## 1 Introduction  
Offshore drilling is a mechanical process in which a wellbore is drilled into the seabed. In an offshore drilling system, a subsea well is drilled from a drilling rig using a subsea wellhead located below the rig, and a wellhead stack is mounted on the subsea wellhead [1]. Drilling in the ocean is largely classified into bottom supported rigs and floating rigs; it can be further classified into platform, jack-up, submersible, semi-submersible, and drillship. The mud circulation system is the modern solution to an environmentally sensitive drilling operation. The circulation system on the rig is fully self-supporting, requiring only the discharge of drill cuttings [2]. The mud circulation system performing functions ranging from mud mixing and supply to mud recovery. The system increases the lifetime of drill bits and bearings by preventing the wear and damage of drill bits when drilling is carried out deep in the ground. The system can be divided into five subsystems: bulk transfer system (BTS), mud mixing and storage system (MMSS), mud supply system (MSS), mud treatment system (MTS), and mud control system (MCS). Figure 1 shows the overall configuration of the main parts of the mud circulation system. The subsystems have the following roles:  
* BTS: Storage and transportation of mud material
* MMSS: Preparation and storage of mud by mixing the mud material with water
* MSS: Injection of mud into the borehole
* MTS: Processing of mud recovered from the borehole
* MCS: Integrated control and monitoring of the above four systems  
In the drilling system, mud is used as the drilling fluid and is a key element in the drilling operations. The fluid composition varies according to the additives that constitute the fluid. The mud is a liquid suspension that contains various additives, which provides the specific properties required for drilling fluids, including specific gravity and viscosity. The mud circulation system is responsible for circulating the mud during drilling to remove rock cuttings. The final subsystem of the mud circulation system is the MMSS. In this system, the mud to be reused is controlled while considering the changed mud properties after circulation and the properties of the mud required for the current well. To make the mud suitable for reuse, materials such as barite and bentonite, which are called bulk, are mixed and stored in the mud mixing system and then supplied to the drill bit using a pump. Barite increases the density of the mud, whereas bentonite increases the viscosity and volume of the mud. The bulk transfer performance of the BTS is one of the important design factors of the drilling system because the density and viscosity of the mud mixed inside the mud mixing system must be kept constant to maintain the overall stability of the drilling system. Figure 2 shows a schematic of a typical BTS installed inside a drillship. The BTS generally refers to the technology and equipment used to transport bulk such as raw materials or products in a plant or  
Figure 1: Schematic of mud circulation system, including MTS and BTS. factory using air pressure generated in a certain pipe. The BTS has many advantages such as dust minimization in the field, process simplification, and reduction in maintenance and environmental costs. The bulk storage tank is mainly installed at the bottom of an offshore structure. Bulk is considerably denser and is more affected by gravity than other fluids. In a drillship or a floating production, storage, and offloading unit, the distance from the tank top to the upper deck is approximately 30-40 m. Therefore, it is important to consider the pressure loss problem inside the vertical pipe from the tank to the deck. To transport the bulk at the target transport rate without clogging, a technique is needed to optimize the extreme pressure loss inside the vertical pipe. In addition, the operating pressure, air volume, and transport rate accuracy determine the system and operating costs. Hence, a system optimization technology is required.