Difference between revisions of "Category: FracDesign"

Latest revision as of 06:49, 10 December 2018

Brief

pengtools fracDesign

fracDesign is a software for designing a hydraulic fracture treatment in pengtools.

For the given set of reservoir, fluid and proppant properties fracDesign calculates the pumping schedule which will create the optimal fracture geometry to achieve maximum well’s productivity.

fracDesign algorithm is based on widely used fracture PKN and KGD models (see ^[1]). Pumping schedule realizes the optimal fracture geometry and assures uniform placement of the proppant (see ^[2]). If the optimum placement cannot be realized by traditional means, a TSO design option is available. Like any other model fracDesign inevitably uses a number of mathematical idealizations.

fracDesignis available online at www.pengtools.com.

Typical applications

Calculating the pumping schedule required to achieve optimal fracture geometry in design mode
Providing the input pumping schedule for more complex fracture simulators to use as a fracture design starting point (initial guess)
Optimization of hydraulic fracture design with Unified Fracture Design^[2]
TSO design for high permeable and soft formations where high fracture flow conductivity (width) is needed
Simulation of the fracture geometry based on the given pumping schedule with PKN and KGD models in simulation mode
Sensitivity studies: By modifying various input parameters, an intuitive feel for their relative importance in treatment design and final fractured well performance can be rapidly acquired

Math & Physics

w_{f,hydr,max,PKN}=9.15^{\frac{1}{(2 + 2 n)}}\ 3.98^{\frac{n}{(2 + 2 n)}}\ \left ( \frac{1+2.14n}{n}\right )^{\frac{n}{(2 + 2 n)}}\ K^{\frac{1}{(2 + 2 n)}}\ \left ( \frac{q_i^n h_f^{1-n} x_f}{E'} \right )^{\frac{1}{(2 + 2 n)}}

- hydraulic maximum fracture width PKN (ref^[1] eq 9.53)

w_{f,hydr,max,KGD}=11.1^{\frac{1}{(2 + 2 n)}}\ 3.24^{\frac{n}{(2 + 2 n)}}\ \left ( \frac{1+2n}{n}\right )^{\frac{n}{(2 + 2 n)}}\ K^{\frac{1}{(2 + 2 n)}}\ \left ( \frac{q_i^n x_f^2}{h_f^n E'} \right )^{\frac{1}{(2 + 2 n)}}

- hydraulic maximum fracture width KGD (ref^[1] eq 9.55)

E'=\frac{E}{1-\nu^2}

- plain strain modulus

w_{f,hydr,avg} = w_{f,hydr,max} * \gamma

- hydraulic average fracture width

\gamma_{PKN}=\frac{\pi}{5}

- shape factor PKN (ref^[1] eq 9.10)

\gamma_{KGD}=\frac{\pi}{4}

- shape factor KGD (ref^[1] eq 9.24)

w_{f,prop}=\frac{M_{prop}}{2 x_f h_f (1-\phi_{prop}) \rho_{prop}}

- propped fracture width

V_i = V_f + V_L

- mass balance equation (ref^[1] eq 8.1)

V_i = q_i t_e

- injected volume into one fracture wing

A_f = x_f h_f

- the area of one face of one wing for rectangular fracture shape

A_f = x_f h_f \frac{\pi}{4}

- the area of one face of one wing for elliptic fracture shape

V_f = A_f w_{hydr,avg}

- volume of fluid contained in one fracture wing

V_L = K_L 2 A_f C_L \sqrt{t} + 2 A_f S_p

- volume of fluid leak-off to formation through the two created fracture surfaces of one wing

q_i t = A_f w_{hydr,avg} + K_L 2 A_f C_L \sqrt{t} + 2 A_f S_p

- mass balance equation (ref^[2] eq 4.6)

\eta = \frac{V_f}{V_i}

- fluid efficiency

Opening time distribution factor K_L

Nolte opening time distribution factor K_L

2 K_L=\frac{8}{3} \eta + ( 1 - \eta) \pi

- (ref^[1] eq 8.36)

Carter opening time distribution factor K_L

K_L=-\frac{S_p}{C_L \sqrt{t_e}} - \frac{w_{f,hydr,avg}}{2C_L\sqrt{t_e}} + \frac{w_{f,hydr,avg}}{2 \eta C_L \sqrt{t_e}}

(ref ^[2] eq 4.8)

where:

