Meeting Quality Standards in Oil and Gas Extraction with Ultrasonic Transducers
Baker Hughes saves 30% on prototyping costs by using ultrasonic simulations to study acoustic wave propagation, capture experimental responses, and optimize transducers used for testing extracted oil and gas.
By Mackenzie McCarty
September 2025
Before oil and gas can be used for heating homes, fueling cars, and generating electricity, they go through extensive refining, transporting, extracting, and testing processes. Baker Hughes focuses on the first step, also known as the upstream step, of this process, specifically using cement bond logging technology to assess gas quality. The company uses multiphysics simulation software to design and improve its ultrasonic transducers used during pulse-echo and pitch-catch testing, two commonly used methods for testing extracted oil and gas.
Exploring Oil and Gas Extraction
When a hole is drilled into a well to extract gas in the upstream process, the well must be reinforced to control the flow of fluid within it. Cement bonding evaluation is an important procedure in this process. After drilling a borehole, cement is injected between the casing and the formation to prevent fluid communication between producing zones in the borehole. As Haiqi Wen, a lead scientist at Baker Hughes, explained, the cement sheath creates a hydraulic seal that prevents fluid communication and blocks the escape of fluid to the surface.
The two commonly used ultrasonic tools that are run on wireline into the well to gather accurate estimates of well integrity and fluid zone isolation are called cement-bonding logs (CBL) and variable-density logs (VDL). The results of the CBL are in the form of one waveform that can be used to determine the bonding quality between the casing and the cement based on the waveform's amplitude and decay coefficient. The VDL is "more like a visual representation of all the waveforms, and you can have more information for the bonding quality between the formation and the cement," said Wen (Figure 1).
Testing oil and gas at the point of extraction ensures that the product meets quality standards before continuing through the rest of the process. The test identifies impurities that could affect the value or usability and analyzes composition and production rates, which, as Wen explained, helps to optimize production. The testing also gathers data that allows operators to understand reservoir conditions, identify any safety concerns, and guide future improvements.
Piezoelectric transducers are used in the upstream, or testing, part of the process. Wen and his team used the COMSOL Multiphysics® software to model their piezoelectric transducers (Figure 2). Through the software's built-in multiphysics capabilities, they coupled fluid to the piezoelectric transducers, elastic waves to pressure acoustics, and an external electrical circuit to the terminal of the piezoelectric element. These couplings allowed them to accurately examine how multiple physics phenomena interact and model the transformation of voltage signals to elastic waves, as well as fluid–structure interaction at the transducer's boundary with customized circuit parameters.
"I put absorbing layers at the boundary to absorb incoming waves," said Wen, before adding that "the boundary also performs frequency filtering and scanning functions. Only one eighth of the model is simulated to save time and energy, but by applying mirrored datasets, we can obtain the full model response and data."
A key component of transducer design is the thickness of the piezoelectric transducer compared to the wavelength and matching layer. In this design, the transducer thickness is set as half of the wavelength, while the matching layer thickness is set as one quarter of the wavelength.
Wen explored two different methods, form assembly versus form union, while building the transducer dimensions and mesh settings. Form assembly creates a discontinuous mesh at the interface, while form union creates a continuous mesh. "I think form union is usually a little bit more robust, but then you dump much finer elements at the interface so that might make your simulation just slightly slower in some cases," said Wen.
Reducing Prototyping Costs with Simulation
Wen built a simplified, axisymmetric 2D transducer model as well as a full 3D model (Figure 3) and validated both models against experimental testing. The simulation sends out a brief pulse signal that strikes the cement surface of the well. When the bonding quality is good, the receiver will not show many strong signals because the materials are all securely bonded without any voids or cracks between them. In this scenario, the signal passes through the surface. Conversely, if the bonding quality is poor, the receiver shows a reflected signal due to the signal hitting cracks or voids.
