Design of Mud Electrical Parameters Measurement System Based on FPGA

my country has a vast geographical area and rich natural resources. Among them, oil is the blood of my country's industry and an important energy source that supports the rapid development of my country's economy. It is related to national energy security and social stability [1]. However, the process of oil extraction is full of challenges. In order to obtain real-time formation image information at the drill bit and examine the impact of mud on drilling, it is usually necessary to measure the formation electrical parameters [2] and transmit these electrical parameters back to the ground control console, so as to obtain and analyze the formation distribution information in real time.

The FPGA - based mud electrical parameter measurement system is designed to meet the above industrial needs. In order to obtain accurate mud electrical parameters, the mud is injected into a specific annular container, with the mud as the dielectric of the container, and then the complex impedance value of the annular container at a specific excitation frequency is measured to deduce the mud electrical parameters.

1 Measurement method and principle
1.1 Measurement method
The mud electrical parameter measurement adopts an indirect measurement method, that is, the electrical parameters of the mud are inferred by measuring the complex impedance of a special annular container containing the mud to be measured. The measurement of the complex impedance Zx is to load a known voltage excitation Vin on the measured impedance, and then measure the current Iz flowing through the measured impedance, so as to calculate the measured impedance Zx=Vin/Iz. The measurement principle is shown in Figure 1. The output of terminal ① is V3=-Iz·Rs, from which Iz=-V3/Rs can be deduced, where Rs is the sampling resistor.

Figure 2 Schematic diagram of the equivalent model of the ring capacitor

Then the equivalent impedance of the ring capacitor is:

in:

The parameters r1 and r2 represent the inner and outer radii of the annular capacitor, respectively, and h represents the height of the annular container. Simplifying equation (1), the real and imaginary parts of Zeq can be obtained as follows:

Substituting equation (2) into equation (3), further deduction can be made to obtain the resistivity ρ and dielectric constant ε of the medium:

From the above derivation, it can be known that the electrical parameters of the mud can be indirectly obtained by measuring the equivalent impedance of the annular container.

2 System composition The FPGA
- based mud electrical parameter measurement system consists of an FPGA core controller module, an amplitude/phase detection module, a direct digital frequency synthesizer module (DDS for short), a monitoring module, a filter network, and two signal conditioning modules. The FPGA controls the DDS module to generate two identical sinusoidal excitation signals CH0 and CH1, of which CH0 is sent to the reference channel 1 of the amplitude and phase detection circuit after passing through the signal conditioning circuit 1, and CH1 is loaded on the measured impedance after passing through the power amplifier, and then the current flowing through the measured impedance is converted into voltage through the IV conversion circuit, and the voltage signal is then transmitted to the 2 channels of the amplitude/phase detection circuit after passing through the analog bandpass filter network.