OVERVIEW
I just make a summary of my master’s research here for your quick review about what I did. My academic background is more in well logging and applied geophysics. I am skilled in acoustic logging modelling in analytical and numerical solutions. As for my hobbies, I like playing Pingpong, Badimiton and Basketball. I am the person who likes studying and traveling in the field. I have been to Russia and Italy as an exchange student.
In my master’s research. I used a poro-elastic FDTD method to characterize Stoneley wave reflection and transmission across permeable and fractured formations and developed a new FDTD method which can simulate elastic wave propagation in the medium that contain elastic, porous and cracked porous subregions. Please click Master’s research slides or slides button on the top for details. If you want some text description, please refer to different parts of the content in the following. For the education and academic purposes, some codes related to this project will be shared in the future. If you have any questions, please email me or make comments in the contact section.
Content
1. Stoneley wave reflection and transmission across permeable and fractured formations
2. Finite-difference modeling of multipole acoustic logging in the cracked porous formations
3. 3D FDTD modeling dipole acoustic logging and LWD remote detection
- The first two works are finished in my master study. The third one is a group project I participated in, and I will introduce what I did in the project.
1.Stoneley wave reflection and transmission across permeable and fractured formations
In the acoustic logging field, Stoneley wave is a powerful tool to identify and evaluate permeable layers and fractures, calculate permeability, and analyze borehole diameter variation. Particle displacement induced by Stoneley waves is perpendicular to the borehole wall, pushing the fluid flow in and out. This makes Stoneley waves sensitive to fluid exchange between borehole and formations. Stoneley wave is also a kind of symmetric guided wave which propagates along the borehole wall. It’s able to reflect from and transmit across permeable formations, fractures, diameter change (See Slide 8).
As for Stoneley wave reflection and transmission, people used to propose a method called one dimensional effective wavenumber method combining simplified BR theory to study Stoneley wave reflection and transmission coefficients of the model on the left （See Slide 9）. This method has fast calculation speed and is widely used in the well logging software, but it considers only 1-dimensional path wave propagation and doesn’t consider the interaction between pore fluid and formation frame. Also, it cannot model the complex permeable structures, such as fractured zone distributing finitely in radial and axial direction.
In this case, we use finite-difference numerical method to model wave propagation in porous media which are governed by Biot dynamic poroelastic equations. Taylor expansion is used to approximate the dynamic permeability through which the complexity is reduced. After calculation with reasonable parameters, this approximation is effective in the acoustic-loggging-frequency range with permeability below 100 Darcy. Therefore, a robust numerical method, which can investigate the model on the right, can be developed. (See Slide 10) As for finite-difference scheme, PML implementation and interface processing, I do not expand them here (Refer to
(2022). Stoneley wave reflection and transmission across permeable formations and fractured zones：Comparison of analytical and numerical modeling results. In Chinese J. Geophys. (in Chinese).).Then we test and validate our algorithm because dynamic permeability is approximated by using Taylor expansion. (See Slide 11) This is a borehole model surrounded by homogenous porous formation. Source and receivers are in the borehole. We can simulate it using the finite-difference method of this research and the real axial integral (RAI) analytical method, and the results of two methods match very well in terms of permeability of 1Darcy and 50 Darcy. Through parameters setting, we equivalent the highly permeable porous media to a fractured zone which composes of multiple fractures.
As you can see in the Slide 12, many factors (such as fractures, permeable formations et al) can induce Stoneley wave reflection and transmission. In the real subsurface fractures can finitely propagate in the radial direction, and permeability can distribute inhomogeneously in the formation. We can use the FD method to investigate those two situations. By the way, the mind that highly permeable layer can represent the fractured zone has already been validated (Kostek et al., 1998).