\eta=\frac{w_{f,hydr,avg}(w_{f,hydr,avg}+2S_p)}{4\pi {C_L}^2 t_e} \left ( exp(\beta^2) erfc(\beta) + \frac{2\beta}{\sqrt\pi} - 1 \right )

(ref ^[2] eq 4.9)

and:

\beta=\frac{2C_L \sqrt{\pi t_e}}{w_{f,hydr,avg} + 2S_p}

(ref ^[2] eq 4.9)

Nolte G-function for opening time distribution factor K_L

g_0(\alpha)=\frac{2 + 2.06798 \alpha + 0.541262 \alpha^2 + 0.0301598 \alpha^3}{1 + 1.6477 \alpha + 0.738452 \alpha^2 + 0.0919097 \alpha^3 + 0.00149497 \alpha^4}

(ref ^[2] eq 4.12)

where:

\alpha_{PKN} =\frac{2n+2}{2n+3}

\alpha_{KGD} =\frac{n+1}{n+2}

Pumping schedule

According to Nolte^[3] the schedule is derived from the following assumptions:

the whole length created should be propped
at the end of pumping, the proppant distribution in the fracture should be uniform
the proppant schedule should be of the form of a delayed power law with the Nolte's exponent and the fraction of pad being equal

\epsilon= \frac{1-\eta}{1+\eta}

- Nolte exponent

t_{pad}=\epsilon t_e

- pad pumping time

c_e=\frac{M_{prop}}{2\eta V_i}

- proppant concentration at the end of pumping

c=c_e \left ( \frac{t-t_{pad}}{t_e-t_{pad}} \right )^{\epsilon}

- slurry concentration vs time

dt_{stage}=\frac{t_e - t_{pad}}{N_{stages}}

- ramping stage duration

c_{stage} = \frac {\int \limits_{t_{start}}^{t_{end}} c_e \left ( \frac{t-t_{pad}}{t_e-t_{pad}} \right )^{\epsilon} dt}{t_{end}-t_{start}}

- ramping stage slurry concentration

c_a=\frac{c}{1-\frac{c}{\rho_{prop}}}

- conversion form slurry concentration (proppant mass per unit of injected slurry) to clean concentration (proppant mass per unit of injected clean/base/"neat" fluid)

Flow Diagram

Design mode

Simulation mode

Workflow

Design mode

Input the fracture height, h_f
Run optiFrac to get optimum x_f and w_{f, prop}
Calculate maximum and average hydraulic fracture widths : w_f,hydr,max and w_f,hydr,avg
Calculate opening time distribution factor, K_L
Solve mass balance equation for total pumping time, t_e
Calculate fluid efficiency, η
Calculate Nolte's exponent, ε
Calculate pad time, t_pad
Calculate proppant concentration at the end of pumping, c_e
Calculate slurry concentration vs time curve, c vs t
Set the number of stages, N_stage
Calculate slurry concentration at each stage, c_stage

Simulation mode

Input the fracture height, h_f
Input the pumping schedule, dt, c_stage for each N_stage
For each stage duration, dt
1. Set the x_f
2. Calculate maximum and average hydraulic fracture widths : w_f,hydr,max and w_f,hydr,avg
3. Calculate opening time distribution factor, K_L
4. Solve mass balance equation for total pumping time, t_stage
5. Iterate until t_stage=dt
Move to the next stage

Note that: Distribution of the proppant in the fracture is not modelled in the simulation mode. Only geometry evolution and byproducts are simulated under assumption that proppant is uniformly distributed in fracture.

TSO Design

TSO effect is supported by the fracDesign using the TSO Design option.

TSO occurs when dry-to-wet fracture width ratio, δ, is becoming larger than some critical value set by the user.

Dry-to-wet fracture width ratio, δ, is specified by user in the Fracture tuning input section. The value near 0.7 is recommended in Economides, Oligney, Valko (2002).

If TSO Design option is ON and during conventional design critical dry-to-wet width ratio, δ, was reached fracture length stop to grow and width became a function of injected proppant. Then we add additional step with injected concentration equivalent to critical dry-to-wet width ratio. Duration of this step is calculated in order to place all the proppant.

If TSO Design option is OFF and during conventional design critical dry-to-wet width ratio, δ, was reached we stop addition of proppant at this place and show the warning message:

”Tip screen-out occurs. Not all the proppant is placed. Try TSO design.”

