Constant Water Flow System with Thermal Water Flow Sensor and

Variable Frequency Pump

Xiang Zheng Tu

 

It has been reported that electrical energy consumed by pumps, fans and compressors represents a significant proportion of the electricity used around the world. It is estimated that in industrial processes and building utilities, 72 % of electricity is consumed by motors, of which 63 % is used to drive fluid flow in pumps, fans and compressors.

Many heating, cooling and ventilation distribution systems operate at a constant flow rate, even though peak demand may only be required for a few hours. The conventional response to meeting the changing demand for heating and cooling within a building is to restrict flow to individual rooms, while maintaining peak flow in the central system. However, through the use of this approach, considerable energy is used and equipment lifetime is shortened.

For saving energy a better approach is to use a variable speed drive on pumps and fans to vary air or water flow to meet more precisely changing load demands. As shown in the above figure, a constant water flow system comprises a variable frequency pump and a POSIFA’s thermal flow sensor. When the water flow decreases in the user pipe the thermal flow sensor measurement signal decreases. This signal feedback to the variable frequency inverter and results its output frequency decreased. With decreased frequency the operation speed of the variable frequency pump is also decreased and the water flow in the user pipe starts to drop back as to original balance. When the water flow increases the similar process will happen only the direction is opposite.

There is an everyday analogy that can help explain the efficiency advantage of a variable frequency pump.  Imagine you are driving a car. If you are driving on a highway and entering a population area, speed must be reduced so that you do not risk your own and other lives. The best possible way to do that is to reduce motor-rotation speed by taking your foot off the gas pedal and, if necessary, changing to a lower gear. Another possibility would be to use the same gear, keeping your foot on the gas, and at the same time reducing speed simply by braking. This would not only cause wear in the engine and brakes, but also use a lot of fuel and reduce your overall control of the vehicle, which is the case for a "control valve."

In most traditional cases, the variable frequency pumps are controlled to maintain a constant pressure within air ducts or water pipes in which the pressures are measured by pressure differential flow sensors. The differential pressure flow sensor is based on Bernoulli’s Equation, where the pressure drop is a squared function of the fluid velocity.

This relationship can limit the ability of differential pressure sensors to measure large flow ranges. Generally the flow measurement range of 10-100 flow units (10:1 flow turndown) would require a differential pressure flow sensor range of 1-100 differential pressure units (100:1 differential pressure turndown). Therefore, the actual 10:1 flow turndown requires a 100:1 differential pressure flow transmitter turndown.

It would be much better to use the thermal flow sensors replacing the pressure differential flow sensors for controlling the variable frequency pumps. The thermal flow sensor measurement is based on heat transfer from a heated element. The measurement is in mass flow, and additional pressure and temperature correction is not required which is not like the pressure differential flow sensors. They also provide excellent accuracy and repeatability and are easy to install.

POSIFA’s Mass Air Flow Sensor making the first Electronic Cigarette

to Adapt to User’s Draw

Xiang Zheng Tu

United States Patent 9,635,886 disclosed an electronic cigarette with a thermal flow sensor based controller as shown in the following figure.

The controller comprises a housing; a battery, a controller assembly; an air for allowing air to enter into the housing, a mouthpiece; a fluid reservoir; an atomizer; at least a light emitting diode; and a display. The thermal flow sensor is fabricated using micro-electro-mechanical systems (MEMS) technologies which is amenable to create the electronic cigarette with a thermal flow sensor based controller having stable evaporated liquid delivering, immediately response to smoker inhalation, like normal cigarette inhalation resistance, low power consumption, and no accidental actuation take place.

The controller has been used for new electronic cigarettes recently launched by Blu MAX in Brighton.

The new generation of e-cigarette, blu MAX™ boasts Responsive Draw™ technology that gives users complete control over their in-hale. The innovation has been created to provide smokers and vapers with an experience closer to smoking a cigarette than ever before, without the harmful tobacco or tar substances.

