We investigate a theoretical model of the pulsatile motion of a contaminant-doped semi-infinite bubble in a rectangular channel. We examine the fluid mechanical behaviour of the pulsatile bubble, and its influence on the transport of a surface-inactive contaminant (termed surfinactant). This investigation is used to develop a preliminary understanding of surfactant responses during unsteady pulmonary airway reopening. Reopening is modelled as the pulsatile motion of a semi-infinite gas bubble in a horizontal channel of width 2$a$ filled with a Newtonian liquid of viscosity $\mu$ and constant surface tension $\gamma$. A modified Langmuir sorption model is assumed, which allows for the creation and respreading of a surface multilayer. The bubble is forced via a time-dependent volume flux $Q(t)$ with mean and oscillatory components ($Q_{M}$ and $Q_{\omega }$, respectively) at frequency $\omega $. The flow behaviour is governed by the dimensionless parameters: Ca$_{M} \,{=}\,\mu Q_{M}/(2a\gamma $), a steady-state capillary number, which represents the ratio of viscous to surface tension forces; Ca$_{\Omega } \,{=}\,\mu Q_{\omega }/(2a\gamma $), an oscillatory forcing magnitude; $\Omega \,{=}\,\omega \mu a/\gamma $, a dimensionless frequency that represents the ratio of viscous relaxation to oscillatory-forcing timescales; and $A\,{=}\,2\hbox{\it Ca}_{\Omega }/\Omega $, a dimensionless oscillation amplitude. Our simulations indicate that contaminant deposition and retention in the bubble cap region occurs at moderate frequencies if retrograde bubble motion develops during the oscillation cycle. However, if oscillations are too rapid the ensuing large forward tip velocities cause a net loss of contaminant from the bubble tip. Determination of an optimal oscillation range may be important in reducing ventilator-induced lung injury associated with infant and adult respiratory distress syndromes by increasing surfactant transport to regions of collapsed airways.

The goal of this paper is to examine the evaluation of interfacial stresses using a standard, finite difference based, immersed boundary method (IMBM). This calculation is not trivial for two fundamental reasons. First, the immersed boundary is represented by a localized boundary force which is distributed to the underlying fluid grid by a discretized delta function. Second, this discretized delta function is used to impose a spatially averaged no-slip condition at the immersed boundary. These approximations can cause errors in interpolating stresses near the immersed boundary. To identify suitable methods for evaluating stresses, we investigate three model flow problems at very low Reynolds numbers. We compare the results of the immersed boundary calculations to those achieved by the boundary element method (BEM). The stress on an immersed boundary may be calculated either by direct evaluation of the fluid stress (FS) tensor or, for the stress jump, by direct evaluation of the locally distributed boundary force (wall stress or WS). Our first model problem is Poiseuille channel flow. Using an analytical solution of the immersed boundary formulation in this simple case, we demonstrate that FS calculations should be evaluated at a distance of approximately one grid spacing inward from the immersed boundary. For a curved immersed boundary we present a procedure for selecting representative interfacial fluid stresses using the concepts from the Poiseuille flow test problem. For the final two model problems, steady state flow over a bump in a channel and unsteady peristaltic pumping, we present an ’exclusion filtering’ technique for accurately measuring stresses. Using this technique, these studies show that the immersed boundary method can provide reliable approximations to interfacial stresses.

