Requirements for circuit design for natural gas calorific meters

Xiang Zheng Tu

The project is divided into two phases as:

·      The first phase is designing circuit for measuring the component mole fraction of a natural gas using POSIFA’s thermopile thermal conductivity sensors.  

·      The second phase is combining this circuit with an available mass flow measuring circuit. So as to obtain a complete circuit for natural gas calorific measurement.

A natural gas calorific meter comprises a MEMS thermal flow sensor and a MEMS thermopile thermal conductivity sensor which are provided by POSIFA Microsystems Company. The thermal flow sensor measures natural gas mass flow. A natural gas is a naturally occurring gas mixture, consisting of methane, ethane, propane and nitrogen. The heating value of a natural gas changes with its composition changes. The thermopile thermal conductivity sensors measure the component gas mole fraction in the natural gas flow. With the measured natural gas mass flow rate and component mole fraction the natural gas calorific flow rate and total calorific value can be calculated and displayed accordingly.

The component gas mole fraction of a natural gas can be measured based on the fact that the temperature curve of each component gas thermal conductivity coefficient is unique for each one, but highly correlated. A quaternary linear regression can be used to model the relationship between two or more explanatory variables and a response variable of a natural gas system by fitting a linear equation to observed data.

The thermopile thermal conductivity sensor is configured to have a polysilicon resistor used as heater (resistance = 250 to 350 Ω) and a thermopile used as temperature difference detector (resistance ~200 kΩ). In order to establish a quaternary linear system the heater must be driven using three square pulse voltage steps V₁, V₂, V₃.  The square pulse voltage can be shown as: 

After driving the heater a temperature difference between the hot junctions and cold junctions of the thermopile is established and a corresponding thermopile voltage is generated as:

Three square pulse voltages are used to successively heat the heater in the way as:

With resulting thermopile voltages a quaternary linear regression can be obtained as:

Y₁ =b₁₀ +b₁₁ N_Ethane +b₁₂ N_Propone +b₁₃ N_Nitrigen                     (1)

Y₂ =b₂₀ +b₂₁ N_Ethane +b₂₂ N_Propone +b₂₃ N_Nitrigen                      (2)

Y₃ =b₃₀ +b₃₁ N_Ethane +b₃₂ N_Propone +b₃₃ N_Nitrigen                      (3)

And an identity as

x_Methane +x_Ethane +x_Propone  +x_Nitrigen=1                                     (4)      

Where Y₁, Y₂ and Y₃ are the measured thermopile voltages when the heater is driven By 5, 7, and 9V square pulse voltages respectively, b₁₀ through b₃₃ are the parameters of the quaternary linear regression equation, which are determined by several experimental measurements, and N_Methane,  N_Ethane,,  N_Propone ,  N_Nitrigen  are the mole fraction of methane, ethane, propane, nitrogen.

With the measured values of Y₁, Y₂, Y₃, and the values obtained by fitting parameters b₀₁ through β₃₄, the values of N_Methane,  N_Ethane,,  N_Propone ,  N_Nitrigen  can be calculated by solving the equations (1) through (4).

A digital processing algorithm can also be build based on the equations (1) through (4). Using the obtained algorithm and the related program the component gas mole fraction of a natural gas coming from any different sources can be determined by operating a microcontroller.

                            

With the purpose of canceling the offset of the thermopile voltage of a thermopile thermal conductivity sensor a differential preamplifier is configured to have a sealed thermopile thermal conductivity sensor used as a reference input voltage. The sealed sensor may be filled with pure methane gas but not allowed to contact with natural gas to be measured. So its thermopile voltage will not change with the measured natural gas. Since the thermopile voltage of the exposed thermopile thermal conductivity sensor not only comprises natural gas signal and but also pure natural gas signal. After differential amplifying all common model signals will be canceled. That means the output of the amplifier should be no offset, no temperature drift and no noise. 

In the second phase the natural gas composition measurement circuit is incorporated with an available natural gas flow measurement circuit. The combined circuit is so called natural gas calorific measurement circuit.

Heating value of a natural gas can be calculated as:

Heating value = ( ṁ N_MethaneM_Methane/M_Mix) (HV_Methane) + ( ṁ N_EthaneM_Etane/M_Mix) (HV_Ethane)

+ ( ṁ N_PropaneM_Propane/M_Mix) (HV_Propane)                                          (5)                                                

Where: HV_n = heating value of natural gas component n, in BTU/SCF
N_n = mole or volume fraction of natural gas component n. 

ṁ = mass flow rate.

M_n = natural gas component mole quality.

M_Mix = natural gas average quality.

The following table shows the heating value of natural component gas: