The present application is related to and claims the priority benefit of German Patent Application No. 10 2016 121 226.1, filed on Nov. 7, 2016 and International Patent Application No. PCT/EP2017/075798 filed on Oct. 10, 2017, the entire contents of which are incorporated herein by reference.
The present invention relates to a method for determining the properties of a hydrocarbon-containing gas mixture and an apparatus therefor. The relevant gas mixtures are, in particular, natural gas or biogas.
Natural gas is a fossil fuel. It has a storage-facility-dependent composition. The principal constituent of natural gas is methane, with a molar fraction of, for example, 75% to 99%. Natural gas frequently also contains larger fractions of ethane (1% to 15%), propane (1% to 10%), butane, and ethene. Further minor constituents are hydrogen sulfide, nitrogen, carbon dioxide, and water vapor.
Biogas is a combustible gas mixture of varying composition which is produced by fermentation of biomass of any type. In the crude state, it contains, in particular, methane (up to 60%) and carbon dioxide as main constituents. Also included are nitrogen, oxygen, hydrogen sulfide, water vapor, and ammonia. Hydrogen sulfide and ammonia must be removed before burning or before feeding into the natural gas network. It is also advantageous to remove carbon dioxide before combustion.
In order to be able to reliably control combustion processes, it is necessary to quickly recognize the current calorific value of a gas mixture that is being fed directly to a process.
The Wobbe index W, which is defined as the quotient of the calorific value per unit volume H and the root of the relative density, serves as a technically more relevant characterization of the calorific value. The relative density is the quotient of the density ρ of the fuel gas and the density of dry air ρ0 under the same pressure and temperature conditions:
Gas mixtures of natural gas having the same Wobbe index can easily be exchanged during operation of a burner. Instead of comparing the density gradient, the equivalent coefficient of the mean molar masses of the gas and dry air can also be used.
The patent specifications, DE 69 231 977 T2 and U.S. Pat. No. 5,311,447 A1, disclose methods for determining the calorific value of a gas mixture from the thermal conductivity, the heat capacity, the optical absorption, and the viscosity of the gas mixture.
Publication GB 2 296 091 A describes a method for determining the calorific value or the Wobbe index of a gas mixture on the basis of its thermal conductivity, density, viscosity, and sound velocity. MEMS AG, under the designation Gas QS, offers a sensor which, on the basis of the thermal conductivity, the heat capacity, and the density of a gas mixture, determines its calorific value or Wobbe index.
The still unpublished patent application DE 102015117468.5 discloses a method for the method for determining the Wobbe index or the calorific value as well as the inert gas fraction of gas mixtures that have, in particular, natural gas or biogas, on the basis of the viscosity and the density or sound velocity.
However, the gas network increasingly serves as an energy store for alternatively generated gas from “Power to Gas” (H2) and “Biogas” (CH4+CO2) enriched with liquid petroleum gas (C2H6+C3H8). This significantly changes the gas composition in the network. The gas quality that reaches the consumer fluctuates widely, and fast changes can occur. The hydrogen fraction can be up to 20%. The Wobbe index is suitable only to a limited extent as a measure for good burner control, because H2 behaves differently than natural gas.
There is therefore a need for a simple, robust, and reliable method and corresponding measuring devices for determining properties of a gas mixture, in particular, its calorific value, when it contains hydrogen. It is therefore an aim of the present invention to provide such a method and such an apparatus.
The aim is achieved according to the invention by the method according to independent claim 1 and the device according to independent claim 11.
The method according to the invention for determining properties of a hydrocarbon-containing gas mixture which, in particular, has natural gas or biogas comprises:
allowing the gas mixture to flow through a measuring arrangement;
determining a pressure- and temperature-dependent thermal conductivity value, an associated temperature measurement, and an associated pressure measurement of the flowing gas mixture;
determining a hydrogen fraction XH2 of the gas mixture on the basis of the thermal conductivity value, the associated temperature measurement, and the associated pressure measurement;
determining a pressure- and temperature-dependent density measurement of an associated temperature measurement and of an associated pressure measurement of the flowing gas mixture;
determining a value for the mean molar mass or the standard density of the gas mixture on the basis of the density measurement, the associated temperature measurement, and the associated pressure measurement;
determining a value for the mean molar mass or the standard density of a residual gas mixture reduced by the hydrogen fraction on the basis of the mean molar mass of the gas mixture and of the hydrogen fraction;
determining a pressure-dependent and temperature-dependent viscosity measurement, an associated temperature measurement, and an associated pressure measurement of the flowing gas mixture;
determining a value for the Wobbe index of the residual gas mixture on the basis of the viscosity measurement, the associated pressure measurement, and the associated temperature measurement; and
determining a first value CVW for the calorific value of the residual gas mixture on the basis of the mean molar mass or the standard density of the residual gas mixture and of the Wobbe index of the residual gas mixture.
