Patent Description:
Liquefied natural gas (hereinafter, "LNG") is becoming an increasingly important fuel because the high energy content makes it efficient for transportation. LNG is natural gas which has been processed and liquefied by cooling to a low temperature. An example of typical transportation conditions is at a temperature of about -<NUM> and <NUM> kilopascals (absolute). The composition of LNG differs significantly from source to source and based on the processing applied to the LNG. Typical compositions may include nitrogen, methane, ethane, propane, and higher order hydrocarbons (with four or more carbons in the chain). Due to the variation in composition, it is difficult to know the energy content and burning properties of the different LNG mixtures at the point of delivery. LNG composition can greatly affect the value of the LNG mixtures, and it is necessary to assess the LNG content before purchase.

The current practice for determining energy content of discharged LNG is to measure the volume of LNG and calculate the mean density and mean calorific value from a composition analysis from a gas chromatograph. A common equation used is Eq. (<NUM>): <MAT> In Eq. (<NUM>), VLNG is the volume of LNG measured in the LNG Carrier's tanks, δLNG is the density of LNG calculated based on the chromatographic analysis and temperature of LNG, and HLNG is the mean mass-based Gross Calorific Value (GCV) of LNG calculated through chromatographic analysis of LNG.

As can be seen, existing systems require the use of chromatographs to determine relative composition of the gases. Gas chromatographs take significant time to make determinations, as the sampling and analysis process is slow. Further, chromatography is expensive and cannot be performed in real time. During the time it takes to analyze a sample, the composition of the flowing LNG could change dramatically, making the chromatographic determinations impractical for purposes of determining energy content of the LNG being assessed. Typical LNG and other liquid line measurements include simpler parameters, such as density, viscosity, pressure, and speed of sound (hereinafter, "SOS"). Measurement of these parameters is more practical on-line. However, these measurements are not direct measurements of energy content. Inferential determinations are ones in which there is not a direct relationship between the parameters being measured and the variable being calculated from the measured parameters. If typical fluid measurements taken at line conditions could be applied to inferential relationships to infer energy content, the resulting inferences could benefit from greater sampling rate and recency. The process would also benefit from avoiding costly sampling and chromatography procedures.

Accordingly, there is a need for systems that use inferential relationships with typical LNG measurements to determine live energy content values.

<CIT>discloses to use the density of the liquid phase, together with temperature and pressure, to determine the methane number of liquefied natural gas.

The invention comprises a method for inferring the energy content of a flow fluid in the gaseous state according to claim <NUM>. Further embodiments of the invention are disclosed in claims <NUM>-<NUM>.

The invention comprises also an apparatus for inferring the energy content of a flow fluid in the gaseous state according to claim <NUM>. Further embodiments of the invention are disclosed in claims <NUM>-<NUM>.

<FIG> and the following description depict specific examples to teach those skilled in the art how to make and use the best mode of embodiments of inferring energy content. For the purpose of teaching inventive principles, some conventional aspects have been simplified or omitted. Those skilled in the art will appreciate variations from these examples that fall within the scope of the present description. Those skilled in the art will appreciate that the features described below can be combined in various ways to form multiple variations of energy content inferences.

The invention does not necessarily correspond to the examples described below; its scope is defined by the independent claims.

When isolating the type of fluid to particular classes, for instance, natural gas mixtures, it can be seen that simple relationships between typically measured quantities in fluid flow arrangements can be used to infer energy content of the fluids. This is especially true if the measurements and inferential relationship are determined based on quantities in the liquid state in order to infer the energy content in the gaseous state. When the terms "infer" or "inferring" are used in verb form, it should be understood that this means to determine using inferential associations, for instance, using inferential relationships. This inferring can be done without any direct measurements of heat related metrics, for instance, thermal conductivity, heat capacity, and thermal diffusivity. Further, the inferring can be done without other traditional considerations for determining energy content, such as permittivity, laminar resistances, turbulent resistances, and refractive index. Also, the inferring can be done without artificially generating temperature and/or pressure drops across the measurement equipment beyond those temperature and pressure drops associated with typical flow measurement device interactions with the fluid.

Because these relationships are relatively simple for specific classes of gases, for instance, natural gas mixtures, the inferential relationships may be represented as linear combinations of the simple measurements in the liquid state with associated coefficients. For instance, the inferential relationship may be so simple that it merely accounts for measurement(s) of the fluid in the liquid state, perhaps at line conditions. The relationship may incorporate a corresponding coefficient for the measurement of the fluid in the liquid state. In an embodiment, the corresponding coefficient may have a temperature dependent relationship such that the corresponding coefficient varies with measured temperature of the fluid in the liquid state. In an embodiment, each of the measured values of the liquid in the fluid state (except, potentially, temperature) that are used in the inferential relationship, may have a different corresponding temperature dependent coefficient. It should be noted that, despite the mixture being called natural "gas," natural gas mixtures in both the liquid (i.e. LNG) and gaseous states are contemplated when using the term, natural gas. It should be noted that the specification is not limited to natural gas mixtures and may apply to other classes of fluid with energy content that may be in the liquid and gaseous states.

The inferential relationship may further have a shift term (A) that serves as a reference value relationship for the energy content. The shift term may also be temperature dependent (K<NUM>(T)). In embodiments of the invention, one of the measured values of the fluid in the liquid state is a measured density of the fluid in the liquid state. The measured density may be an element of a density term (B) of the inferential relationship. The density term (B) may be a product of the measured density and the corresponding coefficient for the measured density. In an embodiment outside the scope of the claims, the relationship may be a sum of the shift term and the density term.

In another embodiment outside the scope of the claims, the measured values of the fluid in the liquid state may further include a measured speed of sound of the fluid in the liquid state. The relationship may further account for the measured speed of sound. For instance, the relationship may further have a speed of sound term that incorporates the measured speed of sound. In this embodiment, the speed of sound term may be the measured speed of sound multiplied by a corresponding coefficient that corresponds to the speed of sound. In an embodiment outside the scope of the claims, the relationship may be a sum of the shift term, the density term, and the speed of sound term. In still other embodiments outside the scope of the claims, the speed of sound may be substituted with a viscosity measurement. For instance, the relationship may have a viscosity term that incorporates the measured viscosity. In this embodiment the viscosity term may be the measured viscosity multiplied by a corresponding coefficient that corresponds to the measured viscosity. In an embodiment outside the scope of the claims, the relationship may be a sum of the shift term, the density term, and the viscosity term.

Relationships, outside the scope of the claims, in which one measured quantity of the fluid in the liquid state that is not a measured temperature is incorporated may take the form of Eq. (<NUM>) <MAT> In Eq. (<NUM>), the IECGas is the inferred energy content value of the fluid in gaseous form. A is a shift term. B is a density term, as shown here, but it should be appreciated that other measured terms may be used instead in Eq. (<NUM>).

In all embodiments, the shift term (A) may be expressed as a constant or may be expressed as a temperature dependent quantity (K<NUM>(T)), perhaps having a simple relationship with temperature, as shown in Eq. (<NUM>): <MAT>.

The density term (B) may be expressed as a product of a measured density of the fluid in a liquid state (ρliquid) with a coefficient that corresponds to the measured density (K<NUM>), as shown in Eq. (<NUM>): <MAT>.

In an embodiment, the coefficient that corresponds to the measured density (K<NUM>) may be a temperature dependent coefficient (K<NUM>(T)), such that Eq. (<NUM>) becomes Eq. (<NUM>).

In an embodiment, outside the scope of the claims, Eq. (<NUM>) may take the form of Eq. (<NUM>) <MAT>.

It should be appreciated that embodiments where some or all of the coefficients and shift term are constants and do not vary with temperature.

