by iteration for each time step since the last filling (step 102). If a filling is detected (step 103; "O", step 104), the method calculates the delivered liquid mass mdeliv and the liquid temperatures T1, gas Tg, masses of liquid ml and gas mg after filling according to the model above. As long as a filling is not detected (N, steps 103 and 105), the process continues to calculate by iteration for each time step the values of liquid temperature T1, gas temperature Tg, mass of liquid ml and mass of gas mg. To initialize the first temperature values of the liquid T1 and the gas Tg, the method makes the following assumptions: the first calculation point corresponds to the moment of a complete filling (100%) when the liquid level h1 = Hmax is maximum and the minimum gas level the gas is saturated at steady state.

The first assumption is based on the fact that liquid is evacuated during an overflow (the operator must make sure during a filling). The second hypothesis is based on the fact that during a filling a large part of the gas condenses (top filling in particular), the remaining gas can be considered at equilibrium.

The iteration of the computation until convergence makes it possible to lead to a reliable initial value for the temperature of the liquid TIO (FIG. 4).

The real pressure differential DPreal can then be calculated by equation 12 as a function of this initial liquid temperature TIO, as a function of the temperature of the gas Tg, as a function of the measured pressure differential DP = u and as a function of the constants p (Step 200 Figure 4).

The real pressure differential value DPreal makes it possible to calculate the density of the liquid at this instant pi according to the formula of step 201. With hg the height of gas, pg the density of the gas, hl, the height of liquid, g being the terrestrial attraction.

Depending on the pressure and the liquid density obtained, a new temperature TM for the liquid can be calculated (step 202, for example applying an equation representing the liquid temperature T1 as a polynomial function of the pi density). .

The difference between the new calculated temperature value TM and the previous TIo is calculated. If this difference Diff is greater than a threshold S, the procedure starts again at step 200 using the new value of the calculated temperature TM. Otherwise the new temperature TM is adopted as the initial temperature.

Then, after initialization (initial liquid temperature adopted), the differential equation for the gas and liquid temperatures is solved by iteration (for example by the Euler method).

Claims

According to these equations, the estimation procedure can be carried out as follows: Initialization of the integration step with the liquid and gas temperatures obtained at the previous iteration and measurement of the differential pressure DP, Differential correction according to the equation 12Calculation of liquid and gas heights, volume, mass and densityEstimation of new liquid and gas temperature values by discretizing equations 26 and 31Calculating the differences between the new temperatures obtained and the previous temperatures, If the differences are above a convergence threshold, the iteration is repeated with the last obtained temperature values. This process is used to estimate the temporal evolution of the temperatures as long as a new filling is not detected. Filling is detected during a measured differential pressure increase greater than a fixed threshold. Determining the level of filling of the reservoir thus makes it possible to determine the quantity of fluid that is available in the reservoir at each instant. CLAIMS

1. Method for determining in real time the filling level of a cryogenic reservoir (1) intended to contain a two-phase liquid-gas mixture in which is calculated at each time step (t, t + Δt ...) for the liquid and optionally for the gas at least one of: the level, volume or mass contained in the tank (1), the method measuring at each time step the pressure differential (DP = PB-PH) (in Pa ) between the upper and lower parts of the tank and at least one of the pressures (PH, P1) of said differential, characterized in that the method: calculates by a thermal model at each time step (t, t + Δt ...) the average temperatures of the liquid (Tl) and the gas (Tg) in the tank (1) from the measured pressure differential (PB-PH) and at least one of the pressures (PH, P1) of said differential,

calculates the evolution over time (t, t + Δt ...) at least the density of the liquid (pi) (in kg / m ³ ) from the average temperature of the liquid (Tl) and pressures (PH) (PB) in the tank,

- calculates the liquid level (hl) (in m) in the tank (1) by applying the general law of hydrostatics to the liquid of the type: dP = - pl.g.dhl from the density of liquid ( pi) calculated (with dP the variation of the pressure of the liquid, pi the density of the liquid, g the terrestrial acceleration, and dhl the variation of the height of the liquid).

2. Method according to claim 1, characterized in that the method calculates the density of the liquid (pi) and at each instant (t + Δt ...) from a part of the average temperature of the liquid (Tl) obtained and estimated at the previous instant (t) and, secondly, the pressure differential (PB-PH) and at least one of the measured pressures (PH, Pl) of said differential (DP).

