450742 Optimization Models for Shale Gas Well Refracture Treatments
Optimization Models for Shale Gas Well
Markus G. Drouven1, Diego C. Cafaro2 and Ignacio E. Grossmann3
1,3Department of Chemical Engineering
Carnegie Mellon University
Pittsburgh, PA 15213, USA
2INTEC (UNL CONICET)
Güemes 3450, 3000 Santa Fe, Argentina
Shale gas wells are well-known for their characteristically steep decline curves. In fact, some shale wells produce more than half of their total estimated ultimate recovery (EUR) within the first year of operation. The initial production peak after well completion is caused by the sudden release of previously trapped hydrocarbons in the pores of the reservoir. The subsequent decline is ultimately driven by pressure depletion and the ultra-low permeability of the shale play. Upstream operators oftentimes struggle with the production decline curves. For one, they are contractually obligated to providing steady gas deliveries to midstream distributors over time which is difficult to accomplish given the characteristic, dramatic production decline immediately after wells are turned in line. Moreover, as Cafaro and Grossmann  suggest and Drouven and Grossmann  confirm, operators need to maximize the utilization of production and gathering equipment such as pipelines and compressors in order to stay profitable. In reality, however, production and gathering equipment is usually sized based on the initially high production rates. This means that within a matter of months shale gas wells feed into oversized pipelines and compressor stations, and equipment utilization drops. Worse even, in order to satisfy contractual gas delivery agreements, operators see themselves forced to open up new wells continuously to honor their obligations, and hence the process is repeated over and over again.
Refracturing presents a promising strategy for addressing the characteristically steep decline rates of shale gas wells . The core idea behind refracturing is to restimulate the reservoir such that it yields previously untapped hydrocarbons and improves the overall production profile of a well. Whether or not a refracture treatment will reinvigorate a shale gas well depends on a number of factors including the characteristics of the reservoir and the initial completion design. Historically, refracture treatments have been applied predominantly to shale gas wells suffering from low production rates due to known suboptimal initial stimulations and completions. However, Dozier et al.  argue that even wells with effective initial treatments have shown significant production improvements when restimulated after an initial period of production and partial reservoir depletion.
The problem addressed in this paper can be stated as follows. We assume that a candidate shale gas well has been identified for refracturing. For this well, a long-term production forecast as well as the production profile after additional refracture treatments at any point in time over the planning horizon is given. A gas price forecast along with expenses for drilling, fracturing, completions and refracturing operations are also available as problem data. The problem is to determine: (a) whether or not the well should be refractured, (b) how often the well should be refractured over its entire lifespan, and (c) when exactly the refracture treatments should be performed. The objective is to maximize either: (a) the estimated ultimate recovery (EUR) of the well, or (b) the net present value (NPV) of the well development project.
First, we present a continuous-time nonlinear programming (NLP) model to determine whether or not a shale gas well should be refractured, and when to schedule the refracture treatment. The proposed NLP model relies on the assumption that the well productivity profile follows a decreasing power function of time. To predict well performance prior to and after a refracture treatment, we propose an effective forecast function that mimics real-life curves. Next, we extend the proposed framework to allow for multiple refracture treatments and present a discrete-time mixed-integer linear programming (MILP). In an attempt to reduce solution times to a minimum, we compare three alternative formulations against each other (big-M formulation, disjunctive formulation using Standard and Compact Hull-Reformulations) and find that the disjunctive models yield the best computational performance. Finally, we apply the proposed MILP model to two case studies to demonstrate how refracturing can increase the expected recovery of a well and improve its profitability by several hundred thousand USD.
 Cafaro, D. C.; Grossmann, I. E. Strategic Planning, Design, and Development of the Shale Gas Supply Chain Network. AIChE J. 2014. doi: 10.1002/aic.14405.
 Drouven, M. G.; Grossmann, I. E. Multi-Period Planning, Design and Strategic Models for Long-Term Quality-Sensitive Shale Gas Development. AIChE J. 2016 (accepted for publication).
 Jacobs T. Renewing Mature Shale Wells Through Refracturing. SPE News. 2014, May Issue.
 Dozier, G., Elbel, J., Fielder, E., Hoover, R., Lemp, S., Reeves, S., Siebrits, E., Wisler, D., Wolhart, S., Refracturing works. Oilfield Review. 2003; 10(8):38-53.