Brazilian Journal of Chemical Engineering MODELING AND ANALYSIS OF UNSTEADY FLOW BEHAVIOR IN DEEPWATER CONTROLLED MUD-CAP DRILLING

A new mathematical model was developed in this study to simulate the unsteady flow in controlled mud-cap drilling systems. The model can predict the time-dependent flow inside the drill string and annulus after a circulation break. This model consists of the continuity and momentum equations solved using the explicit Euler method. The model considers both Newtonian and non-Newtonian fluids flowing inside the drill string and annular space. The model predicts the transient flow velocity of mud, the equilibrium time, and the change in the bottom hole pressure (BHP) during the unsteady flow. The model was verified using data from U-tube flow experiments reported in the literature. The result shows that the model is accurate, with a maximum average error of 3.56% for the velocity prediction. Together with the measured data, the computed transient flow behavior can be used to better detect well kick and a loss of circulation after the mud pump is shut down. The model sensitivity analysis show that the water depth, mud density and drill string size are the three major factors affecting the fluctuation of the BHP after a circulation break. These factors should be carefully examined in well design and drilling operations to minimize BHP fluctuation and well kick. This study provides the fundamentals for designing a safe system in controlled mud-cap drilling operatio. Keyword: Deep water; Controlled mud-cap drilling; Unsteady flow; Mathematical model; Kick detection.


INTRODUCTION
Due to the depletion of onshore oil and gas resources, the oil-gas industry has extended its search for resources to deep-water areas.However, deepwater drilling is facing many problems and challenges, including pore pressure prediction uncertainties, narrow pressure margins, and high equivalent circulation density (ECD) (Shaughnessy et al., 1999;2007;Stave, 2014).These problems and challenges not only lead to the inability to design wells for traditional kick tolerances, but also make a well technically undrillable due to lack of drilling window right below the previous casing/liner shoe.Controlled mud cap (CMC) drilling is the solution to all of these problems and challenges, and improve safety and efficiency in the well construction process (JPT staff, 2013;Stave, 2014;Malt and Stave, 2014;Godhavn et al, 2014;Børre and Sigbjørn, 2014).
CMC drilling is a kind of subsea mud-lift pump drilling system technologies.Figure 1 shows a schematic of a CMC drilling system.The mud-lift pump is placed in water and return mud and cuttings to surface through a mud return line (MRL).The technique allows for precise control of bottom hole pressure (BHP) during drilling by regulating the mud  right-hand side term takes into account the boundary pressure at the mud level in the drill string and the annulus.The third right-hand side term is related to friction, and the last right-hand side term represents the driving mechanism caused by the hydrostatic pressure imbalance between the drill string and the annulus.All symbols are defined in the Nomenclature section.
The final expression for the equation of motion for the length of mud, Ann L , in the annulus is ob- tained: These two equations are solved numerically in a computer program.

Numerical Formulation
Because the mud level is not changing very rapidly, the numerical integration need not to be excessive.The explicit Euler method is locally secondorder accurate but first-order globally accurate (Bewley, 2012).Provided that the time step is small enough, the explicit Euler method will yield good results for the problem.The simplest and most intuitive way of integrating the above scheme is by using the explicit Euler method, which takes the following form for Equation (1): The explicit scheme of the length of the mud column in annulus is Eq. ( 3) can be easily solved using the velocity and position of the previous time step to solve for the acceleration of mud in annulus in each time step.The acceleration is then used to obtain the velocity of mud in annulus, which in turn is used to calculate the position of the liquid level in annulus.In practice, the routine can be summarized as follows:  Use Eq. (3) to update the acceleration based on the level position and velocity at the previous time step;  Use Eq. ( 4) to update the level position based on the new velocity.
This procedure is repeated for each time step until the maximum time is reached.

Initial Conditions
After a circulation break, the initial mudflow velocity in the drill string is equal to that in the string before a circulation break: During normal circulation, the length of the mud column within the drill string is equal to the well depth: The annulus pressure at subsea level is approximately equal to the seawater hydrostatic pressure; therefore, the length of the mud column within the annulus can be calculated using the following equation: ( 0)

RESULT AND ANALYSIS Model Verification
Field experimental test for the unsteady flow after a circulation break are not currently available for a CMC drilling system.In 2007, Akira Ogawa et al. studied the flow in a U-tube in a laboratory (Ogawa et al, 2007).They adopted 3 non-Newtonian fluids to carry unsteady flow experiments in a U-tube: 68% glycerin solution, 1.8% acrylic co-polymer solution     The BHP can be predicted based on the mudflow velocity and mud level in the annulus (Figure 8).The BHP is the sum of the hydrostatic pressure and friction pressure loss in the annulus.During unsteady flow, a fluctuation in the BHP can occur.Fig. 8 shows that the BHP rapidly decreases within the first few seconds due to the disappearance of the SPP.Subsequently, the BHP increases as the increase in the pressure resulting from the rising mud level in the annulus is larger than the decrease in the pressure caused by reduced annulus flow velocity; when these two equal to each other, the BHP reaches to a new high point; and then the increase in the pressure resulting from the rising mud level in the annulus becomes less than the decrease in the pressure caused by reduced annulus flow velocity, and the BHP decreases gradually and tends to a constant.The fluctuation in the BHP can threaten drilling safety as it can lead to the occurrence of kick.

Applications
Under normal circulation conditions in CMC drilling, the SPP is non-zero, a kick can be detected

) Mud Densi
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4) Mud Visc
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5) Drill Strin
The calcul or drill string 19.5 mm an nd The wellbore mud is incompressible; therefore, the volumetric flow is conserved, which implies that the rate of volumetric change over time is the same inside the drill string and the annulus: According to the energy balance equation, the following formula can be obtained: where A Ann is the cross-sectional area of annulus in m 2 ; bit P is the friction pressure loss in the drill bit in Pa.The friction pressure loss calculation is well established, and the detailed method used to calculate Thus, the final expression for the motion equation for the length of mud column Ann L in the annulus can be obtained: Figure 1: S After a ci teady flow c rilling in C arrow-margi low, the mu rill string du rill string an evel in the ri which may le earance of th BHP, resultin an be used t uvkam-world urrently not ring additio Therefore, th must be know ufficient mo which has mo Figure 3: glycerin so Figure 4: acrylic co-

Figure 6 :Figure 7 :
Figure 6: Change of annulus flow velocity over time after the surface pump is shut down

Figure 8 :
Figure 8: Transient BHP after the surface pump is shut down.
Figure 9: with and w Figu Figure 14: Figure

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