A Short Note on Modeling Wave Propagation in Media with Multiple Sets of Fractures

Wave propagation and scattering in fractured formations have been modeled with finite-difference programs and the use of equivalent anisotropic media description of discrete fractures. This type of fracture description allows a decomposition of the compliance matrix into two parts: one accounts for the background medium and another accounts for the fractures. The compliance for the fractures themselves can be a sum of compliances of various fracture sets with arbitrary orientations. Non-orthorgonality of the fractures, however, complicates the compliance matrix. At the moment, we can model an orthorhombic medium (9 independent elastic constants) with the two orthogonal fracture sets. However, if the fractures are non-orthogonal, this results in more general anisotropy (monoclinic) for which we need to specify 11 independent parameters.. Theoretical formulation shows that the finite difference program can be extended to simulate wave propagation in monoclinic media with little additional computational and storage cost.United States. Dept. of Energy (Award No. DE-FC26-02NT15346)Massachusetts Institute of Technology. Earth Resources Laborator

Inversion of Shear Wave Anisotropic Parameters in Strongly Anisotropic Formations

Deepwater reservoirs use highly deviated wells to reduce cost and enhance hydrocarbon recovery. Due to the strong anisotropic nature of many of the marine sediments, anisotropic seismic imaging and interpretation can improve reservoir characterization. Sonic logs acquired in these wells are strongly dependent on well deviations. Cross-dipole sonic logging provides apparent shear wave anisotropy in deviated wells, which can be far from the truth. Although anisotropic parameters have been successfully obtained using data from wells of several deviations or using single well data based on weak anisotropy approximation, estimation of strong shear wave anisotropy from single well data remains a challenge. Using sensitivity analysis, we find Stoneley wave velocity has good sensitivity to qSV and SH wave velocities in deviated wells. We create a linear inversion scheme to estimate shear wave anisotropy using SH, SV, and Stoneley wave velocities logged in one well. We first apply the method to laboratory measurements from boreholes of various deviations relative to the symmetry axis of an anisotropic material. We then apply the method to a field data set acquired in a deviated well. We also compute the vertical and horizontal shear wave velocity logs in this well using the inverted elastic shear wave constants.Massachusetts Institute of Technology. Earth Resources Laborator

MRF-PINN: A Multi-Receptive-Field convolutional physics-informed neural network for solving partial differential equations

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in scenarios of reconstructing the physics field and solving the inverse problem. Considering the advantages of parameter sharing, spatial feature extraction and low inference cost, convolutional neural networks (CNN) are increasingly used in PINN. However, some challenges still remain as follows. To adapt convolutional PINN to solve different PDEs, considerable effort is usually needed for tuning critical hyperparameters. Furthermore, the effects of the finite difference accuracy, and the mesh resolution on the predictivity of convolutional PINN are not settled. To fill the gaps above, we propose three initiatives in this paper: (1) A Multi-Receptive-Field PINN (MRF-PINN) model is established to solve different types of PDEs on various mesh resolutions without manual tuning; (2) The dimensional balance method is used to estimate the loss weights when solving Navier-Stokes equations; (3) The Taylor polynomial is used to pad the virtual nodes near the boundaries for implementing high-order finite difference. The proposed MRF-PINN is tested for solving three typical linear PDEs (elliptic, parabolic, hyperbolic) and a series of nonlinear PDEs (Navier-Stokes PDEs) to demonstrate its generality and superiority. This paper shows that MRF-PINN can adapt to completely different equation types and mesh resolutions without any hyperparameter tuning. The dimensional balance method saves computational time and improves the convergence for solving Navier-Stokes PDEs. Further, the solving error is significantly decreased under high-order finite difference, large channel number, and high mesh resolution, which is expected to be a general convolutional PINN scheme

Sonic Logging in Deviated Boreholes in an Anisotropic Formation: Laboratory Study

