2.1. Homogenization strategy

In order to overcome the problem of regime dependent for component fraction measurements, four methods are used commonly: 1) multi-beam gamma-ray densitometry [8−10]; 2) flow imaging tomographic systems[11,12]; 3) dual modality technique, including transmitted and scattered gamma-ray counting [13–15] and using artificial neural network as a pattern recognition technique[16]; and 4) using a homogenization mechanism to remove all of the possible regimes [17]. Flow homogenization before measurement, is an elegant strategy, which causes the mixture density to be the same across the pipe cross section, and therefore reduces the number and difficulty of measurements required. Homogenization simplifies the flow rate measurements, and reduces the slip between the phases. It makes individual phases have the same velocity, removes all the possible flow regimes except homogenous one, and makes a regime independent component fraction measurement.

2.2. Gamma-ray densitometry

Gamma-ray attenuation obeys the Lambert-Beer’s exponential decay law:

where, I is the measured intensity; I₀ is the initial intensity; α_i and μ_i are the component fraction and linear attenuation coefficient of individual phases, respectively; d is the effective inner diameter of the pipe; and B is the buildup factor due to scattered radiation. Assuming that the pipe is filled with a two-phase mixture and B =1, by the establishment of the good geometry conditions, the component fractions can be extracted as

where, α₁ and α₂ are the dispersed and carrier phase fractions, respectively; I_mix is the mixture count rate; and I₁ and I₂ are the count rates relating to the calibration stage, with the pipe being fully filled by the dispersed and carrier phases at each time. While working with a suspension, it is impossible to fill the loop by the solid (dispersed) phase entirely. Thus, one can consider a maximum permissible fraction of t≤1. In this case, the component fractions can be calculated by

3.1. Mechanical design

3.1.1. Homogenization tank

For converting a suspension to a homogenized mixture, calculations were done on various kinds of parameters of the homogenization tank, and finally we used a 4" diameter (a common oil pipe diameter) cylindrical tank with dished bottom to maximize suspension quality, in height of 60 cm, enough for placing the meters. On the tank wall, there were two Plexiglas windows opposite to each other, used as a material of low γ-ray attenuation coefficient and to make more accurate measurements by reducing the statistical errors. Sixteen 45° PBT(Pitched Blade Turbine) type impellers were used, each consisting of four flat blades of 1 cm width and 2 mm thickness.

According to the standard handbook of industrial mixing [18], the best compromise between shearing and flow pumping was decided to achieve complete homogenization. In order to deliver a uniform suspension, which means practically uniform in particle concentration and size distribution in the tank, we calculated the just suspended impeller speed (N_js) and obtained the uniform suspended impeller speed by using a speed ratio. The speed was calculated by[19]:

$N_{\text{js}}=S{v}^{0.1}{[g_{\text{c}}(-{\rho }_{\text{L}})/{\rho }_{\text{L}}]}^{0.45}{\chi }^{0.13}{d}_{\text{p}}{}^{0.2}{D}^{-0.85}$ (5)

where, N_js is in rps; S is a dimensionless number related to the impeller type, the ratio of impeller diameter to tank diameter, and the ratio of impeller bottom clearance to tank diameter; v is the kinetic viscosity of the liquid (m²/s), g_c=9.81 m²/s the gravitational acceleration constant; ρ_S is the density of particle (kg/m³); ρ_L is the density of liquid (kg/m³); χ is the mass ratio of suspended solids to liquid; d_p is the mass-mean particle diameter (m); and D is the impeller diameter (m). Assuming, water as the carrier phase, S=4.4 and a mass ratio equivalent to the maximum permissible solid to liquid mass fraction of unity, using a speed ratio of 1.71, the impeller speed versus the particle density, calculated at different particle sizes, is shown in Fig.3(a).The least-required speed increases with the particle density and size, to achieve a uniform suspended particle-water mixture.

Fig. 3.Full-screen View

The impeller speed versus particle density at different particle sizes for the homogenization (a) and suspension (b) tanks.

3.1.2. Suspension tank

To achieve a complete off-bottom suspension, calculations were performed on important parameters. To avoid cavitation due to the central interface vortex forms with the commencement of impeller motion and subsequently air bubbles entering the loop, the volume of the tank at a conservative estimate considered to be fourfold the homogenization one. A Φ10"×30 cm tank having, with dished bottom, was used. The slurry height to tank diameter ratio was always less than one. We used only one 30° PBT type impeller, with four flat blades of 4 cm width and 2 mm thickness. A complete off-bottom suspension means that no particle remains at the tank bottom for over 1–2 s. The required impeller rotation speed was calculated using Eq.(5), assuming water as the carrier phase, S=7.2 and a mass ratio of unity. The impeller speed versus the particle density, calculated at different particle sizes, is shown in Fig. 3(b). The least-required impeller speed increase with the particle density and size, too, to achieve a complete of bottom suspension. Under the same conditions, it is easier to reach an off-bottom suspension than to reach a homogenization.

By implementing two separate inlets to the two tanks, solid phase was allowed to be slowly added to the liquid one, while circulating the mixture between the two tanks for a better suspension. Fig.4 shows schematically the homogenization and suspension tanks and impellers used in each of them.

Fig. 4.Full-screen View

Schematic diagrams of the homogenizer and suspension/emulsion tanks.

