CN100346856C - Rectification tower automatic control and optimization method - Google Patents

Abstract

The present invention relates to a method for controlling and optimizing a distillation tower, which is characterized in that a distillation tower is controlled according to the balanced relation of materials and the balanced relation of components and is optimized by a surrogate model. The drawing-out ratio (being short for light and heavy product ratio in the following) a heavy product at the bottom of the tower to a light product at the top of the tower is used as a main controlled variable according to the rectification principle, the balanced relation of the materials and the balanced relation of the components in the distillation tower, and the light and heavy product ratio, the temperature and the reflux ratio are controlled through regulating reflux quantity and the thermal load of a reboiler so that the stable operation is achieved. An actual process is simulated through process simulating software, and a neural network model is trained and used as the surrogate model for process optimization. The surrogate model is used for operation optimization by utilizing the testing data of raw materials and products so that the clamping side optimization of the products is achieved, and the present invention increases the yield of high-value products and realizes energy saving and consumption reduction of a device at the premise of ensuring the qualified quality of the products.

Description

A kind of automatic control and the optimization method of rectifying column

Technical field

The present invention relates to the automatic control and the optimization method of rectifying column, belong to chemical industry rectifying column and production process automation field.

Background technology

In petroleum refining, chemical process, almost each device has all related to liquid-liquid separation process, and rectifying column is to realize dissolving each other the main process unit that thing liquid-liquid separates.

Rectifying column is different with separation accuracy according to the product number, can be divided into two classes: a class is called fractionating column, purpose is very complicated to be divided into a plurality of products as raw materials such as oil by boiling range with forming, therefore except that at the bottom of cat head, the tower, there are a plurality of product side lines, as atmospheric and vacuum distillation unit atmospheric distillation tower, catalytic cracking unit main fractionating tower or the like, the main measurement index of its product quality is boiling range and similar parameters; Another kind of is rectifying column, and purpose is that each key component of forming in the simple relatively raw material is separated, and the fine degree of separation looks to produce needs decision.Each rectifying column has only two products at the bottom of cat head, the tower, and each component can only mainly be present in cat head or the bottom product, and as gas separation unit propylene rectification tower, styrene device phenyl ethylene rectification tower or the like, the main measurement index of product quality is the content of impurity.

N class key component in liquid-liquid mixture to be separated, then need N-1 rectifying column at least.Rectifying column is the process apparatus according to the design of rectifying principle.The column plate of rectifying column temperature from top to bottom raises gradually, after raw material enters rectifying column from the middle part, carries out flash distillation on each layer column plate, realizes separating purpose.The gaseous substance that cat head overflows goes out device through the condensation rear section as overhead product, and part is as refluxing as control measures.The liquid phase substance of extracting out at the bottom of the tower is after the reboiler heating, and the vaporization part is returned tower as main thermal source, and liquid phase part goes out device as bottom product.Reasonably design reflux ratio, obtain enough separation accuracies; Regulation and control cat head column bottom temperature makes cat head bottom product impurity content all meet standard.

Because the popularity that rectifying column is used, the control of rectifying column just had crucial meaning with optimizing.By control and optimization to rectifying column, make the device smooth operation, improve product percent of pass, reduce the loss of high-value product in the low-value product, energy-saving and cost-reducing simultaneously, reduce the thermic load of reboiler.Therefore, the control to rectifying column just has high economic benefit with optimization.

Existing rectifying column control of product quality scheme has almost all adopted the mode based on the soft measurement of product quality.As the intelligence control method (patent No. 02111034) of propylene rectification tower in the ethylene unit, the intelligence control method of ethylene rectifying column in the ethylene unit (patent No. 02148476) etc.By setting up the product quality soft-sensing model of rectifying column, utilize the process real time datas such as temperature, pressure, flow of rectifying column, online real-time counting yield quality realizes control on this basis and optimizes.This soft sensor modeling realizes that it is feasible that the fractionating column cut point calculates, but be difficult to reach the requirement of rectifying column, because the precision of soft-sensing model input variable such as flow detection is low, output variable is an impurity concentration, the order of magnitude is usually in some thousandths of to ten thousand/several, and the Chang Weiyi position effective digital, truncated error is big.Simultaneously, because the needs of rectifying, the general number of plates is all many, and for improving the separative efficiency of column plate, its return tank and column plate amount of savings are relatively large with the ratio for the treatment of capacity in addition.This has the characteristics of big delay, large time constant with regard to the dynamic characteristic that has caused rectifying column.When operating condition changed, product quality changed and to reach stable time quite long, had exceeded the acceptance level of PREDICTIVE CONTROL.This also is unfavorable for the control scheme based on the soft measurement of product quality.

