US 3891836 A
A processing system comprising a plurality of individual units is optimized by first estimating the yields of the individual units at a standard set of operating conditions and then establishing optimum flow rates using a linear programming model or similar mathematical tehniques. Individual units are then controlled and locally optimized consistent with a sensitivity analysis which is performed by treating a proposed change in operating conditions of an individual unit as a disturbance in the unit yield column of the linear programming model. The overall system may then be optimized for the changes in operating conditions by determining and establishing new flow rates. The steps of changing operating conditions and establishing new flow rates may be repeated until the sensitivity analysis reveals that any further change in operating conditions will not further improve the profit of the overall system.
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United States Patent Lee June 24, 1975 APPARATUS FOR OPIIMIZING I MULTIUNIT PROCESSING SYSTEMS m ry Examinerloseph F. Ruggiero  Inventor: Wooyoung Lee, Cherry Hill, NJ. Anomey' Agem or Flrm c' Huggeu  Assignee: all? Oil Corporation, New York.  ABSTRACT A processing system comprising a plurality of individl Filed: ual units is optimized by first estimating the yields of A L No; 454,620 the individual units at a standard set of operating con- I pp ditions and then establishing optimum flow rates using Related Application Data a linear programming model or similar mathematical I63] Continuation-in-part of Ser. No. 246,445, April 21, tehniques. Individual units are then controlled and lol972,abandoned. cally optimized consistent with a sensitivity analysis which is performed by treating a proposed change in  U-S- Cl. 3 5l-l2; 235/150 /1 operating conditions of an individual unit as a distur-  Int. Cl. G06f 15/46; 606g 7/58 bance in the unit yield column of the linear r0 ram- P 8  Field of Seard 235/1501. ming model. The overall system may then be opti- 235/l5l.l2; 444/1 mized for the changes in operating conditions by determining and establishing new flow rates. The steps of  References Cited changing operating conditions and establishing new UNlTED STATES PATENTS flow rates may be repeated until the sensitivity analy- 3 075 700 M963 Bishop H 235/150}l sis reveals that any further change in operating condi- 3:079:079 2/1963 p i et a] H 235/1501 tions will not further improve the profit of the overall 320L572 8/1965 Yetter 235/!5] y 3,594,559 7/1971 Pemberton 235M501 X 3,62l,2l7 11/1971 Carr 235/1501 x 18 C|a|m5- 19 D'awmg Figures OVERALL SYSTEM COMPUTER i817 2 T y-1a, r- 7" 7 -1 l l M I 1 I'm a f i LOCAL 2 l I LOAL LOCAL 12, come j I come COMP. UNIT l UNlT UNIT- 1 5 6 lS l 12;, "1| l I j l I 1212 I LOCAL I COMP. D3 l i umt '29 141 i I 3 l i I25 I213 l UNIT l UN" 2 10 I 7 i bg M ii 12 1 I UNIT 1 1 I I2 4 l2 I 4 t\ 5 I L f" J PATENTEI] JUN 2 4 I975 AM 5 mm W m 4 llllll... N M Wm U I, L I MWM W3 E 3 LC 44 Q a a 0 M f I 4 2 PATENTEDJUN24 I975 3.891, 836
SHEET 2 ESTIMATE UNIT COSTS AND YIELDS AT STANDARD OPERATING CONDITIONS Fig Z TRANSMIT COSTS AND YIELDS TO SYSTEM PLANNING /24 SOLVE LP FOR T TRANSMITTED YIELDS TRANSMIT LOCAL /26 OBJECTIVE FUNCTION AND LP SOLUTION TO LOCAL UNITS DETERMINE IF A CHANGE IN YIELD OF UNIT WILL CORRECT SATISFY LOCAL LP OBJECTIVE FUNCTION SOLUTION IF CHANGE SATISFIES LOCAL OBJECTIVE 30 FUNCTION, TRANSMIT TO SYSTEM PLANNING PATENTEDJUN24 I975 3.891.836
SHEET 3 ESTIMATE UNIT COSTS AND YIELDS AT STANDARD SYSTEM PLANNING i /24 SOLVE LP FOR J TRANSMITTED YIELDS TRANSMIT LOCAL 26 OBJECTIVE FUNCTION AND LP SOLUTION TO LOCAL UNITS T Ml FA HANGE I N YI IE LD g T T WILL TRANSMIT CORRECTED SATISFY LOCAL LP SOLUTION TO OBJECTIVE FUNCTION SYSTEM PLANNING IF CHANGE SATISFIES LOCAL OBJECTIVE FUNCTION, CORRECT my 30a LP SOLUTION SOLVE LP AT OVERALL SYSTEM COMPUTER USING ESTIMATED YIELDS CHANGE IN YIELDS WILL SATISFY LO OBJECTIVE FUNCTION DETERMINE IF IF CHANGE SATISFIES LOCAL OBJECTIVE FUNCTIONJRANSMIT CHANGE TO LOCAL UNIT DETERMINE IF LOCAL UNIT CAN MAKE CHANGE IF LOCAL UNIT CAN TO SYSTEM COMPUTER MAKE CHANGE, TRANSMIT CORRECT PATENTEDJuN24 I975 3. 891. 8 36 SHEET 5 OVERALL 54 SYSTEM COMPUTER I 'lg- 4 A 56 56 x! CA /48 i I GASOLINE CRuOE 1 --l FUEL CRUDE 2'---"""" PROCESSNG HEATING OIL CRUDE 3/i/v JET FUEL 3 L 52 CRuOE 4 L 50 LOCAL COMP.
