Regularized ridge regression models to estimate static elastic moduli from wireline measurements: case study from Southern Iraq

Elastic moduli such as Young’s modulus (E), Poisson’s ratio (v), and bulk modulus (K) are vital to creating geomechanical models for wellbore stability, hydraulic fracturing, sand production, etc. Due to the difficulty of obtaining core samples and performing rock testing, alternatively, wireline measurements can be used to estimate dynamic moduli. However, dynamic moduli are significantly different from elastic moduli due to many factors. In this paper, correlations for three zones (Nahr Umr shale, Zubair shale, and Zubair sandstone) located in southern Iraq were created to estimate static E, K, and ν from dynamic data. Core plugs from the aforementioned three zones alongside wireline measurements for the same sections were acquired. Single-stage triaxial (SST) tests with CT scans were executed for the core plugs. The data were separated into two parts; training (70%), and testing (30%) to ensure the models can be generalized to new data. Regularized ridge regression models were created to estimate static E, K, and ν from dynamic data (wireline measurements). The shrinkage parameter (α) was selected for each model based on an iterative process, where the goal is to ensure having the smallest error. The results showed that all models had testing R2 ranging between 0.92 and 0.997 and consistent with the training results. All models of E, K, and ν were linear besides ν for the Zubair sandstone and shale which were second-degree polynomial. Furthermore, root means squared error (RMSE) and mean absolute error (MAE) were utilized to assess the error of the models. Both RMSE and MAE were consistently low in training and testing without a large discrepancy. Thus, with the regularization of ridge regression and consistent low error during the training and testing, it can be concluded that the proposed models can be generalized to new data and no overfitting can be observed. The proposed models for Nahr Umr shale, Zubair shale, and Zubair sandstone can be utilized to estimate E, K, and ν based on readily available dynamic data which can contribute to creating robust geomechanical models for hydraulic fracturing, sand production, wellbore stability, etc.

Viscoelastic Properties in Cancer: From Cells to Spheroids

AFM-based rheology methods enable the investigation of the viscoelastic properties of cancer cells. Such properties are known to be essential for cell functions, especially for malignant cells. Here, the relevance of the force modulation method was investigated to characterize the viscoelasticity of bladder cancer cells of various invasiveness on soft substrates, revealing that the rheology parameters are a signature of malignancy. Furthermore, the collagen microenvironment affects the viscoelastic moduli of cancer cell spheroids; thus, collagen serves as a powerful proxy, leading to an increase of the dynamic moduli vs. frequency, as predicted by a double power law model. Taken together, these results shed new light on how cancer cells and tissues adapt their viscoelastic properties depending on their malignancy and the microenvironment. This method could be an attractive way to control their properties in the future, based on the similarity of spheroids with in vivo tumor models.

Improved estimation method for dynamic bulk moduli of sandstones subjected to hydrostatic stress.

<p>We designed and modified an experimental method to simultaneously measure the stress-strain (static moduli) and stress dependence of S and P-wave velocities of rocks (sandstone) under hydrostatic pressure by a Hoek’s cell. Dynamic moduli were calculated from the direct measurement of ultrasonic P- and S-wave velocities at a central dominant frequency of 1 MHz, while static moduli was recorded by strain gauges. The hydrostatic pressure was applied with a fixed rate at 1MPa/minute. We observed that the dynamic bulk moduli can be up to 44% higher than the static moduli in sandstones with porosity ranging from 8% to 24%. The results are in agreement with the existing empirical equations for soft rocks. Our experimental results demonstrate that the dynamic bulk’s modulus ranges from 4-13GPa, while the static bulk modulus ranges from 2-11GPa. We measured dynamic Young’s modulus and Poisson’s ratio at four different time periods (before applying the stress, right after the unloading, 20 days, and 60 days after the experiment) to investigate the effect of time on stress relaxation and eventually on the properties of the sandstones. All the samples showed an increase of Young’s modulus right after the stress application and then a gradual decrease of this value over time because of this relaxation; however, most of the samples could not reach the original state due to irreversible deformation at micro-level. Dynamic moduli show greater sensitivity to the irreversible deformations as compared to static moduli (even within the elastic limits). Dynamic moduli of porous material are also more sensitive to the microstructure than the static ones. Independent P and S-wave measurement for this study showed that the estimation of the S-wave velocity from the recorded P-wave velocity is not an accurate procedure and introduces a big error in the final calculation of the dynamic moduli. It also confirmed that by registering an accurate P-wave velocity the UCS (Unconfined Compressive Strength) value can be accurately estimated for sandstones. This demonstrates the great potential of dynamic studies as a non-destructive method to estimate this value for porous materials.</p>

Effect of Side Groups on the Hydrolytic Stability of Thiolated and Disulfide Cross-linked Polyaspartamides

Thiolated polyaspartamides either with N,N-dimethyl-2-aminoethyl (DME), N,N-dimethyl-3-aminopropyl (DMP) or 2-hydroxyethyl (HE) side groups were synthesized to study the effect of side groups on the hydrolytic stability of these polymers. The chemical structure of linear polymers was confirmed by 1H NMR spectroscopy, while thiol content was determined by Ellman's assay. Hydrolytic stability of thiolated polyaspartamides was studied by viscosity measurements and results suggested main-chain degradation in the presence of DME side groups. Polyaspartamides with DMP or HE side groups showed considerable stability. Thiolated polyaspartamides were converted to their disulfide cross-linked hydrogels and the gelation process was followed by oscillatory rheology. Time-dependence of dynamic moduli indicated the degradation of hydrogels containing DME side groups, while stable moduli were observed for hydrogels containing DMP or HE side groups. This structure-dependent aqueous degradation of polyaspartamides can be useful in different biomedical fields.

Dynamic Moduli of Polybutylene Terephthalate Glass Fiber Reinforced in High-Temperature Environments

The aim of this work was to show the evolution over time of the dynamic moduli in components made of Polybutylene Terephthalate reinforced with glass fiber when they are held to temperatures close to the glass transition temperature over time. For this purpose, PBT samples reinforced with short, glass fibers of Ultradur® material with 0%, 20%, and 50% in weight content were tested. Dynamic moduli showed an increment with glass fiber content showing a nonlinear behavior with the temperature. The evolution of storage modulus was depicted by means of a modified law of mixtures with an effectiveness factor depending on temperature and fiber content, whereas the evolution over time was obtained with a time–temperature transformation generated with the TTS Data Analysis software of TA-instruments for a given temperature. Storage modulus showed a linear relationship with glass fiber content when components were held to temperatures near to their respective glass transition temperature, obtained from the maximum of loss modulus curve with temperature. In summary, the value and evolution of dynamic moduli of PBT samples improved with glass fiber content, allowing us to increase the durability of components when they are submitted to high-temperature environments.