Responsive Draw™ is unlike any other technology in the e-cigarette market; responding to the strength of the in-hale, users can take in as much or as little vapour as they like, depending on their needs and mood. The sleek new e-cigarette also imitates the visual sensations of traditional drawing with its intelligent light system that illuminates with the intensity of the draw. “blu MAX is different from other vaping products due to its ‘Mass Air Flow’ technology making it the first electronic cigarette that adapts to the user’s draw.

In other words, vaping blu MAX is more enjoyable, since this is the first e-cigarette that responds to the intensity of your draw.” Titus Wouda Kuipers, CEO Fontem Ventures. blu MAX™ will be available on sale from the 17th November, exclusively in Brighton stores.

Experiment design for measuring component of gas mixtures

using thermal conductivity sensors

Xiang Zheng Tu

 

Gas mixture is the combination of two or more gases. One example of a mixture is air which is made up of nitrogen, oxygen, and smaller amounts of other gases. The other gases include water vapor (humidity), carbon dioxide, and methane. These gases may pollute our air at any given time or place and affect human health and safety or environment protection. To avoid these things happen, many gas sensors are used to monitor the levels of the gases in the atmosphere so as to maintain each gas concentrations below a safe levels. They are recommended for carbon dioxide: 5000ppm, methane: 1000ppm and humidity: 30% to 50% (relative humidity).

All gases conduct heat to differing degrees, and the amount of heat transferred by a gas is determined by its thermal conductivity. This property can be exploited in sensing because each gas has a different thermal conductivity. POSIFA’s Thermal Conductivity Sensors use this property to accurately measure one of the three gases present in a pseudo-ternary gas mixture such as air, water vapor (humidity) and carbon dioxide or air, water vapor (humidity) and methane. The “pseudo-ternary” means the dry air here is treated as a simple gas.

The detection principle of thermal conductivity sensors is as follows. Temperature differences are produced between the hot junctions and cold junctions of one or tow thermopiles. The hot junctions and cold junctions are positioned on a hot plate and a frame both are created in a silicon substrate, respectively. The hot plate is heated by applying a required electrical power to a resister positioned a long the hot junctions. Heat is transferred from the hot plate to the substrate via thermal conduction through the gas mixture filled the cavity under the hot plate. A temperature gradient is established due to the thermal flow energy in the gas mixture. The temperature difference or thermopile(s) output for the thermal conductivity sensor, therefore, is a direct measure of the thermal conductivity of the gas mixture. Heat loss due to radiation, convection and heat conduction through the terminals of the hot plate has been minimized by the sensor MEMS structure.

According to Wassiljewa’s equation the thermal conductivity k_m for a mixture of three gases 1, 2 and 3 can be expressed as:

k_m = k₁ / (1 + A₁₂  x₂  / x₁ + A₁₃ x₃ / x₁) + k₂  / (1 + A₂₁ x₁ / x₂  + A₂₃ x₃ / x₂)

+ k₃  / (1 + A₃₁ x₁ / x₃  + A₃₂  x₂ / x₃)                                      (1)

Where k₁, k₂ and k₃ are the thermal conductivity of gases 1 (air) , 2 (water vapor) and 3 (carbon dioxide or methane), x₁, x₂ and x₃ are the mole fraction of gases 1, 2 and 3, and A_12, A_13, A₂₁, A₂₃, A₃₁ and A₃₂ are Wassiljewa’s coefficients which are the functions of the molar masses and viscosities of the two related gases.

The thermal conductivity of the pseudo-ternary gas mixture does not vary linearly with the composition of the mixture. As seen from the equation (1) if the changes of the mole fraction of the gases are small enough the equation will be reduced as:

k_m ≈ a₁ x₁ + a₂ x₂ + a₃x₃                                                          (2)

Where a₁, a₂ and a₃ are constants related to the thermal conductivities k_1, k₂ and k₃ respectively. For the water vapor (humidity) and carbon dioxide and air, water vapor (humidity) and methane the above mentioned assumption is true.

