Dynamic Correlation Integration

 Real Time Optimization Technology and

Its Industrial Application


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Dynamic Correlation Integration Real

Time Optimization Technology and Its Industrial Application






OptimiPro Control Technology Co., Ltd.







Without modifying process and adding equipment, real time operational optimization of production procedure could gain obvious economic benefit just by changing operation conditions. It is an efficient and effective technology without much investment., so that it has great research and application values.


To describe operational optimization of procedures, the following formulae are generally used:






Wherein, J denotes the objective function, J denotes the optimum of objective function; R denotes the operational condition, or called tuning variable.  denotes the optimum of tuning variable, and hg denote constraint functions.


Formula and are constraints of tuning variables. Generally they are appointed functions of processes. However, mapping  between x and J is an unknown function. To get, two methods are commonly used: Mathematical Modeling and Online Search Methods.


1.  Mathematical Modeling Method



The principle of modeling method is that building a mathematical modeling between objective function J and tuning variable x firstly, then evaluating  by nonlinear or linear programming based on the mathematical modeling and constraints.


According to different model building principles, mathematical modeling could be classified into mechanism and experience modeling.


Mechanism modeling combines operation mechanism equations of all parts of equipment in the system according to flow structures on the basis of mass and energy balance principles, which forms a set of mathematical equations adaptable for real production procedures. Finally, decide the relation between the objective function and tuning variable x according to systematical input and output, price, and so on.


Whereas, if the described procedure is too complex, or the mechanism itself is not clear, and or basic equation is not accuracy enough, it is often difficult to build mechanism model. What’s more, mechanism model of a system are generally without universality; it is even necessary to modify or change completely the model just when there are product changes or slightly process modification.


Experience modeling is to fabricate the experiential relation between the tuning variable and objective function based on plenty of data of experiments and daily operational report forms.  The advantages of this kind of modeling are simple and universal. No matter how complex and different is the procedure or system, same simple method could be used to build the model, and no special process knowledge and pretest equations are needed.


However, the reliability of this method is not very good. If the operational scope depart or overstep the data sampling scope when the model is built during online application, the model may cause too much error to be applied. Slightly change of process equipment may cause huge change of model structure, resulting in failure of modelling works.


2.  Online Search Method

Search method is a kind of universal method, which basic principle is to change the value of tuning variables on line, observe the changing of objective function, then decide whether the changing direction of tuning variables is right. In principle, many nonlinear programming methods, such as golden section and gradient, could be used on line. However, this method is often very sensitive to disturbance. It is well known that objective function is function not only of tuning variables, but also of other uncontrollable variables (environmental variables).  So that when the objective function is changed, it is difficult for us to decide whether it is caused by changes of tuning variables or disturbance.  In present online search methods, the relationship between tuning variables and objective function are generally taken as sole cause and effect relation. Therefor, when there is environmental disturbance, wrong judgment may be made, which could even cause reverse actions.


It is needed to point out, no matter modeling or direct search method, that all are generally built on the basis of the mathematical descriptions of ~.  The relationship between objective function J and x is defined as algebra map, not including environmental disturbance items. As a result, calculation methods educed from this is only adaptable to static and non-disturbance systems in principle. 


In fact, situations are much more complicated. Firstly, tuning variables not only have cause and effect relationship with objective function logically, but also have dynamic procedures by time. That is, when tuning variables change, objective function doesn’t change immediately, but has a transition procedure. Secondly, from the view of real conditions of lots of industrial procedures, objective functions often fluctuate. It is difficult to find a static condition. This is generally caused by those immeasurable and uncontrollable severe disturbances. For example, in production procedure, changes of component of feed often are uncontrollable. Due to difficulties of online component measurement, these variables usually are immeasurable. On the other hand, a lot of procedures are sensitive to changes of component. As a result, influence of changes of component on objective function is often larger than that of controllable temperatures, pressures, and other factors, which could amount to several decade times some time. Therefore, fluctuation caused by the variation of tuning variables often is “submerged” in the disturbance of component on function targets. In this dynamic disturbance situation, any research task on realizing tuning operation has both practical and academic meanings.


A kind of tuning theory based on dynamic correlation integration newly appeared provide a new method to solve above-mentioned problems. To solve problems radically, description of problems by this method is different from ~. It treats tuning variables and objective functions as a dynamic system, takes tuning variables as a mean-controllable random process, and adds dynamic disturbance items in objective functions. After serial research, feasible answers to the problems are found. In final educed dynamic correlation integration technology, real time optimization could be carried out without mechanism or static modeling. This method could be applied for industrial production processes, which is with complex mechanism, strong disturbance, many tuning variables, and hard for modeling.

Brief Introduction of Dynamic Correlation Integration Technology   


 1.     What Is Dynamic Correlation Integration and Dynamic Correlation Integraiton Optimizer

Dynamic Correlation Integration is a kind of operation relating to random process. The defination of dynamic correlation integration between random process x(t) and y(t) are:


Here, T,M are two relevant constants.


Dynamic correlation integration optimizer is a kind of special nonlinear differential equation:



F1,F2 are two fixed real functions.