"In this work, I compared the wave propagation and the pressure response. As you can see, the wave propagation looks almost identical," said Wen. With this finding, Wen concluded that the axisymmetric 2D model was the optimal model in this case, as it takes less time to run but still produces almost identical results to the 3D model. However, he also noted that if the model was not axisymmetric, it would have been necessary to use the 3D model.
The 3D model results were obtained by evaluating the pressure response at the yz-cut plane, where x = 0 (shown at right in Figure 3). "For this pressure probe response, the 2D model is almost overlapping with the 3D model," said Wen. He compared the results using LiveLink™ for MATLAB®, an interfacing product that connects the COMSOL Multiphysics® software with the MATLAB® software (Figure 4).
The COMSOL simulation results and measurement data aligned well at the near field, as shown in LiveLink™ for MATLAB® (Figure 5). The results indicated that the maximum pressure is located on the axis, with the transducer's center frequency in this data being 280 kHz amplitude. However, as Wen pointed out, "there are some discrepancies we are trying to resolve." One example of this is the presence of side lobes in the measurement data, which were not present in the simulation results. Another inconsistency is that local cancellations were observed in the simulation results, whereas the measurement data shows a continuous decay.
"I think the issue may be related to the modeling of the piezoelectric material because in the real application it is actually a composite material. However, in our current study, we are treating it as a homogeneous material," Wen said. "We are still trying to improve this."
"Overall, simulations have been saving us about 30% on prototyping costs," said Wen. "In the past, when we needed to order new transducers, we would usually order a batch of different transducers with different specs. But now that we have been using simulation software like COMSOL®, we just need to verify that there are a few good designs in the batch. Then, we just need to order those designs instead of ordering all of the new transducer designs and testing which one performs the best," said Wen.
Pulse-Echo and Pitch-Catch Testing
Furthering their work, Wen and his team used COMSOL Multiphysics to simulate and optimize pulse-echo and pitch-catch testing. Their pulse-echo simulation highlights an ultrasonic nondestructive testing (NDT) technique that sends out ultrasonic pulse waves to identify defects in materials or analyze the reflective waveforms for information. Wen and his team sent out waves that were reflected by a metal casing, with the transducer acting as both a transmitter and receiver. The waveform data was analyzed after being measured by a point probe.
Wen uses the Hilbert transform to extract the waveform envelope. Wen explained that from this step, "you can take the FFT (fast Fourier transform) off of it to get one of the frequency peaks, and that peak is actually corresponding to the internal reflection within the casing. When you send the signal, there is the first reflection, but there is actually internal reflection" (Figure 6). The casing measurements can then be calculated based on the frequency.
The Hilbert transform was used to extract the envelope of the wavelength in pitch-catch testing, which makes it possible to track the amplitude of the peaks. The peaks in this study are represented by the blue and red dots at specific points in Figure 7. Wen plotted the wave amplitude as a function of the transducer spacing, which allowed the exponential curve to fit. (Note that this effect is not shown in Figure 7.) He compared the different results between the free pipe water and foam cement to understand the material properties within the domain.
"The challenge is that you can see the peak of fairly low amplitude. In real applications, it is going to be very challenging because you will naturally suffer from poor signal-to-noise ratio, especially if you go to higher frequencies," said Wen. He explained that it will be harder to capture meaningful signals when the acoustic waves are being sent and received very quickly.
Simulating the two testing methods in COMSOL Multiphysics allows for increased efficiency in gathering data from the ultrasonic pulse waves, and modeling the transducer conserves resources while optimizing the design. Simulation helps Wen and his team explore how the wave propagates through different materials and determine what causes the final waveform to look the way it does. "That is really something that simulation can provide where we cannot get information out of the test experiments," Wen explained. Ultimately, simulation helps Baker Hughes improve efficiency and accuracy in the upstream step of the oil and gas production process.
Reference
- C. Fang et al., "A Novel Cementing Quality Evaluation Method Based on Convolutional Neural Network," Appl. Sci., October 2022; https://doi.org/10.3390/app122110997