In an embodiment outside the scope of the claims, in which more than one measured quantity of the fluid in the liquid state (the more than one measured quantity not including a measured temperature in the terms but having coefficients potentially dependent upon temperature) is used in the inferential relationship, the inferential relationship may take the form of equation (<NUM>): <MAT>.

The shift term (A) and the density term (B) may be as expressed in Eqs. (<NUM>) to (<NUM>). In an embodiment outside the scope of the claims, where the speed of sound of the fluid in the liquid state is one of the more than one measured quantity used in the inferential relationship, the relationship may have a speed of sound term (C), as shown in Eq. (<NUM>).

The speed of sound term (C) may be expressed as a product of a measured speed of sound of the fluid in the liquid state (SOSliquid) with a coefficient that corresponds to the measured speed of sound (K<NUM>), as shown in Eq. (<NUM>): <MAT>.

In an embodiment, the coefficient that corresponds to the measured speed of sound (K<NUM>) may be a temperature dependent coefficient (K<NUM>(T)), such that Eq. (<NUM>) becomes Eq. (<NUM>).

In an embodiment, outside the scope of the claims, the relationship expressed in Eq. (<NUM>) may be expressed as Eq. (<NUM>).

In various embodiments outside the scope of the claims, in which more than one measured quantity of the fluid in the liquid state (the more than one measured quantity not including a measured temperature in the terms, but having coefficients potentially dependent upon temperature), a viscosity measurement of the fluid in the liquid state may be used instead of or in addition to the speed of sound. In this embodiment, a viscosity term (D) might be used in addition to or instead of the speed of sound term (C).

The viscosity term (D) may be expressed as a product of a measured viscosity of the fluid in the liquid state (ηliquid) with a coefficient that corresponds to the measured viscosity (K<NUM>), as shown in Eq. (<NUM>): <MAT>.

In an embodiment, the coefficient that corresponds to the measured viscosity (K<NUM>) may be a temperature dependent coefficient (K<NUM>(T)), such that Eq. (<NUM>) becomes Eq. (<NUM>).

In an embodiment outside the scope of the claims, the inferential relationship may be a sum that incorporates a viscosity term (D) with a density term (B) and a shift term (A) and not a speed of sound term (C) as shown in Eq. (<NUM>): <MAT>.

In an embodiment outside the scope of the claims, the relationship of Eq. (<NUM>) may be expressed as Eq. (<NUM>).

In still another embodiment outside the scope of the claims, all of the shift term (A), density term (B), speed of sound term (C), and viscosity term (D) may be accounted for in the inferential relationship. For instance, the inferential relationship may be a sum of the shift term (A), density term (B), speed of sound term (C), and viscosity term (D), as shown in Eq. (<NUM>).

The inferential relationship may further account for any number of terms (hereinafter, "higher order terms") with squared or higher order exponentials of measured parameters used (hereinafter, "higher order measurements"), for instance, squares or higher order exponentials of one or more of measured density of the fluid in the liquid state, measured speed of sound of the fluid in the liquid state, and viscosity of the fluid in the liquid state. The inferential relationship may have corresponding coefficients for each of the higher order measurements. The corresponding coefficients of the higher order measurements may each have temperature dependencies. The higher order measurements may be represented in the inferential relationships in higher order terms. In various embodiments, the higher order terms may be products of each higher order measurement and each corresponding coefficient. One or more higher order terms may be incorporated into the inferential relationships as further sums, for instance, further sums of the higher order terms that would be added to the right side of any of Eqs. (<NUM>), (<NUM>), (<NUM>), (<NUM>), (<NUM>), (<NUM>), (<NUM>), and (<NUM>). An embodiment of the invention comprises the right side of equations (<NUM>) or (<NUM>) with at least one higher order term added.

In an embodiment, the inferential relationship may be quadratic in certain terms and may take the form of Eq. (<NUM>): <MAT> In Eq. (<NUM>) K<NUM>(T) and K<NUM>(T) are temperature dependent coefficients for squared density and squared viscosity measurement values respectively. An alternative embodiment is contemplated where the coefficients are constants that do not vary with temperature (ie. K<NUM>-K<NUM> are constants). This provides quadratic relationships between each of density and viscosity with the inferred energy content of a gas.

In an embodiment outside the scope of the claims, each of the terms of the inferential relationship may only have one of a measured value and a higher order measured value.

The temperature dependency of one or more of the temperature dependent coefficients (e.g. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), and/or K<NUM>(T)) can be determined by any number of relationships. For instance, the relationship between a coefficient and temperature could be linear, an embodiment of which is shown in Eq. (<NUM>): <MAT> In Eq. (<NUM>) G and H are constants (hereinafter, "coefficient constants") that can be determined by analysis means, for instance, regression, over several different gas mixtures at different ranges of temperatures. Each term may have a temperature dependent coefficient, and each temperature dependency of the coefficient may have at least one term-specific coefficient constant (e.g. G and/or H may be term-specific coefficient constants for the exemplary "xth" term in Eq. (<NUM>)). The "x" subscript is merely to denote that the coefficient relationship described in Eq. (<NUM>) is generic to any corresponding measurement value (or higher order measurement value, e.g. squared measured density) in the inferential relationship. "Relationship elements" may include one or more of the coefficients and coefficient constants. For the purposes of the specification, if a structure of inferential relationship is determined, the structure for instance of the form of one or more Eqs. (<NUM>)-(<NUM>), the inferential relationship may be characterized by this structure and relationship elements.

In another embodiment, the temperature dependency of one or more of the temperature dependent coefficients (e.g. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), and/or K<NUM>(T)) can be determined by a quadratic relationship with temperature, an embodiment of which is shown in Eq. (<NUM>): <MAT> In Eq. (<NUM>), G, H, and I may be constants that can be determined by analysis means, for instance, regression, over several different gas mixtures at different ranges of temperatures. Again, the "x" subscript is merely to denote that the coefficient relationship described in Eq. (<NUM>) is generic to any corresponding measurement value (or higher order measurement value) in the inferential relationship. Each of the temperature dependent coefficients (e.g. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), and/or K<NUM>(T)) may have different values of one or more of G, H, and I and/or may have different ordered polynomials in temperature for each of the coefficients such that more or fewer coefficients are used. One or more of the relationships expressed in Eqs. (<NUM>)-(<NUM>) could be used to infer values of one or more of MN, a LFL, a WI, a GHV, and a NHV from typical measurements taken at line conditions.

Examples of these implementations are shown in <FIG> and their corresponding descriptions.

<FIG> shows a block diagram of an embodiment of a flow fluid measuring system. The system <NUM> has a vibratory sensor <NUM>, an optional speed of sound sensor <NUM>, and an optional additional vibratory sensor <NUM>. It should be appreciated that any vibratory sensor <NUM> system could be used, for instance, a Coriolis flow meter, a fork densitometer, a fork viscometer, and/or the like. The same applies to the optional vibratory sensor <NUM>. In various embodiments, multiple vibratory sensors <NUM> of the same or different types may be used in series to determine measurements to be used in inferential determinations of energy content.

The vibratory sensor <NUM> and/or <NUM> can be used to provide typical flow fluid and/or fluid flow measurements of a fluid that interacts with the vibratory sensor. Typical measurements provided by vibratory sensors <NUM> and/or <NUM> may include, for instance, one or more of density, viscosity, speed of sound, mass flowrate, and volumetric flowrate of a fluid in a liquid state. The vibratory sensor <NUM> and the optional additional vibratory sensor <NUM> may be different types of vibratory sensors, such that they are structured differently and/or may provide different measurements from one another. For instance, the vibratory sensor <NUM> may be a fork viscosity meter and the optional additional vibratory sensor <NUM> may be a Coriolis flow sensor. This is merely exemplary, and all variations of potential flow sensors <NUM> and/or combinations of flow sensors <NUM> and optional additional flow sensors <NUM> are contemplated.