Find according to the operating process analysis of actual rectifying column with based on the simulation study of flowsheeting software: when the operating condition variation of rectifying column, product quality changes and to reach stable time quite long, but heavy product is extracted ratio out and can be produced significant change faster at the bottom of cat head light product and the tower, and often vibrate, it is the main cause that causes the operation shakiness of tower.Heavy product is extracted ratio out and is departed from and satisfy the needed material balance relationship of product quality indicator and component balanced relation is the major influence factors that influences the product quality of tower at the bottom of cat head light product and the tower, and the process that has large time delay for rectifying column like this, it is very long to influence the duration, that is to say that current interference to the influencing meeting and just can display of product quality, at this moment regulates just late again after the long period.Therefore, can be at the bottom of cat head, tower operating condition change that (reflux temperature that causes as the start and stop of cat head Air-cooled Unit, climate change changes, tower bottom steam variations in temperature etc.) and feed conditions when changing (as variations such as feed rate, feeding temperatures) and causing weight product rate of change, it is constant to keep it to stablize, can overcome the disturbance factor that causes that further product quality changes, the product quality of keeping tower is steady, the product quality analysis data that so just can wait until new moment tower arrives, and carries out the optimization of a new round and the fine tuning of product quality.For the interference that feed component changes, when the analysis data that comprises feed component arrives, to recompense when optimization at this moment and product quality fine tuning, this mainly can be realized by feedforward compensation.

Summary of the invention

Purpose of the present invention: propose a kind of novel rectifying column control and optimization method.According to the material balance relationship and the component balanced relation of rectifying principle and rectifying column, adopt weight product ratio as main controlled variable, by regulating capacity of returns and reboiler thermic load, control weight product ratio, temperature, reflux ratio reach quiet run.By the mechanism mathematical model of flowsheeting software or any other rectifying column, realize emulation, and the neural network training model is as the agent model of process optimization to real process.Utilize the analysis data of raw material and product, use agent model to carry out operation optimization, reach the edge optimization of product, guaranteeing to increase the yield of high-value product under the qualified prerequisite of product quality, and implement device is energy-saving and cost-reducing.

The invention is characterized in: this method contains following off-line training and 2 stages of on-line implement successively:

Off-line training step contains following steps:

Steps A 1: use the rectifying column of HYSYS flowsheeting software simulation reality, and act on behalf of neural network model according to process data and product quality data foundation optimization that this simulation softward produces; This steps in sequence is undertaken by following substep:

Steps A 1.1: use HYSYS flowsheeting software simulation rectifying column, and model parameter is adjusted, to obtain and actual approaching analog result according to the on-the-spot real data that collects by Distributed Control System;

Steps A 1.2: process data and product quality data sample that above-mentioned flowsheeting software is produced carry out standardization by following formula:

x ^o＝(x-m _x)/σ _x，

Wherein x is an initial data, x ^oStandardized data for correspondence;

m _x, σ _xArithmetic mean of instantaneous value and the standard deviation of representing this data sample respectively;

Described data sample obtains by following steps: changes operating condition, obtains process data and product quality data under the different operating modes, thus the multi-group data that obtains;

Steps A 1.3: set up final neural network model according to the multi-group data sample that steps A 1.2 obtains, this model is that final training error and predicated error are a minimum model in a plurality of neutral nets:

$C_{\mathrm{top}}^o={\mathrm{NN}}_{\mathrm{top}}({(D/B)}^o,T_{\mathrm{top}}^o,T_{\mathrm{bot}}^o,{(R/F)}^o,{(Q/F)}^o),$

$C_{\mathrm{bot}}^o={\mathrm{NN}}_{\mathrm{bot}}({(D/B)}^o,T_{\mathrm{top}}^o,T_{\mathrm{bot}}^o,{(R/F)}^o,{(Q/F)}^o),$

NN wherein _Top, NN _BotThe expression neural network model, actual is 5 * 10 * 1 RBF network;

Steps A 2: actual rectifying column is carried out test modeling, set up the following step response model of capacity of returns, reboiler thermic load and overhead product flow, bottom product flow, tower top temperature, column bottom temperature:

$\left[\begin{array}{c}{D}_c\\ B_c\\ T_{\mathrm{top}}\\ T_{\mathrm{bot}}\end{array}\right]=f(G,\left[\begin{array}{c}R\\ Q\end{array}\right]),$