It could adjust set point sp in real time, making objective function J amount to its maximum value.


2.  Characteristics of Dynamic Correlation Integration Technology

Compared with previous optimal technologies, dynamic correlation integration technology has following characteristics:



l        Permit dynamic fluctuation and disturbance existing in tuning variables and objective function of procedure, and the statistic properties of those fluctuation and disturbance are unknowable.


l        Unnecessary to build static and dynamic models in advance. Only if there is self balanced property and knowing approximately transition time.


l        Make use of natural fluctuation during normal operation, no additional test signal is needed. Therefore, its jamming to procedure operation is very little.


l        This technology has strong anti-disturbance feature. Even in severe interfere case, i.e. objective-function changes caused by other factors, such as material property, larger than useful signal (tuning variables causing changes of objective functions), it still could work normally. There is no this kind of strong anti-disturbance property ever before.


l        This optimizer is strong Robust. It still could work normally even when the dynamic and static characteristics have excursion.

3.     Applied Requirements For Dynamic Correlation Integration Optimizer

Dynamic correlation integration technology could apply for procedures that could meet the following requirements:


lIt must be a continuous production process. This technology could not be used in Batch process.


lIts optimized objective function must be able to be measured or calculated online. Because dynamic correlation integration needs continuous curve of objective function. Laboratory analytical data, which be gotten once for each several hours, cannot be adopted.


l The processes are controlled by DCS. For real time optimizer is a 24hour continuous close loop, which requires high reliability of computer control system. DCS system could meet these requirements.



Examples of industrial application


1.  Optimal Energy Recovery

Equipment used for optimal energy recovery is showed in Fig. 1.

The whole equipment actually is a jacketed heat exchanger. Water flows into it through control valve to smaller container. When water level reaches a fixed height, water flows out of the equipment from overflow port. Incoming water flow  is controlled in constant. Temperature of incoming water is.  Water in container  is heated by an electrical heater; water temperature T1 is controlled at fixed value. Larger container  is jacketed outside of  to form a jacket. Water flows into the jacket from control valve, and spill out from overflow port. Incoming temperature of jacket water is, but leaving temperature of it is. The flow W2 is controlled by computer.


The equipment is a heat recovery system, aiming at recovery heat from container. Obviously, heat recovered in each unit time is:  


Where,  denotes specific heat of water.


To recover the heat, it is a much to make water get kinetic energy  and overcome energy consumption  required by resistance in transportation pipe. Wherein,  denotes loss coefficient,  denotes pipe inner diameter. So, total recovery energy of the system is:


Because  and  are functions of time, and , could be seemed as constants. The above formula could be actually showed as follows:


Where, and are constants.


From theoretical analysis, it could be seen that the larger, the more heat recovered; and reach saturation state finally. For the final temperature of  couldn’t be lower than. Whereas, the larger the, the more kinetic energy is consumed. So, there shall be an optimal  which could make recovered energy from the system maximum.


In experiment, we adopt dynamic correlation integration optimizer to optimize  on line at real time and get good results.


Fig. 2     Optimal Energy Recovery Experiment


Experimental curve is showed in Fig. 2.




2.  Real Time Optimization of Solvent Dewaxing Process

In petrochemical enterprises, production of lube oil is an important part of processing of crude oil. And solvent dewaxing is the most adopted process presently. Adopting computer two-level real time optimization, the system make use of dynamic correlation integration technology to optimizing solvent ratio in close loop online, getting obvious economic benefit without changing process, adding equipment, and much investment.


Process description


In refineries, all oil (raw oil) after reduced pressure distillation contains lubricant oil and paraffin components at different ratio. To separate the lubricant oil and paraffin, freeze dewaxing process is widely used in industry. For freezing point of wax is pretty high, it is only necessary to cool and freeze raw oil, paraffin could be crystallized from raw oil and separated from lubricant oil by filtrating.

However, for cooling reason, raw oil becomes very viscidity, which influences transportation and filtration of oil and prevents crystallizing of paraffin severely. To reduce the viscosity of oil products, solvent is added many times into raw oil with the development of freezing degree. It is showed in Fig. 3.


It could be seen from Fig. 3 that raw oil is distributed into 5 branches. There are 3 crystallizers in each branch. After ammonia-cooling, ketone-benzol solvent, coming from solvent recovery system, is added into raw materials. In branch 1, flow ratios of injecting solvent 1 and solvent 2 to raw oil is called 1B1S1B2S solvent ratio. Each raw oil flows through 3 crystallizers and mixes with third solvent (3S), then enter into container 1C1. Raw oil from C1 has fully crystallized and enters into filter. Main component of the filtrate is mixture of lubricant oil and solvent, being sent to C5 and C6. Filtrate in C5 is sent to recovery section to remove solvent and distil lubricant oil. Paraffin from filter still contains some lubricant oil and solvent, and is sent for recovering and distilling. To improve filtrating effect, a stream of solvent is spraied into the filter, which is called washing solvent (WS). The ratio of washing solvent to total raw oil is called wash solvent ratio.



