Thixotropy effects on drilling hydraulics

Highlights

• A computationally inexpensive model is proposed to model thixotropy in drilling fluids.

• Thixotropy causes fluctuation in bottomhole pressure.

• High flow rate and yield stress do not guarantee efficient hole cleaning.

• Pressure fluctuations and cuttings transport depend on fluid’s temporal response to shear rate changes.

Abstract

Thixotropy is the reversible breakdown of fluid microstructure when sheared. The microstructure achieves a new steady-state once shearing stops. Drilling fluids are thixotropic due to their rheological makeup which means that fluid microstructure has a time-dependent response to changes in applied shear rate. In contrast to the literature focusing on the time-independent nature of drilling fluid, few studies have focused on the time-dependent response and even fewer have considered cuttings transport while doing so. The purpose of this study is to investigate the fundamental relationship between thixotropy and drilling hydraulics. An algorithm is developed to model thixotropy using flow history. The results show that the addition of drill cuttings does not directly affect the thixotropic behavior, rather the steady-state response is impacted which consequently changes the thixotropic response. Since the fluid microstructure takes time to respond to shear rate variations, viscosity lags behind shear rate variations causing annular pressure loss to fluctuate. The magnitude of pressure fluctuations is inversely proportional to characteristic time and directly proportional to stretching exponent. At smaller characteristic time coupled with smaller stretching exponent, high yield stress deteriorates cuttings transport. For larger values of characteristic time and stretching exponent, a clear trend is not observed, and further investigation is recommended. Nevertheless, when the thixotropic behavior of drilling fluid is considered, the results show that high flow rates and yield stresses do not guarantee efficient hole cleaning. Out of the two industrial fluid samples discussed, WBM yields higher pressure fluctuations and better cuttings transport compared to OBM. Since the proposed algorithm does not differentiate between the types of drilling fluids, this is due to WBM's smaller characteristic time and larger stretching exponent. It is suggested that a fluid exhibiting a slower response to shear rate changes causes higher pressure fluctuations and better cuttings transport.

Introduction

As wells continue to get deeper, longer, and more complicated, the drilling windows tend to shrink and the need to accurately predict drilling hydraulics has become increasingly critical to successful drilling operations. The rheology of drilling fluid sits at the core of the functions that it is supposed to perform and has been extensively studied in relation to the above-mentioned parameters.

Some of the early studies on rheology and drilling hydraulics focused on the development of empirical models using experimental methods for example Pigott (1941), Hall et al. (1950), and Williams Jr et al. (1951). As computational technology advanced, the focus began to shift on analytical/semi-analytical computer-based models such as those by Gavignet and Wick (1987), Gavignet and Sobey (1989), and Clark and Bickham (1994). With the turn of the century, high fidelity numerically solved models rose in popularity such as those by Bilgesu et al. (2002), Ofei et al. (2014), and Amanna and Movaghar (2016). For a detailed review of this topic, refer to Nazari et al. (2010), Kelin et al. (2013), Li et al. (2014a), and Li et al. (2014b).

Despite an abundance of literature, contradictory results and disagreements exist to date. One of the earliest studies in this field was conducted by Williams Jr et al. (1951) who concluded that low viscosity fluids had better cuttings carrying capacity. On the contrary, Sifferman et al. (1974) concluded that high viscosity yielded better cuttings carrying capacity and the effect of flow rate increased until it reached a plateau after which it had no considerable impact, rather it only caused increased frictional losses. Buscall et al. (1982) observed that higher yield stress improved cuttings transport and thus, was as important as viscosity. Hussaini and Azar (1983) and Okrajni and Azar (1986) reported that at low and medium velocities, an increase in the yield stress and gel strength improved cuttings transport. Tomren et al. (1986) and Ford et al. (1990) observed the same trend for fluid viscosity. In line with the results of Williams Jr et al. (1951), Larsen et al. (1997), Li et al. (2001), Saasen et al. (2002), Valluri et al. (2006), Kelessidis et al. (2007), Duan et al. (2009), Ozbayoglu et al. (2009), Ozbayoglu and Sorgun (2010) and Piroozian et al. (2012) also concluded that low viscosity fluid was preferable for efficient hole cleaning. Mohammadzadeh et al. (2016) showed that high yield stress was favorable for cuttings transport and increased viscosity improved cuttings transport though this effect leveled off at high values. Contradictory to this, Sayindla et al. (2016) reported that high yield stress is detrimental to cuttings transport. Werner et al. (2017) also suggested that low yield stress favored cuttings transport. Epelle and Gerogiorgis (2018) showed that increased viscosity enhanced cuttings carrying capacity for small particles, but this was not always the case for large particles. Huque et al. (2020) concluded that higher yield stress benefitted cuttings carrying capacity. To summarize, some authors have recommended high yield stress and viscosity whereas some have recommended exactly the opposite. Most of the authors have favored high flow rates irrespective of yield stress and viscosity but increasing flow rates result in higher pressure losses, thus excessive ECD and also increased erosion. Moreover, Cameron (2001) showed that high flow rates can also deteriorate fluid's cuttings carrying capacity.