In the slide 12-15, I just show some calculation cases and do not go much detail in analysis. We firstly use the 1-dimensional effective wavenumber method and the finite-difference method to investigate single and multiple porous layers. Stoenley wave refection and transmission coefficients (Dash lines are calculated by 1D effective wavenumber method; Solid lines are from the FD method) are calculated using two methods. We can see these two results agree very well in both reflection and transmission coefficients in the frequency of 0-2kHz. Due to the physics of Stoenely wave, we can see different trend variation of Stoeneley wave reflection and transmission coefficients in the porous formation. Then, Due to the flexibility of finite difference method, we can study the fractured model (See slide 16-18). This is the model that low-porosity and permeability formation contains a fractured zone with finite radial and axial extension. We can change its thickness, radial extension and permeability distribution. In this case, I use cosine function to control the permeability distribution. When dominant permeability area moves from the bottom to the top, the high frequency components of Stoneley wave reflection coefficients become less. The Stoenely wave transmission coefficient is only related to the total permeability of the fractured zone. All the results have been compiled into a journal paper (
(2022). Stoneley wave reflection and transmission across permeable formations and fractured zones：Comparison of analytical and numerical modeling results. In Chinese J. Geophys. (in Chinese).)
2.Finite-difference modeling of multipole acoustic logging in cracked porous formations
People use waves of different frequencies to investigate different scales problems. In addition to geometrical effect on scattering wave, fluid flow effect on wave propagation cannot be ignored, especially in the acoustic and ultrasonic frequency range. According to previous studies, three kinds of scales of fluid flow can cause wave dispersion and attenuation: Macroscopic flow of the Biot mechanism, mesoscopic flow of the double porosity mechanism and microscopic flow of the squirt-flow mechanism. (See slide 22) In the last Stoneley wave research work, the fluid flow in fractured and porous formation is based on Biot mechanism. In this work, we focus on this squirt-flow mechanism. My advisor Prof.Tang proposed a cracked porous medium elastic wave theory which includes the effect of squirt flow and is the evolution of the Biot theory.
This theory has good application in formation evaluation, such as inversion of crack density and fluid properties identification. As for forward modelling of acoustic logging in the cracked porous formation, the analytical method is quite mature. There are many published papers. However, it is universe that the heterogeneous subsurface has stratified cracked porous formations, which cannot be modeled by analytical method. Therefore, it is necessary to develop a flexible numerical method to model elastic wave propagation in the heterogeneous cracked porous formation.
Let’s look at the governing elastic wave equations (See slide 23). The main difference between Biot poroelasitc equations and these equations is that there has an additional term which is the squirt-flow factor. I looked for many references, there are few papers solving this type of equations using a numerical method. I got inspiration from computational rock physics and viscoelastic modeling, this problems are finally solved.
As a new numerical method, I use analytical method to validate its results(See slide 26). The model on the left is a borehole surrounded by a homogeneous cracked porous formation. We model the cases of saturated hard formation and soft formation. The source center frequencies are 8 kHz and 20 kHz for monopole, 3kHz for dipole, respectively. (See slide 27-30)
These are waveforms excited by monopole and dipole and received at 3m away from the source in the borehole. We can see that the results of two methods agree quite well in the cases of different crack densities. Then, test the effect of squirt-flow effect. Also, these are the results of the soft formation case. Results of two methods match very well. We also test the effect of squirt-flow factor. When the formation contains the squirt-flow mechanism, the leaky p-wave attenuates a lot.
Finally, this method can simulate the borehole wavefield of stratified formations (See slide 31-34). This is the model that a porous formation containing a cracked porous interlayer surrounding the borehole. This is the amplitude diagram of synthetic sound pressure waveforms. We can see very clearly the different wave components change in amplitude and reflected waves. Also, we have the amplitude diagram of the model without interlayer. I change the crack aspect ratio of the interlayer and extract the waveform at the 5 meter. The calculated attenuation is close to the analytical result. (see the draft
(2022). Finite-difference modeling of multipole acoustic logging in cracked porous formations. Unpublished Draft.)
Outcome of above two section:
- 2.5D FDTD and analytical codes including Biot and squirt-flow mechanism
- A journal paper published in Chinese Journal of Geophysics (In Chinese)
- A draft of this work written in English
3.3D FDTD modeling dipole acoustic logging and LWD remote detection
- The third part is a project I participated in (See slide 37). Dipole acoustic logging remote detection is a new technology developed in recent years. It uses the scattering wave received in the borehole to image the geological faults and near wells. In this project, I used 3D FD codes to simulate the wave-field in the whole process of wave radiation, scattering and reception of borehole waves, and compared simulated waveforms with analytical results.
Outcome of this section:
- Comparisons between 3D FDTD results and analytical results
Feiyue Xia(夏飞月)
Ph.D. Student of Petroleum Engineering
Ph.D. Student at UT Austin. My research interests are borehole geophysics, rock physics and petrophysics.