Deepwater field development requires drilling of deviated or horizontal wells. Most formations encountered can be highly anisotropic and P- and S-wave velocities vary with propagation directions. Sonic logs acquired in these wells need to be corrected before they can be applied in formation evaluation and seismic applications. In this study, we make use of a laboratory model made of an approximate transversely isotropic Phenolite to study acoustic logging in deviated wells. We drill holes at various deviations relative to the symmetry axis in the Phenolite block. Then we perform monopole and dipole sonic measurements in these holes and extract the qP, qSV, SH, and Stoneley wave velocities using the slowness-time domain semblance method. The velocities measured using monopole and dipole loggings vary with borehole deviations. We also measure the qP, qSV, and SH wave velocities using body waves at the same angles as the well deviations. We then compute the theoretical qP, qSV, SH, and Stoneley wave velocities based on an equivalent transverse isotropic model of the Phenolite. We find the qP, qSV , and SH wave velocities obtained using the body wave measurement and acoustic logging method agree with the theoretical predictions. The Stoneley wave velocities predicted by the theory also agree reasonably well with the logging measurements.Massachusetts Institute of Technology. Earth Resources LaboratoryMassachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

Experimental and Theoretical Studies of Seismoelectric Effects in Boreholes

In a fluid-saturated porous formation, an impinging seismic wave induces fluid motion. The motion of fluid relative to the rock frame generates an electric streaming current. This current produces electric and magnetic fields, which are called seismoelectric and seismomagnetic fields, respectively. When there is a fracture or a discontinuity, a radiating electromagnetic wave is also generated, in addition to local fields. Seismoelectric and seismomagnetic fields depend on the amplitude, frequency, and mode of the seismic wave, as well as the formation porosity, permeability, pore size, and fluid conductivity. In this paper, we describe laboratory results of seismoelectric and seismomagnetic fields induced by an acoustic source in borehole models. We use a piezoelectric source for acoustic waves and a point electrode and a high-sensitivity Hall-effect transducer for measuring the localized seismoelectric and seismomagnetic fields in fluid-saturated rocks. The dependence of seismoelectric conversions on porosity, permeability and fluid conductivity are investigated. Three components of the seismomagnetic field are measured by the Hall-effect transducer. At a horizontal fracture, the acoustic wave induces a radiating electromagnetic wave.Massachusetts Institute of Technology. Earth Resources LaboratoryMassachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

Finite Difference Modeling of Seismic Responses to Intersecting Fracture Sets

Fractured reservoir characterization is becoming increasingly important for the petroleum industry. Currentmethods for this task are developed based on effectivemedia theory, which assumes the cracks or fractures in a reservoir are much smaller than the seismic wavelength. A discrete fracturemodel has to be used for large-scale fractures. We describe an approach of using a finite difference method for modeling seismic wave propagation in rock formations with intersecting fracture sets. We then use the code to study the behavior of seismic waves, particularly scattering due to such fracture sets with various spacing and compliances. The scattering pattern due to fractures varies azimuthally. We find that converted PS and PSP waves from the bottom of the fractured layers show strong interference by the scattered waves. We observe coherent scattered waves in shot gathers parallel to the fracture orientation and significant backscattering at near offsets and forward scattering at far offsets in the gathers normal to the fracture orientation. When two sets of fractures are present, scattering becomes stronger and more complex scattered waves appear in the gathers. The scattering becomes stronger with increasing the fracture compliances and decreasing spacing (still on the order of seismic wave length). When the fracture sets are not orthogonal to each other, the gathers still show coherent scattering in the fracture orientations. Azimuthal characteristics of the scattered waves may be used to analyze fracture orientations, spacing, and relative compliance of intersecting fracture sets.Shell GameChangerMassachusetts Institute of Technology. Earth Resources Laborator

Domain selection combined with improved cloning strategy for high throughput expression of higher eukaryotic proteins