The vibratory sensor <NUM> and/or <NUM> may be mounted in a pipe or conduit, a tank, a container, or other fluid vessels. The vibratory sensor <NUM> and/or <NUM> can also be mounted in a manifold or similar structure for directing a fluid flow. However, other mounting arrangements are contemplated and are within the scope of the description and claims.

In an embodiment, the vibratory sensor <NUM> and/or <NUM> may be a fork meter, for instance a fork viscosity meter or a fork density meter. The vibratory sensor <NUM> and/or <NUM> may have a meter electronics <NUM>, a driver <NUM>, a first tine 104a, a second tine 104b, a response sensor <NUM>, a temperature sensor <NUM>, and a communication link <NUM>. The vibratory sensor <NUM> operates to provide fluid measurements. The vibratory sensor <NUM> may provide fluid measurements including, for instance, one or more of a fluid density (ρ), fluid temperature (T), a fluid viscosity (η), a mass flowrate, a volumetric flowrate, and a pressure (P) for a fluid, including flowing or non-flowing fluids. This listing is not exhaustive, and the vibratory sensor <NUM> and/or <NUM> may measure or determine other fluid characteristics.

The meter electronics <NUM> is a processing circuit that processes raw signal data for taking measurements and/or processing programming modules. The meter electronics <NUM> may be an embodiment of the computer <NUM> shown in <FIG>. The meter electronics <NUM> controls operation of the driver <NUM> and the response sensor <NUM> of the vibratory sensor <NUM> and can provide electrical power to the driver <NUM> and the response sensor <NUM>. For example, the meter electronics <NUM> may generate a drive signal and provide the generated drive signal to the driver <NUM> to generate vibrations in the first tine 104a. The first tine 104a is an immersed element of the vibratory sensor <NUM>. The generated drive signal can control the vibrational amplitude and frequency of the first tine 104a. The generated drive signal can also control the vibrational duration and/or vibrational timing. It should be noted that the meter electronics <NUM> may represent multiple components and products that are used in unison but perhaps sold separately. For instance, the meter electronics <NUM> may comprise electronics of the meter and the electronics of other communicably coupled elements, for instance, a transmitter or other device the use of which requires the meter and its electronics.

The driver <NUM> is an element that drives motions. The first tine 104a is an element that is vibrated and interacts with a fluid. The driver <NUM> may receive drive signals from the meter electronics <NUM> to vibrate the first tine 104a. The second tine 104b is another immersed element that has a resulting vibration, perhaps driven by the vibration of the first tine 104a. The second tine 104b is coupled to a response sensor that measures the vibratory response of the second tine 104b, such that the relationship between the vibratory response of the second tine 104b and the driver signal applied to the driver <NUM> that drives the first tine 104a, is representative of properties of the fluid. These vibrations may be driven to allow for flow fluid and/or fluid flow measurements to be determined by the meter electronics <NUM>. The temperature sensor <NUM> is a device that measures temperature. Fluid flow and/or fluid flow measurements may have temperature dependencies, so the temperature sensor <NUM> may provide temperature data to the meter electronics <NUM> for use in the measurements.

The meter electronics <NUM> can receive a vibration signal or signals from a response sensor <NUM> that detects motion and/or vibrations of the second tine 104b. In an embodiment, the meter electronics <NUM> may drive the vibratory element in a phase lock, such that the command signal provided to the driver <NUM> and the response signal received from the response sensor <NUM> are phase locked. The meter electronics <NUM> may process the vibration signal or signals to generate a density (ρ) measurement, for example. The meter electronics <NUM> processes the vibration signal or signals received from the response sensor <NUM> to determine a frequency of the signal or signals. Further, or in addition, the meter electronics <NUM> processes the vibration signal or signals to determine other characteristics of the fluid, such as a viscosity (η). In alternative embodiments, the meter electronics <NUM> may also determine a phase difference between upstream and downstream signals, that can be processed to determine a fluid flow rate, for example. As can be appreciated, the phase difference is typically measured or expressed in spatial units such as degrees or radians although any suitable unit can be employed such as time-based units. If time-based units are employed, then the phase difference may be referred to by those in the art as a time delay between the vibration signal and the drive signal. Other vibrational response characteristics and/or fluid measurements are contemplated and are within the scope of the description and claims.

The meter electronics <NUM> can be further coupled to a communication link <NUM>. The meter electronics <NUM> may communicate the vibration signal over the communication link <NUM>. The meter electronics <NUM> may also process the received vibration signal to generate a measurement value or values and may communicate the measurement value or values over a communication link <NUM>. In addition, the meter electronics <NUM> can receive information over the communication link <NUM>. For example, the meter electronics <NUM> may receive commands, updates, operational values or operational value changes, and/or programming updates or changes over the communication link <NUM>. In various embodiments, the communication link <NUM> may be an embodiment of or communicatively coupled to a communicative coupler <NUM>.

The vibratory sensor <NUM> and/or <NUM> may provide a drive signal for the driver <NUM> using a closed-loop circuit. The drive signal is typically based on the received vibration signal. The closed-loop circuit may modify or incorporate the vibration signal or parameters of the vibration signal into the drive signal. For example, the drive signal may be an amplified, modulated, or an otherwise modified version of the received vibration signal. The received vibration signal can therefore comprise a feedback that enables the closed-loop circuit to achieve a target frequency or phase difference. Using the feedback, the closed-loop circuit incrementally changes the drive frequency and monitors the vibration signal until the target phase is reached, such that the drive frequency and vibration signal are phase locked at or near the target phase.

Fluid properties, such as the viscosity (η) and density (ρ) of the fluid, can be determined from the frequencies where the phase difference between the drive signal and the vibration signal is <NUM>° and <NUM>°. These desired phase differences, denoted as first off-resonant phase difference φ1 and second off-resonant phase difference φ2, can correspond to the half power or 3dB frequencies. The first off-resonant frequency ω1 is defined as a frequency where the first off-resonant phase difference φ1 is <NUM>°. The second off-resonant frequency ω2 is defined as a frequency where the second off-resonant phase difference φ2 is <NUM>°. Density (ρ) measurements made at the second off-resonant frequency ω2 can be independent of fluid viscosity (η). Accordingly, density (ρ) measurements made where the second off-resonant phase difference φ2 is <NUM>° can be more accurate than density (ρ) measurements made at other phase differences.

In some embodiments, the vibratory sensor <NUM> may only determine one of the density (ρ) and viscosity (η) with another implement determining the other of the density (ρ) and viscosity (η), the other implement perhaps being a different vibratory meter.

Various embodiments of the vibratory sensor <NUM> are contemplated, and the embodiment shown in <FIG> is merely for exemplary purposes. Any vibratory sensor <NUM> may be used, for instance, the fork meter described or a Coriolis flow sensor.

The optional speed of sound sensor <NUM> is a sensor that detects the speed of sound of a fluid. The optional speed of sound sensor <NUM> may determine a speed of sound of a fluid in a liquid state to determine the energy content of the fluid in the gaseous state. The optional speed of sound sensor <NUM> may transmit a sound, using a sound transmitter, through the liquid fluid to be measured and receive, with a sonic sensor, the response. The speed of sound may then be determined based on the time of transit and the distance between the sound transmitter and the sonic sensor. This is merely exemplary and other methods of measuring speed of sound by the optional speed of sound sensor <NUM> are contemplated.

