(527g) Optimization Models for Shale Gas Well Refracture Treatments

 Optimization Models for Shale Gas Well

Refracture Treatments

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

¹mdrouven@cmu.edu, ²dcafaro@fiq.unl.edu.ar ³grossmann@cmu.edu

Abstract

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 [1]
suggest and Drouven and Grossmann[2] 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 [3]. 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. [4] 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.

References

[1] 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. 

[2] 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).

[3] Jacobs T. Renewing Mature Shale Wells
Through Refracturing. SPE News. 2014, May Issue.

[4] 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.