Acoustic measurements based on guided sonic and ultrasonic wave propagation in multilayered structures are used for several different applications in the Oil and Gas (O&G) industry. One of these applications is borehole sonic logging where the propagation characteristics of these waves are recorded and analyzed as function of well bore depth. Petrophysicists can then develop methods to use these real-time measurements to estimate porosity, permeability, formation mechanical properties, fracture & lithology identification, stresses in thin layers, and borehole integrity.
These inversion methods for analyzing sonic measurements are based on high fidelity, physics-based models and signal process algorithms to provide engineers reliable information so that they can make informed decision on the availability and safe production of hydrocarbons in an optimal time frame. The physics-based models that are required to generate the necessary synthetic data sets in real-time are computationally intensive, both in time and memory (RAM) This limits their integration into an integrated workflow that will help an engineer make informed decisions in real-time based on these sonic measurements.
OnScale have developed fast time domain multiphysics FEA solvers and seamlessly integrated them with cloud high performance compute (HPC) capabilities that addresses these constraints. Further, OnScale can execute massively parallel simulations with an almost linear scalability, allowing users to consider problems far in excess of anything previously attainable from legacy FEA packages
Sonic Logging Principle
Borehole Sonic Logging is based on the principle of measuring the travel time of Compressional (P), Shear (S) and Stoneley waves propagating along a borehole with different radial depths into the formation. The borehole could be filled with fluid/mud (open hole) or could have multiple casings (cased hole). The sonic waves are excited using a sonic logging tool which consists of a piezoelectric transmitter (source) and array of hydrophones (receivers) placed along the borehole axis (Figure 1).
The source is configured in the form of either a monopole or a dipole pressure pulse. Typically, the operating frequency range for these measurements is from 0.5 to 20 kHz. This helps to probe several meters into the formation. The receivers measure the time it takes for the acoustic pulse to travel in the formation in various forms while undergoing dispersion and attenuation. When the sound energy arrives at the receiver, having passed through the formation, it does so at different times in the form of different types of wave. This is because different types of wave travel with different velocities in the formation or take different pathways to the receiver.
Figure 2 shows a typical waveform recorded at one of the receivers for monopole excitation in a fluid-filled borehole. The first wave arrival is the compressional or longitudinal wave (P-wave). It is usually the fastest wave and has a small amplitude. The next wave arrival is usually the transverse or shear wave (S). This is slower than the P-wave, but usually has a higher amplitude. The next succeeding wave arrivals are the guided surface waves which are the Rayleigh waves, Stoneley waves, and mud waves. The velocity of wave propagating in the formation and its dispersive characteristics can be determined based on the distance between the transmitter (Tx) and the receiver (Rx). Interpretation of these measured borehole guided wave velocity and dispersions are based on monitoring changes relative to a modeled dispersion signatures associated with a reference borehole geometry. Different inversion schemes are then applied to estimate the formation properties, porosity and permeability. Hence accurate and fast modeling tools are required to generate a large database (library) of physics-based dispersion signature for all possible scenarios encountered in the downhole environment including the sonic measurement system.
Figure 1. Configuration of a fluid-filled (OH) borehole with a sonic measurement tool at the center of borehole and surrounded by formation (OnScale).
Figure 2. Typical waveform recorded for monopole excitation (OnScale).
Several methods based on analytical approach, mode search and finite-difference-time-domains (FDTD) have been employed to generate synthetic dispersion signatures. However, these methods based on several assumptions do not account for all the complexity in the borehole geometry and the surrounding formation. Hence these synthetic borehole signatures may not provide the correct reference for estimating the required parameters based on the measured data. In order to account for these complexities finite-element (FE)-method based several codes have also been employed. However, the simulation time and memory taken by these FE codes to generate synthetic data sets is several orders of magnitude higher than analytical and FDTD methods. Hence in order to augment the development of data driven sonic digital platforms it becomes necessary to generate synthetic physics data sets in real time for sonic logging.
OnScale removes these inherent barriers in legacy FEA products by combining a suite of world class proprietary powerful Multiphysics time domain solvers with cloud HPC. The cloud gives users access to HPC level compute power on an on-demand basis. This removes the high cost of entry and allows users to pay only for simulation they need. This enables engineers to solve a wide range of tough advanced engineering problems that would previously have been impossible. Furthermore, the OnScale solver architecture is specifically designed to take advantage of the massive parallelism that the cloud can offer. This combination of scalable cloud with Multiphysics FEA offers users a step change in simulation capability. Given this solver architecture, an OnScale user can generate these sonic-logging data sets orders of magnitude faster than before fast, facilitating the integration of high-fidelity, physics-based models in the development of real-time sonic measurement workflows.