Although not depicted, one or more of the vibratory sensors <NUM> and/or <NUM> may be a Coriolis flow sensor. Coriolis flow sensors may determine phase differences in measured oscillations due to Coriolis forces to determine mass flowrate and/or density of a fluid, perhaps a fluid in a liquid state and/or a fluid in a gaseous state. In an embodiment, neither of the vibratory sensor <NUM> and the optional additional vibratory sensor <NUM> are fork meters (such that the vibratory sensor <NUM> shown in <FIG> is different from the vibratory sensor <NUM> of this embodiment). In another embodiment, the vibratory sensor <NUM> may be a gas density meter that relies on vibrating. The manners in which vibratory sensor(s) <NUM> and/or <NUM> and optional speed of sound sensors <NUM> measure and determine measured quantities is well-established in the art, and further disclosure is omitted for brevity.

A computer system, for instance, a meter electronics <NUM> of the vibratory sensor <NUM>, may be configured to use one or more typical flow fluid and/or fluid flow measurements to infer a value of an energy content metric for the fluid in the gaseous state, for instance, using any of the relationships expressed in Eqs. (<NUM>) to (<NUM>) and other examples taught by this specification.

Examples of typical energy content metrics include methane number (hereinafter, "MN"), lower flammability limit (hereinafter, "LFL"), Wobbe Index (hereinafter, "WI"), gross heating value (hereinafter, "GHV"), and net heating value (hereinafter, "NHV"). In the embodiments disclosed in this specification, the inferred energy content may be one or more of a MN, a LFL, a WI, a GHV, and a NHV.

MN is an energy content measurement that may represent the knock potential of a fluid when combusted. It describes a likelihood that the fuel will combust uncontrollably. An embodiment of a relationship to find MN is shown in Eq. (<NUM>): <MAT> In Eq. (<NUM>), MN is methane number and ( <MAT>) is atomic hydrogen to carbon ratio (e.g. ( <MAT>) for methane is four for methane which has four hydrogens and one carbon). To determine this directly, one would have to know the composition of a fluid mixture, something difficult to determine at line conditions.

LFL is an energy content measurement that represents the minimum composition of the gas in a mixture with air at which combustion will occur. An embodiment of a relationship to find LFL is shown in Eq. (<NUM>): <MAT> In Eq. (<NUM>), LFL is the lower flammability limit, i is an index referencing each component of the mixture, xi is the relative proportion of the component i, and LFLi is a lower flammability limit of the component i. Methods using this relationship are limited by needing to know composition. Composition can be difficult to determine at line conditions.

WI is an energy metric that represents interchangeability of fuel gases. The WI is a calorific value relative to the root of the specific gravity. Eq. (<NUM>) shows an embodiment of a relationship for determining WI: <MAT> In Eq. (<NUM>), WI is Wobbe Index, CV is calorific value, and SG is specific gravity of the fluid. Again, traditional measurements for determining calorific value require knowing relative composition of the mix and require a composition determination. Composition determinations may be impractical when determining or inferring live measurements at line conditions.

GHV and NHV are both heating values, often referred to as calorific values. The difference between GHV and NHV is that NHV is reduced by the amount of heat that would result from condensing any water vapor in the mixture. An embodiment of a method for determining GHV is shown in Eq. (<NUM>): <MAT> In Eq. (<NUM>), GHVV is the gross heating value (in volume units), %CO<NUM> is carbon dioxide composition of the mix by volume and %N<NUM> is nitrogen composition of the mix by volume. Eq. (<NUM>) is the AGA <NUM> equation relationship in volumetric units. It should be noted that only terms for carbon dioxide and nitrogen are shown, but more elements exist in the equation for other substances which are omitted for brevity. In some systems, Eq. (<NUM>) yields calorific value in BTU per cubic foot at <NUM> pounds per square inch pressure and <NUM>°F.

A mass unit equivalent of the AGA <NUM> equation may also be used. An embodiment of the mass unit equivalent is shown in Eq. (23A): <MAT> In Eq. (23A), GHVM is the gross heating value (in mass units), MC is carbon dioxide composition by mass, MN is nitrogen composition by mass, and SG is specific gravity.

To get NHV, one could use the resulting GHV of either of Eqs. (<NUM>) or (23A) and subtract from it the heat of condensation of any water vapor of the mix. Again, this will require a composition determination. Composition determinations may be impractical when determining or inferring live measurements at line conditions.

In an embodiment in which the inferential relationship does not depend on velocity of sound of a fluid in a liquid state, a single vibratory meter <NUM>, perhaps a fork viscosity meter (hereinafter, "FVM") may be used to determine the inferred energy content of a fluid in a gas state based on measurements taken of the fluid in a liquid state. The measurements taken by the FVM may include a measured density and a measured viscosity. These measured quantities taken of the fluid in the liquid state may be used to infer energy content of the fluid in a gaseous state. In an embodiment in which a FVM (e.g. vibratory sensor <NUM>) is used, a separate Coriolis flow sensor (e.g. optional additional vibratory sensor <NUM>) may still be used to determine mass flowrate of a fluid in a liquid state. When both mass flowrate and energy content are determined by any of the systems disclosed in this specification, the systems may further derive from the mass flowrate and the energy content of a fluid in a liquid state an energy flowrate of a fluid, such that the flow of a fluid in a liquid state is measured in energy the fluid flowing can provide in a gaseous state per unit time.

In another embodiment, the inferential relationship does depend on measured speed of sound of a fluid in the liquid state. In this embodiment, an optional speed of sound sensor <NUM> may be used to determine the speed of sound of a fluid in a liquid state. In an embodiment in which the speed of sound of a fluid in a liquid state is used and a density of a fluid in a liquid state is used, the speed of sound measurements of a fluid in a liquid state determined by the optional speed of sound sensor <NUM> may be transmitted to another computer, perhaps a meter electronics of a vibratory sensor <NUM> and/or <NUM>, in order to infer an energy content of the fluid in a gaseous state in the another computer. In this embodiment, one or more of a density and a viscosity of a fluid in a liquid state may be determined by the vibratory sensor <NUM> and/or <NUM> and used with the transmitted speed of sound measurement of a fluid in a liquid state to infer the energy content of the fluid in a gaseous state.

Further embodiments are envisioned in which multiple vibratory sensors <NUM> and/or <NUM> are each used to measure one or more of mass flowrate, density, and viscosity of a fluid in a liquid state, and/or the optional speed of sound sensor <NUM> is used to measure the speed of sound of a fluid in a liquid state. All combinations of potential hardware and software arrangements based on the types of sensors disclosed and the measurements potentially used in the inference of energy content are contemplated by this specification.

<FIG> shows a block diagram of an embodiment of a computer system <NUM>. In an embodiment, the computer system <NUM> may be a meter electronics, for instance, the meter electronics <NUM>. In various embodiments the computer system <NUM> may be comprised of application specific integrated circuits or may have a discrete processor and memory elements, the processor elements for processing commands from and storing data on the memory elements. The computer system <NUM> may be an isolated physical system, a virtual machine, and/or may be established in a cloud computing environment. The computer system <NUM> may be configured to accomplish any method steps presented in this description and may execute all functions associated with the disclosed modules.

The computer system may have a processor <NUM>, a memory <NUM>, an interface <NUM>, and a communicative coupler <NUM>. The memory <NUM> may store and/or may have integrated circuits representing, for instance, an analysis module <NUM>, an inference module <NUM>, and a measurement module <NUM>. In various embodiments, the computer system <NUM> may have other computer elements integrated into the stated elements or in addition to or in communication with the stated computer elements, for instance, buses, other communication protocols, and the like.

The processor <NUM> is a data processing element. The processor <NUM> may be any element used for processing such as a central processing unit, application specific integrated circuit, other integrated circuit, an analog controller, graphics processing unit, field programmable gate array, any combination of these or other common processing elements and/or the like. The processor <NUM> may have cache memory to store processing data. The processor <NUM> may benefit from the methods in this specification, as the methods may enhance the resolution of calculations and reduce error of those calculations using the inventive structures presented.

