2. Basic Design

7/23/2019 2. Basic Design

1/6

Basic Design

It is advantageous to start any fracturing treatment design from the point of view

of the reservoir. We should first resolve such important issues as the type and

amount of proppant placed into the pay layer and the corresponding optimallength and width, withoutconsidering the technical details of inducing the fracture

and placing the proppant. Once we determine the amount of proppant required

and the desired half length, the next step is to select the fluid system and slurry

injection rate.

(For a discussion of the equations used in determining these parameters, refer to

the II!" section titled #$uantitative %escription of Fracture &rowth,# which

appears under the heading #Hydraulic Fracturing Fundamentals.#'

t this point we assume that we have sufficient information to start the

calculations. )hat is, we assume that we *now the fracture height hf, the plane

strain modulus +, the injection rate qi, the viscosity , the -arter lea*off coefficient

-and the spurt loss coefficient "p. We also assume a specified target length, xf.

(/on0/ewtonian rheology will 1e considered later.'

Pumping time2)he first 1asic design step is to determine the pumping time, te,

using the com1ination of a width equation such as 3/ and a simple material

1alance. )his part of a typical design procedure is summari4ed as follows5

1. Calculate the wellbore width at the end of pumping from the PKN (or any other)

width equation:

2.

. Con!ert wellbore width into a!erage width:

".

6. ssume a 7 8.986 (or a similar value for other geometries, i.e., 8.9:;

for the 3&% model and 8.


2/6

#electing a$ the new un%nown& a $imple quadratic equation ha$ to be $ol!ed

1) Calculate in'ected !olume

and fluid efficiency

e may refine the abo!e $imple de$ign by con$idering $e!eral factor$& $uch a$ de!iation of

permeable and fracture height$ and nonNewtonian rheology.

If the permea1le height, hpis less than the fracture height, it is convenient to use

apparent lea*off and spurt loss coefficients. )he apparent lea*off coefficient is the

#true# lea*off coefficient (the value with respect to the permea1le layer'

multiplied 1y the factor rpshown in Table 1.

PKN K*+ ,adial (-igure 1&Ratio of permeable to

fracture area: radial geometry)
http://figurewin2%28%27../asp/graphic.asp?code=5575&order=0%27,%270%27)http://figurewin2%28%27../asp/graphic.asp?code=5575&order=0%27,%270%27)http://figurewin2%28%27../asp/graphic.asp?code=5575&order=0%27,%270%27)


3/6

Figure 1

Table 1: =atio of permea1le to total surface, rp

)here are several ways to incorporate non0/ewtonian 1ehavior into the width

equations. convenient procedure is to add one additional equation connecting

the equivalent /ewtonian viscosity with the flow rate. ssuming ower aw

1ehavior for the fluid, we can calculate the equivalent /ewtonian viscosity for the

average cross section. fter su1stituting the equivalent /ewtonian viscosity intothe 3/ width equation we o1tain

(1)


4/6

Proppant schedule/nce we %now the pumping time& we can e$tabli$h a proppant $chedule.

/ur goal i$ to determine the pad !olume and the particular cur!e of proppant concentration

!er$u$ time that we ha!e to follow during pumping. 0o carry out the de$ign $ugge$ted by

Nolte (13)& we need to $pecify 'u$t one additional parameter: ce& the ma4imum proppant

concentration that i$ technically po$$ible for the in'ected $lurry.

Ideally, the proppant schedule results in a uniform proppant concentration in the

fracture at the end of pumping, with the value of the concentration equal to ce.

We derive the schedule from the requirements that

the whole length created $hould be propped

at the end of pumping, the proppant distri1ution in the fracture should 1e

uniform

the schedule curve should 1e of the form of a delayed power law, with

the exponent and fraction of pad (' 1eing equal.

5t i$ important to notice that once we %now the ma4imum proppant concentration and the

height& length and width at the end of pumping& we can calculate the total ma$$ of proppant

that will be placed into one wing by

(2)

e $hould u$e thi$ equation to $elect the in'ection rate and fluid rheology corre$ponding to

the $pecified de$ign goal of placing the proppant of ma$$ 2Minto the formation. 6t thi$ $tage&

Mandxf are already $pecified and cei$ u$ually con$trained by technical limitation$7 i$

thu$ the only parameter that we can ad'u$t& which we do by changing the fluid rheology and

the in'ection rate.

general procedure for determining the proppant schedule is as follows5

1) Calculate the e4ponent of the proppant concentration cur!e :

2) Calculate the pad !olume and the time needed to pump it:

and


5/6

) Calculate the required proppant concentration (ma$$8unit in'ected $lurry !olume)cur!e& which i$ gi!en by

where cei$ the ma4imum proppant concentration of the in'ected $lurry.

9' -alculate the mass of proppant placed into one wing5

9) Calculate the propped width:

where pi$ the poro$ity of the proppant bed and pi$ the true den$ity of the proppant

material.

Note that in the abo!e procedure$& the in'ection rate qirefer$ to the slurry(not clean fluid)

in'ected into one wing. 0he obtained proppant ma$$& M& al$o refer$ to one wing. 0he

concentration$ are gi!en in ma$$ per unit !olume of $lurry& and any other type of

concentration (e.g.& added ma$$ to unit !olume of neat fluid) ha$ to be con!erted fir$t.

!ore complex proppant schedule procedures may ta*e into account proppant

movement (1oth in the lateral and the vertical directions', variations in the slurry

viscosity with time and location (due to temperature, shear rate and solid contentchanges', width required for free proppant movement, etc.

If the resulting propped width and also the amount of proppant differ from the

design goal, we may consider using another type of fluid and?or consider using

equipment providing a higher maximum proppant concentration.

Other design considerations2 )here are several other chec*s we have to conduct

during the initial treatment design. For instance, at the end of the pad injection,

the current hydraulic width should 1e large enough to accommodate proppant (a

width of three proppant diameters is considered sufficient'.


6/6

considera1le part of a treatments costs relate to pump horsepower. )he

product of surface treating pressure and injection rate provides the theoretically

required pumping power5

(3)

0he theoretical energy requirement i$ the power multiplied by in'ection time:

(4)

0o obtain the actual power and energy requirement$& we ha!e to account for the mechanical&

electrical and other efficiencie$ of the equipment.

)he predicted surface treating pressure is the sum of the closure pressure plus

the friction losses in the tu1ulars and through the perforations, minus the

hydrostatic head5

(5)

Pumping co$t$ $hould be a function of both the power and the energy requirement$.

(ll of the calculations outlined in this section can 1e easily programmed. "etting

up a customi4ed fracture0design program is advantageous when we need to

compare 1ids from different service companies or ma*e quic* decisions at the

location. It also helps us to understand the output and underlying approximations

of larger, more complex, fracture simulator software pac*ages.'

Documents

2. Basic Design