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
6. Water Supplies
Demand Fulfillment per Pad Availability
TtFffwaWS tfIi
tif ∈∈∀≤∑∈
,,,,
1,,1,, >∈∀+= −− tPpSSepCapSepCap stptptp τ
1,,,, >∈∀≤∑∈
tPpSepCapGF tpJj
tpj
18
( ) ]
[)4/1(
,,,
,,
,,,,,,
,,,,,,
1,,
,
,,,
,,,,,,,
∑∑
∑∑
∑∑∑∑
∑∑∑∑
∑∑
∑
∑∑
∑ ∑∑∑∑∑
∈ ∈
∈∈
∈ ∈∈ ∈
∈ ∈∈ ∈
∈ =
∈
∈ ∈
∈ ∈∈ ∈∈ ∈
−
+−
−−
−−
−−
−
−
−
+++=
Ff Iitififff
Pp
CompExptp
Jj
CompExptj
Pp Ll
LiqPipeExptlplp
Pp Kk
GasPipeExptkpkp
Jj Pp
GasPipeExptpjpj
Ii Jj
GasPipeExptjiji
Ii
n
ntni
WellExp
Pp
SepExptp
Ii Jjtjitti
Tt Pptptt
Pp Lltlpttl
Pp Kktkpttk
t
WSlvarfix
WkcWkc
DlkpDlkp
DlkpDlkp
ynkd
Sks
GFndshgc
NFndlpgpLFndethpGFndgaspdrNPV
i
MINLP Model
Objective Function
Max
Sales Income Shale Gas Cost
Drilling/Fracking Cost
Pipeline Cost
Gas Plant Cost
Compressor Cost
Water Cost
Concave Cost
19 19
Branch-Refine-Optimize (BRO) Algorithm (You& Grossmann, 2010)
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)
22 22
• Pipeline Network and Compressors
Optimal Supply Chain Structure
11 ½” 11 ½”17 ½”
3255 HP
5 ¾”1608 HP
1096 HP
16 ½”
15” 976 HP
14 ½” 13” 12 ½”
12½”
12 ½” 18”
23
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11
i9
i8
i7
i6
i5
i4
i3
i2
i1
0
10
20
30
Number of Wells Drilled at Every Pad per
Period
Total Number of Wells Drilled
Per Period
Water Scarcity
23
Optimal Drilling Strategy
24 24
Optimal Drilling Strategy
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11
i9
i8
i7
i6
i5
i4
i3
i2
i1
0
10
20
30
Number of Wells Drilled at Every Pad per
Period
Total Number of Wells Drilled
Per Period
Phase 1: Intensive Drilling Phase 2: Flow Maintenance
25
25
• Methane Sales Flow
Optimal Production Profile
17 ½”
3255 HP
5 ½”
12 ½” 11 ½” 11 ½”
0
20
40
60
80
100
120
140
160
180
200
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16
MMcf/day = Billon BTU/day
26
26
• Ethane Sales Flow
Optimal Production Profile
17 ½”
3255 HP
5 ½”
12 ½” 11 ½” 11 ½”
0
100
200
300
400
500
600
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16
Mgal/day
27
• Quarter 1 Drilling and Water Supply Water
Supplies
Depleted
Optimal Operation
28
Optimal Operation
• Quarter 2 Drilling and Water Supply
29
Optimal Operation
• Quarter 3 Drilling and Water Supply
30
Optimal Operation
• Quarter 4 Drilling and Water Supply
31
-322.475
-651.378
-86.993
-7.063
-10.862
-1300
-1100
-900
-700
-500
-300
-100
100
300
500
t1 t2 t3 t4 t5 t6 t7 t8 t9 t10 t11 t12 t13 t14 t15 t16
MM$
Compressors
Water
Drilling/Fracking
Processing Plant
Pipelines
LPG Sales
Ethane Sales
CH4 Sales
31
Economic Analysis
• Cash Flow
Discounted Payback Period 3 years
32
Real World Case Study
150 well pads 4 wells per pad Dry gas (95% methane) 10 years (40 time periods) No gas plants
MINLP Model 4,815 discrete variables 12,226 continuous variables 16,815 constraints 20 hours CPU-time 8% Gap
33
0
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
t10 t11 t12 t13 t14 t15 t16 t17 t18 t19 t20 t21 t22 t23 t24 t25 t26 t27 t28 t29 t30 t31 t32 t33 t34 t35 t36 t37
ACH
ACK
Toby
ABW
ACL
ABZ
ABV
ACO
ACI
ACG
ACF
ACD
ACA
ACE
ACC
ACN
ACJ
ACV
ACM
ACB
33
Real World Case Study • Drilling Strategy Well Pads
Quarters
Number of Wells Drilled & Fracked
Up to 4 Wells Drilled per Pad per Period
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
34
Conclusions
1. Proposed Multiperiod MINLP Model for Shale Gas Production
3. Branch-Refine-Optimize Algorithm for Large-scale Nonconvex MINLP
4. MINLP model leads to systematic optimization of Shale Gas Production Systems
2. Model determines: a) Structure of supply chain: - Plants of Natural Gas - Pipelines and Compressors b) Operation supply chain:
- Drilling strategy - Supply of water