Flowing signals are produced during the flow of oilgas-water mixed fluid, which can be used in the corelation measurement to change the problem of the measurement of velocity into the problem of measuring the time interval.

As is shown in Figure 1, the same kind of sensors, which are named as upstream and downstream sensors and have a distance of L, are installed along the flow pipe. As the mixed fluid flows through the sensors, the energy beam or energy field produced by the sensors will

be modulated irregularly, and then the outputs of the sensors will be changed with the modulated signals of the flow. So the outputs of the upstream and downstream called x(t) and y(t) are signals related to the patterns of the measured fluid. When the measured fluid flows stably through the sensors, the modulated signals x(t) and y(t) can be considered separately as two sample functions of x_k(t) and y_k(t) that come from the ergodic stationary random process.

According to the “Solidification” flow pattern assumption proposed by G. I. Taylor, the irregular modulation of the signal x_k(t) at the upstream sensor will repeatedly appeared at the downstream sensor after a certain time,which is named as the transit time, and we can detect the signal y_k(t) at the downstream sensor that has been irregularly modulated by the fluid. That is the signal x_k(t) and y_k(t) have great similarity besides the last one has a time lag named transit time. In fact, the “Solidification” flow pattern assumption can not fully reflect the patterns of the oil-gas-water three-phase flow, but we can approximatively think that the change of the flow pattern is so little that it can be ignored when the distance of the upstream sensor and the downstream sensor is small enough. This requires that we must obtain a stable periodic flow of the fluid during testing, and then we can think the “Solidification” flow hypothesis is basically satisfied. So we can describe this as:

So, the cross-correlation functionis written as:

As thereflects the interaction and the similarity of the two waves described as x(t) and y(t) here, we can know from the characteristics of the correlation function that obtains the maximum value when when. That is to say, the peak of the correlationfunctioncorresponds to the time value which exactly is the transit time when the mixed fluid flows from the upstream sensor to the downstream sensor. As the distance between the upstream sensor and the downstream sensor L is known, we use A to describe the cross-sectional area of the pipe that the mixed fluid flows past, so we can obtain the flow Q:

where is the flow velocity.

As all these results are obtained under the ideal conditions, we must consider many other factors during the tests such as the change of the flow patterns when the mixed fluid flows from the upstream sensor to the downstream sensor. This may lead to the decrease of the similarity of the signals and equal to add a random disturbance signal to the sensor, which will inevitably lead to the measurement error.

The correlation function of the flow signal x(t) and y(t) can be obtained by using the correlation algorithm in frequency domain [11], which has its unique advantages compared with other algorithms. In frequency domain, we can use the Fast Fourier Transform (FFT) to improve the computing speed and the real-time, and we can also obtain a higher precision.

The correlation algorithm in frequency domain is used to calculate the correlation between the two flow signals in frequency domain. If is the FFT of x(t) and is the FFT of y(t), according to the WienerKhintchine formula, the bilateral cross-spectral density functionis the Fourier transform of the correlation function.So we can get:

As is shown in Figure 2, we can get the correlation function by doing like this. First of all, do the FFT of x(n) and y(n) separately and get X(k) and Y(k) in frequency domain, then calculate the conjugation of X(k) and multiplied with Y(k) to get. The correlation function can be obtained by doing the IFFT of.

From Figure 2, we can get the correlation function in frequency domain easily after doing the calculation of FFT and IFFT which can be done by the software MATLAB. So the advantages of calculating the correlation function in frequency domain are obvious.

The sensor pipe is made by glass fiber reinforced plastics (FRP), and six silver-plated copper ring-type electrodes are smoothly embedded on the inside wall of the insulator pipe. As is shown in Figure 3, the two most outside ring-type electrodes at both ends of the insulator pipe E1 and E2 are called incentive electrode, which are used to apply excitation to the conductivity sensor. The four ring-type electrodes in the middle of the insulator pipe are called upstream sensor composed of two ring-type electrodes B1 and B2 and downstream sensor made up of two ring-type electrodes C1 and C2. The up-stream sensor and downstream sensor output the signals that have been irregularly modulated by the fluid. The signal conditioning circuit blocks are used to amplify, filter and demodulate the signals that have been modulated by the mixed liquid. Then, the data used to calculate the flow will be sent to the computer to be analyzed and processed.

Many factors such as the material of the sensor, the size of the conductance sensor, the size of the ring-type

electrodes and the distance between the rings will directly impact the sensitivity of the sensor and the reasonableness and the reliability of the measuring results. So how to get all the right parameters is very important. The ANSYS finite element software is used to simulate the distribution of the electric potential and give the reasonable parameters of the size of the ring-type electrodes and the distance between the rings. After the simulation is completed and the feasibility is demonstrated, the conductance sensor pipe can be made according to simulation results.

It is necessary to set up a special simulated experimental system to verify the reasonability of the conductance sensor and the measurement scheme. First of all, we should mix the three-phase fluid as evenly as possible. Second, the conductance sensor must be installed in the pipeline system through which the mixed fluid will flow. Third, the fluid must be circulated in different ways and the waste liquid can be eliminated easily.

After considering all the factors, the experimental system was finally set up in the laboratory, which contains screw pump, frequency converters, air compressor, air purifier, flow control valve, check valve, spherical valve, flow steady devices, straight pipe, conductance sensor, standard flow meter, mass flow meter, gas meter, static mixer, mixing tank, recycling tank, plastic hose and so on. The schematic diagram of the system is shown in Figure 4, in which the S1 - S14 are spherical valves.

As the oil, gas and water must be mixed evenly according to the certain percentage during the experiments, some equipments are very important in the system such as the oil and water mixing tank, the air compressor supplying certain amount of gas, and the static mixer mixing the three-phase fluid. The amount of the oil and water can be measured before they are mixed in the mixing tank, and the gas will be measured by the standard gas meter before mixing with the oil-water two phase flows in the static mixer. In order to reduce the pulse interference of the fluid, oil-water mixed fluid and gas must be regulated by the steady regulator devices. Transparent pipes are installed in the pipeline system so as to observe the flow pattern of the fluid in real time. There are more than fourteen flow control valves installed in the pipeline system, so we can change the ways and directions of the mixed fluid whenever it is needed. The three-phase flow must be precipitated, separated and recycled after the experiments.