The memory <NUM> is a device for electronic storage. The memory <NUM> may be any non-transitory storage medium and may include one, some, or all of a hard drive, solid state drive, volatile memory, integrated circuits, a field programmable gate array, random access memory, read-only memory, dynamic random-access memory, erasable programmable read-only memory, electrically erasable programmable read-only memory, cache memory and/or the like. The processor <NUM> may execute commands from and utilize data stored in the memory <NUM>.

The computer system <NUM> may be configured to store any data that will be used by the analysis module <NUM>, the inference module <NUM>, and the measurement module <NUM> and may store historical data for any amount of time representing any parameter received or used by the analysis module <NUM>, the inference module <NUM>, and the measurement module <NUM> in the memory <NUM>, perhaps with time stamps representing when the data was taken or determined. The computer system <NUM> may also store any data that represents determinations of any intermediates in the memory <NUM>. While the analysis module <NUM>, the inference module <NUM>, and the measurement module <NUM> are displayed as three separate and discrete modules, the specification contemplates any number (even one or the three as specified) and variety of modules working in concert to accomplish the methods expressed in the specification.

The analysis module <NUM> is a programming module that determines an inferential relationship between an energy content of a fluid in a gaseous state and parameters of the fluid measured while the fluid is in a liquid state. The analysis module <NUM> may use any methods and equations disclosed in this specification to determine the inferential relationship, for instance, the methods disclosed in the description of <FIG> and Eqs. (<NUM>)-(<NUM>). The analysis module may determine, using an evaluation procedure, for instance, regression or a machine learning algorithm, the inferential relationship using existing data. For instance, analysis may be performed on various relationships that incorporate various measured parameters of a fluid in a liquid state and converge the resulting inferred energy content to known, measured energy content of the fluid in a gaseous state. For instance, the analysis module <NUM> may receive data representing one or more of measured density of the fluid in the liquid state, measured speed of sound of the fluid in the liquid state, and/or measured viscosity of the fluid in the liquid state and corresponding measured values of energy content of the same fluid in the gaseous state and determine values of inferential relationship elements in the inferential relationship that relate the measured parameters of the fluid in the liquid state to the measured energy content values of the same fluid in the gaseous state. In various embodiments, the inferential relationship will have elements that are temperature dependent such that the determination of the inferential relationship, by the analysis module <NUM>, also requires receiving values of measured temperature of the fluid in a liquid state, the measured temperature perhaps taken contemporaneously or substantially contemporaneously with the other measured values. Inferential relationship elements may include measured parameters, higher powers of measured parameters, coefficients (perhaps corresponding coefficients that correspond to one or more of measured parameters or higher powers of the measured parameters), temperature dependencies of various coefficients, and/or the like. The inferential relationship may be described by one or more of Eqs. (<NUM>)-(<NUM>), and the analysis module may use one or more of the relationships expressed in Eqs. (<NUM>)-(<NUM>) to determine the inferential relationship. The analysis module <NUM> may further use equations with higher order terms of measurement values (for instance, quadratic terms) to determine the inferential relationship, as taught in this specification.

The analysis module <NUM> may use only some measured values to determine the inferential relationship. For instance, in an embodiment, the analysis module <NUM> may receive a measured quantity value of a fluid in a liquid state to determine a term that corresponds with the measured quantity (e.g. A, B, C, and/or D). The analysis module <NUM> may incorporate temperature measurements of the fluid in a liquid state to establish temperature dependency of coefficients and, perhaps a shift term (A). In this embodiment, the analysis module <NUM> may determine a corresponding coefficient that corresponds to the measured quantity value and multiply the measured quantity value by the corresponding coefficient that corresponds to the measured quantity value to generate a term that corresponds to the measured quantity value. The analysis module <NUM> may conduct an evaluation procedure to determine the coefficient that corresponds to the measured value using the measured quantity value of the fluid in the liquid state and a measured energy content of the fluid in a gaseous state. In an embodiment, the corresponding coefficient and/or the shift term is temperature dependent, such that the corresponding coefficient and/or the shift term is not a constant. In this embodiment, the analysis module <NUM> may determine, by the evaluation procedure, the relationship between the measured temperature of the fluid in the liquid state and the corresponding coefficient and/or the shift term.

The analysis module <NUM> may use different inferential relationships for each of the types of inferred energy content, depending on which measurements and terms are appropriate for each of the types of inferred energy content. For instance, one or more of a measured density, measured temperature, measured viscosity, measured speed of sound, higher order values of measurements, and the like may be used in the inferential relationship. The measuring of one or more measured quantities used in determining elements of the inferential relationship (for instance, coefficient constants) may be accomplished by the system <NUM> using the computer system <NUM>, and/or the computer system <NUM> may receive the measured data from sources that have already determined measurements and corresponding measured energy content values.

The analysis module <NUM> may determine or receive from a user an inferential relationship with elements, for instance, the structure of the inferential relationship (e.g. relationships expressed by Eqs. (<NUM>)-(<NUM>)) and relationship elements (e.g. coefficients, coefficient constants, and temperature and/or pressure dependent relationships to determine coefficients, potentially ones reflected in the relationships expressed in Eqs. (<NUM>)-(<NUM>)). The coefficients and/or coefficient constants of the Eqs. and/or the elements used to determine the coefficients may be determined by the analysis module <NUM>, for instance, using a regression or other statistical or probabilistic technique. The structure of the inferential relationship may be determined by the analysis module <NUM> (e.g. may determine best relationship for each energy content metric) or may be supplied by the user or meter electronics <NUM>. The resulting inferential relationship elements may be associated by the analysis module <NUM> with one or more of the energy metric being determined, the flow fluid, and a class of flow fluids of which the flow fluid is a member. The data regarding the one or more of the energy metric, fluid type, and fluid class may be supplied by a user or may be determined and/or identified by the analysis module <NUM>. The resulting inferential relationship, relationship elements, and data associations therewith may be stored in the computer system <NUM> that determined the inferential relationship with the analysis module <NUM> or may be transmitted to a different computer system <NUM>, perhaps a meter electronics <NUM> of a vibratory sensor <NUM> (or directly coupled hardware).

The inference module <NUM> uses the inferential relationship having predetermined elements (for instance, predetermined relationships between terms and/or predetermined coefficient constants) to infer inferred energy content values. The inferential relationship stored may have predetermined and/or prestored elements, for instance, the structure of the inferential relationship (e.g. relationships expressed by Eqs. (<NUM>)-(<NUM>)) and relationship elements (e.g. coefficients, coefficient constants, and temperature and/or pressure dependent relationships to determine coefficients, potentially ones reflected in the relationships expressed in Eqs. (<NUM>)-(<NUM>)). The coefficients of the Eqs. and/or the elements used to determine the coefficients may be predetermined and prestored in the computer system <NUM> (or directly coupled hardware). The inferential relationship elements may be associated by data with one or more of the energy metric being determined, the flow fluid, and a class of flow fluids of which the flow fluid is a member. The data regarding the one or more of the energy metric, fluid type, and fluid class may be supplied by a user or may be determined and/or identified by the inference module <NUM>. The data associations may assure that the inference module <NUM> uses the best inferential relationship elements and energy content metric for a particular application. The inference module <NUM> may retrieve, from memory <NUM>, the appropriate relationship elements for the particular flow fluid and application. From this the inference module <NUM> may evaluate the inferential relationship to determine the energy content of a fluid in a gaseous state from measurements taken of the fluid in the liquid state.