Wherein f is a convolution algorithm;

G is the step response model that test modeling is set up;

The on-line implement stage comprises following steps:

Step B1: host computer initialization:

Be provided with: the timer cycle;

Overhead product impurity divides rate C _TopWeight w _Ctop

Bottom product impurity divides rate C _BotWeight w _Cbot

The weight w of thermic load amount Q _Q

The weight w of the actual weight product ratio amount of transfiniting Δ η _η

The tower top temperature amount of transfiniting Δ T _TopWeight w _Ttop

The column bottom temperature amount of transfiniting Δ T _BotWeight w _Tbot

The weight w of the reflux ratio amount of transfiniting Δ r _r

Making fitness function J is the constant C onst that positive number is set;

Step B2: be carved into when judging control not:

If be carved into during control, then carry out next step; Otherwise, wait for;

Step B3: host computer through the OPC communication interface by the rectifying column field data below the Distributed Control System collection and deposit real-time data base in: overhead product amount D, bottom product amount B, tower top temperature T _Top, column bottom temperature T _Bot, capacity of returns R, thermic load amount Q and inlet amount F; Be calculated as follows cat head, bottom product flow behind the liquid level dynamic compensation simultaneously, change the product flow measured deviation that causes with the product savings of avoiding producing because of level fluctuation at the bottom of cat head, the tower:

D _c＝D+(h _top(L _top，new)-h _top(L _top，old))/t，

B _c＝B+(h _bot(L _bot，new)-h _bot(L _bot，old))/t，

H wherein _Top, h _BotBe the function that liquid level is converted to the quality amount of savings based on the container Mathematical Modeling;

L _{Top, new}, L _{Top, old}Be respectively current and a period of time return tank of top of the tower liquid level detected value before, its numerical value is got percentage;

L _{Bot, new}, L _{Bot, old}Be respectively still liquid level detected value at the bottom of the tower before current and a period of time, its numerical value is got percentage;

T is that the time interval of being got is calculated in compensation;

Actual weight product ratio:

η＝D _c/B _c；

Step B4: host computer judges whether to obtain new product quality analysis data:

If obtain new product quality analysis data, then execution in step B5; Otherwise, change step B6 over to;

Step B5: based on the product quality analysis data described neural network model of genetic algorithm optimization, with the more excellent controlled variable of search, reach the assurance product quality, reduce capacity of returns, reduce the purpose of these two performance variable values of reboiler thermic load, described controlled variable is meant weight product ratio, tower top temperature, column bottom temperature and reflux ratio; This steps in sequence contains following each substep:

Step B5.1: colony of initialization:

Set the value of individual in population number n, each individual b _iBe to be designated as { D/B, T _Top, T _Bot, R/F, the data group of Q/F}, wherein each variable is all evenly got a plurality of values in 5～10% the closed interval about of current operating value, finally is combined into the data group individuality that has nothing in common with each other;

Step B5.2: read neural network model, calculate each individual fitness according to neural network model and following formula, described fitness is

Fit＝Const-(w _CtopC _top+w _CbotC _bot+w _QQ)；

Step B5.3: determine to select each individual number of times according to following formula,, eliminate the little individuality of fitness, generate new colony to keep the big individuality of fitness:

$\mathrm{Num}\left(b_i\right)=\mathrm{Fit}\left(b_i\right)/\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{Fit}\left(b_j\right)*n,i=\mathrm{1,2},...,n;$

Step B5.4: from the colony that step B5.3 obtains, select p at random _c* n is right, p _c=0.05～0.1, at every couple of individuality { b _i, b _jIn select k variable in the data group at random, be calculated as follows new value, and replace old value, form new individuality:

b _i，new{k}＝Rand*b _i，old{k}+(1-Rand)*b _j，old{k}，

b _i，new{k}＝(1-Rand)*b _i，old{k}+Rand*b _j，old{k}，

Wherein Rand is [1,2] interval interior equally distributed random number;

Step B5.5: from the colony that step B5.4 obtains, select p at random _v* n, p _v=0.02～0.05, each individuality is selected certain variable in the data group at random, increases or reduce a percentage 1～5% at random;

Step B5.6: in the colony that step B5.5 is obtained, suitably remove the repeating data of selecting in the operation, remain unchanged to guarantee the individual in population number;

