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Assuming cuttings sphericity 1.0, the volume of individual cuttings is.

Substituting Eqs. (A.9) and (A.10) into Eq. (A.8) results in

Substitution of Eqs. (A.7) and (A.11) into Eq. (A.13) yield:

Substituting Eq. (A.14) into Eq. (A.2) results in:

1 2 rgv<sup>2</sup> <sup>g</sup> <sup>¼</sup> <sup>1</sup> 2 rg0v<sup>2</sup> <sup>g</sup><sup>0</sup> þ

rewritten in the same form of Angel's equation as:

where

178 Drilling

Nomenclature

An total nozzle area, mm<sup>2</sup>

Wg <sup>¼</sup> <sup>100</sup><sup>f</sup> <sup>g</sup>D<sup>2</sup>

1 2 rgv<sup>2</sup> <sup>g</sup> <sup>¼</sup> <sup>1</sup> 2 rg<sup>0</sup> vg<sup>0</sup>

C choke flow coefficient (≈1.2 according to Guo and Liu [2])

Vc <sup>¼</sup> <sup>4</sup><sup>π</sup> 3

<sup>m</sup> <sup>¼</sup> <sup>D</sup><sup>2</sup>

The energy requirement for grinding all particles in a unit volume of gas is then expressed as.

It is understood that crushing energy should be from rotating drill bit, drill string, and the flowing gas. Assuming the fraction of the crushing energy from the flowing gas is fg, we have

<sup>h</sup>WirshROP

1 ffiffiffi d <sup>p</sup> � <sup>1</sup> ffiffiffiffi D p � �

<sup>h</sup>WirshROP

ffiffiffiffiffiffiffiffiffiffiffi 1 þ n � � p <sup>2</sup>

1 ffiffiffi d <sup>p</sup> � <sup>1</sup> ffiffiffiffi D p � �

Qg<sup>0</sup>

Qg<sup>0</sup>

<sup>100</sup><sup>f</sup> <sup>g</sup>D<sup>2</sup>

To make the model easy to be adopted in existing computer models, this equation can be

<sup>n</sup> <sup>¼</sup> Wg 1 <sup>2</sup> rg0v<sup>2</sup> g0

D 2 � �<sup>3</sup>

<sup>h</sup>hROP

<sup>40</sup>Qg0D<sup>3</sup> (A.11)

W ¼ mw (A.12)

Wg ¼ f <sup>g</sup>mw (A.13)

(A.10)

(A.14)

(A.15)

(A.16)

(A.17)

Jun Li<sup>1</sup> \*, Yulong Yang<sup>1</sup> , Boyun Guo<sup>2</sup> and Gonghui Liu<sup>1</sup>

\*Address all correspondence to: lijun446@vip.163.com

1 China University of Petroleum, Beijing, China

2 University of Louisiana at Lafayette, USA
