This disclosure relates generally to a calibration method used when determining quality of a gas.
High-quality gas is typically worth more than low-quality gas. If gas is offered for sale, its price may depend on its quality. Determining the quality of other gases, such as atmospheric gas, indoor air, etc., may be useful for environmental reasons.
Components are the chemically independent constituents of a gas. Natural gas, an example type of gas, is made of several components, some of which are hydrocarbons. The quality of natural gas may be based on the enthalpy of combustion of its individual components.
One technique for determining the quality of gas involves optical sensors, which may suffer from drift and loss of calibration. Optical sensors that measure gas are especially susceptible because of fluctuating temperatures and pressures. Optical sensors used for gas content measurement typically require precision of better than ±0.5%. Such precision requires relatively complex mechanical systems.
An example method of calibrating a detected intensity of gas components includes measuring an intensity of a reference gas, measuring an intensity of a calibration gas, and calibrating a measurement of an intensity of a test gas using at least a measurement of the intensity of the reference gas and at least a measurement of the intensity of the calibration gas.
An example gas quality assessment system includes a detector configured to determining an intensity of a provided gas. A manifold is configured to selectively communicate a test gas, a reference gas, or a calibration gas to the detector as the provided gas. A controller is configured to determine a calibrated intensity measurement of the test gas, wherein the calibrated intensity measurement is calibrated based on an intensity measurement of the reference gas and the calibration gas.
The various features and advantages of the disclosed examples will become apparent to those skilled in the art from the detailed description. The figures that accompany the detailed description can be briefly described as follows:
Referring to
Gas G communicates through the pipeline 30 from a supply 42 to a destination 46. The example gas G is natural gas. The supply 42 is a utility company. The destination 46 is a home or business.
The example meter 10 determines the composition of the natural gas within the interior 38 (and thus the composition of gas within the pipeline 30). The composition is used to determine the quality of the natural gas within the interior 38 and the pipeline 30.
In one example, a provider of the supply 42 utilizes the quality information when determining how much to charge the destination for the gas G. The meter 10 is mounted to the pipeline 30 between the supply 42 and the destination 46. In other examples, the meter 10 may be utilized at location of the supply 42, at the location of the destination 46, or at some other location.
The meter 10 includes a controller 50 that is operationally linked to the infrared light source 14, the filter 18, and the detector 22. To monitor the components of the natural gas within the interior 38, the controller 50 initiates the movement of infrared light waves 54 within the meter 10. The waves 54 propagate from the infrared light source 14. The waves 54 are mid-infrared spectrum waves ranging. The waves 54 pass through the gas G within the interior 38.
In this example, the infrared light source 14 generates waves within the mid-infrared spectrum. The filter 18 allows some of the waves 54 to reach the detector 22, and blocks some of the waves 54 from reaching the detector 22. The example filter 18 may be a cross-interference/broadband filter device that ensures only waves having certain lengths are detected by the detector 22.
In another example, the infrared light source 14 generates some, rather than all, the waves in the mid-infrared spectrum. In such an example, the filter 18 is not used. Another filter, such as a cross-interference filter, may still be used however.
The distance D between the infrared light source 14 and the detector 22 is the optical path length of the waves 54. As the waves 54 move through the gas G toward the detector 22, alkanes in the gas G absorb some of the light. For the wavelengths that pass through the filter 18, the detector 22 detects the light that has not been absorbed by alkanes in the gas G. The detector 22 includes optical sensors for detecting the light. As known, the optical sensors may experience drift and loss of calibration.
The controller 50 utilizes this information about the detected light to determine the percentage of the waves 54 that have been transmitted through the gas G to the detector. The percentages detected by the detector 22 represent the percentages of the waves 54 that have not been absorbed by alkanes in the gas G.
Referring to
In this example, the reference gas from the reference gas supply 42a is an inert gas, which has substantially no interference with waves 54 within the meter 10. Dry air and nitrogen are example types of reference gases.
The example calibration gas from the calibration gas supply 42b is a gas having a known chemical signature or composition, such as pure methane. Another example calibration gas may be a natural gas having a known chemical composition and signature.
In this example, the test gas from the test gas supply 42c is a natural gas having an unknown chemical signature.
Referring to
Referring now to
In one example, an operator may be interested in ultimately determining the quality of the test gas, which may be a natural gas. In such an example, the reference gas is first provided to the meter 10 for a period of time. The reference gas is turned off and the calibration gas is turned on and provided to the meter 10 for a period of time. Then the calibration gas is then switched off and the test gas is turned on for a period of time. The period of time is dependent on the instrument and desired accuracy.
The respective intensities of the reference gas, the calibration gas, and the test gas, are then plotted as shown in
In this example, both the reference gas and the calibration gas are used to calibrate the intensities of the test gas. In another example, a reference gas and calibration source that is not a gas (i.e. a liquid or solid) is used to calibrate the intensities of the test gas.
The measurements of the intensity of the test gas may be adjusted (or calibrated) based on the identified variations within the system. The adjusted intensities of the test gas are then used to determine the quality of the test gas, which can then be plotted as shown in
Referring to
The step 204 utilizes Beer's law to determine the concentrations of components using Equation 1 and absorption coefficients and path length from step 205.