Objective function and tuning variables


In ketone-benzol dewaxing process, a key index is yield of dewaxed oil rate of lubricant oil to raw oil, which is influenced by feed amount of each solvent and distribution mode. Tuning task is to choose proper ratio of flow 1B1S, 2B1S,…5B1S, 1B2S, 2B2S,…,5B2S, 3S and WS to make yield of dewaxed oil maximum.


Apparently objective function of optimization is yield of dewaxed oil, tuning variables are these solvent ratios. By adjusting the solvent ratios modifying crystallizing condition to improve filtration efficiency and maximize the yield of dewaxed oil.



Constrains are permitted scope in optimization, for example, range of each tuning variables. Total solvent ratio (the sum of solvent flow injected to the process/feed flow) is a key index that is related to energy consumption. In addition, capacity of solvent recovery system is constrained. Upper limit of total solvent ratio could be added to the optimal process.



Real Time Optimization


In this real time optimization system, two-level computer optimal control is adopted. By dynamic correlation integration technology, the system collects data online for each two minutes and calculates correlation integration, 10 optimal solvent ratios are given each hour, which are sent to basic controllers as setpoints for execution.


Economic benefits and long-time operational effect


Generally, yield of dewaxed oil could be improved 0.5-2%(absolute percent) by adopting the system. The increment of yield is related to original level of operation, raw material properties, filters, and so on of the plant. Table 1 is the yield compared-condition after adopting this system.


Table 1. Yield compared-condition after adopting the system.

Raw oil type

Manual operation

Real time optimization

Increment of yield















3.  Real Time Optimization for Catalytic Cracking

Fluid Catalytic Cracking Unit (FCCU) is important equipment in petroleum processing, which cracks wax oil and final residuum to liquid hydrocarbon, gasoline and diesel oil (with higher economic value) under the action of catalyst. Its operation state influences yields of all products directly and economic benefits.




Process of a catalytic cracking is showed in Fig. 4.


Vacuum residue and wax oil from tank farm are mixed with deasphalted propane oil; after heat exchanging with mass flow of fractionation system, mixed with cycle oil and oil slurry, sprayed into lift pipe reactor through atomization device at the lower part of lift pipe.


Atomized raw oil, sprayed steam and high-temperature catalyst from reproducer are mixed at the lower part of reactor, mounting up along with lift pipe to joining catalytic cracking reaction. Reacted oil and gas with catalyst is sent to settler from the top of lift pipe. Oil and gas with catalyst enters into crude cyclone separator, then separated oil and gas is sent to two sets of high effective cyclone separators. Finally, oil and gas leaves the settler, entering into fractionation system for product separation.


Most of separated catalyst through the dipleg of crude cyclone separator is pre-stripped by steam and then enters stripping zone of the settlers. Entrained oil and gas is stripped out of catalyst. Stripped catalyst, waiting for regeneration, is separated into two flows. One flow enters into first regenerator for burning regeneration; the other flow enters into second regenerator, with half-regenerated catalyst from first regenerator, waiting for burning regeneration together. Regenerated catalyst is transported to lift pipe reactor for recycle.


Oil and gas from settler enters into fractionation tower. After separation, crude gasoline is yielded at the top of the tower; light diesel oil is yielded at the middle of the tower and sent to successive section. Cycle oil slurry and cycle oil backflow to feed section to mix with new feeding and are sent to the reactor for recycle.



Objective function and optimized variables


There maybe many objective functions of FCCU. In this example, multi-objective mode is used, i.e. optimal target could be switched according to requirements. If liquid hydrocarbon is main product, take yield of liquid hydrocarbon as objective function; if gasoline is main product, take yield of gasoline as objective function; if diesel oil is main product, take yield of diesel oil as objective function. For the total economic benefit of the unit, take economic benefit of processing each barrel of raw material as objective function.


When selecting optimized variables, important and easy controllable variables in reaction-regeneration sections are considered. In the example FCCU, the following variables are taken as online optimized variables:


l        Outlet temperature of lift pipe    

l        Flow rate of pre-stripping steam

l        feed temperature

l        Ratio of residuum

l        Ratio of cycle oil

l        Ratio of cycle oil slurry

l        Drained oil slurry


For constrains, liquid level of fractionation tower, upper and lower limitations of optimized variables, and product distribution are considered, and dynamic correlation integration optimization technology is used.


Applied effect


To test the function and effect of the catalytic cracking real time optimization, manual operation and computer online optimization are carried out under same conditions. The results are shown in table 2:


Table 2 shows the variation of yields of main products from default values (manual operation) to optimized values.


Table 2  yield variation of main products of each optimal process

Objective function

Main product

default yield%

Optimal yield%


Yield of liquid hydrocarbon






Yield of gasoline





Yield of diesel oil

Diesel oil




From table 2, it could be seen that yields of each main product is increased, indicating the validity of real time optimization.


In table 3, benefit variation in the total economic benefit mode is illustrated. For a 7140000 barrel/a plant, USD 428, 970,000 benefit is obtained each year after adopting this real time optimization technology.



Table 3  Economic Benefit Effect of Optimal Process


Default value

Optimized value

Increment USD/barrel

benefitUSD/barrel raw material