LUBE I PROCESSING l I LUBE OIL Fig 5 A 24 CONSTRAINTMI) 2 x CONSTRAINTMZ) PATENTEI] JUN 2 4 1915 SHEEI SHEET PATENTEDJIJN 24 I975 NEW 300 SIMPLEX MQLTIPLI ERS NEW COSTS NEW BASIS MATRIX liq- I982 202 17 /2002 LT@Q1V SHEET PATENTED JUN 24 I975 lsp SHEET 2|4 CHECK IF c; 20
PATENTEDJUN 24 ms SW TCH NG SHEET PATENTED JUN 2 4 I975 W on w m m m 2 4 a w w w w a m a ll lllllllllllll ll c 8 PATENTEDJUN 24 ms sum 14 13 8 91; 8 36 o o o o c STORE l 11 1 soo STORE Ap 502 COMPUTE SENSITIVITY COEFFICIENTS 5' o 504 5= 1 6 A S1 Em COMPUTE NEW X's o sos J 4 1+ -m COMPUTE NEW INVERSE BASIS MATRIX 5, 50s I o I Q Q g m 0 I1 S -m COMPUTE NEW SIMPLEX MULTIPLIERS 51o 'm 2K S C COMPUTE NEW COST COEFFICIENTS 1 APPARATUS FOR OPTIMIZING MULTIUNIT PROCESSING SYSTEMS RELATED APPLICATION This is a continuation-in-part of copending application Ser. No. 246,445, filed Apr. 21, 1972, now abandoned which is incorporated herein by reference.
BACKGROUND OF THE INVENTION This invention relates to a method for optimizing large, complex processing systems comprising a plurality of individual units.
A number of techniques are available for optimization of such large processing systems. Linear programming is one of the most widely used techniques, and modern refinery complexes are optimized by linear programming almost without exception. However, a linear programming model is at best an approximation of a real physical system. For example, it is commonly assumed that the yield information incorporated into the LP (linear programming model) is relatively fixed and the coefficients of the constraint equations which represent these yields are also fixed. In reality, however, these yield coefficients are dependent upon the operating conditions of the units and any change in the operating conditions for a single unit will of necessity affect the operation of other units.
In many instances, the operating conditions may be closely controlled. Local unit managers have appropriate tools (i.e., mathematical models, optimizers, and process control computers) for the local optimization and control of their individual units. As a result, large amounts of detailed information about the processes are continuously generated which are valuable for accurate adjustment of operating conditions. Each process unit can thus be locally optimized and controlled continuously.
However, any change in operating conditions of a unit which locally optimizes the unit will not necessarily optimize the overall system. In fact, a change in operating conditions which optimizes the local unit may have an adverse effect on the overall system. As a result, changes in operating conditions of the individual units have been discouraged or avoided for fear of the adverse effect on the overall system.
Changes in the operating conditions of individual units have been avoided for another reason. Any attempt to change the operating conditions at an individual unit would necessarily render the LP and its solution obsolete since the yield coefficients in the LP for a particular unit would change. Such a change would therefore require the LP to be solved again and prior art computer techniques for solving LPs are extremely cumbersome and complex. In the case of a digital computer, a great deal of computer time is required to solve an LP, particularly where the LP described a complex processing system.
Because of the foregoing difficulties associated with making the changes in operating conditions in the prior art, individual local objective functions consistent with the overall objective function of the system have been assigned and every effort has been made to maintain those operating conditions at the individual units which will satisfy the local objective functions rather than change to better operating conditions. In other words, no effort is made to deliberately change the operating conditions at the units to optimize the overall system.
Sensitivity analyses such as that disclosed by C. S. Bightler and D. J. Wilde, Hydrocarbon Processing, 44, No. 2, 111 (1965) have been proposed to determine the effect of changes in LP constraints on the operation of a system. However, no specific method has been proposed to take advantage of the sensitivity analysis for changes in the yield coefficients of an LP which optimizes the overall system, i.e., making changes in the operating conditions which will optimize the overall system as indicated by the sensitivity analysis.
SUMMARY OF THE INVENTION It is an object of this invention to provide an improved method of and apparatus for controlling the operation of a processing system including a plurality of individual processing units supplied by a plurality of feed streams of materials being transformed by the units into a plurality of product streams flowing from the units where the marginal product yield and the marginal product cost for each unit are dependent upon the operating conditions.