The output Seebeck voltage of the thermopile(s) of the thermal conductivity sensor U_seebeck can be expressed as:

U_seebeck = S k_m                                                                            (3)

Where S is sensitivity of the sensor, which is the determined by the input power and the parameters of the sensor structure. It has been shown that it is the functions of the width of the hotplate, length of the palate supporting beams and path of the cavity filled with the gas mixture.

It should be noticed that the three component mixture has 2 degrees of freedom and the mole fraction of gas 1 can be calculated by equation:

x₁ + x₂ + x₃ = 1                                                                          (4)

Combine of equation (3) and (4) results an equation as:

U_seebeck = b₁ + b₂ x₂+ b₃ x₃                                                                                       (5)

Where b₁ is a bias term in the output Seebeck voltage of the sensor so that the solution of the equation is no zero solution, and b₂, b₃ are sensitive to component 2 and 3 mole fractions, respectively. Since the output is expressed in unit of V, the coefficients b₁, b₂ and b₃ are expressed as the same.

A three factorial experimental design may be used for determining the coefficients b₁, b₂ and b₃ by the experimental measurements of the thermal conductivity sensors.The design includes three treatments x₁, x₂ and x₃ of the experimental variable, nine levels L₁, L₂, _L3 and L₉ of the control variable and nine observations and has 9 different cells as shown below. In the design the means for the columns provide the researcher with an estimate of the main effects for treatments and the means for rows provide an estimate of the main effects for the levels. The design also enables the researcher to determine the interaction between treatments and levels.

 

The general linear model is a statistical linear model.  The general linear model system of equations may be expressed elegantly using matrix notation as:

Representing the indicated vectors and matrix with single letters, the form of the general linear model system of equations may be changed as:

U = X B + E                                       (7)

{\displaystyle \mathbf {Y} =\mathbf {X} \mathbf {B} +\mathbf {U} ,}

Where U is a matrix with series of multivariate measurements, X is a matrix that might be a design matrix, B is a matrix containing parameters that are usually to be estimated and E is a matrix containing errors or noise.

Given the data U and the design matrix X, the general linear model fitting procedure has to find a set of B values explaining the data as good as possible. The time course values predicted by the model are obtained by the linear combination of the predictors:

U = X B                                             (8)

A good fit would be achieved with B values leading to predicted values which are as close as possible to the measured values u. By rearranging the system of equations, it is evident that a good prediction of the data implies small error values:

E = U – X B = U – u                         (9)

An intuitive idea would be to find those beta values minimizing the sum of error values. Since the error values contain both positive and negative values (and because of additional statistical considerations), the general linear model procedure does not estimate B values minimizing the sum of error values, but finds those B values minimizing the sum of squared error values:

E’ E = (U – X B)’ (U – X B) > min    (10)

The term E’ E is the vector notation for the sum of squares. The apostrophe symbol denotes transposition of a vector or matrix. The optimal B weights minimizing the squared error values are obtained non-iteratively by the following equation:

B = (X’ X)^-1 X’ U                                (11)

The term in brackets contains a matrix-matrix multiplication of the transposed, X', and non-transposed, X, design matrix. This term results in a square matrix with a number of rows and columns corresponding to the number of predictors. This X'X matrix corresponds to the predictor variance-covariance matrix. The variance-covariance matrix is inverted as denoted by the "-1" symbol. The resulting matrix (X'X)^-1 plays an essential role not only for the calculation of beta values but also for testing the significance of contrasts. The remaining term on the right side, X'U, evaluates to a vector containing as many elements as predictors. Each element of this vector is the scalar product of a predictor time course with the observed voxel time course.

