G Factor From Drilling Fluids Processing Handbook

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Crews need to be alert to torn screens no matter what shaker is used.

This is especially true during slow drilling, when drill pipe connections

are infrequently made. When riser-assist pumps are used, flow should

be periodically directed to different shakers during connections. This

allows screens to be properly inspected and replaced, if needed.

7.5.4 g Factor

The g factor refers to a ratio of an acceleration to Earth’s gravitational

acceleration. Jupiter has a mass of 418.6 1025 lb and Earth has a mass

of 1.317 1025 lb. A person on Earth who weighs 200lb would weigh

320 times as much on Jupiter, or 64,000 lb. A person’s mass remains

the same on Earth or Jupiter, but weight is a force and depends on

the acceleration of gravity. The gravitational acceleration on Jupiter is

320 times the gravitational acceleration on Earth. The g factor would

be 320. (As a point of interest, Mars has a mass of 0.1415 1025 lb, so

the g factor would be 0.107; a 200-lb person would weigh only 21.4 lb

on Mars.)

The term ‘‘ g force’’ is sometimes used incorrectly to describe a g factor.

In the preceding example, the g force on Earth would be 200 lb and the

g force on Jupiter would be 64,000 lb. This is because the acceleration

of gravity on Jupiter would be 320 times the acceleration of gravity onEarth.

Calculation of g Factor

Accelerations are experienced by an object or mass rotating horizontally

at the end of a string. A mass rotating around a point with a constant

speed has a centripetal acceleration (Ca) that can be calculated from

the equationCa ¼ ro2

where r is the radius of rotation and o is the angular velocity in radians

per second.

This equation can be applied to the motion of a rotating weight on

a shale shaker to calculate an acceleration. The centripetal acceleration

of a rotating weight in a circular motion with a diameter (or stroke) of

2r, in inches, rotating at a certain rpm (or o) can be calculated from

the preceding equation,

ðCaÞ ¼ ð1=2ÞðdiameterÞfog2:

136 Drilling Fluids Processing Handbook



Ca ¼ 1

2ðstroke, in inchesÞ

1 ft

12 inches

RPM 2 radians

revolution

1 minute

60 seconds

2

Combining all of the conversion factors to change the units to ft/sec2:

Caðin ft/sec2Þ stroke, in inches

ðRPMÞ2

Normally this centripetal acceleration is expressed as a ratio of the value

to the acceleration of gravity:

No. of g’s ¼ Ca

32.2 ft/sec2 ¼ ðstroke, in inchesÞ ðrpmÞ

2

70490 :

Shale shakers are vibrated by rotating eccentric masses. A tennis ball

rotating at the end of a 3-ft string and a 20 lb weight rotated at the

same rpm at the end of a 3-ft string will have the same centripetal accel-

eration and the same g factor. Obviously, the centripetal force, or the

tension in the string, will be significantly higher for the 20-lb weight.

The rotating eccentric weight on a shale shaker is used to vibrate the

screen surface. The vibrating screen surface must transport solids across

the surface to discard and allow fluid and solids smaller than the screen

openings to pass through to the mud tanks. If the weights rotated at a

speed or vibration frequency that matched the natural frequency of the

basket holding the screen surface, the amplitude of the basket’s vibration

would continue to increase and the shaker would be destroyed. This will

happen even with a very small rotating eccentric weight. Consider a child

in a swing on a playground: Application of a small force every time the

swing returns to full height (amplitude) soon results in a very largeamplitude. This is a case in which the ‘‘forcing function’’ (the push every

time the swing returns) is applied at the natural frequency of the swing.

When the forcing function is applied at a frequency much larger than

the natural frequency, the vibration amplitude depends on the ratio

of the product of the unbalanced weight (w) and the eccentricity (e) to

the weight of the shaker’s vibrating member (W ); or

vibration amplitude ¼ we

W :

The vibration amplitude is one half of the total stroke length.

Shale Shakers 137





As noted previously (in the Linear Motion Shale Shakers subsection),

only a portion of the energy transports the cuttings in the proper

direction in unbalanced elliptical and circular vibration motion designs.

The remainder of the energy is lost due to the peculiar shape of the

screen bed orbit, as manifested by solids becoming nondirectional ortraveling in the wrong direction on the screen surface. Linear motion

and balanced elliptical designs provide positive conveyance of solids

throughout the vibratory cycle because the motion is straight-line

rather than elliptical or circular.

Generally, the acceleration forces perpendicular to the screen surface

are responsible for the liquid and solids passing through the screen, or

the liquid capacity. The acceleration forces parallel to the screen surface

are responsible for the solids transport, or the solids capacity.On a linear motion shaker, the motion is generally at an angle to the

screen. Usually the two rotary weights are aligned so that the accele-

ration is 45 to the screen surface. The higher liquid capacity of linear

motion shale shakers for the same size openings in the screens on

unbalanced elliptical or circular motion shakers seems related primarily

to the fact that a pool of drilling fluid is created at the entry end of the

shale shaker. The pool provides a liquid head to cause a higher flow rate

through the screen. The linear motion moves the solids out of the pool,

across the screen, and off the end of the screen.

On a linear motion shaker with a 0.13-inch stroke at 1500 rpm, the

maximum acceleration is at an angle of 45 to the shale shaker deck.

The g factor would be 4.15. The acceleration is measured in the direction

of the stroke. If the shale shaker deck is tilted at an upward angle from

the horizontal, the stroke remains the same. The component of the

stroke parallel to the screen moves the solids up the 5 incline.

vy1

1 2

1 2

Position A

Position B

Shale Shakers 139



Relationship of g Factor to Stroke and Speed of Rotation

An unbalanced rotating weight vibrates the screen deck. The amount of

unbalanced weight combined with the speed of rotation will give the

g factor imparted to the screen deck (see preceding paragraphs). The

stroke is determined by the amount of unbalanced weight and its dis-

tance from the center of rotation and the weight of the shale shaker

deck. (This assumes that the vibrator frequency is much larger than

the natural frequency of the shaker deck.) Stroke is independent of the

rotary speed.The g factor can be increased by increasing the stroke or the rpm, or

both, and decreased by decreasing the stroke or rpm, or both. The stroke

must be increased by the inverse square of the rpm reduction to hold the

g factor constant. Examples are given below to hold 5 g’s constant while

varying stroke length at different values of rpm:

5 g’s @ 0.4400 stroke at 900 rpm 4 g’s @ 0.3500 stroke at 900 rpm




7.5.5 Power Systems

The most common power source for shale shakers is the rig electrical

power generator system. The rig power supply should provide constant

voltage and frequency to all electrical components on the rig. Most

drilling rigs generate 460 alternating-current-volt (VAC), 60 Hz, 3-phasepower or 380 VAC, 50 Hz, 3-phase power. Other common voltages are

230VAC, 190 VAC, and 575VAC. Through transformers and other

1 2

Position C

Position D

140 Drilling Fluids Processing Handbook

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G Factor From Drilling Fluids Processing Handbook