**8. Proppant fall rates**

The rate of fall for proppant is normally calculated using Stoke's Law which can be written as:

Using a value of 1393 cps of apparent viscosity in Stoke's Law gives a total proppant fall of 15 feet during the four hour period. Almost perfect transport is achieved by a fluid system having

Fracturing Fluids

23

http://dx.doi.org/10.5772/56192

This example may appear to be extreme but it is actually conservative. The Fall Rate Correction was reduced from 80% to 50% and the time it takes to heat up to reservoir temperature was ignored. The main point to be taken from this is that the viscosity requirements for a frac fluid can be overestimated by an order of magnitude and sufficient proppant transport can be

Treating pressure is fairly insensitive to viscosity as the pressure is proportional to viscosity raised to the ¼ power. However as discussed above the viscosity estimate can easily be off by an order of magnitude which can have a drastic impact on treatment behavior. An order of magnitude would be (10 0.25 = 1.8) so the treating pressure would be 80% greater than antici‐ pated. This could cause undesired height growth and result in treatment failure. For jobs where the control of net pressure to prevent height growth is important, fluid viscosity is a critical

[1] Api, R. P. M, Recommended Practice for Measurement of Viscous Properties of Com‐

[2] Api, R. P. Recommended Practice for Presenting Performance Data on Cementing

[3] GidleyJohn L., et.al., Recent Advances in Hydraulic Fracturing SPE Henry L. Doher‐

[4] ElyJohn W., Stimulation Engineering Handbook, PennWell Publishing Company,

achieved with a fluid having a reference apparent viscosity of 50 to 100 cps.

a final reference apparent viscosity of only 50 cps.

**9. Viscosity and fracture treating pressure**

parameter.

**Author details**

Carl Montgomery

**References**

NSI Technologies, Tulsa, Oklahoma , USA

pletion Fluids, Jul-(2004). , 01.

087814417(1994).

and Hydraulic Fracturing Equipment, Feb-(1995). , 01.

ty Series Monograph Chapter 7, 155563020(1989). , 12

Fall Rate = V (ft/sec) = 1.66x10<sup>5</sup> D2 /μf SGprop– SGfluid

Where:

D = the average proppant diameter in feet

μf = the apparent viscosity of the fluid in Cps

SG prop = the specific gravity of the proppant (i.e. 2.65 for sand)

SGfluid = the specific gravity of the fluid (i.e. 1 for water)

Stokes's Law is generally not valid for Reynolds numbers much in excess of unity15 or for hindered settling due to proppant clustering in static fluids16. For crosslinked fluid the actual fall rate may be much less than Stokes Law. Hannah and Harrington17 present lab data that shows that proppant in crosslinked fluids falls at a rate which is reduced by about 80% when compared to non-crosslinked linear gels with the same apparent viscosity. The rate of proppant fall in foams and emulsions is also much less than would be indicated by using the apparent viscosity in Stoke's Law18. Another factor affecting proppant fall is the particle concentration which increases slurry viscosity (Figure 11). This retards or hinders the proppant fall because of clustered settling16 in static fluids. Finally the slurry flowing down a fracture is generally much lower that the shear rate of 170 or 511 sec-1 used to report the fluid apparent viscosity.

When all of these factors are put together they can significantly affect the viscosity. To provide an example consider a crosslinked gel which has a reference apparent viscosity at 170 sec-1 of 50 cps after four hours at reservoir temperature.


Using a value of 1393 cps of apparent viscosity in Stoke's Law gives a total proppant fall of 15 feet during the four hour period. Almost perfect transport is achieved by a fluid system having a final reference apparent viscosity of only 50 cps.

This example may appear to be extreme but it is actually conservative. The Fall Rate Correction was reduced from 80% to 50% and the time it takes to heat up to reservoir temperature was ignored. The main point to be taken from this is that the viscosity requirements for a frac fluid can be overestimated by an order of magnitude and sufficient proppant transport can be achieved with a fluid having a reference apparent viscosity of 50 to 100 cps.
