minlp model and solution strategies for the long-term...

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


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


30

Optimal Operation


31

-322.475

-651.378

-86.993

-7.063

-10.862

-1300

-1100

-900

-700

-500

-300

-100

100

300

500


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

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