A Novel Analytical Fracture-Permeability Model Dependent on Both Fracture Width and Proppant-Pack Properties

Summary For an empty fracture, the fracture permeability (kf) is mainly influenced by the effect of viscous shear from fracture walls and can be analytically estimated if the fracture width (wf) is known a priori (i.e., kf=β2wf2/12, where β2 is the unit-conversion factor). For an adequately propped fracture, the fracture permeability is mainly influenced by the proppant-pack properties and can be approximated with the proppant-pack permeability (kf=kp, where kp is proppant-pack permeability). It can be readily inferred that as the effect of viscous shear fades (or the proppant-pack effect becomes pronounced), there should be a regime within which both the viscous shear and the proppant-pack properties exert significant influences on the fracture permeability. However, the functional relationship between fracture permeability, viscous shear (or fracture width), and proppant-pack properties is still elusive. In this work, we propose a new fracture-permeability model to account for the influences of the proppant-pack permeability, proppant-pack porosity (ϕp), and fracture width on the fracture permeability. This new fracture-permeability model is derived from a modified Brinkman equation. The results calculated with the fracture-permeability model show that with different values of the Darcy parameter, the fluid flow can be divided into viscous-shear-dominated (VSD) regime, transition regime, and Darcy-flow-dominated (DFD) regime. If the Darcy parameter is sufficiently large, the effect of proppant-pack permeability on fracture permeability can be neglected and the fracture permeability can be calculated with the VSD fracture-permeability (FP) (VSD-FP) equation (i.e., kf=β2ϕpwf2/12). If the Darcy parameter is sufficiently small, the effect of viscous shear on fracture permeability can be neglected and the fracture permeability can be calculated with the DFD-FP equation (i.e., kf=kp). Both the VSD-FP and DFD-FP equations are special forms of the proposed fracture-permeability model. For the existing empirical/analytical fracture-conductivity models that neglect the effect of viscous shear, one can multiply these models by the coefficient of viscous shear to make these models capable of estimating the fracture conductivity with large values of Darcy parameter.

Quality Control of Display Devices for Medical Radiodiagnosis Employing the Standard TG18, GSDF and JND

Introduction: This work presents a study on the procedures for evaluating the quality of imaging display devices in radiology, considering the characteristic luminance curve obtained experimentally versus the Just Noticeable Difference (JND) and the lifetime of digital display devices. Materials & Methods: The evaluations were done using image patterns published by the American Association of Physicists in Medicine on Digital Imaging and Communication in Medicine (DICOM) and the Grayscale Standard Display Function (GSDF), viewed in DICOM software, with various shades of gray. A digital luximeter was used as the luminance meter. A correlation with the time of use of the devices was performed to classify the digital devices as primary (suitable for medical diagnosis) or secondary (suitable only for visualization of medical images). Results & Discussion: Among the monitors evaluated, those with a resolution between 2 and 5 megapixels were classified as primary for up to 50, 000 hours of use, and some above that time limit present behavior equivalent to secondary monitors. Monitoring the temporal evolution of the use of devices is important to avoid errors in medical diagnosis. Conclusion: The use of a calibrated digital luximeter with an illuminance unit conversion factor in luminance defined by this equipment was shown to be an alternative to replace a photometer when this latter is not available.