(735d) Mixed-Integer Programming Models for Long-Term, Quality-Sensitive Shale Gas Development

 Mixed-Integer Programming Models for Long-Term, Quality-Sensitive Shale
Gas Development

Markus
G. Drouven¹ and Ignacio E. Grossmann²

Department of Chemical Engineering

Carnegie Mellon University

Pittsburgh, PA 15213

¹mdrouven@cmu.edu, ²grossmann@cmu.edu

Abstract

The
production of shale gas from unconventional resource plays is transforming the energy
landscape in the United States. Advances in production technologies, notably
the dual application of horizontal drilling and hydraulic fracturing, allow the
extraction of vast deposits of trapped natural gas that, until recently, were
uneconomic to produce. The Energy Information Administration predicts that
shale gas will account for 50% of total U.S. natural gas production by 2040 [1]. Natural gas
demand is also expected to increase in the electric power and nearly all other industrial
sectors. The future development of shale gas resources requires an extensive expansion
of the existing gas production, transmission, and processing infrastructure.
Virtually all stages of the shale gas supply chain need to be expanded and upgraded
to match the ever growing natural gas supply and demand [3]. Since the
necessary capital investments for drilling rigs, pipelines, boosting stations and
midstream processing facilities are substantial, the long-term planning of
upstream production and natural gas transmission is a key challenge.

The
problem addressed in this work can be stated as follows. Within a potential
shale gas development area an upstream operator has identified a set of
candidate well pads from which shale gas may or may not be extracted. To
extract the gas the operator can develop, i.e., drill and fracture a limited
number of wells at every candidate pad. Ultimately, the operator wishes to sell
extracted gas at a set of downstream delivery nodes which are typically located
along interstate transmission pipelines. For this purpose a gathering system
superstructure has been identified. This superstructure specifies all feasible,
alternative options for laying out gathering pipelines to connect candidate
well pads with the given set of delivery nodes. In addition, the superstructure
indicates candidate locations for compressor stations as well as the location
of existing processing plants.

The
long-term shale gas development problem involves planning, design and strategic
decisions. In terms of planning decisions the operator needs to decide: a)
where, when and how many wells to drill at every candidate well pad, b) whether
selected wells should be shut-in and, if so, for how long, and c) how to
allocate drilling rigs over time. The design decisions involve: a) where to lay
out gathering pipelines, b) what size pipelines to install, c) where to
construct compressor stations, and d) how much compression power to provide. Finally,
we consider strategic decisions that include: a) the selection of preferred
downstream delivery nodes, b) the arrangement of delivery agreements, and c)
the procurement of take-away capacity. The upstream operator's objective is to
determine the optimal development strategy by making the right planning, design
and strategic decisions such that the net present value is maximized. 

The
shale gas development problem requires operators to size equipment that is part
of the shale gas gathering system such as pipelines and compressors. We take
advantage of the discrete nature of the respective design variables, i.e., standardized
pipeline diameters and compressor sizes, and systematically derive disjunctive
models based on Generalized Disjunctive Programming (GDP) that yield tight
continuous relaxations. Disjunctive models are usually transformed into
mixed-integer constraints using either a Big-M (BM) or a Hull-Reformulation
(HR) [3]. The continuous relaxation of the (HR) is at least as tight as and
generally tighter than the (BM), but it requires disaggregated variables and
constraints which increase its size. Similar to Castro & Grossmann [4], we
show that in this particular case the proposed equipment sizing models can be
transformed by means of a compact Hull
Reformulation. This compact reformulation does not require the introduction of
disaggregated variables or constraints and, hence, yields the best possible
reformulation of the disjunctive models.

In
general, the composition of the extracted shale gas can vary significantly
within a shale play. In the Marcellus play, for instance, the gas quality
ranges from ?wet gas?, which contains heavier hydrocarbons such as ethane,
butane or propane, to ?dry gas?, which is almost exclusively methane, i.e., nearly
pipeline-quality gas. In practice, a cluster of shale wells will feed different
gas qualities into a gathering system at varying production rates over time.
Hence, the composition of the gas delivered to midstream processors or
downstream transmission lines varies temporally. These variations can create
major challenges since upstream operators have to satisfy strict gas quality
specifications at delivery nodes. Hence, it is critical to consider composition
variations in shale gas development areas. In light of this reality we emphasize
that the long-term shale gas development problem is highly quality-sensitive, i.e., the quality of the gas extracted within a
particular development area determines decisively which development strategies
are profitable and which ones may not even be feasible. In this work we address
the quality-sensitive shale gas development problem with multiple delivery
nodes, i.e., mixing and splitting within the gathering system is explicitly
permitted. This problem corresponds to a network flow pooling problem that we
model as a nonconvex MINLP. The non-convexities arise from bilinear terms in
the flow balances around splitting nodes. We present a solution strategy that
relies on an MILP approximation coupled with a restricted MINLP that yields
near-global solutions in a reasonable period of time.

The
proposed optimization model is applied to a set of real-world case studies based
on historic development data that is provided by one of the largest upstream
operators in the Marcellus Shale region. The results demonstrate clearly that
previous, uncoordinated development strategies led to over-sized gathering systems
that were heavily under-utilized at times. Moreover, the case studies allow us
to actually quantify the economic value of advanced, computational tools in
this domain. 

References

[1]
U.S. Energy Information Administration (EIA). Annual Energy Outlook with
Projections to 2040. April 2013.

[2] Goellner, J. F. Expanding the Shale
Gas Infrastructure. AIChE CEP August
2012, 49-52.

[3] Grossmann, I.E.; Trespalacios, F.
Systematic Modeling of Discrete-Continuous Optimization Models through
Generalized Disjunctive Programming. AIChE
J. 2013. 59 (9). 3276-3295.   

[4]
Castro, P. M.; Grossmann, I.E. Generalized Disjunctive Programming as a
Systematic Modeling Framework to Derive Scheduling Formulations. Ind. Eng. Chem. Res. 2012, 51, 5781-5792.

[5]
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.