Also if concentration of injected slurry became larger then defined by user maximum concentration we stop addition of proppant and show the warning message:

”Maximum concentration reached. Not all the proppant is placed. Try TSO design”

Comparison study

1. fracDesign Comparison Study 1 Warpinski. The fracDesign calculates 4 cases described in the paper and shows good agreement in results.

Main features

PKN and KGD fracture geometry models
optiFrac workflow on fracture geometry optimization
Slurry concentration versus time pumping schedule as plot and table
Fracture length and width profiles vs time plots
Net pressure profiles vs time as plot and table
Practical pumping constrains and Fracture tuning options
Detailed output table with calculated fracture design parameters
Sensitivity option with benchmark to potential
Simulation mode: calculating the fracture geometry from the given pumping schedule
Hydraulic fracturing proppant catalog with predefined proppant properties.
"New model" button resets input values to the default values.
Switch between Metric and Field units.
Save/load models to the files and to the user’s cloud.
Export pdf report containing input parameters, calculated values and the chart.
Share models to the public cloud or by using model’s link.
Continue your work from where you stopped: last saved model will be automatically opened.
Download the chart as an image or data and print (upper-right corner chart’s button).

Nomenclature

A

= surface area, m²

c_a

= clean concentration (proppant mass per unit of injected clean/base/"neat" fluid), kg/m³

C_L

= leak-off coefficient, m/s^0.5

c

= slurry concentration (proppant mass per unit of injected slurry), kg/m³

dt

= time step, sec

E'

= plain strain modulus, Pa

E

= Young's Modulus, Pa

h

= height, m

K_L

= opening time distribution factor, dimensionless

K

= rheology consistency index, Pa*sⁿ

M

= mass, kg

n

= rheology flow behavior index, dimensionless

q

= slurry injection rate for one wing, m³/sec

S_p

= spurt loss coefficient, m

t

= pumping time, sec

V

= volume, m³

w

= width, m

x_f

= fracture half-length, m

Greek symbols

\delta

= dry to wet width ratio at the end of pumping, usually 0.5-0.7

\epsilon

= Nolte exponent, dimensionless

\eta

= fluid efficiency, fraction

\gamma

= geometric factor in vertical direction, dimensionless

\nu

= Poisson's ratio, dimensionless

\phi

= porosity, fraction

\pi

= 3.1415

\rho

= density, kg/m³

Subscripts

avg = average

e = end of pumping

f = fracture

gross = gross

hydr = hydraulic

i = injected

KGD = Khristianovic-Geertsma-de Klerk geometry

L = leak-off

max = maximum

net = net

pad = pad

PKN = Perkins-Kern-Nordgren geometry

prop = propped or proppant

r = reservoir

References

↑ ^1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 Valko, Peter; Economides, Michael J. (1995). Hydraulic fracture mechanics. Texas A & M University: John Wiley and Sons.
↑ ^2.0 ^2.1 ^2.2 ^2.3 ^2.4 ^2.5 ^2.6 Economides, Michael J.; Oligney, Ronald; Valko, Peter (2002). Unified Fracture Design: Bridging the Gap Between Theory and Practice. Alvin, Texas: Orsa Press.
↑ Nolte, K.G. (1986). "Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline" (SPE-13278-PA). Society of Petroleum Engineers.

Pages in category "FracDesign"

The following 8 pages are in this category, out of 8 total.

T

[HFM1995-1] 1.0 ^1.1 ^1.2 ^1.3 ^1.4 ^1.5 ^1.6 Valko, Peter; Economides, Michael J. (1995). Hydraulic fracture mechanics. Texas A & M University: John Wiley and Sons.

[UFD2002-2] 2.0 ^2.1 ^2.2 ^2.3 ^2.4 ^2.5 ^2.6 Economides, Michael J.; Oligney, Ronald; Valko, Peter (2002). Unified Fracture Design: Bridging the Gap Between Theory and Practice. Alvin, Texas: Orsa Press.

[Nolte1986-3] Nolte, K.G. (1986). "Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline" (SPE-13278-PA). Society of Petroleum Engineers.

