Category: OnPlan

Brief

pengtools onPlan

onPlan is a fracture simulation tool for designing a hydraulic fracture treatment.

onPlan is developed under cooperation agreement between pengtools and Moscow Institute of Physics and Technology Oil&Gas Center LLC.

onPlan utilizes the Planar3D class model with advanced numerical optimization which allows to achieve high accuracy in predicting fracture geometry and fast simulation time.

onPlan integrates the Unified Fracture Design^[1] concept which enables comparison of the designed frac geometry with the optimal one to maximize the performance of the fractured well.

onPlan is available online at www.pengtools.com.

Typical applications

Simulation of the single vertical well fractures in low stress contrast environments with a high risk of fracture breakthrough into overlying gas or underlying water
Optimization of hydraulic fracturing with Unified Fracture Design^[1]
Understanding post-fracturing production performance
Sensitivity studies

Main features

Fracture design charts: height, width, length, pressure vs time; height vs width; width vs length; height vs length. All showing propped and hydraulic values.
Fracture design Type Curves (Plot of J_D as a function of C_fD using I_x and N_p as parameter) showing the current fracture design and the optimal one.
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.
Proppant catalog with predefined proppant properties.
Users reference data for benchmarking vs actual.
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

Math & Physics

Basic equations of Planar3D model:

P(x,y)=-\frac{E}{8\pi(1-\nu^2)}\Delta \int \limits_{\Omega}^{}\frac{h(x^', y^')dx^'dy^'}{ \sqrt{((x-x^')^2+(y-y^')^2}}

( 1 ) - elastic reaction of formation

\frac{\partial}{\partial t} h C_i + div q_i = v_i

,

V_p = V_p + \Delta V

( 2 ) - 2D equation of multifluid flow and proppant transport

The model accounts for the effect of proppant bridging and gravitational setting.

Type Curves

The Type Curves shows the dimensionless productivity index, J_D, at steady and pseudo-steady state as 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”^[2]. 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 ^[2]. 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.

Flow Diagram

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=\frac{M_{prop}}{Out Zone Growth} \frac{h_{net}}{h_{gross}}

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}

h_f=h_{gross} * Out Zone Growth

the fracture height

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 ^[2]:

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^[2].

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) ^[2].

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)^[2]. N=3 in the optiFrac.