In an embodiment, it should be appreciated that the determination of elements of the inferential relationship (for instance, predetermined relationships between terms and/or predetermined coefficient constants) may be conducted by a first system, and the predetermined elements determined in that first system may be used in live inferences of energy content in a second system. In this embodiment, the computer system <NUM> for the first system may have one or more of the analysis module <NUM> and the measurement module <NUM>, but not have the inference module <NUM>. In this embodiment, the computer system <NUM> for the second system may have one or more of the inference module <NUM> and the measurement module <NUM>, but not have the analysis module <NUM>.

In another embodiment, a computer system <NUM> may be used to both determine the elements of the inferential relationship (for instance, predetermined relationships between terms and/or predetermined coefficient constants) and deploy the inferential relationship to infer energy content values from live line condition measurements. In this embodiment, the computer system <NUM> may have one or more of the analysis module <NUM>, inference module <NUM>, and the measurement module <NUM>.

The measurement module <NUM> is a programming module that takes raw data from sensors and processes the raw data to determine flow fluid and/or fluid flow measurements. The flow fluid and/or flow fluid measurements may include one or more of measured density, pressure, viscosity, speed of sound, temperature, mass flowrate, and/or the like. In various embodiments, various hardware elements may be incorporated into the system. Each of the different hardware elements in system <NUM> may have different embodiments of the measurement module <NUM>. For instance, the vibratory sensor <NUM> may measure one or more of density and viscosity, using an embodiment of the measurement module <NUM>. The optional speed of sound sensor <NUM> may measure speed of sound of the flow fluid using its own embodiment of the measurement module <NUM>. The optional additional vibratory sensor <NUM> may determine mass and/or volumetric flowrate of the flow fluid using its own embodiment of measurement module <NUM>.

The capabilities of the analysis module <NUM>, the inference module <NUM>, and the measurement module <NUM> are contemplated and reflect the methods that are performed in the flowcharts presented. All methods in this specification are contemplated with respect to each flowchart and orders specified or, when it is specified that the order does not matter, inform the flowcharts, but all methods and capabilities of the analysis module <NUM>, the inference module <NUM>, and the measurement module <NUM> are contemplated for the purposes of any method claims that follow this description.

Also, in embodiments where the computer system <NUM> is a meter electronics <NUM>, the meter electronics <NUM> may comprise a number of communicatively coupled elements. The hardware that interacts to form the cohesive computer system <NUM> that is the meter electronics <NUM> may be of different components, for instance, a traditional meter electronics array communicatively coupled to a corresponding and/or compatible transmitter. In an embodiment, the meter electronics <NUM> may have at least some elements of its processor <NUM> in the integral meter electronics elements of the vibratory sensor <NUM> and at least some elements of the memory <NUM> in the transmitter coupled to the vibratory sensor <NUM>.

The interface <NUM> is an input/output device used to communicatively couple the data computer system <NUM> to external compute elements. The interface <NUM> is capable of connecting the computer system <NUM> to external elements, using known technologies, the external elements including, for instance, universal serial bus, Prolink, serial communication, serial advanced technology attachments, HPC type connections, Gigabit Ethernet, infiniband, and/or the like. The interface <NUM> may have a communicative coupler <NUM>. The communicative coupler <NUM> is used to couple the computer system <NUM> with components external of the computer system <NUM>, for instance, with external compute devices or facilitating data transfer between one or more of the vibratory sensor <NUM>, the optional speed of sound sensor <NUM>, and the optional additional vibratory sensor <NUM>. In an embodiment in which the computer system <NUM> is a meter electronics <NUM> comprised of multiple compatible and potentially separably couplable elements (e.g. traditional meter electronics of a vibratory sensor <NUM> and a transmitter), the communicative coupler <NUM> may communicatively couple the elements. In an embodiment, the communicative coupler <NUM> may be an embodiment of the communication link <NUM>.

<FIG> show flowcharts of embodiments of methods for inferring and using an energy content. The methods disclosed in the flowcharts are non-exhaustive and merely demonstrate potential embodiments of steps and orders. The methods must be construed in the context of the entire specification, including elements disclosed in descriptions of <FIG> and <FIG>, system <NUM> and computer system <NUM> disclosed in <FIG> and <FIG>, the analysis module <NUM>, inference module <NUM>, and/or measurement module <NUM>.

<FIG> shows a flowchart of an embodiment, broader than the scope of the claims, of a method <NUM> for inferring an energy content. The system <NUM>, vibratory sensor <NUM>, optional speed of sound sensor <NUM>, optional additional vibratory sensor <NUM>, computer system <NUM>, analysis module <NUM>, inference module <NUM>, and measurement module <NUM> referred to or implicitly used in method <NUM> may be the system <NUM>, vibratory sensor <NUM>, optional speed of sound sensor <NUM>, optional additional vibratory sensor <NUM>, computer system <NUM>, analysis module <NUM>, inference module <NUM>, and measurement module <NUM> referred to in method <NUM> as disclosed in <FIG> and <FIG>, although any suitable system <NUM>, vibratory sensor <NUM>, optional speed of sound sensor <NUM>, optional additional vibratory sensor <NUM>, computer system <NUM>, analysis module <NUM>, inference module <NUM>, and measurement module <NUM> referred to or implicitly used in method <NUM> may be employed in alternative embodiments. All methods for accomplishing these steps disclosed in this specification are contemplated, including all of the capabilities of the system <NUM>.

Step <NUM> is inferring, by the inference module <NUM>, an inferred energy content of a fluid in the gaseous state from an inferential relationship between the inferred energy content of the fluid in the gaseous state with at least one measurement taken of the fluid in the liquid state. Step <NUM> may be conducted by an inference module <NUM> of a vibratory sensor <NUM> and/or an optional additional vibratory sensor <NUM>. The inferring may be based on relationships expressed in one or more of Eqs. (<NUM>)-(<NUM>). The values of the input parameters for the inference may be provided by one or more of the vibratory sensor <NUM>, the optional speed of sound sensor <NUM>, and the optional additional vibratory sensor <NUM>.

In other embodiments, the method shown in <FIG> may have other steps in addition to or instead of the step listed above. Subsets of the step listed above as part of the method shown in <FIG> may be used to form their own method. The step of method <NUM> may be repeated in any combination and order any number of times, for instance, continuously looping in order to provide live or continuous line condition inferred energy content values.

<FIG> shows a flowchart of an embodiment, broader than the scope of the claims, of a method <NUM> for inferring an energy content. The system <NUM>, vibratory sensor <NUM>, optional speed of sound sensor <NUM>, optional additional vibratory sensor <NUM>, computer system <NUM>, analysis module <NUM>, inference module <NUM>, and measurement module <NUM> referred to or implicitly used in method <NUM> may be the system <NUM>, vibratory sensor <NUM>, optional speed of sound sensor <NUM>, optional additional vibratory sensor <NUM>, computer system <NUM>, analysis module <NUM>, inference module <NUM>, and measurement module <NUM> referred to in method <NUM> as disclosed in <FIG> and <FIG>, although any suitable system <NUM>, vibratory sensor <NUM>, optional speed of sound sensor <NUM>, optional additional vibratory sensor <NUM>, computer system <NUM>, analysis module <NUM>, inference module <NUM>, and measurement module <NUM> referred to or implicitly used in method <NUM> may be employed in alternative embodiments. All methods for accomplishing these steps disclosed in this specification are contemplated, including all of the capabilities of the system <NUM>. Method <NUM> may be an embodiment of step <NUM>, and step <NUM> may be an embodiment of method <NUM>.

Step <NUM> is receiving, by an inference module <NUM>, measured values of relevant input parameters of the fluid in a liquid state. In an embodiment, the relevant input parameters may be one or more of density, viscosity, temperature, pressure, and speed of sound. In an embodiment, the inference module <NUM> may be stored in the vibratory sensor <NUM>. The vibratory sensor <NUM> may use its own measurement module <NUM> to measure quantities, for instance, one or more of density, viscosity, and temperature of the flow fluid. The vibratory sensor <NUM> may receive a measured speed of sound from the optional speed of sound sensor <NUM> if the embodiment of the inferential relationship calls for use of a speed of sound quantity. In an embodiment, the vibratory sensor <NUM> may optionally receive a mass flowrate from the optional additional vibratory sensor <NUM>.

