Simulation of Ultrasonic Borehole Imaging

OnScale is working with leading oil and gas companies to optimize their ultrasonic sensors and measurement systems. This article will cover a range of applications, from basic sensor design, to downhole imaging and flow measurement.

6 min read


Understanding the complex, highly coupled behaviour of electromechanical sensors and their performance within a system is critical. OnScale allows users to simulate device behaviour, quickly assess design changes and ultimately optimize the designs.

OnScale is working with leading oil and gas companies to optimize their ultrasonic sensors and measurements systems. A range of applications from basic sensor design, to downhole imaging and flow measurements will be presented in this article.

Why simulate on the cloud?

Simulation is an important tool for engineers working in competitive markets. Technology companies risk losing their competitive advantage unless they continue to innovate, and simulation plays a central role in this.

Through accelerated design and innovation and reducing the requirement for physical prototypes, it allows companies to bring cutting edge products to the market much faster than before.

This is where the flaws of legacy simulation packages become ever more apparent. The speed of simulations is a common issue that limits the number of simulations that can be carried out over a practical timeframe. There is typically a high upfront cost for the legacy simulation packages and restriction is not only on the software functionality, but on the number of users who have access to it.

Moving to a cloud-based simulation platform addresses these issues with additional advantages. The cloud enables direct access to HPC hardware allowing much larger and comprehensive simulations to be performed. Thousands of simulations can also be executed in parallel, opening the possibility of large design studies that were not feasible with legacy CAE packages.

Who are OnScale?

OnScale removes the barrier inherent in legacy simulation products by combining a suite of powerful Multiphysics Finite Element solvers, with cloud high-performance computation (HPC). Whilst OnScale offers on-demand access to HPC compute power, it also removes the high cost of entry by simply allowing users to pay only for the time (Core Hours) spent solving a problem on the cloud.

Transducer Design Study

A simple design study was carried out on an ultrasonic transducer. The aim was to achieve a 1MHz resonant frequency, with high sensitivity, bandwidth and unimodal behaviour. This type of device could be applied to either downhole imaging, flow measurement or even non-destructive testing (NDT). There are two main varieties of active materials used in these sensors: the first uses a monolithic slab of PZT to create a very simple device; the second uses a composite structure made of both PZT and inert polymer.

OnScaleFigure 1. Simple device created from a slab of PZT (left) and a piezocomposite plate (right) with PZT pillars (green) and epoxy filler (red) both plates are 20x20 mm.

Piezocomposites offer improved performance over monolithic PZT as it provides a better acoustic impedance matching to the load, higher piezoelectric coupling coefficients and significantly reduces parasitic resonances. Piezocomposites can also be tailored to any given application, making them the material of choice for biomedical imaging, sonar and NDT. As a simple comparison the simulated impedance of the monolithic PZT plate was compared directly to that of a 1-3 piezocomposite.

Both devices have been simulated in OnScale with both simulations being completed in 4 minutes. Plotting the electrical impedance of both devices highlights some of the key advantages of a piezocomposite device:

OnScaleFigure 2. Simulated results from the direct comparison between a monolithic PZT plate and a piezocomposite.

There is a significant reduction in lateral resonances, resulting in a much smoother unimodal response. The electromechanical coupling coefficient has been improved, which as a result improves the efficiency of the device. Finally, both the transmit and receive sensitivity improvement offers a better signal-to-noise ratio (SNR).

Extracting mode shape videos at the electrical resonance of the device also highlights the more efficient behavior of the piezocomposite. In the monolithic PZT simulation lateral modes result in a non-uniform surface displacement, which is inefficient. The piezocomposite has a more piston like response, helping transfer energy to the load.

OnScaleFigure 3. PZT shows overtones of the width modes interfering with the thickness modes (left) piezocomposites have a more piston like response, which further improves efficiency (right).

Borehole Imaging Case Study

This next case study looks at using piezocomposite sensors within a borehole imaging application. In downhole logging, ultrasonic tools are typically used to interrogate structures outside the casing and assess bond integrity. Challenges with their design include not only the design of the sensor array itself, but also predicting wave propagation through layers of inhomogeneous materials. Since the layers can contain both solids and liquids it is necessary to consider both acoustic and elastic wave propagation during a single simulation. OnScale allows all the material interactions to be considered in a single simulation with minimal effort.

OnScaleFigure 4. 2D model structure used to assess focal performance and crosstalk.

A phased array based ultrasonic logging tool was considered. The device had a 90 mm outer diameter and is designed to sit within a 150mm inner diameter casing. The array is centered at 250 kHz and has a total of 128 elements. The simulation began with a simple 2D model of the device, prior to moving to the full 3D simulation. The 2D model can be used to quickly assess both focal performance and crosstalk, before using it to determine the performance of a cementing defect inspection.

The array is phased to focus the pulse on the inside diameter of the casing. A wide range of phenomena can be seen, including crosstalk through the array and wave propagation through not only the water but also the casing itself. Each simulation takes under 30 seconds, making it a very effective way of evaluating array performance before performing a full 3D analysis.

OnScaleFigure 5. Acoustic velocity from a borehole imaging array simulated with OnScale.

With the baseline simulations executed, we can explore a more interesting case. In this example, the cementing on the outside of the casing is incomplete, and a section of the cement is replaced with drill mud shown in Figure 6.

OnScaleFigure 6. Structure with added defects (mud) added allows the imaging performance of devices to be assessed.

OnScale can be used to simulate a synthetic aperture imaging approach where all transmit elements are fired sequentially and each time, the receive voltage on all array elements is recorded. This can be used to construct a full imaging of the casing and surrounding structure. Rather than digress into imaging algorithms a much simpler approach has been taken, by plotting the pulse echo response on each of the top 64 elements, we can look at whether the presence of the drill mud is detectable.

All 64 pulse echo signals are presented in a B-scan image. It can see that the front wall reflection from the casing is very uniform regardless of concreate condition, which would be expected. However, the ringdown of this casing signal is affected by the presence of the concreate, and where it is missing, an indication of this can be seen in the image. Extracting the raw signal data, it can be shown that the ringdown is extended from 7us in the baseline case to 34us in defect case. This indicates that it is indeed feasible to detect defects on the far side of the casing with this system.

OnScaleFigure 7. Initial reflection from casing is the same regardless of concrete condition (left) Signals in the defect area (25 - 39) show much longer ringdown (middle) finally the ringdown is extended from 7 to 34us in the defect area (right).

2D simulations give some insights into the performance of borehole imaging systems, but for many effects a full 3D simulation is required. Beams are often designed to propagate at an angle relative to the axis of the pipe, and 3D misalignments can cause significant degradation in imaging performance. These effects are all considered by extending the initial 2D simulations to 3D. When comparing these directly to the 2D results the receive voltage on the 3D model is smaller, because of beam spreading along the axis of the pipe. This is a more realistic assessment of the performance of the system.

OnScaleFigure 8. Results show a smaller signal in 3D (red) due to beam spreading along the pipe.


OnScale’s cloud-based simulation platform represents a huge opportunity for engineers. The ability to run simulations in parallel allows engineers to move away from traditional iterative design processes and has been described as revolutionary by our customers. Additionally, the ability to simulate full 3D devices allows engineers to further de-risk their designs and solution prior to prototyping and experimental testing.

For more check out the full webinar here that features more on:

  • Full transducer structure study

  • Piezoelectric sensor study

  • Flow measurement study

  • 3D flow meter study accelerated using MPI

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