This paper describes the planning, logistics, and technology used in Cascade and Chinook, the two largest deepwater highpressure perforation jobs successfully executed to date in the Gulf of Mexico (GoM). These Lower Tertiary well completions have gross perforation intervals over 800 feet and downhole pressures higher than 19,000 psi. This paper discusses the technology used in the planning stages to predict gunshock loads on completion equipment, and the logistics and procedures used to minimize costs, rig time and risks while maintaining safe operations.Perforating several intervals in one run was required to complement a single-trip multi-zone frac-pack system in which all downhole packers, screens and service tools are run at once, and all zones are stimulated in a single trip. Perforating all intervals with long gunstrings and then frac packing multiple zones in a single trip saves substantial rig time compared with performing conventional stacked frac packed completions requiring multiple trips per perforated zone.Thousands of perforating jobs are conducted successfully worldwide each month. However, there are a small number of jobs, typically high-pressure deepwater wells, where gun shock is a real and significant risk. When planning perforation jobs in deepwater high-pressure wells, engineers strive to minimize the risk of equipment damage due to perforating gunshock loads, such as bent tubing and unset packers, and a potential fishing job. For Cascade and Chinook, peak gunshock loads were evaluated with software that predicts the pressure waves in the completion fluid, and the associated structural loads on all well components. Fast gauge pressure data shows that predicted wellbore pressure transients are sufficiently accurate both in magnitude and time when the input reservoir response data is close to the actual field data.We discuss in detail the logistics and procedures used for loading and transportation of guns, building the BHA, and running the gun string in the well. The logistics for mobilizing over 700 lbs of explosives requires extensive planning to minimize time and costs. Minimizing the time needed for each gun connection is crucial to minimize rig time, and several approaches were employed.The logistics and procedures outlined in this paper led to a rig time reduction of over 67% for the execution of the largest deepwater high-pressure perforation jobs done to date in the Gulf of Mexico.

Numerous effects (e.g., airway wall buckling, gravity, airway curvature, capillary instabilities) give rise to nonuniformities in the depth of the liquid lining of peripheral lung airways. The effects of such thickness variations on the unsteady spreading of a surfactant monolayer along an airway are explored theoretically here. Flow-induced film deformations are shown to have only a modest influence on spreading rates, motivating the use of a simplified model in which the liquid-lining depth is prescribed and the monolayer concentration satisfies a spatially inhomogeneous nonlinear diffusion equation. Two generic situations are considered: spreading along a continuous annular liquid lining of nonuniform depth, and spreading along a rivulet that wets the airway wall with zero contact angle. In both cases, transverse averaging at large times yields a one-dimensional approximation of axial spreading that is valid for the majority of the monolayer. However, a localized monolayer remains persistently two dimensional in a region at its leading edge having axial length scales comparable to the length scale of transverse depth variation. It is also shown how the transverse spreading of a monolayer may be arrested as it approaches a static contact line at the edge of a rivulet. Implications for Surfactant Replacement Therapy are discussed.

Summary Thousands of well-perforation jobs are executed successfully around the world each month; however, certain perforation jobs require special design considerations to minimize the risk of equipment damage, such as bent tubing and unset packers, from perforating gunshock loads. Perforating guns generate pressure waves in the completion fluid and stress waves in structural components. The magnitude, duration, and timing of these waves depend on job parameters that can be adjusted by the design engineer, such as type, length, and loading of guns; number of shock absorbers; distance from sump packer to bottom of guns; and distance from completion packer to top of guns. The sensitivity of peak loads and gun-string movement to key design parameters can be evaluated with a software tool specifically developed to predict well-perforation-induced transient fluid-pressure waves and the ensuing structural loads. All relevant aspects of well-perforating events are modeled, including gun carrier filling after firing, wellbore pressure waves and associated fluid movement, wellbore pressurization and depressurization by reservoir pressure, and the dynamics of all relevant gun-string components, including shock absorbers, tubing, and guns. Existing fast-gauge pressure data from a large number of perforation jobs were used in previous jobs to verify that predictions made by using software simulation are sufficiently accurate, both in magnitude and time; thus, the transient pressure loading on well components is sufficiently accurate to predict the structural dynamics response and the associated gun-string loads. In this paper, we present case studies that show how key elements used for gunshock mitigation are simulated, and the sensitivity of peak loads and deformation to gun-string elements, such as shock absorbers, gun types and loading, tubing size and weight, and packer placement. With this software, we evaluate the dependence or sensitivity of peak loads and gun-string movement on/to key design parameters, and, when necessary, design changes are made to reduce potentially unsafe load conditions. The design verification and optimization methodology described in this paper significantly reduces the risk of nonproductive time and fishing operations. Key technologies described in this paper enabled the successful execution of many deepwater high-pressure (HP) perforation jobs, including Petrobras’ Cascade and Chinook, the largest deepwater HP perforation jobs performed to date in the Gulf of Mexico.