Step B5.7: in the colony that step B5.6 is obtained, repeating step B5.2～B5.6 is tending towards a stationary value until the fitness of individual in population maximum, though perhaps do not reach till the iterations that stationary value reached setting; Take out the optimal solution of the individuality of this maximum adaptation degree, and this is separated as the target of controlling described each controlled variable as optimization calculating;

Step B6: as performance variable, as controlled variable, rectifying column is carried out multivariable prediction control with weight product ratio, tower top temperature, column bottom temperature and reflux ratio with capacity of returns and reboiler thermic load; This steps in sequence contains following each substep:

Step B6.1: judge whether off-duty mistake of above-mentioned optimization: if the off-duty mistake, then weight product ratio with the mean value of 1～2 hour actual value before as target, tower top temperature, column bottom temperature and reflux ratio with the center line of control bound as target; If moved, then the optimal solution that step B5.7 is obtained is as the target of described each controlled variable;

Step B6.2: read step response model, and press step response model, the computing formula of weight product ratio η and the hybrid prediction model of following formula generative process:

Reflux ratio r:

r＝R/D _c；

Step B6.3:, realize the multivariable prediction control of rectifying column according to the hybrid prediction model of process:

At first, set the control bound: the control limit of weight product ratio is based on the control target, the permission percentage that setting departs from, get 0～10%, the control limit of tower top temperature, column bottom temperature and reflux ratio is revised on the Distributed Control System operation interface according to Rectification Tower Design parameter and operating experience by the operative employee.

Secondly, set soft priority: reflux ratio＞temperature＞weight product ratio; Wherein, temperature comprises tower top temperature and column bottom temperature;

Once more, the control goal-setting is the amount of the transfiniting weighted calculation value minimum of each variable:

J _c＝w _η|Δη|+w _Ttop|ΔT _top|+w _Tbot|ΔT _bot|+w _r|Δr|，

J wherein _cBe the control object function;

Δ η, Δ T _Top, Δ T _Bot, Δ r is respectively controlled variable η, T _Top, T _Bot, r exceeds the value of control limit, poor for corresponding control limit when each controlled variable value transfinites is 0 when not transfiniting;

w _η, w _Ttop, w _Tbot, w _rBe respectively controlled variable η, T _Top, T _Bot, r actual weights, determine by following formula:

$w_{\mathrm{\η}}=w_{\mathrm{\η}}^o/{\mathrm{\σ}}_{v,\mathrm{\η}},w_{\mathrm{Ttop}}=w_{\mathrm{Ttop}}^o/{\mathrm{\σ}}_{v,\mathrm{Ttop}},w_{\mathrm{Tbot}}=w_{\mathrm{Tbot}}^o/{\mathrm{\σ}}_{v,\mathrm{Tbot}},w_r=w_r^o/{\mathrm{\σ}}_{v,r},$

W wherein _η ^o, w _Ltop ^o, w _Lbot ^o, w _r ^oBe respectively controlled variable η, T _Top, T _Bot, r the standardization weights, according to above-mentioned soft priority level initializing;

σ _{V, η}, σ _{V, Ttop}, σ _{V, Tbot}, σ _{V, r}Be respectively controlled variable η, T _Top, T _Bot, r standard deviation;

Step B7: the value of the controlling value of capacity of returns and reboiler thermic load and each controlled variable of response, this control cycle finishes, and gets back to step B2 and waits for following one-period.

Use proof: the present invention makes the operation of rectifying column more steady, and the impurity of cat head, bottom product descends, and energy consumption also descends simultaneously, and under the identical operations expense higher separating degree is arranged.

Description of drawings

Fig. 1. the principle process chart of rectifying column device.

Fig. 2. control and a kind of implementation of optimizer in host computer: a, execute-in-place flow chart; B, the host computer operational flowchart.

Fig. 3. the block diagram of off-line training modeling: a, the training step of the neural network model of optimization, b, the step response model identification step of control.

Fig. 4. the program flow diagram of rectifying column on-line optimization control.

The specific embodiment

Optimize the foundation of agent model (neural network model)

Flowsheeting software or other Analysis on Mechanism model carry out analog simulation by the modelling by mechanism mode to multiple chemical process unit, by parameter adjustment, can reach enough degrees of accuracy and instruct production.Owing to adopt the mechanism mode, can in a big way, guarantee accuracy to the actual cell process simulation.But because the complexity that mechanism is calculated, amount of calculation is bigger, be difficult to online use, and software price is high.

