Thermopile Flow Sensors with Differential pressure sensors for Measurements of Mass Flow Rate, Density and Void Fraction of Gas-Liquid Two-Phase Flow Fluids

Tu Xiang Zheng

Gas-liquid two-phase flow exists broadly in chemical, petroleum and metallurgical industries. The measurements of gas-liquid two-phase flow parameters in real time without separating the phases is desirable in order to reduce costs, increase production and reach excellence in oil and gas transport. Although many measurement techniques have been developed, it is yet difficult to measure some flow parameters because of the complexity of the two-phase flow. It is necessary to explore new measurement techniques.

This paper proposes a measurement technique of gas-liquid two-phase flow parameters which has the advantages of low cost, simple structure and non-intrusiveness. This technique is based on the combined use of a thermopile flow sensor and a differential pressure sensor. The setup is shown in the above figure which consists of a venture, a bypass tube, a thermopile flow sensor, and a differential pressure sensor. The thermopile flow sensor is installed at the central point of the bypass flow tube and the differential pressure sensor is used to measure the pressure difference between the inlet and the outlet pressure of the bypass tube. The mass flow rate measured by the thermopile flow sensor can be used to derive the main mass flow rate passing through the venture according to a ratio dependent on the setup structure. Knowing the mass flow rate and pressure difference the density of the gas-liquid two-phase fluid can be obtained. The void fraction of the gas-liquid two-phase fluid can be further calculated using know pure liquid density and pure gas density.  

As can be seen from the above figure, there are two flow loops: the venture loop and the bypass loop. In accordance with the nature of these two parallel loops, it is reasonable to have their pressure drop to be equal.

According to the homogeneous model of two-phase flow two phases travel at equal velocities and mix well; therefore, they can be treated as if there is only one phase.

Using Bernoulli's equation in the special case of incompressible flows (such as the flow of water or other liquid, or low speed flow of gas), the theoretical mass flow rate through the venture can be given by:

m_v = C_vA₂{2(p_up-p_down)/ρ[1-(A₂/A₁)²]}^1/2   (1)

where m_v is the mass flow rate of the fluid, C_v is the discharge coefficient = (actual flow rate) / (theoretical flow rate), A₁ and A₂ is the cross-sectional area of the venture in the indicated section of the venture, p_up, p_down are the fluid's static pressure in the indicated section of the venture, and ρ₁ is the fluid's density passing through the venture.

Similarly, the theoretical mass flow rate through the bypass tube can be given by:

m_b = C_bA₃[2(p_up-p_down)/ρ₂]^1/2                       (2)

where m_b is the mass flow rate of the fluid, C_b is the discharge, A₃ is the cross-sectional area of the bypass tube, p_up, p_down are the fluid's static pressure in the indicated section of the bypass tube, and ρ₂ is the fluid's density passing through the bypass tube.

In arriving at the homogeneous model for two-phase flow, area averaging is performed for both phases and the density ρ₁ and ρ₂ must be equal a similar ρ. Forever the void fraction α of the two-phase fluid must satisfied the relation:

  ρ = (1-α)ρ_l + αρ_v                                           (3)

where ρ_l and ρ_v are the densities of the pure liquid and the pure gas, respectively.

It is clear that a thermopile flow sensor with a differential pressure sensor can be used to measure the mass flow rate, density and void fraction of a gas-liquid two-phase flow. A proposed setup comprises a thermopile, a differential pressure sensor, a venture tube and a bypass tube. Using the venture equation and the homogeneous model form the mass flow rate measured by the thermopile flow sensor and the pressure difference measured by the differential pressure sensor the density and the void fraction of the two-phase fluid can be derived respectively. This technique requires the gas and the liquid mixes so well that the mixture can be seen as one single phase approximately. The mixing degree of the gas and the liquid affects the measuring accuracy. For un-complete mixing two-phase fluid correction is needed to improve the accuracy.