Flow displacement in eroded regions inside annular ducts

Abstract

This work presents a numerical study of the displacement of two fluids through vertical annular ducts with an enlargement in the cross section. This flow is found in cementation operations in the oil industry. A successful cementing operation is obtained when the cement slurry is able to effectively displace the drilling fluid from the annular space between the wellbore and the casing. The process is very complex, since both fluids can have non-Newtonian behaviour, and the flow is time-dependent. In addition, in many situations the wells have some eroded regions, where the cross-sectional area is larger than the regular well annular cross section. The optimization of the displacement efficiency is important not only because of the cost of the process, but also due to security problems, since a unsuccessful operation may result in the collapse of the oil well. The displacement efficiency is a function of the fluids rheology, the density ratio, the flow rate, and the geometry. This work presents an analysis of the influence of rheology, flow rate and geometry on the displacement process inside annular ducts with an eroded region. The governing conservation equations are solved for an axisymmetric flow using the finite volume method. The multiphase problem is dealt using the volume of fluid method. Flow pattern along the eroded region and the displacement efficiency are presented and discussed for different pairs of fluids. The results show that the displacement through the eroded region is better for larger aspect ratios (or longer eroded regions). It is also observed that inertia tends to shift the interface towards the exit wall of the eroded region, leading to lower displacement efficiencies. Keywords Viscoplastic fluids Á Yield stress Á Eroded wells Á Fluid displacement 8 j Volume occupied by phase j in the cell control volume 8 Greek symbols a Symmetry factor b Displacement efficiency Dp Pressure drop in the developed region of the tube _ c Intensity of the rate-of-strain tensor _ c c Characteristic shear rate _ c cr Critical rate-of-strain modulus g c Characteristic viscosity g r Viscosity ratio

A Review of Rheological Modeling of Cement Slurry in Oil Well Applications

“…Zhou et al [291] developed a new model to look at gas migration in non-Newtonian fluids with yield stress and the factors affecting the wellhead pressure change by the analysis of variance (ANOVA). Naccache et al [292] performed a numerical simulation to study the displacement of two fluids (e.g., cement slurries and drilling fluids) in vertical annular pipe in the cementing operation in the petroleum industry. For the multiphase fluid problem, the governing equations were solved by using the ANSYS FLUENT.…”

Deslocamento Axissimétrico De Fluidos Miscíveis Em Anulares Com Expansão Abrupta

“…Já NACCACHE et al (2018) [7] analisaram o deslocamento de pares de fluidos imiscíveis através de um duto anular contendo uma erosão na parede do duto externo, simulando numericamente o deslocamento 2-D do fluido de perfuração durante o processo de cimentação primária, com diferentes propriedades reológicas e diferentes números de Reynolds. Consideraram um fluido visco-plástico deslocando um fluido newtoniano, um fluido newtoniano deslocando um fluido visco-plástico e também o deslocamento entre dois fluidos visco-plásticos.…”

“…Alguns trabalhos científicos recentes estudaram o comportamento hidrodinâmico do deslocamento do fluido de perfuração por um sistema de cimentação. Dentre eles destacamos os estudos realizados por NACCACHE et al (2018) [7], apresentando um estudo numérico sobre o deslocamento de dois fluidos através de um duto vertical contendo um alargamento abrupto na seção transversal.…”

“…) A correlação, µ(c), ideal irá depender da escolha do par de fluidos e a função utilizada para deslocamentos miscíveis envolvendo fluidos newtonianos é a exponencial, dada por (2)(3)(4)(5)(6)(7)(8)(9)(10)(11):…”

“…Na equação (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12), η é um dos parâmetros de controle adimensionais do nosso problema e representa a razão entre as viscosidades em escala logarítmica, onde µ 1 é a viscosidade dinâmica do fluido injetado e µ 2 , a do fluido deslocado:…”