On Shut-In Based Production Optimization of Shale-Gas Systems
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The use of shale gas as an energy resource has increased extensively over the last decade, with emerging new technologies causing shale gas to become the largest source of growth in the US natural-gas supply. Ecient utilization of shale-gas resources is, however, very challenging, with wells being inherently dynamic and elds typically consisting of hundreds of geographically distributed wells and production pads. The characteristic system of low-permeable matrix blocks and interconnecting fracture networks makes shale-gas wells particularly suited for intermittent shut-in based production schemes, a property which can be utilized both as a means of preventing liquid loading and for meeting varying gas demands and prices. This thesis concerns the development of ecient optimization schemes and shale-gas well- and systems models for scheduling of well shut-ins in large-scale shale-gas systems. The thesis is divided into four parts. The rst part describes the development of novel shale well and reservoir proxy models, together with mixed integer models for computation of shut-in times for shale multi-well pads. The scheme applies short shut-ins in order to prevent liquid loading in late-life wells, and tracks an assigned reference rate for a set of wells producing at a shared pad. Following a spatial and temporal discretization of the PDE governing the reservoir proxy model, we use logic-based generalized disjunctive programming (GDP) as a basis for modeling well shut-ins and constraints on well switchings. This formulation lends itself both to a complete MILP reformulation and reduced size MINLP reformulations. A computational study shows that the complete MILP formulation retains best computational performance for increasing problem sizes. Moreover, we demonstrate how a structured shut-in schedule prevents the oscillating rates caused by a naive shut-in approach, however, at the expense of a complex shut-in pattern. The second part of the thesis addresses shut-in scheduling for preventing liquid loading in large, distributed shale multi-pad systems. The proposed scheme optimizes shut-in times and a distinct reference rate for each multi-well pad, minimizing deviations from the individual pad rates while ensuring that the total produced rate tracks a given short-term gas demand for the entire eld. An extended tuning procedure for the proxy models are presented, using preltering of prediction errors as weight-selection in a least-squares formulation for parameter estimation in the proxy models. By using an embedded GDP model for describing the states of the system, we derive an MILP reformulation of the entire shale multi-pad scheduling problem. The resulting MILP model renders a block-separable structure, facilitating the solution by a Lagrangian relaxation scheme. The resulting decomposition scheme is developed with a trust-region cutting-plane method for solving the Lagrangian dual, and a combined xing and Local-Branching based heuristic for recovering primal feasible solutions from the Lagrangian. In the third part of the thesis, the use of shut-ins is further developed as a means of meeting seasonal varying gas demands from natural-gas power plants. To this end, the proposed scheme argues that shale-gas reservoirs can be used to shift storage of gas used for meeting varying demands, from separate underground storage units operated by local distribution companies to the gas producers themselves. This chapter contains slightly modied well and reservoir proxy models with a more accurate nonlinear tubing model. Moreover, a tight convex-hull reformulation of an GDP model is derived and utilized in the scheduling formulation. Model reformulations and SOS2 approximations are applied to render a large-scale MILP, which we solve by a Lagrangian relaxation scheme. Finally, we implement a receding horizon strategy to address operational uncertainties and varying gas spot-price. Illustrative case studies show a signicant economic potential for shale-well operators by adopting the proposed scheme, and a viable approach for generating companies to secure a rm gas supply for meeting seasonal varying electric-power demands. The last chapter of the thesis presents an Objective Feasibility Pump (OFP) designed for nding good feasible solutions in short computation times for dicult convex MINLPs. The algorithmic development uses a multi-objective optimization formulation to systematically design a heuristic that balances the two goals of quickly obtaining a feasible solution and preserving solution quality. A set of user-dened parameters allows for emphasizing either short computation time or solution quality. The eciency of the proposed heuristic is evaluated by extensive computational testing on a large set of convex MINLP test problems. As the algorithmic framework of the OFP is quite generic, we further demonstrate applicability of the proposed heuristic on nonconvex MINLPs by solving a nonlinear shale-well scheduling problem.
Has partsKnudsen, Brage Rugstad; Foss, Bjarne Anton. Shut-in based production optimization of shale-gas systems. Computers and Chemical Engineering 2013 ;Volum 58. s. 54-67 http://dx.doi.org/10.1016 /j.compchemeng.2013.05.022 This article is reprinted with kind permission from Elsevier, sciencedirect.com
Knudsen, Brage Rugstad; Grossmann, Ignacio E.; Foss, Bjarne Anton; Conn, Andrew R.. Lagrangian relaxation based decomposition for well scheduling in shale-gas systems. Computers and Chemical Engineering 2014 ;Volum 63. s. 234-249 http://dx.doi.org/10.1016/j.compchemeng.2014.02.005 This article is reprinted with kind permission from Elsevier, sciencedirect.com
Knudsen, Brage Rugstad; Whitson, Curtis Hays; Foss, Bjarne Anton. Shale-gas scheduling for natural-gas supply in electric power production. Energy 2014 ;Volum 78. s. 165-182 http://dx.doi.org/10.1016/j.energy.2014.09.076 This article is reprinted with kind permission from Elsevier, sciencedirect.com
Sharma, Shaurya; Knudsen, Brage Rugstad; Grimstad, Bjarne André. Towards an objective feasibility pump for convex MINLPs. Computational optimization and applications 2015 The final publication is available at Springer via http://dx.doi.org/10.1007/s10589-015-9792-y
Deler av appendix dvs enkelte figurer, er publisert i følgende artikkel: Knudsen, Brage Rugstad; Foss, Bjarne Anton. Designing shale-well proxy models for field development and production optimization problems. Journal of Natural Gas Science and Engineering 2015 http://dx.doi.org/10.1016/j.jngse.2015.08.005 This article is reprinted with kind permission from Elsevier, sciencedirect.com