Comparison of both MEMS Thermal Conductivity CO₂ Sensors

And Non-dispersive Infrared CO₂ Sensors

Xiang Zheng Tu

 

A major hazardous gas present in the atmosphere which creates various adverse effects to human is carbon dioxide (CO₂). Measurement of CO₂ gas using CO₂ sensor will help to monitor its presence and indicate us above dangerous limits to prevent adversities. In a modern ventilation system CO₂ sensors used as indoor air quality indicators help to ensure a fresh outside air supply to building occupants while simultaneously optimizing energy consumption. For such systems it has been recommended: CO₂ sensors shall be certified by the manufacturer to be accurate within plus or minus 75 ppm at a 600 and 1000 ppm concentration. Carbon dioxide air-conditioning systems have been installed in cars. In these applications the CO₂ leakage detection range is 0-50.000 ppm with a resolution of 10% while the comfort range is 0-5.000 ppm with a resolution of 200 ppm.

A non-dispersive infrared (NDIR) CO₂ sensor is shown in the above first figure. The NDIR sensor comprises an infrared source, a sample cell, an optical filter and a detector system. The infrared source directs waves of light through the cell filled with air containing CO₂ toward the filter and then detector which measures the amount of the light that hits it. As the light passes through the cell, any gas molecules that are the same size as the wavelength of the light absorb the light only, while letting other wavelengths of the light pass through. Next, the remaining light hits the filter that absorbs every wavelength of light except the exact wavelength absorbed by CO₂. Finally, the detector reads the amount of light that was not absorbed by the CO₂ molecules or the optical filter.

The difference between the amount of light radiated by the source and the amount of the light received by the detector is measured. The difference is proportional to the number of CO₂ molecules in the air inside the cell.

The advantages of the non-dispersive infrared (NDIR) CO₂ sensors are selective, sensitive, non contact and reliable. At present time this technology is accepted as a state-of-the-art. But it still has some serious problems such as inherently expensive (at least two components), large size, requiring drift compensation and complex packaging.

So many efforts have been made regarding more miniaturization and lower system costs compared to the non-dispersive infrared CO₂ sensors.

POSIFA Microsystems Company announces a MEMS thermal conductivity CO₂ sensor.

The sensor integrates all CO₂ sensing components in a single silicon microstructure with a micro-hot-bridge, which is not like the non-dispersive infrared CO₂ sensor which is assembled with at least 4 separated components. In additional the micro-hot-bridge the sensor further contains a resistor, a cavity, and a thermopile with its hot junctions near the resistor and cold junctions extending to the silicon frame along the bridge supporting beams.  

The thermal conductivity CO₂ sensor performs a measurement as follows. By applying a voltage to the resistor on the micro-hot-bridge of the sensor, the resistor is heated up and becomes a “hot source”. The cavity is open to the atmosphere and filled with air containing a certain amount of CO₂ gas or air mixture. The air mixture transfers a quantity of heat from the hot source to the cold bottom of the cavity via the air mixture. The quantity of heat is measured by the thermopile. The changes in the thermal conductivity of the air mixture can be detected by measuring the changes of the output Seebeck voltage of the thermopile. With the measured thermal conductivity of the air mixture the concentration of the CO₂ in the air can be calculated by a humidity compensation algorithm which is based on the measurement results using the same sensor operated at two different temperatures.

Compared with the non-dispersive infrared CO₂ sensors, the thermal conductivity CO₂ sensors possess many advantages such as:

• Size reduced to a single silicon chip,
• Milliwatts grade power consumption,
• Milliseconds grade response times,
• Low cost, and
• Able to identify different gases of a gas mixture.

 

It is not be surprised for the last advantage. The thermal conductivities of gases always change with temperature. As shown in the above second figure, the thermal conductivities of gases CH₄, C₂H₆, N₂ and CO₂ increase slight-non-linearly with temperature. Based on this inherent character of the gases distinguishing single components of a gas mixture can be realized by modulating operation temperature of a thermal conductivity sensor.