Step <NUM> is loading, by the inference module <NUM>, an inferential relationship between measurements taken of a flow fluid in a liquid state and inferred energy content of the flow fluid in a gaseous state. The inferential relationship stored in the meter electronics <NUM> may have predetermined and/or prestored elements, for instance, the structure of the inferential relationship (e.g. relationships expressed by Eqs. (<NUM>)-(<NUM>)) and relationship elements (e.g. coefficients, coefficient constants, and temperature and/or pressure dependent relationships to determine coefficients, potentially ones reflected in the relationships expressed in Eqs. (<NUM>)-(<NUM>)). The coefficients of the Eqs. and/or the elements used to determine the coefficients may be predetermined and prestored in the meter electronics <NUM> of the vibratory sensor <NUM> (or directly coupled hardware). One or more of these inferential elements may have been determined in a previously executed method, for instance, an embodiment of the method <NUM> as shown in <FIG>. These elements may have been established in a different computer system with an analysis module <NUM>. These coefficients, structures and/or elements may be specific to one or more of the flow fluid or the class of fluids of which the flow fluid is a member, for instance, by the computer system <NUM> having data stored that represents an association between at least one of the coefficients, coefficient constants, structures, and/or elements and the one or more of the flow fluid and the class of which the flow fluid is a member. The loading may entail the user specifying the flow fluid or the class of fluids of which the flow fluid is a member and loading the associated data representing the inferential relationship. For instance, the inferential relationship may be associated with natural gas mixtures to be used in inferences of natural gas mixture energy contents. In an alternative embodiment, the vibratory sensor <NUM> may be a fixed purpose meter for a particular fluid or class of fluids with the inferential relationship loaded for the specific fluid. In still another embodiment, the meter electronics <NUM> may dynamically identify the flow fluid and apply the appropriate inferential relationship associated with one or more of the flow fluid identified, the class of fluids of which the flow fluid is a member, and the energy content metric to be used for the particular application.

Step <NUM> is inferring, by the inference module <NUM>, an inferred energy content of a flow fluid in a gaseous state based on measurements of the flow fluid in a liquid state. The inferring may use an inferential relationship, for instance, a prestored and/or predetermined relationship. The inferential relationship may be based on one or more of the relationships shown in Eqs. (<NUM>)-(<NUM>). The inference module <NUM> may use any of the capabilities of the inference module <NUM> taught in this specification to accomplish the inferring of Step <NUM>. Step <NUM> may be an embodiment of step <NUM> and/or method <NUM>.

Step <NUM> is optionally inferring, by the inference module <NUM>, an inferred energy content flowrate. Much like a mass or volumetric flowrate, an energy content flowrate can be determined by determining an energy content with a basis (the basis typically being one or more of mass or volume) and applying it to a flowrate in the basis. For instance, if the basis is mass, an energy content may be inferred that is based on a unit of mass and that inferred energy content per unit mass can be applied to a measured mass flowrate in order to yield an inferred energy content flowrate.

In an embodiment, each of the steps of the method shown in <FIG> is a distinct step. In another embodiment, although depicted as distinct steps in <FIG>, steps <NUM>-<NUM> may not be distinct steps. In other embodiments, the method shown in <FIG> may not have all of the above steps and/or may have other steps in addition to or instead of those listed above. The steps of the method shown in <FIG> may be performed in another order. Subsets of the steps listed above as part of the method shown in <FIG> may be used to form their own method. The steps of method <NUM> may be repeated in any combination and order any number of times, for instance, continuously looping in order to provide live or continuous line condition inferred energy content values.

Step <NUM> is receiving, by an analysis module <NUM>, measured values of relevant input parameters. In an embodiment, the relevant input parameters may be one or more of density, viscosity, temperature, pressure, energy content (perhaps of a fluid in a gaseous state), and speed of sound. In an embodiment, the inference module <NUM> may be stored in the vibratory sensor <NUM>. The vibratory sensor <NUM> may use its own measurement module <NUM> to measure quantities, for instance, one or more of density, viscosity, and temperature of the flow fluid. The vibratory sensor <NUM> may receive a measured speed of sound from the optional speed of sound sensor <NUM> if the embodiment of the inferential relationship calls for use of a speed of sound quantity.

Step <NUM> is receiving or determining, by the analysis module <NUM>, a structure of the inferential relationship between an inferred energy content of a flow fluid in a gaseous state and the received measurements of the flow fluid in a liquid state. The analysis module <NUM> may have stored a user supplied preferred structure for the inferential relationship, or the analysis module <NUM> may optimize and determine the best structure for the inferential relationship by trying a variety of different structures of the inferential relationships and determining which is best based on comparison of the results (perhaps by conducting this method multiple times with different flow fluids for determining optimal structure of relationships specific to the flow fluid or a class of fluid of which the flow fluid is a member). Exemplary structures of the inferential relationship are shown in Eqs. (<NUM>)-(<NUM>).

Step <NUM> is determining, by the analysis module <NUM>, from the received measurements and the received or determined structure, relationship elements. These relationship elements may include the coefficients and coefficient constants of relationships expressed by relationships represented by one or more of Eqs. (<NUM>)-(<NUM>). These relationship elements may be specific to the flow fluid or to a class of fluids of which the flow fluid is a member or to which the flow fluid is otherwise related. Step <NUM> may be the core of the determination of the inferential relationship. The determined inferential relationship may be characterizable by the structure and the relationship elements, perhaps for a given fluid. Step <NUM> may use a regression or other analysis technique conducted on a structure into which the measured values are entered. The analysis may be used to determine the relationship elements that best allow the inferential relationship having the selected structure, using the measured values of inputs, to converge the inferred energy content output by the inferential relationship to a measured energy content of the fluid in a gaseous state that corresponds to the actual measured values input. By converging the measured energy content of the fluid in the gaseous state to the inferred energy content produced by the inferential relationship based on measurements taken of the fluid in the liquid state, the relationship elements may be determined that can be used in later energy content inferences.

Step <NUM> is optionally associating, by the analysis module <NUM>, determined relationship elements and/or the structure with the flow fluid. Further associations may be included, for instance, associations with relationships for the energy content metric being used. The associations may be stored in the computer system <NUM> in such a way that the relationship elements and/or the structure is associated with one or more of the flow fluid, a class of fluids of which the flow fluid is a member or to which the flow fluid is related, and/or the particular energy content metric used. The data representing one or more of the relationship elements and the structure may be stored and/or associated with data identifying one or more of the flow fluid, an associated class of fluids, or the energy metric used. The association may be stored in memory <NUM>.

Step <NUM> is optionally transmitting, by the analysis module <NUM>, data representing one or more of the structure, relationship elements, and associations to a different computer system <NUM>. The different computer system <NUM> may be one that does not have the analysis module <NUM>. The different computer system <NUM> may be a meter electronics <NUM> of a vibratory sensor <NUM>. The different computer system <NUM> may use this data as predetermined and/or prestored data to make inferences of energy content of the flow fluid, perhaps even live inferences thereof.

<FIG> show graphs explaining embodiments of inferential relationships for energy content inferences described in the specification. These graphs demonstrate the efficacy of inferring energy content of a flow fluid in a gaseous state based on measurements of the flow fluid in a liquid state.