3. Method according to claim 1 or 2, characterized in that the method calculates the density of the gas (pg) at each instant (t + Δt ...) from a part of the average temperature of the gas (Tg) obtained and estimated at the previous instant (t) and, secondly, the pressure differential (DP = PB-PH) and at least one of the pressures (PH, Pl) measured of said differential.

4. Method according to any one of claims 1 to 3, characterized in that the thermal model calculates at each time step (t + Δt) the average temperatures of the liquid and the gas (Tl, Tg) in the reservoir (1) from the measured differential pressure (DP = PB-PH) and at least one of the pressures (PH, P1) of said differential and from the known liquid and gas temperatures (Tl , Tg) in the previous instant (t).

5. Method according to claim 4, characterized in that the model uses as initial value for the temperature of the liquid (Tl) and gas (Tg), the initial temperature values obtained during a complete filling of the tank (1). ), the level of the liquid (hl) at this known full filling time being the known level of the weir tank (1).

6. Method according to claim 5, characterized in that the model uses the following calculation approximation: the gas after complete filling is at equilibrium liquid-vapor at the pressure of the reservoir.

7. Method according to any one of claims 1 to 6, characterized in that the model uses the following calculation approximation: the liquid and the gas are constantly isothermal each in its respective volume but at respective temperatures which may be different

8. Method according to any one of claims 1 to 7, characterized in that the model calculates at each time step the mean temperatures of the liquid and the gas (Tl, Tg) in the tank (1) from the balance sheets of mass (m) and energy modeled and applied separately to the liquid and gas contained in the tank (1).

9. Method according to claim 8, characterized in that the mass and energy balances modeled and separately applied to the liquid and the gas contained in the reservoir (1) are made at a time (t + Δt) on the basis of the values density and volume of liquid and gas calculated from an estimation of the liquid and gas temperatures at the previous instant (t) and in that the model iterates the calculation of the average temperatures of the liquid and the gas ( Tl, Tg) in the reservoir (1) until the average liquid and gas temperatures (Tl, Tg) calculated at a time (t + Δt) converge from a predetermined value to the temperatures estimated at the previous instant (t) and in that after convergence the process resumes the steps of calculating the temperatures (Tl, Tg) of density (pi) and liquid level (hl) for the following instant (t + 2Δt).

10. Process according to claim 8 or 9, characterized in that the mass and energy balances modeled and applied to the gas use the enthalpy equation according to which the change in the enthalpy (Hg) of the gas corresponds to the exchanges thermal and mass applied to the gas, that is to say taking into account at least one of the following exchanges: the heat exchange between the liquid and the gas, the heat exchange between the outside of the tank (1) and the gas, the heat exchange provided by a possible vaporization heater (3) located generally below the tank, the vaporization of liquid in the tank (1).

11. Method according to any one of claims 8 to 10, characterized in that the mass and energy balances modeled and applied to the liquid use the enthalpy equation according to which the variation of the enthalpy of the liquid (Hl ) corresponds to the thermal and mass exchanges applied to the gases, that is to say taking into account at least one of the following exchanges: the exchange of heat between the outside and the liquid, the heat exchange between the gas and the liquid, the heat exchange provided by a possible vaporization heater located generally below the tank, the vaporization of liquid in the tank (1), the consumption of liquid withdrawn by a user of the tank (1).

12. The method of claim 10 or 11, characterized in that it comprises a temperature measurement in the vicinity of the tank (1), to calculate the heat exchange between the outside and the tank (1).

13. Method according to any one of the preceding claims, characterized in that the measurement of the pressure differential (DP = PB-PH) between the upper and lower parts of the tank is performed by at least one remote pressure sensor connected to the parts. high and low of the tank via respective measuring pipes, characterized in that the method corrects the calculated liquid level (hl) and / or the pressure differential (PB-PH) measured taking into account a difference value of additional pressure (DPpipe) created by the gas in the measuring pipes, the differential of pressure (DP = PB-PH) measured remotely between the high and low parts of the tank being connected to the so-called "real" pressure differential between the high and low parts of the tank (DPreal) according to the formula: DP = PB- PH = DPreal-DPpipe.

