8/2/2019 LP Application Oil Gas
1/25
APPLICATIONOF LINEAR PROGRAMMINGIN OILAND GAS INDUSTRY
Presented by:
Saurabh Jain (R020208031
Shankar Deo Rajpal (R020208032)
ABSTRACTOFPAPERS
8/2/2019 LP Application Oil Gas
2/25
8/2/2019 LP Application Oil Gas
3/25
LP MODEL : TERMS INVOLVED
Decision Variable: Various Alternatives or Courseof Action to look upon
Objective Function: A function associated with anoptimization problemwhich determines how good asolution is,
Constraints: They exist because certain limitationsrestrict the range of a variable's possible values.
8/2/2019 LP Application Oil Gas
4/25
LP MODEL
Objective Function : Max or Min
Subject to Constraints.
nnxaxaxaz ..........2211
1313212111 cxbxbxb 2333222121 cxbxbxb
8/2/2019 LP Application Oil Gas
5/25
8/2/2019 LP Application Oil Gas
6/25
PROBLEM FORMULATION. (CONT.)
Add any implicit constraints, such as non-negativerestrictions.
Arrange the system of equations in a consistentform suitable for solving by computer. For example,place all variables on the left side of their equationsand list them in the order of their subscripts.
8/2/2019 LP Application Oil Gas
7/25
LINEARPROGRAMMING ASSUMPTIONS
Certainty
Divisibility or Continuity
Additivity
Linearity or proportionality
8/2/2019 LP Application Oil Gas
8/25
APPLICATIONOF LINEARPROGRAMMING
LP is one of the most powerful and widespread businessoptimization tools. And may be hard to believe but thetool, can be used in a very large variety of businessproblems. They include:
Product Mix Planning
Transportation
Distribution networks
Human Resource Planning
Financial and Tax Planning
Corporate Restructuring
Facility Planning
Fleet Scheduling
8/2/2019 LP Application Oil Gas
9/25
USING SOFTWAREFOR LINEARPROGRAMMING
Modern optimization techniques have challengedorganizations to rethink the way they conductbusiness both internally and externally, i.e. howefficiently and effectively their entire business is
managed. Some of the softwares are
Lindo
Lingo
Solver
Dataforms
GAMS
8/2/2019 LP Application Oil Gas
10/25
APPLICATIONIN OILAND GASINDUSTRY
Grassroots refinery design/configuration
Selection and evaluation of crude oils and raw materials
Long-range and short-term operations planning
Capital investments evaluation for process equipment
Analysis of the profitability of merging and acquisition plansand the creation of ad-hoc models for joint venture refineries
Evaluation of processing agreements and product exchangecontracts
Evaluation of new process technologies
Control of the refinery performance Product blending control
Down-time planning
Inventory management
8/2/2019 LP Application Oil Gas
11/25
8/2/2019 LP Application Oil Gas
12/25
PAPER 1
The Use of LP & mathematical model inunderground oil production
J.S.Aronofsky & A.C. Williams
Socony Mobil Oil company Inc. New York City This paper describes how linear programming can
be used to solve crude oil production problem forthe purpose of economic planning of coordinatedoperations.
Started with Single well system and then integratedthe to multi well system
8/2/2019 LP Application Oil Gas
13/25
MULTI RESERVOIR SINGLE WELL
8/2/2019 LP Application Oil Gas
14/25
TERM & SUBSCRIPTS USED
Reservoir : is a subsurface pool of hydrocarbonscontained in porous rock formations. The naturallyoccurring hydrocarbons are trapped by overlyingrock formations with lower permeability.
J1, J2.Jj Used for 1 to J Reservoirs
Time period denoted I = 1 to I
Reserve capacity Bj denotes removable oil in JthReservoir.
Pipeline Capacity Ri at time period i
Flow rate qj and Pressure denoted pi
8/2/2019 LP Application Oil Gas
15/25
PROBLEM
It is required to compute that production schedulefor many sources and over a series of time periodsfor which resulting profit is a maximum, and forwhich all assumptions as to
1. behaviour of underground reservoirs,
2. restrictions on surface facilities, and
3. economies requisite to preparing a "profit andloss" statement, are satisfied.
Assumptions from all three categories are requiredin order to present a linear program model that is ofinterest.
8/2/2019 LP Application Oil Gas
16/25
BEHAVIOR OFUNDERGROUNDRESERVOIR
For each reservoir, there must be an expression thatrepresents the technology of flow through porousmediathe behaviour of underground reservoirs. Sucha relationship between the well pressure and theproduction flow rate is given in equation (1).
The function f(T) deserves some special consideration.It describes how the well pressure, pw, changes with
time when the flow rate changes abruptly from zero to aconstant rate, q. It is sometimes referred to as aninfluence function. It is dependent upon properties, suchas: reservoir rock, fluid characteristics, and reservoirgeometry
)(.)(0 fqpp w
8/2/2019 LP Application Oil Gas
17/25
BEHAVIOR OFUNDERGROUNDRESERVOIRCONT
The same equation is superimposed for series of time period for variationof q in different wells. The equation will be as
q denotes production rate of jth reservoir for ith period
Well pressure can take any value provided it does not go below somespecified value Dj.
toJj
toIkkijkjkjwj fqqpp
1
11,1,0 )().()(
jwj Dp )(
8/2/2019 LP Application Oil Gas
18/25
PRODUCTION CONSTRAINTS 1
Cumulative production cannot be greater thenreserve
= ii-1
The constant Bj in this inequality represents theremovable oil in place for Jth Reservoir
Hence there will be J equations for J reservoirs.
I
i jiji Bq1 , .
8/2/2019 LP Application Oil Gas
19/25
TRUNKPIPELINECONSTRAINT
The production rate at any time period should notexceed the pipeline capacity Ri
Thus Ri represents the flow of oil through the ithtime period.
J
j iiji Rq1 , .
8/2/2019 LP Application Oil Gas
20/25
THE OBJECTIVEFUNCTION
To find all sets of qij which satisfy all constraints and theprofit is largest , We wish to maximize.
The term profit is defined to include all economic factorthat are involved in producing and selling crude oil topipeline facility.
All the economic factors pertaining to revenue andexpenses are contained in the profitability index, di,jwhich has the dimensions of dollars and represents totalprofit for the entire lifetime of project.
i
J
j
I
i
jiji dq 1 1,.,
8/2/2019 LP Application Oil Gas
21/25
TOWARDS SCHEDULINGPRODUCTIONRATESFROMMULTIWELLSYSTEM
8/2/2019 LP Application Oil Gas
22/25
MAXIMIZING CDU1 OUTPUT,RIL
CDU1 REVENUE CALCULATION MODEL FORPERIOD 1.12.2001 TO 7.12.2001
DATA REFERENCE - RELIANCE IND.LTD,JAMNAGAR
8/2/2019 LP Application Oil Gas
23/25
8/2/2019 LP Application Oil Gas
24/25
8/2/2019 LP Application Oil Gas
25/25
SOLVER
APPLICATION INEXCEL