Category: OptiFrac

1 Fracturing Optimization Software
2 Typical applications
3 Math & Physics
4 Fracturing Design Optimization Type Curves
5 Fracturing Optimization Flow Diagram
6 Fracturing Optimization Workflow
7 Fracturing Physical Constraints
- 7.1 Maximum net pressure
- 7.2 Minimum fracture width
8 Main features
9 Nomenclature
10 References

Fracturing Optimization Software

pengtools optiFrac

optiFrac is a single well fracture design optimization software.

For the given set of reservoir and proppant properties optiFrac calculates maximum achievable well productivity index (JD) and required fracture geometry.

In production optimization of hydraulic fracturing, it is important to recognize that for a fixed proppant volume, fracture length and fracture width compete to each other. Consequently, there is an optimum fracture length and width that would maximize the dimensionless productivity index of the fractured well ^[1]. Unified Fracture Design provides a methodology whereby for any given proppant volume the best combination of width and length could be determined ^[2].

optiFrac is available online at www.pengtools.com and in AppStore for iPad.

Typical applications

Single fracture design
Optimization of hydraulic fracturing with Unified Fracture Design^[2] method
Calculating optimum fracture design parameters:
- Dimensionless productivity index, J_D .
- Dimensionless fracture conductivity, C_fD .
- Fracture half length, x_f .
- Fracture width, w_f .
- Fracture penetration, I_x .
Understanding post-fracturing production performance
Sensitivity studies

Math & Physics

Fracture Notation

I_x=\frac{2x_f}{x_e}

- penetration ratio ^[2],

C_{f_D}=\frac{k_f w_f}{k x_f}

- dimensionless fracture conductivity ^[2],

N_p={I_x}^2 C_{f_D} = \frac{4 k_f x_f w_f}{k {x_e}^2} = \frac{4 k_f x_f w_f h}{k {x_e}^2 h} = \frac{2 k_f V_f}{k V_r}

- proppant number ^[2],

{\bar{P}_D}^{pss} = \frac{1}{2} ln{\left (\frac{16}{1.78 C_A {I_x}^2} \right )} + f

- pseudo-steady state equation for finite-conductivity fractured wells ^[1],

{\bar{P}_D}^{ss} = \frac{1}{2} ln{\left (\frac{26.4}{1.78 C_A {I_x}^2} \right )} + f

- steady state equation for finite-conductivity fractured wells ^[1],

C_{A}=7.7327 {I_x}^3 - 25.204 {I_x}^2 - 0.7211 I_x + 30.555

- shape factor ^[1].

Fracturing Design Optimization Type Curves

The Type Curves show the dimensionless productivity index, J_D, at steady and pseudo-steady state as a function of C_fD, using I_x as parameter (red curves) and overlapping with the type curve with N_p as parameter (black curves).

The green curve along the maximum points for different N_p values is “Design Optimization Curve”^[1]. This curve represents the target of the designs of the fracture treatments in a dimensionless form.

Type Curves were obtained, through seven hundred runs with a numerical simulator, modeling a fractured well in a closed square reservoir ^[1]. For infinite and finite fracture conductivities, the shape factors, C_A, can be calculated if the P_D is known for a specific value of I_x. The P_D value obtained by numerical simulations. After knowing C_A (which would be a function of I_x), f-function values can be calculated if P_D is known for a specific dimensionless fracture conductivity C_fD and fracture penetration I_x.

Fracturing Optimization Flow Diagram

Fracturing Optimization Workflow

Fracture Plane Dimensions

1. Calculate the N_p:

V_r=h_{net} {x_e}^2

the volume of the reservoir

k_f=k_{prop} * Gel Damage

the fracture permeability

M_f=M_{prop} \frac{h_{net}}{h_f}

the proppant mass in the pay zone

V_f=\frac{M_f}{SG_{prop} (1 - \phi_{prop})}

the fracture volume in the pay zone

N_p=\frac{2 k_f V_f}{k V_r}

the proppant number

2. Read C_fD^opt, I_x^opt, J_D^opt from the Design Optimization Curve of the Type Curve

3. Calculate optimum fracture half-length and width:

{x_f}^{opt}=0.5 x_e {I_x}^{opt}

{w_f}^{opt}=\frac{{C_{fD}}^{opt} {x_f}^{opt} k}{k_f}

Fracturing Physical Constraints

It is important to mention that the Design Optimization Curve could give unrealistic fracture geometry depending on the reservoir permeability, reservoir mechanical properties and target N_p. The two most common scenarios are ^[1]:

The required net pressure for the fracture geometry is too high - “maximum net pressure curve”,
Fracture width is too small (fracture too narrow) - “minimum width curve”.

The area between the “minimum width curve” and the “maximum net pressure curve” is the “working area” (highlighted in yellow) of the whole type curve for the specific rock mechanical properties, reservoir and proppant properties used. Any fracture design for this specific case should be located on the “optimum design curve” anywhere in this working area depending on the desired N_p^[1].

Maximum net pressure

The maximum net pressure during the fracturing treatment should provide a surface pressure less than a certain value (which is surface pressure operational limit) ^[1].

w_{max}=\frac{2 P_{net} h_f (1 - \nu^2)}{E}

w=w_{max} \frac{\pi}{4} \gamma \delta

Minimum fracture width

Fracture propped width should be greater than N times mean proppant diameter (to provide at least N proppant layers in the fracture after closure)^[1]. N=3 in the optiFrac.

Main features

Fracture design Type Curves (Plot of J_D as a function of C_fD using I_x and N_p as parameter).
Design Optimization Curve which corresponds to the maximum J_D values for different N_p.
Design Optimum Point at which J_D is maximized for the given proppant, fracture and reservoir parameters.
Physical constraints envelope.
Hydraulic fracturing proppant catalog with predefined proppant properties.
Users Data Worksheet for benchmarking vs actual.
"Default values" 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
Share models to the public cloud or by using model’s link
Export pdf report containing input parameters, calculated values and plots
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)
Export results table to Excel or other application