Based on our previously developed prototype simulator, a transient cuttings transport simulator using the two-layer model was developed with some modifications and improvements for more practical use. To evaluate functionality and potential of the simulator, a post analysis on hole cleaning were carried out for an actual extend reach well (ERW) drilled in Japan. Simulation results showed that the modified model successfully demonstrated transient distributions of cuttings bed height and annular pressure over the whole trajectory of the well. From the comparison with a conventional steady-state analysis, transient simulation over the whole trajectory was found to be crucial and useful for prediction of behaviors unrecognized by steady-state simulations.
Hole cleaning or effective cuttings transport is one of the biggest challenges in drilling ERWs. Many efforts have been made by researchers to reveal cuttings transport mechanism in their previous works.1,2 Several modeling and simulation methods have been proposed as well as comprehensive experimental studies. There are few simulation tools, however, which satisfy the industry requirement to use for more practical and comprehensive study on hole cleaning.
One of the problems might lie in the situation that most conventional cuttings transport models or numerical simulators are of steady-state calculations. Consequently, most of them are for use of obtaining critical flow rate for a single section of the whole well with a constant hole geometry at a time.
In this study, based on our previously developed prototype simulator,3 a transient cuttings transport simulator was developed with some modifications and improvements for more practical use in field operating conditions. To evaluate functionality and potential of the simulator, a post analysis on hole cleaning were carried out for an actual ERW drilled in Japan. Also a comparison with conventional steady-state analysis is presented in this paper.
The mathematical model uses the two-layer model which describes an isothermal transient 1D flow of solid-liquid two phases in well annulus (Figs. 1 and 2). The basic equations comprise mass and momentum conservation, which are summarized in Appendix A. Required constitutive equations to solve the basic equations are detailed in Appendix B.
Although the model has been originally developed for use of underbalanced drilling with gasified drilling fluids, for simplification of explanation, descriptions in this paper accounts only for a single-phase liquid drilling fluid. The rheology model of drilling fluid is assumed to be power-law.
Modifications described below were made for more practical simulation by use of field data.
Mass and momentum transfer between layers play a significant role in transient fluid flow modeling. In the previous work,3 however, the slope ment and the critical friction velocity u*12 in cuttings entrainment rate formulation, Eq. B-19, were said to be tuning parameters to match simulation results with experimental data for cuttings concentration.
From our experimental observations and parameter sensitivity analysis, an implication that the cuttings entrainment rate should be a function of hole inclination angle, was obtained. Keeping the simple linear form of the entrainment rate equation, the critical friction velocity u*12 in Eq. B-19 was reformulated based on the mechanistic model proposed by Clark and Bickham.4
As shown in Fig. 3, gravity force Fg, drag force FD and lift force FL act on a single spherical cuttings particle just about to move at the surface of deposited bed. These forces can be written in terms of the friction velocity u12, as follows.