A new mathematical model is presented which enables the prediction of various modes of cuttings transport in highly deviated to horizontal annuli that have been observed in laboratories. The model consists of three components - a bed of particles of uniform concentration, a dispersed layer in which particle concentration is varied, and a fluid-flow layer which could be a clear fluid or a turbulent suspension. The model predictions exhibit good agreement with experimental observations.
Over the past 15 years or so, considerable effort has been expended on solving cuttings transport problems in highly-deviated to horizontal wells. The methods by these investigators can be categorized into two main approaches: the first is an empirical approach in which one begins with experimentation to obtain data from scale-up models and then correlate these data by dimensional analysis or semi-theoretical reasoning; the second is a theoretical approach in which one, by analyzing forces involved in the situation with the use of basic principles, develops a set of equations and then numerically solves them with certain physical or mathematical assumptions.
A number of empirical relations exist, but they are, as often the case for experimentally derived relations, limited to very specific ranges of operating conditions. A few mathematical models have also been proposed which are based on simplified theory and, hence, can only simulate a limited range of phenomena observed in laboratories.
The objective of this work is to improve the characterization and evaluation of hole-cleaning performance of drilling fluids in highly-deviated to horizontal annuli, by developing a new mathematical model based on improved understanding of the mechanism and theory of particles transport.
For subsequent numerical analysis, we conceptually categorize the transport process into the following flow patterns as schematically illustrated in Fig. 1.
At high shear (i.e., high flow velocity), mobile particles on the uppermost layer of the bed tend to glide forward on top of a stationary bed forming a dilated 'dispersed layer'. Thus, we have a three-layer-flow pattern: a stationary bed of particles of uniform concentration, a dispersed layer in which particle concentration is varied, and an essentially clear fluid-flow region on top (as shown in Fig. 1(b)).
As the flow velocity is increased, the intensity of turbulent eddies grows in strength and eventually reaches a stage at which these turbulent eddies are strong enough to lift the topmost particles of the dispersed layer into the fluid-flow region and carry them in turbulent suspension mode. At this stage, we have a three-layer-flow pattern but with a slightly different composition to Fig. 1(b) (see Fig. 1(c)): a heterogeneous-suspension layer (also known as 'suspended-load' zone - Fig. 2) on top of a dispersed layer and a uniform-concentration bed which can either be stationary or moving 'en bloc' (the dispersed and uniform-concentration layers are sometimes collectively referred to as the contact-load zone - Fig. 2).
As more and more particles are picked up by turbulent eddies as the flow velocity increases further, the bed will get thinner and thinner and eventually the uniform layer will disappear leaving behind a dispersed layer and a heterogeneous suspension layer. This flow pattern is hereafter referred to as 'two-layer' flow pattern (as shown in the fourth annulus of Fig. 1(d)).