Use flowsheeting software or other Analysis on Mechanism model that the inputoutput data of reflection production process wide variation is provided, carry out the training of statistical model, obtain simply can online use agent model, just can overcome this shortcoming.Simultaneously, use the data training of flowsheeting software or other Analysis on Mechanism model, real process data relatively can also overcome that data have noise jamming in the real process, and data coverage is little, can't obtain real weakness such as steady state data.

In this method, use HYSYS flowsheeting software, set up the flowsheeting of rectifying column, and the flow process analog parameter is adjusted, to obtain and actual approaching analog result according to the Distributed Control System real data.

Set up to optimize and act on behalf of neural network model, input variable is chosen cat head bottom product amount than D/B, tower top temperature T _Top, column bottom temperature T _Bot, capacity of returns charge ratio R/F, thermic load amount charge ratio Q/F, so the data that actual needs obtains comprise overhead product amount D, bottom product amount B, tower top temperature T _Top, column bottom temperature T _Bot, capacity of returns R, thermic load amount Q, inlet amount F.Output variable is respectively overhead product impurity branch rate C simultaneously _Top, bottom product impurity divides rate C _Bot, i.e. cat head bottom product quality.

Change operating condition, obtain process data and product quality data under the different operating modes.It is defective that operating mode has contained product quality, and performance variable, controlled variable and design conditions depart from situations such as bigger.500 groups of data samples of final acquisition.These inputoutput datas are carried out standardization:

x ^o＝(x-m _x)/σ _x，

Wherein x is an initial data, x ^oStandardized data for correspondence;

m _x, σ _xArithmetic mean of instantaneous value and the standard deviation of representing this data sample respectively;

Afterwards, therefrom choose 400 groups of data as training sample, other 100 groups of data are as test sample book.Use training sample to carry out the training of neutral net iteration, and to the neutral net of per step training gained with training sample calculation training error, calculate predicated error with test sample book, when predicated error increases or training error when no longer obviously reducing by reducing to become, this neural metwork training finishes.Use the method to train a plurality of neutral nets, select final training error and predicated error all minimum as training result.

The final neural network model form of setting up is as follows:

$C_{\mathrm{top}}^o={\mathrm{NN}}_{\mathrm{top}}({(D/B)}^o,T_{\mathrm{top}}^o,T_{\mathrm{bot}}^o,{(R/F)}^o,{(Q/F)}^o),$

$C_{\mathrm{bot}}^o={\mathrm{NN}}_{\mathrm{hot}}({(D/B)}^o,T_{\mathrm{top}}^o,T_{\mathrm{bot}}^o,{(R/F)}^o,{(Q/F)}^o),$

NN wherein _Top, NN _BotThe expression neural network model, actual is 5 * 10 * 1 RBF network;

At line computation weight product ratio and carry out index correction (data processing module)

By the rectifying column material balance,

F＝D+B，

Fx _F＝Dx _D+Bx _B，

Wherein F, D, B are feed rate, cat head, bottom product flow;

x _F, x _D, x _BFor light component in charging, cat head, the bottom product divides rate, and x _B＜x _F＜x _D

Then exist

D/B＝(x _F-x _B)/(x _D-x _F)，

Therefore it is constant to desire to keep product quality in the operation, and keeping D/B constant is a primary condition.

Based on the charging analysis data with to the requirement of product purity, can the desirable weight product rate value of primary Calculation.For the multicomponent rectifying column, at the bottom of its each component can concentrate on cat head or tower according to technological design, then in view of the above all components is divided at the bottom of cat head group categories or the tower in the group categories, regard two class components as two kinds of components and handle, just can be equivalent to the bi-component rectifying column.

Because the variation of liquid level can influence the product real-time traffic at the bottom of the cat head tower, therefore will carry out the liquid level dynamic compensation calculates, the liquid level compensating for variations on product flow, is obtained really the flow that flows out in tower, avoid the fluctuation of liquid level and the product savings that produces and the product flow measured deviation that causes.

D _c＝D+(h _top(L _top，new)-h _top(L _top，old))/t，

B _c＝B+(h _bot(L _bot，new)-h _bot(L _bot，old))/t，

D wherein _c, B _cBe cat head, the bottom product flow after the compensation;

h _Top, h _BotBe the function that liquid level is converted to the quality amount of savings based on the container Mathematical Modeling;

L _{Top, new}, L _{Top, old}Be respectively current and a period of time return tank of top of the tower liquid level detected value before, its numerical value is got percentage;

L _{Bot, new}, L _{Bot, old}Be respectively still liquid level detected value at the bottom of the tower before current and a period of time, its numerical value is got percentage;

T is that the time interval of being got is calculated in compensation.

