Modeling of Before Closure Zero Slope Pressure Derivative in a Diagnostic Fracture Injection Test DFIT

Recent diagnostic fracture injection test (DFIT) data presented on a Bourdet log-log diagnostic plot showed derivative slope of 0 in the before closure (BC) portion of the DFIT response. Some works qualitatively describe it as radial flow. This behavior has not been quantitatively analyzed, modeled and matched. The present work disagrees with the hypothesis of radial flow and successfully matches the relatively flat trend in the Bourdet derivative with a model dominated by friction dissipation coupled with tip extension. The flat trend in Bourdet derivative occurs shortly after shut-in during the before closure period. Because a flat derivative trend suggests diffusive radial flow, our first approach was to consider the possibility that an open crack at a layer interface stopped the fracture propagation and caused the apparent radial flow behavior observed in falloff data. However, a model that coupled pressure falloff from diffusive flow into a layer interface crack with pressure falloff from closure of a fracture that propagated up to the layer interface failed to reproduce the observed response. Subsequently, we discovered that existing models could match the data without considering the layer interface crack. We found that data processing is very important to what is observed in derivative trends and can mislead the behavior diagnosis. We succeeded to match one field DFIT case showing an obvious early flat trend. The presence and dominance of geomechanics, coupled with diffusive flow, disqualify the description of the flat trend in Bourdet derivative as radial flow. Instead, flow friction coupled with tip extension can completely match the observed behavior. Based on our model, cases with a long flat trend have large magnitude near-wellbore tortuosity friction loss and relatively long tip extension distance. Further, we match the near wellbore tortuosity behavior with rate raised to a power lower than the usually assumed 0.5. The significance of these analyses relates to two key factors. First, large magnitude near wellbore tortuosity friction loss increases the pressure required for fracture propagation during pumping. Second, tip extension is a way to dissipate high pumping pressure when very low formation permeability impedes leakoff. Matching transient behavior subject to the presence of both of these factors requires lowering the near-wellbore tortuosity exponent.

Effects of the Hydro Anisotropy and the Magnetic Field on the Dynamic Thermo-Bi-Diffusive Flow in a Horizontal Cavity Confining a Porous Medium Saturated by a Binary Fluid

We analyze analytically the effects of anisotropy in permeability and that of a transverse magnetic field on thermal convection in a porous medium saturated with a binary fluid and confined in a horizontal cavity. The porous medium, of great extension, is subjected to various conditions at the thermal and solutal boundaries. The axes of the permeability tensor are oriented obliquely with respect to the gravitational field. Based on a scale analysis, the velocity, temperature, and heat and mass transfer rate fields were determined. These results were validated by the study of borderline cases which are: pure porous media and pure fluid media discussed in the literature. It emerges from this study that the anisotropy parameters influence the convective flow. The application of a transverse magnetic field significantly reduces the speed of the flow and thereby affects the temperature field and the rate of heat and mass transfer.

On The Dynamics of Interstate Diffusion of Firearm Violence and Impact of Firearm Regulations

Objectives : Our purpose was to test the impact of firearm regulations on the firearm violence flow across US state borders. Further we assessed the spatial variations in these impacts across different regions with the goal of identifying state groups that are especially vulnerable to cross-border firearm violence. Methods : Incidence of firearm violence (2000 to 2017) has been modelled as an inhomogeneous diffusion process whose parameters depend on state firearm regulations. Firearm regulations measurement for a state accounted for all 14 law categories across 54 states since 1991 as per State Firearm Law Database. The effects of regulations and other covariates were estimated across all states. Results : Six clusters of states were identified based on the variations of effects within and across those clusters. For 3 of these clusters the diffusive flow parameters were statistically significant. In all of these clusters the deterring effect of regulations on incidence and flow of crime was statistically significant. Conclusion : The clusters can be assigned to 5 descriptive categories based on their roles in the flow of firearm violence : Source states, Transitive states, Destination states, Isolated issue states and Stable . It was found that flow of firearm violence indeed does follow a diffusive process for most categories of states. It has also been recommended that while in-state regulations are important to curb firearm violence flowing into Destination states, they are not adequate unless regulatory stringency is also applied to neighbouring Source and Transitive States.

On The Dynamics of Interstate Diffusion of Firearm Violence and Impact of Firearm Regulations

Objectives – Our purpose was to test the impact of firearm regulations on the firearm violence flow across US state borders. Further we assessed the spatial variations in these impacts across different regions with the goal of identifying state-groups that are especially vulnerable to cross-border firearm violence.Methods – Incidence of firearm violence (2000-2017) has been modelled as an inhomogeneous diffusion process whose parameters depend on state firearm regulations. Firearm regulations measurement for a state accounted for all 14 law categories across 54 states since 1991 as per State Firearm Law Database. The effects of regulations and other covariates were estimated across all states. Results – Six clusters of states were identified based on the variations of effects within and across those clusters. For 3 of these clusters the diffusive flow parameters were statistically significant. In all of these clusters the deterring effect of regulations on incidence and flow of crime was statistically significant.Conclusion – The clusters can be assigned to 5 descriptive categories based on their roles in the flow of firearm violence – Source states, Transitive states, Destination states, Isolated issue states and Stable states. It was found that flow of firearm violence indeed does follow a diffusive process for most categories of states. It has also been recommended that while in-state regulations are important to curb firearm violence flowing into Destination states, they are not adequate unless regulatory stringency is also applied to neighboring Source and Transitive States.

Thermo-Diffusive Flow of Chemically Reacting Fluid in a Saturated Porous Medium for Radiative Heat Flux

A theoretical investigation has been made for a radiating and chemically reacting viscous-fluid of a conducting gas over a vertical porous surface immerse in a saturated porous medium for the impact of magnetic drag-force, buoyancy forces and thermal-diffusion (Soret) order under oscillatory suction and heat absorption. The analytical solutions have been derived for the physical variables related to the governing equations under the appropriate boundary conditions. It is found that the velocity profiles increase with the increasing values of Soret number (S0) and higher Soret number (S0 = 5) shows the large temperature difference. It is noticed that increasing radiation parameter (R) elevated the velocity profiles near the plate. In the effects of Soret number (S0) the velocity profiles are an increasing function for both the cases of M = 0 and M = 10. The validity and accuracy of the flow model is presented and found suitable to proceed the work. In this study, the findings would be useful in many practical areas such as diffusion operations, which involved molecular diffusion of species with molar concentration.