Hear, as a gas mixture of Air, CO₂ and humidity (water vapor) is measured as a gas mixture. The temperature modulation is conducted by applying heating voltages V₁ and V₂ with V₂ higher than V₁. The measured output signals of the thermopile are Y₁ and Y₂ respectively. Then two binary linear equations can be obtained as

Y₁ = b₀₁ + b₁₁ N_CO2 + b₁₂ N_{water vapor}       (1)

Y₂ = b₀₂ + b₂₁ N_CO2 + b₂₂ N_{water vapor}        (2)

Where Y₁ and Y₂ are the output of the thermopile, N_CO2 and N_{water vapor}  are the volume percentage of CO₂ and humidity respectively, b_01, b_02, b₁₁, b_12, b_02, b₂₁ and b₂₂ are constants determined by calibration tests. The volume N_air of Air is found by meeting the equation as

N_air + N_CO2 + N_{water vapor} = 1                   (3)

With the measured Y_1, Y₂ and the known b_01, b_02, b₁₁, b_12, b_02, b₂₁ and b₂₂, N_CO2, and N_water can be found by solving the equations (1), (2) and (3).

All these advantages offer a high potential for mass markets. The most compact thermal conductivity CO₂ sensors have been developed for human breath analysis that will focus on enabling low cost applications but without compromising on accuracy.

Advantages of Thermal Conductivity Water Flow Sensors

over Plastic Spinning Water Flow Sensors

Xiang Zheng Tu

 

Reference to the above figure, a thermal conductivity water flow sensor is made up of two thermopiles, which is used as the sensing temperature difference element and operated in conjunction with a resistive heater element for thermoelectric sensing. The fabrication of such sensors is more complicated since less conventional materials are utilized for fabrication of thermopiles but CMOS (complementary metal oxide semiconductor) compatible processing is possible. The Seebeck effect of thermopiles enables higher sensitivity and unbiased output voltages with no offset or drift.

The thermopiles are constructed with thermocouples in series and so the output voltages due to temperature difference change is summed and increased over that of a single thermocouple. Since the thermal conduction between hot and cold junctions of the thermopiles and Johnson noise increases with increasing number of thermocouples, a high thermal isolation structure is desired in order to maximize temperature difference between hot and cold junctions.

The water mass flow (m) passing through the thermal conductivity sensor is calculated on the basis of the measured temperature difference (T_hot - T_cold) between the hot and cold junctions of the thermopile, and the thermal conductivity (C_p) coefficient (k), electric heat rate (q), and specific heat (C_p) of water, as follows:

m = kq/(C_p(T_hot – T_cold)                                    (1)

The electromotive force, or emf (V) created by the thermopile is directly proportional to the differential temperature (T_hot - T_cold) between the two junctions as

Emf_AB = nS_AB (T_hot - T_cold)                                (2)

Where n is the number of thermocouples of a thermopile and S (V/K) is called the Seebeck coefficient.

Still reference to the above figure, a plastic spinning water flow sensor has a rotor, a bearing, and a shaft, which are mounted in housing. The rotor spins as water passes over it. The measured flow rate is proportional to the rotational speed of the rotor. A variety of methods are used to detect the rotor speed, including a mechanical shaft and an electronic sensor.

Plastic bearings must be lubricated, not only to reduce friction and wear, but, in the case of plain bearings, to prevent them from seizing the shaft which they support. Self-lubricating plastic bearings contain a mix of dry lubricants. In operation, movement between shaft and bearing causes microscopic abrasion of the dry lubricant, filling and smoothing the shaft surface to reduce friction. The resulted micron particles will enter the water flow which is harmful to human health.

Most plastic bearing materials expand when exposed to heat and moisture. This factor is more significant when the running clearance between the bearing and shaft is less than 0.001 in. Plastic bearings and shafts are fabricated by injection molding process which has typical accuracy within 0.005 in. As a result, excessive wear or seizing of the shaft occurs very often.