[1]

[2]

[3]

@@ Line 4: / Line 4: @@
 [[File:fracDesign_i.png|thumb|right|200px|link=https://www.pengtools.com/fracDesign|pengtools fracDesign]]
-[[:category:fracDesign | fracDesign]] is a tool for designing a hydraulic fracture treatment in [[:category:pengtools | pengtools]].
+[[:category:fracDesign | fracDesign]] is a software for designing a hydraulic fracture treatment in [[:category:pengtools | pengtools]].
 For the given set of reservoir, fluid and proppant properties [[:category:fracDesign | fracDesign]] calculates the pumping schedule which will create the optimal fracture geometry to achieve maximum well’s productivity.
+[[:category:fracDesign | fracDesign]] algorithm is based on widely used fracture PKN and KGD models (see <ref name=HFM1995/>). Pumping schedule realizes the optimal fracture geometry and assures uniform placement of the proppant (see <ref name=UFD2002/>). If the optimum placement cannot be realized by traditional means, a TSO design option is available. Like any other model [[:category:fracDesign | fracDesign]] inevitably uses a number of mathematical idealizations.
 [[:category:fracDesign | fracDesign]]is available online at [https://www.pengtools.com www.pengtools.com].
@@ Line 12: / Line 14: @@
 == Typical applications ==
-* Design mode: Calculating the pumping schedule required to achive optimal fracture geometry
+* Calculating the pumping schedule required to achieve optimal fracture geometry in design mode
+* Providing the input pumping schedule for more complex fracture simulators to use as a fracture design starting point (initial guess)
 * Optimization of hydraulic fracture design with '''Unified Fracture Design'''<ref name=UFD2002/>
-* Simulation mode: Simulation of the fracture geometry based on the given pumping schedule with PKN and KGD models
+* TSO design for high permeable and soft formations where high fracture flow conductivity (width) is needed
-* Sensitivity studies
+* Simulation of the fracture geometry based on the given pumping schedule with PKN and KGD models in simulation mode
+* Sensitivity studies: By modifying various input parameters, an intuitive feel for their relative importance in treatment design and final fractured well performance can be rapidly acquired
 ==Math & Physics==
@@ Line 127: / Line 131: @@
 # Input the fracture height, '''h<sub>f</sub>'''
 # Input the pumping schedule, '''dt, c<sub>stage</sub> for each N<sub>stage</sub>'''
-# Input the pumping schedule, '''dt, c<sub>stage</sub> for each N<sub>stage</sub>'''
+# For each stage duration, '''dt'''
-# For each stage duration, '''dt''', iterate until '''t<sub>stage</sub>=dt'''
 ## Set the '''x<sub>f</sub>'''
 ## Calculate maximum and average hydraulic fracture widths : '''w<sub>f,hydr,max</sub>''' and '''w<sub>f,hydr,avg</sub>'''
 ## Calculate opening time distribution factor, '''K<sub>L</sub>'''
 ## Solve mass balance equation for total pumping time, '''t<sub>stage</sub>'''
+## Iterate until '''t<sub>stage</sub>=dt'''
 # Move to the next stage
+Note that: Distribution of the proppant in the fracture is not modelled in the simulation mode. Only geometry evolution and byproducts are simulated under assumption that proppant is uniformly distributed in fracture.
+==TSO Design==
+[[TSO effect]] is supported by the [[:category:fracDesign| fracDesign]] using the '''TSO Design''' option.
+[[TSO effect| TSO]] occurs when dry-to-wet fracture width ratio, '''&delta;''', is becoming larger than some critical value set by the user.
+Dry-to-wet fracture width ratio, '''&delta;''', is specified by user in the Fracture tuning input section. The value near 0.7 is recommended in Economides, Oligney, Valko (2002).
+If '''TSO Design''' option is '''ON''' and during conventional design critical dry-to-wet width ratio, '''&delta;''', was reached fracture length stop to grow and width became a function of injected proppant. Then we add additional step with injected concentration equivalent to critical dry-to-wet width ratio. Duration of this step is calculated in order to place all the proppant.
+If '''TSO Design''' option is '''OFF''' and during conventional design critical dry-to-wet width ratio, '''&delta;''', was reached we stop addition of proppant at this place and show the warning message:
+ ”Tip screen-out occurs. Not all the proppant is placed. Try TSO design.”