Natural gas mixtures are typically predominantly composed of methane with smaller relevant quantities of one or more of ethane and propane. Other petroleum substances, such as higher order hydrocarbons and other substances may be present to a lesser extent. Natural gas is typically composed of between <NUM>% and <NUM>% methane with ranges of ethane content varying from <NUM>% to <NUM>%. Because the compositions have these relatively consistent relationships, the inferential relationships can be based on the measurements that are taken in the liquid phase.

The temperature and density for basic alkanes in a liquid state may be largely linearly related. The relationship between viscosity and temperature and the basic alkanes may have more quadratic character. The inferential relationship may use these correlations to infer the energy content of the flow fluid using measurements of the flow fluid that are better associated with the relative composition of the flow fluid than directly derived heat properties of each component. For all of the graphs, the coefficients of the inferential relationships are presumed to have second order temperature dependence, as shown in Eq. (<NUM>). It should be appreciated that, despite the embodiments using a second order temperature dependency, embodiments are contemplated where the coefficients are constant values or have temperature dependencies of different orders. Embodiments in which the coefficients are also pressure dependent are considered, however, the pressure effects may be small due to the measurements being conducted on a liquid which is likely marginally compressible.

<FIG> shows a graph <NUM> of a fit between measured Wobbe Index values and inferred Wobbe Index values inferred from an embodiment of an inferential relationship. The graph <NUM> has a plurality of data points <NUM> representing relative values of inferred and measured Wobbe Index, a trendline <NUM>, an abscissa <NUM> representing the measured Wobbe Index of the flow fluid, and an ordinate <NUM> representing the inferred Wobbe Index of the flow fluid inferred using the inferential relationship.

The embodiment of inferential relationship is a variant of Eq. (<NUM>), the inferential relationship represented by Eq. (<NUM>): <MAT> In Eq. (<NUM>), WIGas is the Wobbe Index of the flow fluid in the gas state, the K values (i.e. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T)) are coefficients (temperature dependent in this embodiment), ρliquid is the density of the flow fluid in a liquid state, and ηliquid is the viscosity of the flow fluid in a liquid state. It can be seen here that the fit is excellent with a coefficient of determination (R<NUM> value) of.

<FIG> shows a graph <NUM> of a fit between measured methane numbers and inferred methane numbers inferred from an embodiment of an inferential relationship. The graph <NUM> has a plurality of data points <NUM> representing relative values of inferred and measured methane number, a trendline <NUM>, an abscissa <NUM> representing the measured methane number of the flow fluid, and an ordinate <NUM> representing the inferred methane number of the flow fluid inferred using the inferential relationship.

The embodiment of inferential relationship is a variant of Eq. (<NUM>), the inferential relationship represented by Eq. (<NUM>): <MAT> In Eq. (<NUM>), MNGas is the methane number of the flow fluid in the gas state, the K values (i.e. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T)) are coefficients (temperature dependent in this embodiment), ρliquid is the density of the flow fluid in a liquid state, and ηliquid is the viscosity of the flow fluid in a liquid state. It can be seen here that the fit is excellent with a coefficient of determination (R<NUM> value) of.

<FIG> shows a graph <NUM> of a fit between measured lower flammability limit and inferred lower flammability limit inferred from an embodiment of an inferential relationship. The graph <NUM> has a plurality of data points <NUM> representing relative values of inferred and measured lower flammability limit, a trendline <NUM>, an abscissa <NUM> representing the measured lower flammability limit of the flow fluid, and an ordinate <NUM> representing the inferred lower flammability limit of the flow fluid inferred using the inferential relationship.

The embodiment of inferential relationship is a variant of Eq. (<NUM>), the inferential relationship represented by Eq. (<NUM>): <MAT> In Eq. (<NUM>), LFLGas is the lower flammability limit of the flow fluid in the gas state, the K values (i.e. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T)) are coefficients (temperature dependent in this embodiment), ρliquid is the density of the flow fluid in a liquid state, and ηliquid is the viscosity of the flow fluid in a liquid state. It can be seen here that the fit is excellent with a coefficient of determination (R<NUM> value) of.

<FIG> shows a graph <NUM> of a fit between measured gross heating value and inferred gross heating value inferred from an embodiment of an inferential relationship. The graph <NUM> has a plurality of data points <NUM> representing relative values of inferred and measured gross heating value, a trendline <NUM>, an abscissa <NUM> representing the measured gross heating value of the flow fluid, and an ordinate <NUM> representing the inferred gross heating value of the flow fluid inferred using the inferential relationship.

The embodiment of inferential relationship is a variant of Eq. (<NUM>), the inferential relationship represented by Eq. (<NUM>): <MAT> In Eq. (<NUM>), GHVGas is the gross heating value of the flow fluid in the gas state, the K values (i.e. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T)) are coefficients (temperature dependent in this embodiment), ρliquid is the density of the flow fluid in a liquid state, and ηliquid is the viscosity of the flow fluid in a liquid state. It can be seen here that the fit is excellent with a coefficient of determination (R<NUM> value) of.

<FIG> shows a graph <NUM> of a fit between measured net heating value and inferred net heating value inferred from an embodiment of an inferential relationship. The graph <NUM> has a plurality of data points <NUM> representing relative values of inferred and measured net heating value, a trendline <NUM>, an abscissa <NUM> representing the measured net heating value of the flow fluid, and an ordinate <NUM> representing the inferred net heating value of the flow fluid inferred using the inferential relationship.

The embodiment of inferential relationship is a variant of Eq. (<NUM>), the inferential relationship represented by Eq. (<NUM>): <MAT> In Eq. (<NUM>), NHVGas is the net heating value of the flow fluid in the gas state, the K values (i.e. K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T), K<NUM>(T)) are coefficients (temperature dependent in this embodiment), ρliquid is the density of the flow fluid in a liquid state, and ηliquid is the viscosity of the flow fluid in a liquid state. It can be seen here that the fit is excellent with a coefficient of determination (R<NUM> value) of.

The detailed descriptions of the above embodiments are not exhaustive descriptions of all embodiments contemplated by the inventors to be within the scope of the present description. Indeed, persons skilled in the art will recognize that certain elements of the above-described embodiments may variously be combined or eliminated to create further embodiments, and such further embodiments fall within the scope and teachings of the present description, but may be outside the scope of the invention.

It will also be apparent to those of ordinary skill in the art that the above-described embodiments may be combined in whole or in part to create additional embodiments within the scope and teachings of the present description, but possibly outside the scope of the invention.

Claim 1:
A method for inferring energy content of a flow fluid in a gaseous state by a computer system (<NUM>) having a processor (<NUM>) and memory (<NUM>), the memory (<NUM>) having an inference module (<NUM>), characterized by the method comprising inferring, by the inference module (<NUM>), the inferred energy content of the flow fluid in the gaseous state from an inferential relationship between the inferred energy content of the flow fluid in the gaseous state with at least three measurements taken of the flow fluid in the liquid state, wherein the at least three measurements comprise a measured density, a measured viscosity and a measured speed of sound, and the energy content is an energy of the fluid when combusted;
wherein the inferential relationship is a sum of terms, wherein each term has one or more of one of the at least one measurement and one higher order value of one of the at least one measurement wherein each term has a coefficient that corresponds to the term, and wherein the relationship has at least five terms, the at least five terms comprising:
a shift term;
a density term comprising a product of the measured density and the coefficient that corresponds to the density term;
a speed of sound term comprising a product of the measured speed of sound and the coefficient that corresponds to the speed of sound term;
a viscosity term comprising a product of the measured viscosity and the coefficient that corresponds to the viscosity term;
at least one of a higher order viscosity term, a higher order speed of sound term, and a higher order density term, correspondingly comprising a higher order value of the one or more of the measured viscosity, the measured speed of sound, and the measured density, each correspondingly multiplied by the coefficient that corresponds to the viscosity term, the coefficient that corresponds to the speed of sound term, and the coefficient that corresponds to the viscosity term.