<p>Abstract</p> <p>Background</p> <p>Expression of higher eukaryotic genes as soluble, stable recombinant proteins is still a bottleneck step in biochemical and structural studies of novel proteins today. Correct identification of stable domains/fragments within the open reading frame (ORF), combined with proper cloning strategies, can greatly enhance the success rate when higher eukaryotic proteins are expressed as these domains/fragments. Furthermore, a HTP cloning pipeline incorporated with bioinformatics domain/fragment selection methods will be beneficial to studies of structure and function genomics/proteomics.</p> <p>Results</p> <p>With bioinformatics tools, we developed a domain/domain boundary prediction (DDBP) method, which was trained by available experimental data. Combined with an improved cloning strategy, DDBP had been applied to 57 proteins from <it>C. elegans</it>. Expression and purification results showed there was a 10-fold increase in terms of obtaining purified proteins. Based on the DDBP method, the improved GATEWAY cloning strategy and a robotic platform, we constructed a high throughput (HTP) cloning pipeline, including PCR primer design, PCR, BP reaction, transformation, plating, colony picking and entry clones extraction, which have been successfully applied to 90 <it>C. elegans </it>genes, 88 Brucella genes, and 188 human genes. More than 97% of the targeted genes were obtained as entry clones. This pipeline has a modular design and can adopt different operations for a variety of cloning/expression strategies.</p> <p>Conclusion</p> <p>The DDBP method and improved cloning strategy were satisfactory. The cloning pipeline, combined with our recombinant protein HTP expression pipeline and the crystal screening robots, constitutes a complete platform for structure genomics/proteomics. This platform will increase the success rate of purification and crystallization dramatically and promote the further advancement of structure genomics/proteomics.</p

An Experimental Study Of Seismoelectric Signals In Logging While Drilling

Acoustic logging while drilling (LWD) may be complicated because of contamination by waves propagating along the drill collar (the tool waves). In this paper we propose a new method for separating tool waves from the true formation acoustic arrivals in borehole acoustic LWD. The method utilizes the seismoelectric signal induced by the acoustic wave at the fluid-formation boundary. The basis for seismoelectric conversion is the electric double layer (EDL) that exists in most rock-water systems. EDL does not exist at the tool (conductor) water interface. Therefore, there should be no seismoelectric signals due to tool modes. In this paper, borehole monopole and dipole LWD acoustic and seismoelectric phenomena are investigated with laboratory measurements. The main thrust of the paper is the utilization of the difference between acoustic and seismoelectric signals, to eliminate the tool waves and enhance the formation acoustic signals in acoustic LWD.Massachusetts Institute of Technology. Earth Resources LaboratoryMassachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu

Orientation Estimation for Multiple Large Fractures by Scattering Energy

We have done the numerical modeling of seismic response to multiple sets of vertical large fractures by using finite-difference method (FD), which can easily handle media with monoclinic anisotropy. We consider three types of fracture distributions: a set of parallel fractures, two sets of orthogonal fractures and two sets of non-orthogonal fractures intersecting at 45 degrees. We address the seismic scattering response to large fractures by using a 3-layer model and a 5-layer model, where a fractured reservoir is in the middle layer of these two models. Seismic scattered energy is analyzed by the Scattering Index (SI) method to estimate the orientation of these multiple fractures. In both models, SI indicates the correct orientation of the two orthogonal fracture sets but is ambiguous for non-orthogonal fracture sets. Information about the fracture spacing and compliance can also be extracted from the azimuthal SI in some situations. More compliant fracture sets result in higher SI values while the relationship between fracture spacing and SI depends on the source wavelength. Variations in the SI energy can be caused by fracture spacing and compliance variations, and these relationships need further investigation.United States. Dept. of Energy (Award No. DE-FC26-02NT15346)Massachusetts Institute of Technology. Earth Resources Laborator

A comparison of LWD and wireline dipole sonic data

Data measured by both wireline and LWD tools in the same borehole are compared. Discrepancies in shear velocities as calculated from the data are on average around 5% and discrepancies between compressional velocities are less than 3%. The consistency of the bias between logs suggest it is related to the calculation of velocity. Comparison of industry and ERL velocity processing show excellent agreement and give an example of possible spread of velocity data due to processing chain. A short section of data in an unconsolidated zone shows velocity differences of just over 10% with an opposite trend to the over all bias. Dispersion analysis of the waveforms show this is consistent with a damaged zone surrounding the borehole wall caused by drilling.Massachusetts Institute of Technology. Earth Resources LaboratoryMassachusetts Institute of Technology. Borehole Acoustics and Logging Consortiu