Cheng, Cheng
(2015)
Energy-based approach for rapid stimulation of interacting hydraulic fractures.
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
Currently, every oil and gas industry operator’s motivation is aimed toward attaining optimized, low-cost horizontal well completions. The goal is typically to generate uniform, simultaneously-growing hydraulic fractures from 3-6 initiation/entry sites that are spacingd within a certain interval of the wellbore comprising a so-called “stage”. Due to the stress interaction among growing hydraulic fractures, however, it is hard to stimulate all hydraulic fractures to grow simultaneously in the array. This phenomenon, referred to as a stress shadow, inhibits the growth of inner fractures and favors the growth of outer fractures in the array. Recently, we created a new hydraulic fracture simulator, C2Frac,which very rapidly simulates the growth of an array of hydraulic fractures. The simulation helps reduce the negative effects of stress shadow by determining an optimal perforation spacing. In this model, the fractures created from all perforation clusters were restricted to radial, planar growth. This coupled mathematical model uses the power estimate, asymptotic solutions, and local integration to develop a relationship between the fluid flow entering the well bore and friction pressure drop that approximately accounts for the stress interaction between fractures. Utilizing this relationship, C2Frac can determine how the radius, width, pressure, and total fracture area evolve with time and compare them with a fully coupled benchmark model. The solution is found to be sufficiently accurate for practical purposes and C2Frac completes the calculation in less than 2 seconds compared with the benchmark model that took approximately 1 week to solve the same problem.
Perforation loss, that is, the pressure drop of fluid through the perforation tunnel on the casing, is another important but sometimes neglected effect on fracture growth. So we add the perforation loss into C2Frac to simulate how perforation loss influence the total fracture surface area obtained from a growing array of hydraulic fractures that are impacted by the stress shadow effect. Our results show the potential of proper perforation diameter and number to double the fracture surface area generated by a given injected fluid volume though minimizing the negative effect of interaction. This approach is known as “limited entry design”. The investigation concludes with devising limited entry design and optimal spacing for different numbers of entry points.
In summary, C2Frac is shown to provide useful approximation to the growth of arrays of hydraulic fractures under the influence of stress shadow and limited entry. By using a novel energetic approach to account for the coupling among the hydraulic fractures and through judicious use of asymptotic, approximate solutions, C2Frac computes in 10-6-10-5 of the computation time required by the most efficient existing model that fully solves the coupled problem. This enables completion optimization because over a thousand trial cases can be run in a single hour of computation in order to search for the best completion configuration, whereas existing models would require tens of years of processor time to perform the same task.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
4 June 2015 |
| Date Type: |
Publication |
| Defense Date: |
25 March 2015 |
| Approval Date: |
4 June 2015 |
| Submission Date: |
27 March 2015 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
66 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Swanson School of Engineering > Chemical and Petroleum Engineering |
| Degree: |
MSPE - Master of Science in Petroleum Engineering |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Hydraulic Fracturing; Horizontal Well Completions; Perforating; Limited Entry; Fracture Modeling |
| Date Deposited: |
04 Jun 2015 13:41 |
| Last Modified: |
15 Nov 2016 14:26 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/24187 |
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