OnScale enables real time borehole sonic logging simulations:
In this section we provide a case study for a 2D-axisymmetric fluid-filled borehole configuration. Using OnScale fast time domain FEA solvers we simulate the propagation of sonic waves in a fluid-filled borehole surrounded by slow formation. The waves are excited using a monopole pressure pulse having a center frequency of 5 kHz. Figure 3 shows the simulated pressure waveforms recorded at 25 receivers placed along the axial depth of the borehole. The dispersion and slowness profiles of these different waves are then obtained using the SFK-Transform toolbox in MATLAB. To obtain accurate high fidelity results it is necessary to have the total simulation time to be 0.01 secs with a time increment ( t) of 1.65 µs and total degrees of freedom (DoFs) is 252810. The total simulation run time using OnScale cloud computing capabilities (16 cores) is less than 2 secs with a total memory requirement of 56 MB. This is several orders of magnitude faster than any available FE codes and FDTD codes. OnScale’s fully coupled Multiphysics solvers allows users to incorporate all the possible formation intricacies and anisotropy to generate the sonic waveform signatures in real-time.
Figure 3. Typical waveform recorded for monopole excitation in a fluid-filled borehole surrounded by slow formation (OnScale).
Along with this one of the important features of OnScale is the ability to solve 1000’s of case studies in parallel in the same amount of time. Hence, in less than 8 secs. user can generate an entire library of all the possible configurations encountered in downhole environment during sonic logging. OnScale solvers are flexible, which means it can be easily integrated into the sonic inversion workflow and platforms for embedded simulations. An example video of integration using python:
Full 3D OnScale Sonic Logging – Generate high-fidelity physics based sonic-logging libraries
2D-axisymmetric simulations provide an excellent reference for an ideal open borehole configuration. However, the real downhole environment has several multitudes of complexity such as irregular borehole geometry, presence of fractures, thin bedding layers, TI formations, eccentricity of sonic tool and casing etc. Borehole guided sonic waves exhibit varying degrees of sensitivities to these deviations from an ideal case which leads to different slowness and dispersion profile. Hence it becomes important to obtain the waveform signatures from a full 3D model which incorporates all these complexities. The total simulation time for these full 3D models range from few days to weeks using available FDTD and legacy FEA codes. The memory requirements using these codes are in the order of 100’s of GB.
Figure 4. OnScale MPI OnScale MPI Acceleration – 3D OH Sonic Logging
Message Passing Interface provides a way of splitting large models into smaller parts and sharing them between compute nodes on the cloud. Other packages rely on more traditional multithreading approaches, and don’t make efficient use of large numbers of cores. This makes them poorly suited to take advantage of cloud HPC architecture. OnScale’s solvers were written with MPI in mind, and therefore can achieve excellent scaling, ensuring hardware is used efficiently. The key advantage of OnScale MPI is that it allows close to linear scaling of simulation time with compute hardware as shown in Figure 4 for full 3D open hole sonic logging configuration.
Hence, OnScale solver’s unique architecture with Message Passing Interface (MPI) along with cloud computing enables extremely fast full 3D FEA simulations for sonic logging applications. Figure 5 shows the simulated waveforms generated from a full 3D model of fluid-filled borehole surrounded by slow formation.
Figure 5. Full 3D simulations – Typical waveform recorded for dipole excitation in a fluid-filled borehole surrounded by slow formation (OnScale).
The waveforms recorded at 25 receivers placed along the axial depth of the borehole are obtained for a dipole pressure pulse having a center frequency of 5 kHz. To obtain accurate results it is necessary to have the total simulation time to be 0.001 secs with a time increment (∆t) of 1.37 µs and total degrees of freedom (DoFs) of 23 million. The total simulation run time using OnScale MPI (500 parts) and cloud computing capabilities is 6 minutes with a total memory requirement of 4 GB. For the case of monopole pulse the total simulation time is 2 minutes with the same memory requirement of 4 GB. Hence using OnScale fast cloud enabled fully parallel MPI solvers one can generate high fidelity physics-based borehole sonic libraries in less than an hour.
Overall, OnScale fast multiphysics simulations enables to investigate all possible configurations in parallel to generate a large physics-based library in the required amount of time. In a more general sense this all moves into digital twins and augmenting machine learning with physics-based simulations for borehole sonic logging digital platforms.
We would also recommend checking out our 2D Borehole Sonic Logging Simulations step-by-step tutorial!