Primary cementing of vertical wells: displacement and dispersion effects in narrow eccentric annuli

Abstract

Laminar miscible displacement flows in narrow, vertical, eccentric annuli show a wide range of interesting physical phenomena, e.g. static layers and channels, dispersive spikes/fronts and various instabilities. These are of relevance to the primary cementing of wells, where gas leakage and greenhouse gas emissions can result from ineffective cementing. The current popular way to model this process is via a Hele-Shaw approach, reducing the Navier–Stokes equations via scaling arguments and then averaging across the annular gap: the two-dimensional (2-D) gap averaged (2DGA) model. This leads to a reduced model that is computationally efficient and represents some important features of cementing flows, but is also deficient in capturing the effects of dispersion. While three-dimensional (3-D) simulations are able to capture dispersion and most other physical phenomena, they suffer from excessive computational times due to the extreme aspect ratios of cementing geometries and non-Newtonian properties of the fluids. Here we extend the 2DGA approach by modelling the high Péclet number limit of miscible duct displacement flows, to take into account the leading-order effects of dispersion. Our modified dispersive 2DGA model is well able to approximate dispersive effects that are observed by gap-averaging the results of 3-D computations, including geometric effects of eccentricity and instabilities. This represents a marked improvement over the 2DGA approach, while keeping the computational advantages of a 2-D model.

Primary cementing of vertical wells: displacement and dispersion effects in narrow eccentric annuli. Part 2. Flow behaviour and classification

“…In Part 1, this was accomplished by modelling a layered flow explicitly on the gap scale, then deriving the closures related to this structured flow, on averaging across the gap. The dispersive two-dimensional gap-averaged (D2DGA) model was shown to be able to predict dispersive displacements effectively and compared well with the results obtained from 3-D simulations, post-processed by averaging across the annular gap (Zhang & Frigaard 2022).…”

“…The study is mainly based on lab-scale experiments. We also use these to compare with a 3-D computational model and the D2DGA model introduced by Zhang & Frigaard (2022). This provides validation for the modelling approach, which can then be used to study parameter ranges and effects that are difficult to access experimentally, e.g.…”

“…To be consistent, we choose the same dimensionless parameters in the experimental design as used by Zhang & Frigaard (2022). These are the Reynolds number, ; the viscosity ratio, ; the buoyancy number, ; and the annulus eccentricity, .…”

“…The in situ drilling mud in the well is displaced by pumping a sequence of fluids around the well: downwards inside the casing and back upwards in the annulus. Our paper is a sequel to Zhang & Frigaard (2022) (Part 1), which contains a more lengthy introduction to the fluid mechanics literature of primary cementing. At its heart, the process is a displacement flow along a very long narrow annular space, which leads to model simplifications in which behaviour of the fluid in the annular gap is not fully resolved, e.g.…”

“…In Part 1 of the study, Zhang & Frigaard (2022) addressed a shortcoming of the 2DGA modelling approach: that of assuming a uniform (mixed) concentration of fluids in the annular gap, at each point. While valid for turbulent flows, laminar flows are high-Péclet-number miscible displacements that simply do not diffuse fully across the annular gap on the usual time scales of displacement, i.e.…”