Optimization and Engineering

, Volume 20, Issue 4, pp 1227–1248

# Multiperiod optimization model for oilfield production planning: bicriterion optimization and two-stage stochastic programming model

• Utsav Awasthi
• Remy Marmier
• Ignacio E. Grossmann
Research Article

## Abstract

In this work, we present different tools of mathematical modeling that can be used in oil and gas industry to help improve the decision-making for field development, production optimization and planning. Firstly, we formulate models to compare simultaneous multiperiod optimization and sequential single period optimization for the maximization of net present value and the maximization of total oil production over long term time horizons. This study helps to identify the importance of multiperiod optimization in oil and gas production planning. Further, we formulate a bicriterion optimization model to determine the ideal compromise solution between maximization of the two objective functions, the net present value (NPV) and the total oil production. To account for the importance of hedging against uncertainty in the oil production, we formulate a two-stage stochastic programming model to compute an improved expected value of NPV and total oil production for uncertainties in oil prices and productivity indices.

## Keywords

Bicriterion optimization Mixed-integer Nonlinear programming Multiperiod optimization Nonlinear programming Oilfield production planning Stochastic programming

## Constants

c

Linear cost for first stage decisions

disct

discount factor for NPV at time t

gcct

Cost of gas compression at time t

MOw

Maximum amount of oil that can be produced from a well

PIw

Productivity index of well w

pgt

Gas price at time t

pot

Oil price at time t

S

Number of scenarios

Sep

Maximum amount of liquid that can be separated in the separator

TH

Time horizon

wtct

Cost of water treatment at time t

## Sets

s

Scenarios {1…., S}

t

Time {1, 2…, TH}

w

Wells {well 1, well 2, …}

## Functions

g(x, ys)

Stochastic model constraints

GORw,t

Gas oil ratio of a well w at time t, which is a function (fGOR) of cumulative oil produced

Prw,t

Pressure of well w at time t, which is a function (fPR)of cumulative oil produced

WCTw,t

Water cut of well w at time t, which is a function (fWCT) of cumulative oil produced

$$\psi_{s} \left( {x,y_{s} } \right)$$

Second stage problem

## Variables

CCt

Total cost associated with gas compression and water treatment at time t

CRt

Total revenue generated from oil and gas production at time t

NPV

Net present value

rLw,t

Liquid produced from well w at time t

Rorcw,t

Cumulative oil produced form well w at time t

row,t

Oil produced from well w at time t

rgw,t

Gas produced from well w at time t

TrLt

Total liquid produced at time t

Trgt

Total gas produced at time t

Trot

Total oil produced at time t

Trwt

Total water produced at time t

x

First stage decision variables

ys

Second stage decision variables

Z

Total oil production

## Notes

### Acknowledgements

The authors acknowledge financial support from Total and from the Center of Advanced Process Decision-Making at Carnegie Mellon.

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## Authors and Affiliations

• Utsav Awasthi
• 1
• Remy Marmier
• 2
• Ignacio E. Grossmann
• 1
Email author
1. 1.Department of Chemical EngineeringCarnegie Mellon UniversityPittsburghUSA
2. 2.TOTAL SA – CSTJFPauFrance