It is a more specific object of this invention to provide an improved method of and apparatus for controlling the operation of the processing system in a manner so as to encourage and implement changes in operating conditions for the individual units even though those changes do require a change in the linear program model of the processing system.
In accordance with these objects, a preferred embodiment of the invention comprises feed stream computer means for generating initial feed stream signals representing the initial feed stream flow rates for a given yield and cost at each of the units under a given set of operating conditions so as to maximize the profitability of the overall system. Feed stream control means are coupled to the feed stream computer means for controlling the feed stream flow rates in response to the initial feed stream signals. Unit yield and cost computer means generate new yield and cost signals representing new yield and cost for one of the units corresponding to an increase in the profitability of the overall system. Unit control means are coupled to the unit yield and cost computer means for controlling the op erating conditions at the one unit in response to the new yield and cost signals. Another feed stream computer means is coupled to the unit yield and cost computer means for repeatedly and continuously generating new feed stream signals representing new feed stream flow rates in response to the new yield and cost signals. The other feed stream computer means is coupled to the feed stream control means for controlling the feed stream flow rates in response to the new feed stream signals.
It is also a specific object of this invention to provide an improved method of and apparatus for operating and utilizing a linear program model.
In accordance with this specific object, the feed stream computer means includes means for computing the feed stream flow rates x from the linear program model having an overall system objective function of maximizing the profitability.
subject to x +....p x =Q x 2 Ofor alli wherep .Q=
Q is the marginal profit coefficient of the jth unit, x is the flow rate of the ith stream, p j is the yield column of the jth unit and a function of operating conditions, Q is the demand constraint column. a is the yield coefficient of the ith feed stream producing the jth product stream unit, and b,- is the demand coefficient of the ith product stream.
It is another specific object of this invention to assure that all changes in operating conditions at the units improve the overall profitability of the system.
In accordance with this specific object, the unit yield and cost computer means includes means for computing a local objective function where Ac, is the change in the marginal profit coefficient for the mth unit, A is the change in the mth yield column for the mth unit and g" are the simplex multipliers [c. c,,] at the previous operating conditions where Q" is the inverse of the basis matrix in [p,,
- pill- Itis a further specific object of this invention to provide an improved method of and apparatus for correcting the linear program model after permitting a change in operating conditions at one of the operating units.
In accordacne with this specific object, the other feed stream computer means includes means for computing the feed stream flow rates where BRIEF DESCRIPTION OF THE DRAWINGS FIG. 4 is a simplified refinery system operated in accordance with the method of this invention;
FIG. 5 is a graphical solution of a local optimization problem;
FIG. 6 is a block diagram of a processing system operated in accordance with the method depicted in FIG.
FIGS. 7 (a-d) are schematic circuit diagrams of a local computer and process control shown in block form in FIG. 6 where FIG. 7a shows circuitry for computing unit yield and cost coefficients, FIG. 7b shows circuitry for computing the local constraints and the local objective function, and FIGS. 7(c and d) shows circuitry for correcting the linear program model",
FIGS. 8 (a-c) are schematic circuit diagrams of the system computer and control shown in block form in FIG. 6 where FIG. 8a shows circuitry for computing the solution to the linear program model, FIG. 8b shows circuitry for determining the bases in the linear program model and FIG. 8c shows circuitry for controlling the feed stream flow rates to the units;
FIG. 9 is a flow diagram for a programmed digital computer which performs the same correction of the linear program performed by the circuitry of FIGS. 7(0- FIG. 10 is a block diagram of a typical refinery system which is controlled in accordance with this invention;
FIG. 11 is a block diagram of a fluid catalytic cracking unit of the system shown in FIG. 6; and
FIG. 12 is a block diagram depicting the relation and interconnections between the circuit diagrams of FIGS. 7(a-d) and FIGS. 8(ac).
TABLE OF CONTENTS FOR THE DETAILED DESCRIPTION I. Complex Processing System Employing Invention II. Method of Operating Complex Processing System III. General Description of a Simple Processing System IV. Detailed Description of the Simple Processing System Including Analog Computer Control A. Computing Yield and Cost Coefficients at the Local Computer B. Computing an LP Solution at the System Computer C. Computing the Bases of the LP Solution at the System Computer D. Setting the Flow Rate Controls E. Computing and Storing the Inverse Basis Matrix F. Computing the Simplex Multipliers G. Checking Local Optimization H. Checking Local Constraints I. Checking the Local Objective Function j. Correcting the LP Solution 1. Computing Sensitivity Coefficients 2. Computing New X's 3. Computing New Basis Matrix 4. Computing New Simplex Multipliers 5. Computing New Cost Coefficients V. Control of the Simple Processing System with a Digital Computer A. Correction of the LP B. Computing the Local Objective Function VI. Numerical Examples VII. Method of Operating a Complex Refinery System. VIII. Modified Method of Operating a Complex System.