A common theme in all of the above-mentioned studies is that the fluid's thixotropic response is not considered. Drilling fluid, due to its rheological composition, is a typical example of thixotropic fluids (Darley and Gray, 1988). At rest, the microstructure consolidates and viscosity increases with time. When fluid is sheared, the microstructure aligns with flow which leads to a gradual decrease in viscosity as shear rate increases. The term thixotropy was first introduced by Peterfi (1927) to describe the transformation of cytoplasm from a gel-like structure to a solution upon agitation. This paper was followed by several studies on thixotropy that aimed to present an accurate definition of thixotropy. Bauer and Collins (1967) published a review paper on thixotropy and defined thixotropy as reversible reduction in any rheological property of a fluid. The review study conducted by Mewis (1979) defined thixotropy as the reversible decrease in viscosity under shear, a definition which was later endorsed by Barnes et al. (1989). The review study by Barnes (1997) identified thixotropy as the non-linear region on shear stress vs. shearing time graph which was interpreted as microstructure breakdown in fluid. Although a general agreement has developed on the above-mentioned definition of thixotropy, the current argument on thixotropy revolves around the distinction between thixotropy, nonlinear viscoelasticity, and viscoelastic aging and whether to associate the changes in microstructure with shear stress or shear rate. For a detailed discussion on the current debate on thixotropy, refer to the review studies of Mewis and Wagner (2009), de Souza Mendes (2011), and Larson and Wei (2019).

Several mathematical models have been proposed in the literature to model thixotropy. Following Mujumdar et al. (2002), the modeling approaches can be divided into three categories namely: phenomenological approach, the indirect microstructural approach, and direct microstructural approach. As the name suggests, the phenomenological approach intends to define the general behavior of fluid and does not attempt to model the structural changes that take place within a fluid. In the direct microstructural approach, the focus is on modeling the behavior of the bonds between the particles. In recent years, the indirect microstructural approach has found the highest popularity amongst the three approaches. In the indirect microstructural approach, a structural parameter λ is used to model the microstructure of the fluid. A completely broken-down structure is represented by λ = 0 whereas λ = 1 represents a virgin (unbroken) structure. The review studies listed above present a detailed discussion of different modeling techniques.

Most of the studies in the literature on thixotropy in drilling fluids work with fluids in the absence of drill cuttings (Billingham and Ferguson, 1993; Pereira and Pinho, 2002; Herzhaft et al., 2006; Negrao et al., 2010; Cayeux and Leulseged, 2018). Another problem identified by Livescu (2012) was the large number of experimental constants required for modeling thixotropy. Furthermore, WBM, OBM and SBM show varying degrees of thixotropy, and even within each category, the thixotropic response is a function of weighing material and viscosifiers added to base fluid (Skadsem et al., 2019; Cayeux and Leulseged, 2018). The addition of rock cuttings further complicates the situation by affecting the time-independent and time-dependent features of fluid. Mahaut et al. (2008) studied the effect of coarse particles, particles that are much larger than the fluid's microstructure, on the rheological behavior of a thixotropic fluid and concluded that the addition of coarse particles does not affect the structuration rate of a thixotropic suspension. Baldino et al. (2018) noted that settling velocity of cuttings is dependent on competing microstructure breakdown and buildup phenomena. Large particles settled to the bottom as microstructure breakdown dominated microstructure buildup and small particles remained suspended as microstructure buildup dominated microstructure breakdown. Cayeux and Leulseged (2019) showed that the addition of cuttings has a significant impact on flow and consistency indexes, and can be modeled using the model of Herschel and Bulkley (1926).

The purpose of the present work is to gain a better understanding of the interplay between rheology and drilling hydraulics. This study models the thixotropic behavior of drilling fluid and investigates its impact on annular pressure drop and cuttings transport in inclined and eccentric annuli. The viscosity function proposed by de Souza Mendes (2009) is used to model steady-state viscosity and the thixotropic functions based on shear rate step-up/step-down experiments proposed by Dullaert and Mewis (2005) are used to model the transient response. An algorithm is proposed to capture flow history and model the complete response (steady-state and transient) of fluid. Flow is modeled using the mixture approach proposed by Ishii (1975) and is simulated using an open-source CFD software (OpenFOAM v5.0.). The investigation carried out in this study focuses solely on the thixotropic response and thus, viscoelasticity is ignored.