Numerical Optimization of Hydraulic Fracture Stage Placement in a Gas Shale Reservoir

The upstream oil and gas industry focuses increasingly on unconventional gas resources to maintain the level of its hydrocarbon reserves. To unlock the full potential of gas shale reservoirs, horizontal wells are drilled and active stimulation of the reservoirs, in the form of multi-stage hydraulic fracturing, is performed. This new technique has radically changed the energy future of the United States and is on the forefront of changing it in Europe as well. The hydraulic fracturing treatment is a costly, resource intensive and potentially environmentally dangerous procedure. The objective of this thesis is to create a realistic and versatile gas shale reservoir model and optimize the placement and number of hydraulic fracture stages along a horizontal well bore, thereby maximizing the production of gas while minimizing the amount of money that is spent to do so. On the basis of the computationally efficient ensemble based optimization of vertical well placement, an idea coined and investigated by Leeuwenburgh et al. (2010), it is postulated that numerical optimization can aid in finding the optimal placement of hydraulic fracture stages along a horizontal well bore in an equally computationally efficient manner. Three gradient-based optimization algorithms (Ensemble based Optimization: EnOpt (Chen, 2008), Simultaneous Perturbation Stochastic Approximation: SPSA (Spall, 1998) and finite difference gradient estimation) that work with continuous variables, are used to approximate the gradient. Because hydraulic fracture stage locations in a reservoir simulator are commonly treated as discrete variables (well grid block indices), standard implementations of gradient-based optimization are not applicable for optimal hydraulic fracture stage placement. We propose three distinct variable parameterizing placement methods to overcome the inherent continuous to discrete variables conversion issues. After the theoretical arguments about the strengths and weaknesses of the proposed optimization routines, both single well and multiple well scenario experiments are performed. Good results are obtained from the various experiments which favor an optimization with the EnOpt algorithm in combination with the fracture stage interval placement method.

Subject

optimization
hydraulic fracturing
multi-stage
hydraulic fracture
ensemble based optimization
horizontal well
well placement
stimulation
gas shale reservoir
shale gas

To reference this document use:

http://resolver.tudelft.nl/uuid:856057f2-24d4-4078-aa58-e0941b5b21c1

Part of collection

Student theses

Document type

master thesis

Rights

Files

PDF

msc_thesis_sam_holt.pdf

2.06 MB

Close viewer