MINLP Model and Solution Strategies for the Long-Term Planning and Development of Shale Gas Supply Chain Networks Diego C. Cafaro INTEC (UNL – CONICET) Center for Advanced Process Systems Engineering Güemes 3450, 3000 Santa Fe, Argentina and Ignacio E. Grossmann Center for Advanced Process Decision-making Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA 15213, U.S.A. AIChE Meeting, San Francisco November 5, 2013 1
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MINLP Model and Solution Strategies for the Long-Term Planning and Development
of Shale Gas Supply Chain Networks
Diego C. Cafaro INTEC (UNL – CONICET)
Center for Advanced Process Systems Engineering Güemes 3450, 3000 Santa Fe, Argentina
and Ignacio E. Grossmann
Center for Advanced Process Decision-making Department of Chemical Engineering
Carnegie Mellon University Pittsburgh, PA 15213, U.S.A.
AIChE Meeting, San Francisco
November 5, 2013
1
Gas Reserves in World Motivation: Recent Energy Source
2
Shale Gas in US Marcellus Gas Shale
Horizontal drilling Hydraulic fracking
3
Large amount “wet gas”
In 2035 close to 50% from Shale Gas Northeast: from 0.3 trillion scft 2009 to 5.8 trillion scft 2035
Growth in Shale Gas
Goal: Develop Comprehensive Optimization Model for the Design of Supply Chain for Shale Gas Production
4
5 5
Strategic Planning of Supply Chain for Shale Gas Production
• Given: Potential Sites for Well
Pads (i)
Water sources
Ethane
Methane
Structure Supply chain?
Multi-well pads
6 6
Water Supply?
Potential Sites for Well
Pads (i)
Water sources
Ethane
Methane
3 weeks 4-6 weeks 1-3 months
Site Preparation
Drilling Completion Production 20- 40 years
Water acquisition Fracturing
One Quarter Yang et al. (2013)
7 7
Junction pipelines and compressors?
Potential Sites for Junction Nodes
(j)
Methane
Ethane
Water sources
8 8
Where to install gas processing plants?
• Given are:
Potential Sites for Gas
Processing Plants
(p)
0
100
200
300
400
500
600
700
800
900
1000
0 50 100 150 200 250 300 350 400 450
MM$
MMcf/day
Cost Correlations Economy of Scale Functions
9 9
Optimal Design Supply Chain
• The Goal is to Determine: • Number of Wells to Drill in Each Pad at Every Quarter • Site and Capacity of Gas Processing Plants Installed (or Expanded) at
Every Period • Diameter and Length of Pipelines Joining:
– Well Pads and Junction Nodes (Flow Pipelines) – Junction Nodes and Processing Plants (Gathering Pipelines) – Processing Plants and Gas Demand Nodes (Transmission
Pipelines) – Processing Plants and Ethane Demand Nodes (Liquid
Pipelines) • Power of Compressors Installed at Every Period in:
– Junction Nodes – Processing Plants
• Fresh Water Transportation from Reservoirs to Well-Pads at Every Period
10 10
Economic Objective • Maximize NPV:
+ Gas Sales Income + Ethane Sales Income + LPG Sales Income
- Shale Gas Production Cost - Processing Plants Construction/Expansion Cost - Pipeline Construction Cost - Well Drilling and Hydraulic Fracturing Cost - Compressor Installation Cost - Fresh Water Acquisition and Transportation Cost
11
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
0 10 20 30 40 50
MMcf/day
days
i1, i4
i2, i5, i7
i3, i6, i8
i9
11
Well Production Profiles i1 i2 i3
i4 i5 i6
i7 i8 i9
months
12
Natural Gas Price (Seasonal)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 1 2 3 4
$/MMBtu
Quarters12
13
0
10
20
30
40
50
60
70
80
90
0 1 2 3 4
MMgal
Quarters
Water Availability (Seasonal)
F1
F3
F2
F2 F3
13
14 14
MINLP Optimization Model
• MINLP Model comprising: • Discrete Variables: number of wells to drill • Continuous Variables: plants, pipelines, and compressor sizes, flows, etc. • Linear Constraints: shale gas production, flow balances, etc. • Nonlinear Objective Function economies of scale
Remark: Nonconvex MINLP
15
MINLP Model
Main Model Variables Ni,t number of wells drilled in pad i during period t Sp,t plant capacity installed at site p in period t Di,j,t diameter of pipeline installed between nodes i and j
in period t Wj,t compressing power installed at site j in period t GFi,j,t shale gas flow in pipeline i-j during period t GFj,p,t shale gas flow in pipeline j-p during period t GFp,k,t methane flow in pipeline p-k during period t LFp,l,t ethane flow in pipeline p-l during period t
16
MINLP Model
Model Constraints 1. The shale gas production at site i is determined by
the total number of wells drilled, and its age 2. Flow balances at junction nodes
3. Flow balances at plants Methane Ethane
1,,,,
1
1,, >∈∀== ∑∑
∈
−
=− tIiGFSPpwN
Jjtjiti
t
tiiτ
ττ
1,,,,, >∈∀= ∑∑∈∈
tJjGFGFPp
tpjIi
tji
∑∑∈∈
=Kk
tkpJj
tpjG GFGF ,,,, 1,,,,, >∈∀=∑∑
∈∈
tPpLFGFLl
tlpJj
tpjE
17
MINLP Model
Model Constraints 4. Plants, Pipelines and Compressors Sizing 5. Maximum Capacity Constraint
Master Problem: Find a Network 1. Solve an MILP approximation of the MINLP using convex envelopes of
non-linear (concave) cost functions: Global Upper Bound
Reduced Problem: Fix the Network and Refine the Drilling Plan 4. Remove not used pipelines, plants and compressors. 5. Solve the reduced MINLP problem: Lower Bound 6. Refine piecewise linear approximations Bisectioning Intervals
Containing Values of the MINLP solution. 7. Solve an MILP approximation of MINLP using convex envelopes
of non-linear (concave) functions – Reduced Problem Upper Bound
8. Repeat Steps 4 to 7 until the reduced problem optimality tolerance is satisfied
9. Refine the first-step piecewise linear approximation 10.Repeat Steps 1 to 9 until the global optimality tolerance is satisfied.
20 20
Example: Uniform Shale Gas Wetness Shale Gas Composition
CO2, 1 N2, 1
CH4, 74.6
C2H6, 12.8
C3H8, 7.6
C4H10, 2 C5H12, 1 9 well-pads
20 wells per pad 8 potential junctions 3 potential sites plants 10 years (40 periods)
21
21
• Processing Plant
Optimal Supply Chain Structure
Well Pads
Separation Plant
236 MMcf/day
MINLP: 2,343 binary variables, 14,252 constraints, 16,912 continuous variables Total CPU time= 8.5 hours (<3% optimality gap)