Bubbles inevitably form as air is entrained in the water during the pouring process. The formed bubbles can create many problems in plastic spinning water flow sensors, such as:

● decreasing lubricity caused by an air emulsion,
● reduction of thermal conductivity,
● higher noise emission, and
● decrease water output efficiency.

Compare with plastic spinning water flow sensors, the thermal conductivity water flow sensors have the advantages as:

1.     Thermal conductivity water flow sensors have no moving parts, in which there are no any mechanical failures to take place.

2.     Thermal conductivity water flow sensors are MEMS devices with small size, higher sensitivity, higher reliability, low power consumption, ease of fabrication, and low cost.

3.     Thermal conductivity water flow sensors calculate mass flow rather than volumetric flow and do not require temperature or pressure correction, which means there is no additional expense for the purchase and installation of additional equipment.

4.     Thermal conductivity water flow sensors provide excellent accuracy and repeatability over a wide range of flow rates using bypass flow tube design. The sensor is placed in a bypass around a restriction in the main pipe and is sized to operate in the laminar flow region over its full operating range.

It should be emphasized that the thermal conductivity water flow sensors are not influenced by the air bubbles entrained in the water. The effect of the bubbles can be added to the series conductivity by using conductivity of the air-water mixture for the water conductivity. The thermal conductivity of continuous water phase with entrapped air bubbles can be calculated using Maxwell’s model as

k_m= k_c (k_d + 2k_c – 2p_d [ k_c –k_d])/(k_d + 2kc + p_d [k_c –k_d])            (3)

Where:

K_m = conductivity of the mixture,

K_c, k_d = conductivity of continuous and disperse phases, respectively, and

P_d = volume fraction of the disperse phase.

Replacing equation (3) into equation (1), the water mass flow rate measured by the thermal conductivity water flow sensor should be

 m = {(k_d + 2k_c – 2p_d [ k_c –k_d])/(k_d + 2kc + p_d [k_c –k_d])}q/(C_p(T_hot – T_cold)     (4)                        

It can be seen that the measured water mass flow rate does not contain the air bubbles entrained in the water.

0~2000ppm Range and 232ppm Resolution

CO₂ Thermal Conductivity Sensors

Xiang Zheng Tu

 

Figure 1 shows a thermopile thermal conductivity sensor provided by POSIFA Microsystems Company. The sensor mainly comprises a silicon chip, a hot plate suspending over a cavity recessed into the silicon chip, a resistor and a thermopile both disposed on the hot plate. The resistor is heated by applying a square pulse voltage and the thermopile is used to measure the temperature difference between the hot plate and the silicon chip. The temperature difference depends upon the thermal conductivity of the gas or gas mixture filled in the cavity. Since the sensor is ultra miniature its thermal time constant is short enough to allow for heating the sensor to work with very narrow pulses of electricity. So the power consumption throughout sensor's operation is quite low.

Figure 2 shows measurement data for indoor air. The heating square pulse voltage is supplied by Agilent 8110A 150 MHz Pulse Generator. The square pulse voltage is chosen to have: period = 1s, width = 20ms and amplitude = 8.96V. The out voltage of the sensor is measured by a TDS Digitizing Oscilloscope, which is shown as 1.86mV.

Figure 3 shows measurement data for 40% carbon dioxide and 60% nitrogen.

The heating pulse voltage is maintained as the same. The out voltage of the sensor is shown as 1.924V which is higher than the out voltage measured for indoor air. 

Using the above measurement data the sensitivity of the thermopile thermal conductivity sensor for carbon dioxide in nitrogen or in indoor air can be calculated as 1.65mV/1%.

In order to determine the resolution of a practical sensor measurement system in terms of voltage, we have to make a few calculations.

·      Assume the system capable of making measurements across 0 to 5V range,

·      Using a18-bits A/D converter, and

·      Using an averaging technique for reducing the noise contribution from four counts to one count.

Therefore, the smallest theoretical change we can detect is 153μV or 232ppm carbon dioxide in nitrogen. 

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: