The diagram of sand signal detection system is shown in Fig. (1), which contains Instantaneous Sand Production Sub-System (ISPSS) and Sand Production Signal Amplitude Obtaining Sub-System(SPSAOSS), ISPSS can obtain the flow Q₁ and Q. SPSAOSS can obtain the amplitude U of sand signal.

Fig. (1). Principle block diagram for sand production signal detection system.

Doppler Flow meter shown in Fig. (1) is designed based on the Doppler technology, which can obtain Q. This method is described in the literature [8]. Because the sampling number can be counted through computer, then Q₁ is fixed. So the R can be easily computed through equation (11), then the value of R transfers to the computer through the RS-232 bus. The high resister charge signal shown in the Fig. (2) is amplified to the low resister voltage one, which function is to realize impedance transformation. In addition, frequency distribution of sand signal has curtain range, sometimes it exceeds the scope due to the noise generated by pipe vibration, so the first thing is to filter the noise signal, then acquires the amplitude U of sand signal through the PCI bus of data acquisition card.

The structure of sand sensor is shown in Fig. (2), which contains sensitive elements, matching layer, shell and installation mount. The shell of which is made of aluminum, a concave groove is convenient to the install on the pipe outer wall using the fixed belt clip, the materials of which is piezoelectric ceramics. The piezoelectric ceramic piece uses the PSnN-51, and Piezoelectric wafer is thin wafer type, which vibrates along the thickness direction. The produced ultrasonic wave is a longitudinal one [9].

Fig. (2). Structure of sand production sensor.

Sand production sensor only needs to fix on the oil pipe, so it’s contactless to the mixture inside of the pipe. Therefore it does not affect the normal work of the oil and gas transportation process system.

We build the bend pipe model using Fluent software to determine the best location of sand sensor. The material of pipe is stainless steel. The parameters of pipe model are as follows: thickness of pipe wall is 0.004m; the Pipe diameter is 0.08m; the straight pipes of bend pipe is 20m; circular arc radius is 4m; Young’s modulus of stainless steel is 206GPa; poisson ratio is 0.29; the young's modulus of water is 219GPa; the density is 2650 kg/m³. Supposing the inlet velocity of pipe model is 2m/s and 10m/s, the water density is 998.2kg/m³. The material of this model is water. The stress nephogram under the different inlet velocity of pipe model are shown in Figs. (3 and 4) respectively. And the velocity field nephogram under the different inlet velocity of pipe model are shown in Figs. (5 and 6) respectively.

Fig. (3). Stress nephogram under the inlet velocity of pipe model is 2m/s.

Fig. (4). Stress nephogram under the inlet velocity of pipe model is 10m/s.

Fig. (5). Velocity nephogram under the inlet velocity of pipe model is 2m/s.

Fig. (6). Velocity nephogram under the inlet velocity of pipe model is 10m/s.

From velocity nephogram, fluid velocity changes because fluid direction changes at the fluid passing the bend; from the stress nephogram, shock pressure in the bend pipe and straight pipe is not the same, the pressure in the bend pipe is obviously large. Pressure on the elbow inside wall of the lateral increases, the pressure in the inside is reduced, and the maximum stress appears in elbow inside wall of the lateral, namely pressure is the maximum at the lateral on the bend exit, next is the outside of the bent pipe head. Therefore the sensor should install on the exit of bend pipe. The sand velocity direction changed at this position, but the sand signal is still strong. Additionally, the experiment verified that the bend pipe between the sensor and noise resource can reduce the ultrasonic wave on the pipe.

In order to reduce the reflection of sound waves on the pipe surface, increase the effective energy of sound waves, usually it’s needed to join acoustic matching layer between transducer and working medium. Because the material of oil pipe is steel, we should use the organic glass as acoustic conductance material with easily machine shaping, little attenuation for the signal and good acoustic matching characteristics. According to the ultrasonic theory, when the ultrasonic wave shifts from one medium to another one, there will occur reflection and refraction, the theory model is shown in Fig. (7).

Fig. (7). Theory model of matching layer.

Where C₁ and C₂ are the velocity in the medium 1 and medium 2 respectively. Supposing the incident angle of ultrasound in medium 1 is a₁, and angle of reflection is a₂, angle of refraction for longitudinal wave in the medium 2 is β₁, angle of refraction for transverse wave in the medium 2 is β₂. According to the relation between the law of reflection and refraction:

(12)

From equation (12), a₁ is equal to a₂, moreover C₁ is less than C₂, so a₁ < β₁, a₁ < β₂ ,namely the incident angle is less than the angle of refraction.

Because the shear wave can only spread on the surface of pipe wall and internal lateral, but the wave through the pipe wall is generally longitudinal wave, so the sand signal at the interface propagates through the organic glass in the form of longitudinal wave. By the same way, the signal within the organic glass can only propagate in the form of longitudinal wave. The direction of propagation in line with the law of refraction, namely:

(13)

Because the compressional wave velocity is greater than the shear wave in the same medium, a is the incidence angle, β₂ < β₁ < a₁ so, and β₁ increases with a. When the a = 90°,

(14)

From equation (13) and (14), when β₁ is larger than 27.6°, the sand signal can propagate without distortion. Considering the factors such as the degree of bending pipe wall, the angle of inclination for organic glass β₁, choose 45°.

According to the literature [10], the thickness of matching layer, defined as D, which is equal to:

(15)

In this condition, the sound energy of ultrasonic sensor is largest. Where V is the sound velocity of ultrasonic wave in the steel, about 5800m/s, f is the transmission frequency, equal to 640kHz, The thickness of organic glass D can be computed from equation (15), which is about 1cm. The picture of matching layer is shown in the Fig. (8).

Fig. (8). Picture of matching layer.

The designed sand monitoring system is shown in Fig. (9), and used to monitor the sand production. The experimental process is as follows:

Fig. (9). Calibration experimental device for sand carrying ratio.

1. Mixture with oil and sand in the storage tank is injected into the pipe through the screw pump and pipe, which reflows to the recovery tank through a sand filtering net, comes into the storage tank through the submersible pump.
2. Electronic scale is used to measure the sand mass, which is taken as a standard value. The sand sensor is fixed on the pipe. ISPSS and SPSAOSS should be connected correctly, which used to obtain M and U.
3. While we open the sand injection port at pump inlet, sand flows into the tank.
4. Before we open the pump, U_n is measured when no sand pass through the pipe; then open the pump, mixture with sand flows into the pipe, then U_s is measured. Using equation (10) can obtain U.
5. We compute the water volume according to the tank size, measure the sand weight, compute the sand volume according to the sand density. At the same time, sand carrying ratio R is computed according to the equation (11).
6. When we do experiment using sand particles with different diameter repeatedly, then can get the perfect value of K using the curve fitting method.