In Equation 1, O.D. stands for optical density, α(λ) is the absorption coefficient expressed in cm2/mol of a single component of the natural gas mixture at a given wavelength, ci is the concentration of component i expressed in mol/cm3, and l is the optical path length of the measurement cell expressed in cm. The absorption coefficients are calculated or obtained from accepted spectral infrared databases.
In practice the measurement contains error from instrumentation and environment. The error can be traced to physical phenomena of the gas and equipment. Identification and development models for the operation of the equipment and behavior of the gas are impractical. Instead these phenomena are grouped together and considered as a whole based on materials with well characterized properties.
Baseline drift can be corrected by measuring a baseline signal utilizing a reference gas that does not absorb IR radiation at the wavelength of interest.
O.D′=O.D.Test Gas−O.D.Reference Equation 2
The corrected optical density, O.D.′, is the test gas measurement signal with the instrumentation baseline error removed. This is accomplished by subtracting the IR signal of the reference source, O.D.Reference, from the test gas measured signal, O.D.Test Gas.
The correction for instrument error can be accomplished by measuring and then comparing the absorption of IR light by the calibration gas with a known composition. These instrument errors arise from physical phenomena within the test set-up that lead to an apparent deviation in the absorption of IR light.
O.D.′=(α1,λ
In equation 3, αi,λ
ε1,λ
Equation 4 can be solved explicitly for the error term at each measured wavelength, ελ
Beer's law supplies component concentrations at step 206. This information is then used as the input to step 208, the Gibb's rule summarized in Equation 5.
ΔHNatural Gas=ΣiciΔHcombustion,i Equation 5
In Equation 5, ΔHcombustion,i is the alkane heat of combustion for alkane i expressed in kJ/mol from step 210 and ci is the alkane concentration in mol/cm3. In principle, the simple molar addition of the individual heats of combustion gives rise to the Higher Heating Value, 212.
In some examples, the energy flow rate of the mixture of gases is given by:
In Equation 6, Qideal is the energy flow rate given as a function of the volumetric flow rate; {dot over (V)}; compressibility factor, Z(T,P); the density, ρideal; and the mixture heat of combustion equivalent to Higher Heating Value, ΔHideal. The energy content of natural gas is an intensive thermodynamic property. A volume of natural gas has N+1 degrees of freedom, where N is the number of constituents that make up the gas mixture. In order to calculate, the exact energy content value, N+1 measurements are required. In a typical natural gas sample this would mean greater than nine independent measurements. This measurement of nine or more wavelengths corresponds to monitoring the composition of natural gas components from methane (CH3) to octane (C8H18) or higher. In a more specific example of the method 200, the algorithm development for determining the Higher Heating Value or gas quality at step 212 is composed of two equations, Beer's law at step 204 and Gibb's rule at step 208. The data flow between the two equations is shown in
Specifically, the system of linear equations corresponding to the components of the gas need to be solved. The algorithmic development for calculating the Higher Heating Value of a multispecies natural gas mixture is as follows.
The expansion of Beer's law at a given wavelength to take into account multiple gas species is given below.
O.D.λ
This expression states that the absorption of infrared light at a particular wavelength is the summation of individual component absorptions.
The same expression is valid at a different wavelength:
O.D.λ
Both these equations are linear. The optical density and absorption coefficients are unique and different for each wavelength and gas mixture. However, the concentration of the gas species remains constant in each equation. Thus, a system of linear equations can be compiled to convert absorption to concentration. The system of linear equations can be converted to matrix form as shown below:
In Equation 9, provision was made for possibility of using different path length, lj, for the measurements performed at different wavelengths, λj. A simpler representation of this matrix is:
Two methods are available to solve this expression for the concentration vector,
=
The solution above exists for a well defined system. In practice, a system of equations is either over or under determined. In this case an approximation of the solution needs to be made to fit the observed data. This method is normally referred to as the least squares method and is shown below (The superscript T refers to the transpose of the matrix
Accounting for instrument error and taking into account baseline compensation and test gas calibration, this becomes:
=[
The error matrix is represented by:
The simplification of the general error matrix may be applied in the more specific example of non-interacting gas.
Approaches in the past have relied on determining regions of the infrared spectra that could be speciated. In other words, concentrations of all species within a natural gas were determined individually. Only then was the higher heating value calculated. By contrast, some example methods disclosed herein remove this limitation. Specifically, these methods are applicable to convoluted spectral ranges. Convolution is due to multiple alkane absorption coefficients at a particular wavelength contributing to the overall absorption coefficient at a particular wavelength. In this region or with an apparatus that measures a convoluted spectrum, speciation is difficult. However, gas quality still can be determined. This is accomplished by taking the dot product and minimizing the Euclidean Normal, ∥
The higher heating value for natural gas mixture can be determined to an arbitrary accuracy by calculating the Euclidean Normal.
The use of the method described above and minimizing the Euclidean Normal to calculate natural gas quality are features of the disclosed examples. These features were used when evaluating a set of wavelengths in the range of eight to ten microns.
The preceding description is exemplary rather than limiting in nature. Variations and modifications to the disclosed examples may become apparent to those skilled in the art that do not necessarily depart from the essence of this disclosure. Thus, the scope of legal protection given to this disclosure can only be determined by studying the following claims.