In a further development of the invention, the method further comprises determining the inert gas fraction of the residual gas mixture on the basis of the first value for the calorific value and the mean molar mass or the standard density of the residual gas mixture.
In a further development of the invention, the determination of the inert gas fraction comprises the following steps:
determining a second value CVM for the calorific value on the basis of the mean molar mass or the standard density of the residual gas mixture by means of a function which is independent of the viscosity or the Wobbe index; and
determining the inert gas fraction as a function of the first value for the calorific value of the residual gas mixture and the second value for the calorific value of the residual gas mixture.
The determination of the heat conductivity value λ at a given pressure and a given temperature is followed in one embodiment of the invention by a conversion into a standard heat conductivity λref under standard conditions, e.g., with a polynomial in λ, ρ, and T, in particular,
λref=ΣAi·Tti·λli·pvi,
wherein i=0 . . . k is an index of the summands, and the Ai of its coefficients as well as ti, li, and vi are whole number exponents. For example:
λref=A0+A1·T+A2·T2+A3·p+A4·λ+A5·λ·T.
In one embodiment of the invention, the hydrogen fraction XH2 is calculated as a function of the standard heat conductivity.
Determining the mean molar mass M of the gas mixture in one embodiment of the invention comprises calculating the mean molar mass as a function of density, pressure, and temperature,
M=f(ρ,T,p),
e.g., by means of a polynomial in ρ, p, and T, i.e.,
M=ΣBi·Tti·ρri·pvi,
wherein i=0 . . . k is an index of the summands, and the Bi of its coefficients as well as tj, ri, and vi are whole number exponents.
For example:
B0+B1·ρ·T/p+B2·ρ2·T/p+B3·ρ2/p+B4·(ρ·T/p)2+B5·p
The mean molar mass MR of the residual gas mixture can be calculated from the mean molar mass and its hydrogen fraction XH2 as:
MR=(M−XH2·MH2)/(1−XH2),
wherein MH2 is the molar mass of hydrogen.
In a further development of the invention, the determination of the value for the Wobbe index is preceded by the determination of a standard viscosity value of the flowing gas mixture that the flowing gas mixture would have at a standard temperature and a standard pressure, on the basis of the viscosity measurement, the associated temperature measurement, and the associated pressure measurement, wherein the Wobbe index is determined by means of the standard viscosity value of the gas mixture. The standard viscosity resp. standard viscosity can be determined, for example, with a polynomial in η, p, ρ, and T, i.e.,
ηref=ΣCi·Tti·pvi·ηni·ρri,
wherein i=0 . . . k is an index of the summands, and the Ci of its coefficients as well as ti, vi, ni, and ri are whole number exponents. For example:
ηref=C0+C1·η+C2·p+C3·T+C4·T2.
In an embodiment of this further development of the invention, the Wobbe index is calculated with a polynomial, in particular, a square or linear function of the standard viscosity value according to:
W=ΣAi·ηrefni,
wherein i=0 . . . k is an index of the summands, and the Ai of its coefficients as well as ni are whole number exponents.
For example:
W=A0+Aiηref.
The first value CVW for the calorific value of the residual gas may be calculated according to an embodiment of the invention as the product of the Wobbe index with the root from the quotient of the mean molar mass of the residual gas divided by the mean molar mass of dry air, thus:
CVW=W·(MR/Mair)1/2
The second value CVM for the calorific value of the residual gas can be calculated according to an embodiment of the invention as, in particular, a linear function of the mean molar mass M of the residual gas, for example:
CVM=D0+MR·D1,
wherein the Di are constants.
In a further development of the invention, the inert gas fraction Xinert-R-C in the residual gas is determined on the basis of a ratio between the second value for the calorific value of the residual gas and the first value for the calorific value of the residual gas, e.g.,
Xinert-R-C=E·(CVM/CVW−1),
wherein E is a constant.
