ABSTRACT: Wellbore strengthening is an extensively-used method to reduce lost circulation in the petroleum drilling industry, with adding Lost Circulation material to the drilling mud and bridging the fractures on the wellbore to increase maximum stable pressure. In this study, the finite element and Kirsch analytical methods used to model the hoop stress distribution and its effective factors, in one of South Pars gas field's formations, based on Persian Gulf. Findings showed that the compressive stress, in the single fracture model, is raised up to the area of 30° in the fracture initiation state and it will be more in the bridging location across the fracture faces. Furthermore, the hoop stress at the tip of the fracture tends to be tensile; moreover, the compressive stress with higher wellbore pressure on the wellbore, before the area of 60° and after bridging the fracture, is greater than the compressive stress with lower wellbore pressure on the wellbore wall and it will be reversed after the area of 60°. In the multi-fracture model, by moving away from the first fracture, the compressive stress decreases around the 90°, due to the existence of second fracture and the compression stress is raised by increasing the horizontal stress contrast.
Wellbore strengthening is a practical method for reducing lost circulation while drilling formations with narrow drilling mud weight windows. It increases the wellbore's maximum sustainable pressure by bridging drilling induced or natural fractures with lost circulation material (Feng and Gray, 2016). To keep downhole pressure within the mud-weight window, drilling fluids and lost circulation material (LCM) are considered to make wellbore-hydrodynamic pressure low enough to evade downhole lost circulation but high sufficient to avoid borehole instability or kicking(Feng et al., 2015). These drilling fluids and additives cause in the formation hoop stress enhancement, called stress cage, which is a near wellbore area of high stress induced by propping open and sealing narrow fractures at the wellbore/formation boundary (Alberty and McLean, 2004). All lost circulation materials are not same and their type plays a role in terms of both plugging and toughness to better endure displacement pressures. It also, has been confirmed that, mostly, combinations of LCMs act more efficiently compared with the practice of only one type in wellbore strengthening (Savari et al., 2014). Some companies are produced a designer mud which effectively increases fracture resistance while drilling, which can be valuable in both shale and sandstone.it acts by forming a stress cage, using particle bridging and some type of fluid loss mud (Aston et al., 2004). In recent years many deep fundamental studies has been done, related to the lost circulation and wellbore strengthening (Feng and Gray, 2017; Feng et al., 2016). To better understanding of basics of the process of Wellbore strengthening, the effects of several parameters are still not fully understood, and a complete parametric study for each type of formations is necessary to improving field operations. There are plenty of numerical models and analytical solutions which have been developed in recent years for that reason. (AlBahrani and Noynaert, 2016; Wang et al., 2007; Mehrabian et al., 2015; Zhong et al., 2017;Salehi and Nygaard, 2014; Kiran and Salehi,2016; Salehi and Nygaard, 2011; Shahri et al., 2015; Zhang et al., 2016; Zhang et al., 2017;Wang et al., 2018; Chellappah et al., 2018; Feng et al., 2018; Wang, 2018); besides, some research has been done for the usage of wellbore strengthening methods for depleted reservoirs.(Shahri et al., 2014). Furthermore, a set of analytical equations, considered their advantages and disadvantages, are developed for parametric analysis of typical wellbore strengthening approaches. (Morita and Fuh, 2011). A finite-element method is the most important numerical technique, used today to model the wellbore strengthening problems, has been developed to research the effects of major parameters on the distribution of near wellbore hoop stress and fracture width (Feng and Gray, 2016; Arlanoglu et al., 2004; Towler, 2007). In this research, the term hoop stress is generally used to mean the circumferential stress at the wellbore wall. The hoop or tangential stress around a wellbore wall is the main factor in borehole stability and integrity analysis. This research investigates different and effective parameters of wellbore strengthening, related to the formations of south pars gas field in Persian gulf and numerical and analytical methods are used for this purpose; besides, new numerical model with multi fractures has been created to better understanding of wellbore strengthening mechanism and related effective parameters, to investigate of hoop stress around the wellbore and the width of the fractures.