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
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 . 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 . 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) . 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 , 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.
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