Real time production optimization in upstream petroleum production - Applied to the Troll West oil rim Vidar Gunnerud, Bjarne Foss Norwegian University of Science and Technology - NTNU Trondheim, Norway (2007-2014) Outline 1. Problem formulation and today's solution methods and work process at Troll C 2. New Solution method: Dynamic piecewise linearization and Lagrangian decomposition 3. Troll West oil rim Initial results 1
Petroleum production - Decision horizons vary a lot Focus in this work Oilfield Review 2006 2
Production optimization - Optimizing on a day-week horizon Typical optimization problem Maximize oil production while honoring constraints related to the underground hydrocarbon reservoir wells pipelines downstream processing equipment (separators, compressors,...) Decisions variables Production valve on each well (often between 10 and 100 wells) Gas injection valves (on some wells) Routing of the reservoir fluid (often a well may be routed to two different production lines) 3
Platform Sea bed Production optimization - Stylistic view Typical optimization problem One of eight Troll C clusters Maximize oil production while honoring constraints Decisions variables Production valve on each well Gas injection valves Routing of the reservoir fluid Under ground reservoir Typical system boundaries Upstream: Underground hydrocarbon reservoir Downstream: Inlet separator on downstream processing equipment 4
Production optimization - Challenges The optimization problem is a (large) nonlinear programming problem with integer variables Well models can be highly nonlinear Pressure drop models for pipelines are nonlinear Present optimization technology is a constraining factor for real-time production optimization 5
Today s solution methods GORM (Gas-Oil Ratio Model In-House model Simplified reservoir model Models gas coning Adjusted to each well Troll: 100 GORM models GAP (General allocation program) Commercial software Models the flow condition in the network and operational constraints Does not have an appropriate gas coning model Troll: 17 GAP models (clusters) 6 Ref. Duenas, 2007
Todays solution methods Production Data Wellbore Info GOR Prediction Optimal P, inj. rates Routing 7 Ref. Duenas, 2007
8 Today s solution methods The integrated tools
New methodological foundation Methodological foundation for our work Dynamic piecewise linearization To linearize the problem Lagrangian decomposition To split the problem 9
Piecewise linearization of Dynamic piecewise linearization - principle f ( x) = x 2 By a modal formulation a nonlinear function is transformed into a piecewise linear function At most two adjacent s can be non-zero Converts a NP problem to a MILP problem For Troll this means piecewise linear well performance curves piecewise linear pressure drop models 10
Dynamic piecewise linearization - principle Illustration of a dynamical piecewise linearized well performance curve To minimize error due to piecewise linearization, good accuracy and small intervals between interpolation coordinates are needed This again results in a large number of variables and will hence be computationally expensive To handle this, it is possible to dynamically insert interpolation coordinates in demanding areas 11
Dynamic piecewise linearization - principle Solves the problem only containing a small set of interpolation coordinates (coarse resolution) Locates the solution Inserts more interpolation coordinates in that area Re-optimizes Converges when acceptable accuracy close to the solution is achieved 12
Lagrangian decomposition (LD) is a method to decompose an optimization problem into two or more disjoint (and hence smaller) problems LD may be efficient for certain network-type problems Lagrangian decomposition principle Relax the comman constraint The LP problem can be decomposed provided the Lagrangian multiplier for the common constraint is known 13
To solve a Lagrangian decomposed problem is a iterative procedure Solve both problem with initial Lagrangian multipliers Check feasibility with respect to relaxed constraint Calculate new Lagrangian multipliers based on heuristic Feasible objective function give lower bound, Lagrangian function gives upper bound Lagrangian decomposition principle Relaxed constraint Objective function Lagrangian function 14
Constraint to relax gas processing constraint C GAS TOT Lagrangian decomposition Troll C j Clusters q GAS j One of eight Troll C clusters Lagrangian function augmenting the objective function with the common gas processing constraint OIL GAS GAS GAS Max _ Z = q λ ( C q ) j Clusters j TOT j j Clusters Objective for each cluster Max _ Z = q λ q OIL GAS GAS j j j Note: The overall optimization problem can be split into 8 (much) smaller problems! 15
Complete algorithm combining Dynamic piecewise linearization and Lagrangian decomposition Solves the problem for each cluster Calculates the total gas production Compare gas production with total gas capacity constraint Re-optimizes Converges when maximum oil production is found, while honoring the gas capacity constraint 16
17 Implementation
Troll C case and results Tested on two clusters (11 wells) plus pipeline system Results compared with results using GAP (commercial) software Results are promising Challenges numerical instability robustness Problem size are highly scalable (constraints 200-1000, variables 50 000 2 mill) Solution time, highly dependent of problem and problem size (5 min 10 hours) 18
Collabration with CMU Professor Erik Ydstie s group PhD student - Michael Wartmann They have developed an network based analysis of decision making in complex organizations Based on thermodynamics Basic conservation laws for assets and liabilities 19
Collabration with CMU This network based Methodological foundation will be apply to optimization in upstream petroleum production Troll C will be used as test case I will visit CMU Michael Wartmann has/will visit NTNU Professor Ydstie will visit NTNU on regular basis 20
Conclusions and further work New algorithm for production optimization has been developed Algorithm is based on a combination of Lagrangian decomposition and dynamic piecewise linearization of nonlinear models Preliminary test results are promising Focus will lie on further development of Dynamic piecewise linearization Different Lagranigan decomposition methods will be tested Troll C will be used as test case Consider dynamic well models Work will be continued in my PhD thesis project in cooperation with: Hydro (Marta D. Diez) Carnegie Mellon University (Professor Erik Ydstie), Industrial Economy and Technology Management NTNU (Bjørn Nygreen) And others (Dept. of Petroleum Engineering and Applied Geophysics) 21