In a further development of the invention, the method further comprises determining a value for the inert gas fraction)(inert of the flowing gas mixture on the basis of the value for the inert gas fraction of the residual gas mixture Xinert-R and the hydrogen fraction XH2, e.g., according to
Xinert=Xinert-R·(1−XH2).
In a further development of the invention, the method further comprises determining a value for the calorific value of the flowing gas mixture on the basis of the value for the hydrogen fraction, of the specific calorific value of hydrogen, and of the calorific value of residual gas mixture, e.g., according to
CVtotal=CVW·(1·XH2)+CVH2·XH2.
In a further development of the invention, determining the inert gas fraction takes place under the assumption that the inert gas substantially comprises carbon dioxide and nitrogen.
In a further development of the invention, to determine the molar mass of the flowing gas mixture, a value for the standard density value for the density of the flowing gas is first determined under standard conditions on the basis of the pressure- and temperature-dependent density measurement of the associated temperature measurement and of the associated pressure measurement of the flowing gas mixture.
In a further development of the invention, the viscosity and the density of the gas mixture are determined by means of a vibronic sensor, wherein the vibronic sensor is, in particular, a MEMS sensor which has at least one oscillating measuring tube that is flowed through and/or at least one oscillator surrounded by the flowing gas mixture, in particular, in the form of at least one oscillating cantilever or an oscillating tuning fork.
The device according to the invention for determining properties of a hydrocarbon-containing gas mixture, in particular, with a method according to the invention, comprises: a measuring arrangement through which the gas mixture can flow, having a temperature sensor, a pressure sensor, and a vibronic sensor for determining a viscosity measurement and, in some cases, a density measurement of the flowing gas mixture; a thermal conductivity sensor; and an evaluation unit for calculating properties of the flowing gas mixture.
In a further development of the invention, the vibronic sensor is a MEMS sensor which has at least one flow-through, oscillatable measuring tube and/or at least one oscillator surrounded by the flowing gas mixture, in particular, in the form of at least one oscillatable cantilever or an oscillatable tuning fork.
The invention is explained in the following in further detail on the basis of the exemplary embodiments shown in the figures.
The invention is based upon the statistical analysis of the physical properties of several hundred samples of gas mixtures which contain natural gas and hydrogen supplemented by gas mixtures randomly generated within the range of the composition ranges illustrated in
The development of the method according to the invention that is carried out on the basis of the above data is explained in more detail below.
It can be seen that gases with a lower calorific value generally have a higher dynamic viscosity. However, this does not apply to hydrogen, which has a lower viscosity than methane, even though its calorific value is lower. In this respect, the viscosity cannot readily be used as a measurand for determining the calorific value. On the other hand, hydrogen has a considerably higher thermal conductivity than the other gases represented in
As shown in
Aref=A0+A1·T+A2·T2+A3·p+A4λ+A5·λ·T, (1)
wherein the λ is the p, and T is measured thermal conductivity, and the Ai are constants.
This is confirmed by
As already detailed in patent application DE 10 2015 117 468.5, the Wobbe index of a low-hydrogen fuel gas mixture correlates well with its viscosity. The investigations connected with the present invention have shown that the viscosity values for hydrogen-containing fuel gas mixtures correlate with the Wobbe index of the residual gas mixtures that are purified of the respective hydrogen fraction, as depicted in
It is advantageous first to determine a standard viscosity under standard conditions nref from a current viscosity value η(T,p) at a given pressure p and a given temperature T, wherein the Wobbe index must then be calculated on the basis of the standard viscosity under standard conditions. The default viscosity ηref is to be calculated from a current viscosity value, e.g., with a polynomial in η, p, and T, in particular:
ηref=C0+C1·η+C2·p+C3·T+C4·T2 (2)
wherein the Ci are constants.
The Wobbe index W for the residual gas mixture is then determined as a linear function of the standard viscosity, i.e.,
W=Aηref+B, (3),
wherein A and B are constants.
From the Wobbe index for the residual gas mixture cleaned of the hydrogen fraction and determined on the basis of the viscosity measurement, its calorific value can be determined by multiplication with the square root of its specific weight, i.e.,
CVw=W·(MR/Mair)1/2 (4)
The mean molar mass MR of the residual gas mixture required for the calculation is determined on the basis of the density of the gas mixture and its hydrogen fraction.
M=B0+B1·ρ·T/p+B2·ρ2·T/p+B3·ρ2/p+B4·(ρ·T/p)2+B5·p, (5)
wherein the Bi are constants.