14. The method of claim 13, the tank being of the jacketed type with inter-wall volume under vacuum, characterized in that the value of additional pressure difference (DPpipe) is calculated by adding or subtracting the levels of gas and liquid in the measuring pipes taking into account the calculated liquid level (hl) and neglecting the pressure influence of the pipe portions located in the inter-wall space.

15. The method of claim 14, characterized in that when the upper pressure measurement pipe connected to the upper part of the tank is located outside the tank, the additional pressure difference value (DPpipe) is calculated according to a formula of the type: DPpipe = pg_pipe.g. (2len_w + total_length) in which pg_pipe is the density of the gas at ambient temperature (outside the tank), g is the terrestrial acceleration, len_w is the thickness of the tank wall and totaljength the total height of the inner tank and that, when the upper pipe is located inside the tank in the inter-wall space, the additional pressure difference value (DPpipe) is calculated according to a formula of the type: DPpipe = DPside_gas + DPsideJiq;

DPside_gas being the pressure difference in the portion of the pipe connected to the upper part of the tank and facing the gas in the tank, DPsideJiq being the pressure difference in the part of the upper pipe and facing the liquid in the tank ; DPside_gas being obtained according to the formula _S = p DPside_gas ide_ _g as g hg wherein p _S ide_ _g as is the density of the gas calculated in the pipe to a temperature representative of the pipe, g being the gravitational acceleration and the height of hg gas in the tank; DPsideJiq being obtained according to the formula DPsideJiq = p _S ide_ii _q g hl wherein Psidejiq is the density of the gas in the upper pipe located in front of the liquid in the tank calculated at a temperature representative of the pipe, g being the ground acceleration and hl the height of liquid in the tank.

16. A method for dynamically determining the filling level of a cryogenic tank (1) intended to contain a two-phase liquid-gas mixture, according to any one of the preceding claims, comprising a step of measuring a pressure differential (DP = PB-PH) between levels located respectively at the low and high ends of the tank (1), characterized in that it comprises a calculation of a volume and / or a mass of liquid in the tank (1) to from the measured pressure differential (DP), the known or estimated geometry of the reservoir (1) and at least one density of liquid in the reservoir (1), the method further comprising the steps of calculating the following quantities for a moment (t + Δt):

a first step of calculating a density (pi) of the liquid in the tank (1) from the pressure measurements (PB, PH) at the low and high ends of the tank (1) respectively, and the estimated value at the previous instant (t) of a temperature T1 of the liquid in the reservoir (1), a second step of calculating the liquid level (h1) in the reservoir (1) by applying the hydrostatic law to the liquid type: dP = - pl.g.dhl from the density (pi) of the liquid calculated in the previous step, a third step of calculating the pressure level (Pl) at the interface between the liquid phase and the gas phase in the tank (1) from the liquid level (hl) calculated in the tank (1),

a fourth step of calculating the volume of liquid (h1) and gas in the reservoir (1) from the liquid level calculated in the second step, a fifth step of calculating the energy balance applied to the gas of the reservoir ( 1) from the gas enthalpy variation equation and taking into account at least one of the following heat exchanges: the heat exchange between the liquid and the gas, the heat exchange between the outside the tank (1) and the gas, the heat exchange provided by a possible vaporization heater located in the tank, the vaporization of liquid in the tank (1), a sixth step of calculating the energy balance applied to the liquid of the reservoir (1) from the equation of variation of the enthalpy of the liquid and taking into account at least one of the following exchanges: the exchange of heat between the outside and the liquid, the heat exchange between the gas and the liquid, the heat exchange provided by a possible vaporization heater located in the tank, the vaporization of liquid in the tank (1), a seventh step calculating the temperature Tg of the gas from the energy balance of the fifth and sixth stages, and an eighth step of comparing the temperature T (t + Δt) calculated for the following instant at the seventh step with and the temperature T (t) estimated for the preceding instant, and when the difference between the temperature T (t + Δt) calculated for the following instant in the seventh step and the temperature T (t) estimated for the preceding instant is greater than a determined threshold é: a step of returning to the second step and of iteration until convergence, when the difference between the temperature T (t + Δt) calculated for the following instant at the seventh step and the estimated temperature T (t) for the previous moment is less than a threshold (convergence): reiteration of the above steps for the moment (t + 2Δt) with the pressure values measured for this moment.