16 research outputs found
Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids
Primary-cementing displacement flows occur in long narrow eccentric annuli during the construction of oil and gas wells. A common problem is that the displacing fluid fingers up the upper wide side of the annulus, leaving behind a âmud channelâ of displaced fluid on the lower narrow side of the annulus. Tehrani et al. report that the interface between displacing fluid and mud channel can in certain circumstances become unstable, and a similar phenomenon has been observed in our ongoing experiments. Here an explanation for these instabilities is provided via analysis of the stability of two-layer eccentric annular Hele-Shaw flows, using a transient version of the usual Hele-Shaw approach, in which fluid acceleration terms are retained. Two Newtonian fluids are considered, as a simplification of the general case in which the fluids are shear-thinning yield-stress fluids. It is shown that negative azimuthal buoyancy gradients are in general stabilizing in inclined wells, but that buoyancy may also have a destabilizing effect via axial buoyancy forces that influence the base-flow interfacial velocity. In a variety of special cases where buoyancy is not dominant, it is found that instability is suppressed by a positive product of interfacial velocity difference and reduced Reynolds-number difference between fluids. Even a small positive azimuthal buoyancy gradient, (heavy fluid over light fluid), can be stabilized in this way. Eccentricity of the annulus seems to amplify the effect of buoyancy on stability or instability, e.g. stably stratified fluid layers become more stable as the eccentricity is increased
A trust-region SQP method for the numerical approximation of viscoplastic fluid flow
We present a new approach to the problem of stationary viscoplastic duct flow
as modelled by the Herschel-Bulkley model, with Bingham fluids included as a
special case.
While the mathematical formulation of this problem is conventionally based on
a variational inequality, or equivalently, on a nonsmooth minimisation problem
for the flow velocity, we suggest an alternative approach. Considering the
Lagrangian dual in terms of the stress, rather than the velocity, turns out to
be advantageous in numerous ways. The objective functional possesses higher
regularity, which ensures applicability of second order methods. Our numerical
experiments with a trust-region SQP algorithm also demonstrate clearly superior
performance compared to the widely used augmented Lagrangian method, although
no artificial regularisation is introduced into the problem.
Hence, besides providing a new theoretical angle to a classical problem, our
results also pave the way for an entirely new class of numerical approaches to
simulating flows of viscoplastic fluids
Transient effects in oilfield cementing flows: Qualitative behaviour
We present an unsteady HeleâShaw model of the fluidâfluid displacements that take place during primary cementing of an oil well, focusing on the case where one HerschelâBulkley fluid displaces another along a long uniform section of the annulus. Such unsteady models consist of an advection equation for a fluid concentration field coupled to a third-order non-linear PDE (Partial differential equation) for the stream function, with a free boundary at the boundary of regions of stagnant fluid. These models, although complex, are necessary for the study of interfacial instability and the effects of flow pulsation, and remain considerably simpler and more efficient than computationally solving three-dimensional NavierâStokes type models. Using methods from gradient flows, we demonstrate that our unsteady evolution equation for the stream function has a unique solution. The solution is continuous with respect to variations in the model physical data and will decay exponentially to a steady-state distribution if the data do not change with time. In the event that density differences between the fluids are small and that the fluids have a yield stress, then if the flow rate is decreased suddenly to zero, the stream function (hence velocity) decays to zero in a finite time. We verify these decay properties, using a numerical solution. We then use the numerical solution to study the effects of pulsating the flow rate on a typical displacement