The mean molar mass MR of residual gas mixture can be calculated from the mean molar mass and its hydrogen fraction XH2 as:
MR=(M−XH2·MH2)/(1−XH2), (6)
wherein MH2 is the molar mass of hydrogen.
With the mean molar mass MR of the residual gas mixture thus determined, its calorific value can now be determined as CVw on the basis of the Wobbe index in accordance with equation 2.
On the other hand, the calorific value of a gas mixture shows a good correlation to its specific weight as long as the inert gases, nitrogen and carbon dioxide, do not play a role. In this case, the calorific value CVM can be estimated well on the basis of the mean molar mass with
CVM=D0+M·D1 (7),
wherein the Di are constants.
However, if the inert gases include nitrogen and carbon dioxide, the correlation is no longer valid, and the calorific value is overestimated. This makes the present invention useful for calculating a the fraction of inert gases Xinert-R-C in the residual gas mixture, using the deviation between the calorific value on the basis of the viscosity and the calorific value based exclusively upon the mean molar mass, in accordance with
Xinert-R-C=E·(CVM/CVW−1), (8)
wherein E is a constant.
It can be seen from
Xinert=Xinert-R-C·(1·XH2). (9)
The calorific value of the total gas mixture CVtotal is calculated in accordance with
CVtotal=CVW·(1−XH2)+CVH2·XH2. (10)
The gas mixture is comprehensively characterized with the calculated parameters.
In summary,
An exemplary embodiment of the method according to the invention shown in
In a step 20, the hydrogen fraction of the gas mixture is determined, on the basis of the heat conductivity measurement and associated pressure and temperature measurements, in particular, as a linear function of thermal conductivity at standard conditions, which is calculated here in accordance with equation 1.
In a step 30, the mean molar mass of the gas mixture is determined in accordance with equation 5 on the basis of the density measurement and the associated pressure and temperature measurements.
In a step 40, the mean molar mass of a residual gas mixture freed of the hydrogen is calculated on the basis of the mean molar mass of the gas mixture and of the hydrogen fraction.
In a step 50, the Wobbe index of the residual gas mixture is determined on the basis of the viscosity.
In a step 60, the calorific value of the residual gas mixture is determined in accordance with equation 4 on the basis of the mean molar mass of the residual gas mixture and of the Wobbe index of the residual gas mixture.
Optionally, in a step 70, the total calorific value of the gas mixture can be determined in accordance with equation 10 on the basis of the calorific value of the residual gas mixture and the hydrogen fraction.
As a further option, the inert gas fraction Xinert of the gas mixture can be determined in a step 80, details of which are shown in the flow diagram in
First, in a step 82, a second calorific value for the residual gas mixture is determined, on the basis of the mean molar mass of the residual gas mixture, in accordance with equation 7.
Next, in a step 84, the inert gas fraction Xinert-R-C of the residual gas mixture is calculated in accordance with equation 8 on the basis of the ratio of the second calorific value for the residual gas mixture to the calorific value determined via the Wobbe index.
In a step 86, the inert gas fraction of the gas mixture is calculated from this in accordance with equation 9.
The exemplary embodiment of a device according to the invention for carrying out the method according to the invention comprises a measuring cell 110 through which the gas mixture can flow and in which are arranged sensor elements (only schematically illustrated here), viz., a cantilever 122 for determining the viscosity and the density of a gas mixture in the measuring cell, a pressure sensor 124, a temperature sensor 126, and a thermal conductivity sensor 128. The sensor elements are preferably implemented using MEMS technology. The individual sensor principles are known per se to the person skilled in the art and need not be explained in more detail here. The apparatus further comprises an operation and evaluation unit 120 for driving the sensor elements, for evaluating their signals in order to determine the primary measurands, such as viscosity, pressure, temperature, thermal conductivity, and density, and for determining the mean molar mass, the hydrogen fraction, the Wobbe index and/or the calorific value and/or the inert gas fraction of a gas mixture flowing through the measuring cell 110. For this purpose, the operating and evaluating unit comprises a computation unit which can be of compact or modular design and can, in particular, comprise modules spatially separated from one another. The measuring cell 110 is connected, in particular, in a bypass arrangement to a gas line 130, wherein a volume flow of the gas mixture can be driven through the measuring cell 110 by means of a pressure differential across the measuring cell 110, e.g., by virtue of a diaphragm or a Venturi nozzle in the pipeline, or by means of a pump (not depicted here).
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PCT/EP2017/075798 | 10/10/2017 | WO |
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