Mixed Integer Non-linear Optimization for Crude Oil Scheduling

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1 Mixed Integer Non-linear Optimization for Crude Oil Scheduling Ramkumar Karuppiah and Ignacio E. Grossmann niversit Enterprise-wide Optimization Project

2 Introduction Purchasing and Scheduling of crude oil in refineries involves billions of dollars ever ear Simulation tools are used b refiner schedulers to determine feasible schedules Interfaced with Black-box optimization tools Suffer from poor run-times GOA: Derive benefits from use of optimization to obtain crude movement schedules in refiner front-end 2

3 Motivation Economic goals Significant reduction in current costs of scheduling and inventor management is practicall possible Reduced costs in crude-movement scheduling Meet product qualit targets and demands more accuratel Technical goals Improve optimization capabilities inside refiner simulators Predicting ields, crude qualities and tank inventor levels over the whole horizon Integration with Marine Transportation models 3

4 Problem Outline REFINERY Schematic Crude Tanks Distillation Columns Products Crude Arrivals Products Given: 1. Scheduling Horizon 2. Tank inventor (min, max, Optimization initial levels) 3. Available crude tpes and their properties 4. Product propert specifications and demands 5. Bounds on crude and product flows Determine: 1. When to order crudes 2. How much of each crude to order 3. Operating flows of crude between tanks 4. Charges to Pipestills 5. How much of each product to produce 4

5 Simulation Schedulers consider multiple scenarios and perform simulations SIMATION + OPTIMIZATION Start with optimal schedule for simulation Perform what-if analses for sstem perturbations 5

6 Optimization Optimization Mathematical program Defined as getting the best possible solution with respect to an objective and subject to some constraints min s. t. z = f ( x ) g ( x ) h ( x ) = A x + B c T d E e x 0, { 0,1} Continuous variables Discrete variables Solution procedure Modeling aguages: GAMS, AIMMS Solvers: CPEX P and MIP CONOPT NP DICOPT, BARON MINP 6

7 Model Development Rigorous multiperiod formulation to model the important aspects of scheduling ( Discretized time domain ) Time Horizon T-1 T Optimization model Minimize cost objective OR product propert deviation s.t. Tank constraints Crude arrival constraints Pipestill constraints Variable bounds Binar Variables Variables in the model Tank inventories Crude tank transfers Crude shipments Pipestill charges Cuts flows Product flows Cut properties Product Properties Product boiling points Existence of flow in streams 7

8 Model Constraints Crude inflow Tank Constraints Crude outflow Inventor balances I I tot b, t comp jb, t a A Crude composition in tanks I comp jbt Inflow and Outflow restrictions w abt Flow balances c b C b Crude Tank tot tot tot 1 + V abt = I bt + V bct t T, b comp 1 + V jabt = I jbt + V jbct j J, t T, b B a A c b C b tot bt = f I j J, t T, b jbt + w 1 a A, c C, b B, t T bct b b B B Non-linear equations containing Bilinearities 8

9 Model Constraints (Contd ) Crude unloading contraints Crude Arrival Constraints o o Onl one tank can be fed b one vessel at an instance of time Onl one crude tpe can be unloaded at a point in time Distillation Column Constraints Cuts Products Feed Inlet flow and propert restrictions for Distillation Column Yield relations to calculate product flows and properties Allocation constraints o At most two charging tanks can charge a pipestill at an time Product flow and propert balances Product boiling points calculations 9

10 Optimization Model Scheduling problem modeled as a Multiperiod Mixed Integer Non-linear Program (MINP) Discrete variables used to determine which flows should exist and when Model is highl non-linear and non-convex Problem Parameters 11-da horizon, 7 Crude Tanks, 41 Crudes 2 Pipestills, 13 Cuts, 6 Final Products Model statistics Base case Extreme case # Time periods # Properties # Binar variables # Continuous variables # Constraints ,522 18, , , ,540 Need specialized algorithm to solve such large-scale models 10

11 Solution Technique Bi-level heuristic algorithm proposed to solve MINP formulation Mixed-Integer inear Programming (MIP) Relaxation inearize non-linear terms and construct convex envelopes Solve se solution of relaxation to initialize MINP variables x Overestimators x Get rigorous bound on objective value Bilinear term x = w4 x w x w x w x w = 4 + x + x + x + x x x x x nderestimators Original MINP model Solve Get locall optimal solution 11

12 Alternate Solution Method Rolling Horizon Approach to temporall decompose model and solve it Solve single time period and fix inventories in tanks for next time period T-1 T Time Horizon Smaller model Easier to solve temporall decomposed sub-problems Results of this method are similar to full space optimization ower likelihood of finding solutions 12

13 General Remarks ocall optimal schedules obtained for problems where 3 properties are targeted in the products over the entire scheduling horizon Cost objective problems easier to solve than problems with product propert deviation objectives Solution times var between 500 CP secs 5000 CP secs Scaling of data and using good starting points in the optimization are ver important lead to solutions in much reduced solution times 13

14 Conclusions Summar of work Development of a rigorous Mixed Integer Non-linear formulation to model crude oil movement in a refiner front-end Heuristic algorithms to optimize non-linear model to get (locall) optimal schedule Method to obtain a bound on the best possible cost objective Potential future work Target more properties in product specifications Enhance existing model b including downstream processing and crude vessel routing Robust non-linear solver development for solving large-scale refiner scheduling MINPs 14

15 Acknowledgments Corporate Strategic Research, Clinton Kevin Furman Jin-Hwa Song ExxonMobil Engineering, Fairfax Gene Pan Kriengsak Chaiworamukkul Philip Warrick 15