+Also if concentration of injected slurry became larger then defined by user maximum concentration we stop addition of proppant and show the warning message:
+ ”Maximum concentration reached. Not all the proppant is placed. Try TSO design”
 ==Comparison study==
+[[File:Warpinski 1 Net Pressure.png|300px| Net Pressure]]
+. [[fracDesign Comparison Study 1 Warpinski]]. The [[:category:fracDesign | fracDesign]] calculates 4 cases described in the paper and shows good agreement in results.
 ==Main features==
@@ Line 147: / Line 175: @@
 * Sensitivity option with benchmark to potential
 * Simulation mode: calculating the fracture geometry from the given pumping schedule
+* [[Hydraulic fracturing proppant catalog]] with predefined proppant properties.
 * "New model" button resets input values to the default values.
 * Switch between Metric and Field units.
@@ Line 157: / Line 186: @@
 ==Nomenclature==
-:<math>w</math> = width, m
-:<math>n</math> = rheology flow behavior index, dimensionless
-:<math>K</math> = rheology consistency index, Pa*s<sup>n</sup>
-:<math>q</math> = slurry injection rate for one wing, m<sup>3</sup>/sec
-:<math>h</math> = height, m
-:<math>x_f</math> = fracture half-length, m
-:<math>E</math> = Young's Modulus, Pa
-:<math>E'</math> = plain strain modulus, Pa
-:<math>M</math> = mass, kg
-:<math>V</math> = volume, m<sup>3</sup>
 :<math>A</math> = surface area, m<sup>2</sup>
-:<math>t</math> = pumping time, sec
+:<math>c_a</math> = clean concentration (proppant mass per unit of injected clean/base/"neat" fluid), kg/m<sup>3</sup>
+:<math>C_L</math> = leak-off coefficient, m/s<sup>0.5</sup>
+:<math>c</math> = slurry concentration (proppant mass per unit of injected slurry), kg/m<sup>3</sup>
 :<math>dt</math> = time step, sec
+:<math>E'</math> = plain strain modulus, Pa
+:<math>E</math> = Young's Modulus, Pa
+:<math>h</math> = height, m
 :<math>K_L</math> = opening time distribution factor, dimensionless
-:<math>C_L</math> = leak-off coefficient, m/s<sup>0.5</sup>
+:<math>K</math> = rheology consistency index, Pa*s<sup>n</sup>
+:<math>M</math> = mass, kg
+:<math>n</math> = rheology flow behavior index, dimensionless
+:<math>q</math> = slurry injection rate for one wing, m<sup>3</sup>/sec
 :<math>S_p</math> = spurt loss coefficient, m
-:<math>c</math> = slurry concentration (proppant mass per unit of injected slurry), kg/m<sup>3</sup>
+:<math>t</math> = pumping time, sec
-:<math>c_a</math> = clean concentration (proppant mass per unit of injected clean/base/"neat" fluid), kg/m<sup>3</sup>
+:<math>V</math> = volume, m<sup>3</sup>
+:<math>w</math> = width, m
+:<math>x_f</math> = fracture half-length, m
 ===Greek symbols===
 :<math>\delta</math> = dry to wet width ratio at the end of pumping, usually 0.5-0.7
+:<math>\epsilon</math> = Nolte exponent, dimensionless
+:<math>\eta</math> = fluid efficiency, fraction
 :<math>\gamma</math> = geometric factor in vertical direction, dimensionless
 :<math>\nu</math> = Poisson's ratio, dimensionless
@@ Line 183: / Line 214: @@
 :<math>\pi</math> = 3.1415
 :<math>\rho</math> = density, kg/m<sup>3</sup>
-:<math>\eta</math> = fluid efficiency, fraction
-:<math>\epsilon</math> = Nolte exponent, dimensionless
 ===Subscripts===
+:avg = average
 :e = end of pumping
 :f = fracture
 :gross = gross
+:hydr = hydraulic
+:i = injected
+:KGD = Khristianovic-Geertsma-de Klerk geometry
+:L = leak-off
 :max = maximum
 :net = net
+:pad = pad
+:PKN = Perkins-Kern-Nordgren geometry
 :prop = propped or proppant
 :r = reservoir
-:hydr = hydraulic
-:prop = propped
-:PKN = Perkins-Kern-Nordgren geometry
-:KGD = Khristianovic-Geertsma-de Klerk geometry
-:avg = average
-:i = injected
-:L = leak-off
-:pad = pad
 ==References==
@@ Line 242: / Line 270: @@
 [[Category:pengtools]]
+{{#seo:
+|title=Hydraulic Fracturing Design and Simulation Software
+|titlemode= replace
+|keywords=design, optimization, performance, hydraulic fracturing, hydraulic fracturing formulas, hydraulic fracturing proppant, hydraulic fracturing liquids, petroleum engineering
+|description=Hydraulic fracturing formulas for frac design and simulation in fracDesign software at pengtools.com
+}}

Navigation menu

Navigation

Categories

Products

Difference between revisions of "Category: FracDesign"

Latest revision as of 06:49, 10 December 2018

Contents

Brief

Typical applications