Boundary Element Simulations of Compressible Bubble Dynamics in Stokes Flows

Modeling of dynamics of compressible bubbles in acoustic fields at low Reynolds numbers is of interest for a number of contemporary micro- and nanotechnologies. Despite the boundary element method (BEM) is an appropriate method to simulate deformation of three-dimensional bubbles computation of compressible bubbles dynamics using conventional BEM causes difficulties due to degeneration of the resulting system of equations. In the present approach additional relations based on the Lorentz reciprocity principle are used to resolve the problem. The approach is validated by test simulations of dynamics of single bubbles and bubble clusters including strong bubble-bubble interaction in acoustic fields and shear flows.

Compressible bubbles in Stokes flow

The problem of a two-dimensional inviscid compressible bubble evolving in Stokes flow is considered. By generalizing the work of Tanveer & Vasconcelos (1995) it is shown that for certain classes of initial condition the quasi-steady free boundary problem for the bubble shape evolution is reducible to a finite set of coupled nonlinear ordinary differential equations, the form of which depends on the equation of state governing the relationship between the bubble pressure and its area. Recent numerical calculations by Pozrikidis (2001) using boundary integral methods are retrieved and extended. If the ambient pressures are small enough, it is shown that bubbles can expand significantly. It is also shown that a bubble evolving adiabatically is less likely to expand than an isothermal bubble.

THE EVOLUTION OF STABLE FOAM AS A DRILLING MEDIUM

In the late 1960s Stable Foam was developed by Chevron USA as a lightweight circulation medium to clean out production sand in depleted (depleting) wells. In employing this new medium they found that Stable Foam's compressible bubble structure provided up to 10 times the carrying capacity of many common liquid based circulating fluids.These early successes led the industry to expand the use of Stable Foam from cased hole production clean outs to drill-ins, gravel packing, drilling in lost circulation zones, coil tubing, and today its utilisation as an Underbalanced Drilling fluid in depleted reservoirs.Through this evolution Stable Foam has had its successes and failures as well as unique operational concerns which has affected its consideration and utilisation.The following is a breakdown of the major hurdles which have been addressed and overcome, consequently positioning Stable Foam as a viable option for wider use in Underbalanced Drilling:Foam compatibility in water, oil, salt and high temperature environments.MWD and Directional Drilling performance with a compressible fluid.Surface pressure control while drilling.Surface separation and processing of a three phase well return fluid to provide a zero discharge closed loop circuit.