Natural Gas Calorific Meter with Two MEMS Sensors

 Xiang Zheng Tu

As shown in the above figure, a MEMS natural gas calorific meter mainly comprises a MEMS thermal flow sensor and a MEMS thermal conductivity sensor. The thermal flow sensor measures natural gas mass flow rate. Natural gas is a naturally occurring gas mixture, consisting of methane, ethane, propane and nitrogen. The thermal conductivity sensor measures the mole percentage of methane, ethane, propane and nitrogen in the natural gas flow. With the measured mass flow rate and each composition mole percentage the calorific flow rate and total calorific value displayed on the smart phone in the above figure can be calculated.

With the state-of-the-art electronics for the signal process, MEMS natural gas calorific meters have extended dynamic range, enhanced data safety and are easy for network and remote data transmission. They have automatic temperature and pressure compensation and directly provide calorific value. As the MEMS sensor is miniature, the sensor assembly including the electronic control board can be designed into a compact form that is substantially smaller than the mechanical counterpart. This could benefit for the reduction of the cost not only in manufacture but for overall gas distribution management.

The composition of natural gas can be determined based on the fact that the temperature curve of the thermal conductivity coefficient is unique for each natural gas mixture, but highly correlated. A multiple linear regression can be used to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. The model can be expressed as:

Y = β₀ + β₁ x_Ethane + β₂ x_Propone +β₃ x_Nitrigen                                                               (1)

x_Methane + x_Ethane + x_Propone  + x_Nitrigen= 1                                                                  (2)

Where Y is the sensor signal output, β₀, β₁, β₂, β₃ are the parameters of the regression equation, and x_Methane,  x_Ethane,  x_Propone ,  x_Nitrigen are each component mole fraction of natural gas.

These equations describe how the mean response Y changes with the explanatory variables. The observed values for Y vary about their means y and are assumed to have the same standard deviation σ. The fitted values estimate the parameters β₀, β₁, β₂, β₃ of the regression equations. Since the observed values for y vary about their means Y, the multiple regression models include a term for this variation. In words, the model is expressed as DATA = FIT + RESIDUAL, where the "FIT" term represents the expression β₀ + β₁ x_Ethane + β₂ x_Propone +β₃ x_Nitrigen . The "RESIDUAL" term represents the deviations of the observed values y from their means Y, which are normally distributed with mean 0 and variance σ. The notation for the model deviations is ɛ.

The thermal conductivity sensor is excited using three voltage steps V₁, V₂, V_3, resulting in three different operation temperatures. Each operation temperature or driving voltage results a multiple linear regression as follows:

Y_v1 = β_0v1 + β_1v1 x_Ethane + β_2v1 x_Propone +β_3v1 x_Nitrigen                                                  (3)

Y_v2 = β₀v₂ + β_1v2 x_Ethane + β_2v2 x_Propone +β_3v2 x_Nitrigen                                                 (4)

Y_v3 = β_0v3 + β_1v3 x_Ethane + β_2v3 x_Propone +β_3v3 x_Nitrigen                                                  (5)

With measured Y_v1, Y_v2, Y_v3, and estimated parameters β_0v1……β_3v3, the composition mole percentage of a natural gas coming from different sources can be determined in this way: First the sensor is excited by the three voltage steps V₁, V₂, V₃ and each results a sensor signal outputs;

Then the three equations can be obtained for each exciting voltage;

Finally the equations are solved to find each mole fraction of the measured natural gas.

The calorific value of natural gas can be further calculated using the above measured data as flows:

Calorific flow rate =

(ṁ G_Methane) (HV_Methane) + (ṁG _ethane2) (HV_Ethane) + (ṁ G_Propone) (HV_Propone)          (6)                                  

G_Methane = MW_Methne  x_Methane / (MW_Methne  x_Methane +MW_Ethane  x_Ethane

+MW_Propone  x_Propone +MW_Nitrigen  x_Ntrigen  )                                                                 (7)

G_Methane = MW_Ethane  x_Ethane/ (MW_Methne  x_Methane +MW_Ethane  x_Ethane

+MW_Propone  x_Propone +MW_Nitrigen  x_Ntrigen  )                                                                (8)

G_Methane = MW_Methne  x_Methane / (MW_Methne  x_Methane +MW_Ethane  x_Ethane

+MW_Propone  x_Propone +MW_Nitrigen  x_Ntrigen  )                                                                (9)

Where: ṁ = mass flow rate measured by the thermal mass flow sensor, in b/min

HV_n = heating value of gas component n, in BTU/SCF
x_n = mole fraction of gas component n. The table below contains the list of individual component LHV & HHV.

MW = Molecular weight of gas component n.

     

The higher heating value (HHV) refers to a condition in which the water is condensed out of the combustion products. The higher heating value includes the sensible heat and latent heat of vaporization especially for water. In other words, HHV assumes all the water component is in liquid state at the end of combustion.

The lower heating value (LHV), on the other hand refers to the condition in which water in the final combustion products remains as vapor (or steam); i.e. the steam is not condensed into liquid water and thus the latent heat is not accounted for.  The LHV assumes that the latent heat of vaporization of water in the fuel and the reaction products is not recovered.