3.2. Process set-up

Assuming water as the carrier phase and depending on the particle size and density, the minimum required impeller speed for the suspension and homogenization tanks was extracted from Fig.3. We set 20 rps as the maximum attainable speed. Otherwise, closing the control valve of suspension tank allowed initially to make an off-bottom suspension, while the impeller was adjusted to the least-required speed and the solid phase was added to the liquid phase step by step. After several minutes, while the control valve of homogenizer tank kept opened, the valve of suspension tank was opened and the pump was turned on immediately. By adjusting impellers of the homogenizer tank to the desired speed to circulate the mixture for a few minutes, the pump and suspension impeller were turned off, and the valve of homogenizer tank was closed. Finally, a uniform suspension was prepared in the homogenizer tank and the component fraction was measured. We note that depending on dispersed phase tendency (to be settled or floated), the impellers should be adjusted to swirl clockwise or vice versa. Depending on the phase volume fractions in each experiment, certain amount of the phase volumes were prepared and fed to the loop. It is easier to prepare a certain mass, instead of volume, in each experiment, using Eq.(6)

where, β_S, α_S and ρ_S are mass fraction, volume fraction, and density of the solid phase, respectively; and ρ_L is the liquid phase density. The amount of the solid mass was calculated by

where m_L is the mass of liquid phase.

For a suspension, the carrier phase (liquid one) must be entered before the dispersed phase (solid one) is added. For an emulsion, the process is the same but the liquid phase with less density value is considered as the carrier phase.

4.1. Source and detector collimation

The buildup factor is defined as the intensity ratio of the primary and scattered radiations, at any point in a beam, to the intensity of the primary radiation only at that point [20]. Using a pencil-beam detection system with the good geometry conditions, a buildup value of unity can be achieved and component fractions of a homogenized two-phase mixture can be calculated by Eq. 3 or 4. M-C simulations can be done to obtain proper collimators depth and diameter, and to minimum the lead shield volume.

4.2. Radiation shielding

The M-C simulations were to calculate lead shielding so that equivalent dose to individuals was below permissible dose limit of radiation workers. ICRP Publication 60 recommended dose limits of an average of 20 mSv per year over five years (100 mSv in five years) with no more than 50 mSv in a single year [21]. We calculated for a 1 Ci (3.7×10¹⁰ Bq) ¹³⁷Cs source and a cylindrical lead shield, for the air kerma (kinetic energy released per unit mass)rate at 1 m from the source being no more than 20 mSv/y or 10.42 µSv/hr. All simulations were carried out with the MATLAB-based algorithm [22] and the MCNP code, for a ¹³⁷Cs source placed in the center of cylindrical lead shields in height of 10 cm with varying radiuses from 2 cm to 10 cm. The shield thickness was calculated as follows. Compared to distance where the kerma rate was calculated, the source was small enough in size and could be deemed as a point source. Given a specific gamma-ray emission of 7.82×10⁻¹⁴ Sv·m²·Bq⁻¹·h⁻¹, the exposure rate at 1 m from the unshielded source is 3.7×10¹⁰ Bq×7.82×10⁻¹⁴ Sv·m²·Bq⁻¹·h⁻¹/ 1 m² = 0.0029 Sv/h.

With a unity buildup factor, using the gamma-ray attenuation coefficient of 1.24 cm⁻¹ for Pb at 662 keV, the required thickness of lead was calculated at 4.5 cm. Plus one half value layer (HVL) of 0.56 cm for lead at 662 keV, we had the new thickness of 5.06 cm, which is equivalent to 1.24 $\times$ 5.06=6.27 relaxation length, at which the maximum buildup factor was 1.44, calculated by MATLAB-based algorithm and MCNP (not shown). Substituting these values for B and t into the Lambert-Beer equation, the γ-ray dose rate was calculate at 7.84 µSv/h. While the maximum permissible dose rate is 10.42 µSv/h, the shielding thickness can be 5.06 cm.

4.3. Collimator design

The MATLAB-based algorithm was used to simulate ¹³⁷Cs gamma-ray from collimators in depths of 4, 6, 8, 10, 12 and 14 cm and diameters of 1.0, 1.6, 2.0 and 3.0 cm. The detector was placed in a collimator in depth of 4 cm and diameters of 1.0, 1.6, 2.0 and 3.0 cm. The lead cylinders were of 5 cm in wall thickness. All the simulations were done with 10⁸ particles history and maximum error of ±1%. The results are shown in Fig.5(a). The buildup factor decreased with increasing source collimator depth, and tended to a constant value after 8 cm, while it increased with the collimator diameter.

Fig. 5.Full-screen View

Buildup factor (a) and peripheral to total ratio (b) as a function of the source collimator depth, at various collimator diameters.

It must be noted that, a fraction of radiation can pass through the lead shields without any interaction and entered the peripheral area of the detector. The surface flux crosses the peripheral area of the detector must be considered as a main source of noise and removed from the transmitted count rate. The noise was defined as the peripheral-to-total ratio and calculated by dividing the transmitted flux at the detector peripheral area to the sum of transmitted fluxes both at the peripheral and central area of the detector. The ratio versus source collimator depth for various diameters is shown in Fig.5(b). The peripheral-to-total flux ratios decreased with increasing source collimator depth and diameter, tended to be equal values for different source diameters after the depth of 8cm. A greater source collimator diameter means a greater signal-to-noise ratio and accuracy of measurement, subsequently.