Viscosity Based Classification of Displacing Process in Horizontal Annular Cementation
Authors: Zhang Zhuangzhuang , Fu Xinkang , Li Shuailin , Sheng Mao , Huang Zhongwei 
Published: August 2024

ABSTRACT:
Density difference between fluids always exists in cementation, gravity generated stress caused the horizontal well cementation displacement process more complex. In this paper, we investigated the influence of fluid viscosity on cementing, classified the displacement process and further illustrated long time cementing development by simulations. Based on relative value of viscosity, the displacing process are separated into two patterns, call P-1 and P-2. In P-1 pattern, the viscosity of displacing fluid is larger than that of displaced fluid. Interface of two fluids is a regular slop as a consequence of density difference. This slop travels ahead with a constant velocity higher than imposed velocity all around annular. At the tail, gravity caused belt-like displacing fluid exists and theses fluid penetrates into displaced fluids. Generally, belts only arise at top half of annular in case of displacing fluid denser. In P-2 pattern, the viscosity of displaced fluid is larger, and cementing fluids always form stratified structure which is caused by uneven distribution of velocity. This stratified structure tends to have K-H instability leading wavy interface and causes strong mixing. This research provides a new perspective to understand the displacing process in annular cementation.

1. INTRODUCTION
Cementation is a vital operation in well establishment, and it provides guarantees for the following procedure in well drilling and for long-life security of production well. Cementation is a multiphase flow process that contains kinds of fluids which are in different non-Newtonian properties. In addition, it is a multi-stage process with fluids flowing downward in a steel circular tube and then upward in annular formed by tube and wellbore. The up-flow or annular flow obtains more attention compared with tube flow, as the wellbore wall is always irregular and eccentricity often happens, these irregular shape accompanied with fluid properties results in the difficulty of predicting displacement process.
The early research of cementation can be dated to 1910s at least, Knapp (1915) mentioned his research on cementing with Portland cement. The researches of cementing process mainly focus on the mixture zone or interface deformation zone to reveal the spatial-temporal development and how some parameters influence the length of zones. At early stage, Parker et al. (1965) proposed low imposing velocity method, because gelled-pill formed at the joint of different fluids. This pill would keep unbroken at low velocity and assists full displacement of mud. Iyoho & Azar (1980) adopted 1D-dimension method with including only axial velocity and found that the velocity profile mainly depended on fluid properties and average velocity. Haut & Crook (1979) conducted some experiments considering the filtering process of mud and mud cake, he argued that mud cake had influence on displacement and works neglecting mud cake should be carried out carefully. Tehrani et al. (1993) was the first one that reports secondary flow in vertical eccentric well, this secondary flow is the source of azimuthal flow. But according to Nouri, J. M. (1993), even in fully eccentric annular, secondary flow only account for around 2% of the total flow. With the development of equipment and theory, more accurate and complex models were proposed. One of the well-known research should be the Hele-Shaw model which is derived by Bittleston et al. (2002). This is a 2D-dimension method which adopts the radial average of flow field and considers tangential and axial velocity. Also, a group of dimensionless variables are taken into account to make the model more adoptable. From then on, the Hele-Shaw model is modified several times to including more situations, e.g. dispersion effect (Zhang & Frigaard, 2023), turbulence (Maleki & Frigaard, 2018), eccentric annular (Carrasco et al., 2010) and etc. Apart from Hele-Shaw model, some other mathematic method or model were adopted, such as, the lubrication model, augmented Lagrangian method (Pelipenko, 2004), arbitrary Lagrange-Euler method (Roustaei et al., 2015) and Lattice Boltzmann method (Zhao et al., 2016). Also Foroushan (2018) introduced R-T and K-H instability analysis into displacing process to predict whether the displacement is stable or not. Besides, 3D simulations are more available because of advance of computers. To simulated enough long section of annular, Xue et al. (2022) simulated the displacement according to the relative motion principle, in which the displacement is happen as a result of movement of annular-wall instead of the imposing of fluids. Z. Zhang et al. (2022) simulated the washout displacement and figure out the difference of spiral and no-spiral displacement of washout. Renteria et al. (2022) simulated the continuous washout displacement and suggested that the influence of washout on displacement was only restricted to the local zone. In terms of experiments, image acquiring devices and transparent material is widely applied. Malekmohammadi et al. (2010) reported the experiments of vertical well cementation and find that eccentricity of annular would leads that displacing fluid migrates to the wide side of annular resulting in spike of displacing fluid. Renteria & Frigaard (2020) proposed three patterns of horizontal annular displacement, i.e. top, slumping and dispersive pattern, and these patterns are mostly controlled by buoyancy number. In addition, Xu et al. (2020) utilized PIV to investigate the velocity field and argued that turbulent and laminar flow can co-exist in eccentric annular and turbulence is benefit for mud removal. Also some researchers adopted other kinds of data to represent the fluids' movement such as conductivity or density property of fluids (Lund et al., 2020).