For the common horizontal return tank of cat head,

$h_{\mathrm{top}}\left(L_{\mathrm{top},\mathrm{new}}\right)={\mathrm{\ρ}}_{\mathrm{top}}{\mathrm{Len}}_{\mathrm{top}}*(\arccos \left(\frac{(0.5-L_{\mathrm{top},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{top}}}{R_{\mathrm{top}}}\right)*R_{\mathrm{top}}^2$

$-(0.5-L_{\mathrm{top},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{top}}\sqrt{R_{\mathrm{top}}^2-{\left((0.5-L_{\mathrm{top},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{top}}\right)}^2}),$

$h_{\mathrm{top}}\left(L_{\mathrm{top},\mathrm{old}}\right)={\mathrm{\ρ}}_{\mathrm{top}}{\mathrm{Len}}_{\mathrm{top}}*(\arccos \left(\frac{(0.5-L_{\mathrm{top},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{top}}}{R_{\mathrm{top}}}\right)*R_{\mathrm{top}}^2$

$-(0.5-L_{\mathrm{top},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{top}}\sqrt{R_{\mathrm{top}}^2-{\left((0.5-L_{\mathrm{top},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{top}}\right)}^2}),$

And for vertical tower still at the bottom of the tower:

$h_{\mathrm{bot}}\left(L_{\mathrm{bot},\mathrm{new}}\right)={\mathrm{\ρ}}_{\mathrm{bot}}*{\mathrm{\πR}}_{\mathrm{bot}}^2*(0.5-L_{\mathrm{bot},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{bot}},$

$h_{\mathrm{bot}}\left(L_{\mathrm{bot},\mathrm{old}}\right)={\mathrm{\ρ}}_{\mathrm{bot}}*{\mathrm{\πR}}_{\mathrm{bot}}^2*(0.5-L_{\mathrm{bot},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{bot}},$

ρ wherein _Top, ρ _BotBe respectively density of liquid at the bottom of cat head, the tower;

R _Top, R _BotBe respectively the radius of still at the bottom of return tank of top of the tower, the cylindrical tower;

H _Stop, H _SbotBe respectively the detection height of liquid level instrument at the bottom of cat head, the tower;

Len _TopLength for return tank of top of the tower.

Product flow after the compensation more can reflect the actual conditions of device operation, promptly obtains from the actual change of the product volume of tower outflow.

Actual weight product ratio η is calculated as follows:

η＝D _c/B _c。

Each flow is got currency or the arithmetic mean of instantaneous value in 2～10 minutes before this during calculating.Growth average time can improve and overcomes interference performance, but reduces response speed.

Because on-the-spot flow instrument inevitably exists error, so this desirable weight product rate value can not be directly used in to instruct and produce, and need proofread and correct with the weight product rate value of reality.This method adopts adaptively correcting, promptly when using for the first time, gets the D in 1 to 2 hour before this _c, B _cThe historical data arithmetic mean of instantaneous value calculates weight product ratio initial set value, waits until the change amount that provides weight product ratio set when actual product quality analysis data arrives by optimization and product quality fine tuning afterwards.This relative adjustment, can't obtain real weight product rate value in actual applications with regard to having solved owing to the instrument measurement accuracy limitations, and can not realize weight product ratio is controlled to the difficult problem of reasonable value, this also is to restrict for a long time based on direct material balance control scheme directly to realize the problem that controllable quality is difficult to realize.

Set up the forecast model of process

With capacity of returns and reboiler thermic load as performance variable, with weight product ratio, tower top temperature, column bottom temperature, reflux ratio as controlled variable, as the multivariable prediction control scheme of rectifying column.

By carrying out test modeling, can set up the step response model of capacity of returns, reboiler thermic load and overhead product flow, bottom product flow, tower top temperature, column bottom temperature:

$\left[\begin{array}{c}{D}_c\\ B_c\\ T_{\mathrm{top}}\\ T_{\mathrm{bot}}\end{array}\right]=f(G,\left[\begin{array}{c}R\\ Q\end{array}\right]),$

Wherein f is a convolution algorithm;

G is the step response model that test modeling is set up.

Calculate by Analysis on Mechanism then, set up the hybrid prediction model of process.Wherein weight product ratio calculates and provides, and reflux ratio r is calculated as follows:

r＝R/D _c。

Realize the multivariable prediction control (control module) of rectifying column

Based on above-mentioned hybrid prediction model, calculate weight product ratio, reflux ratio in real time and obtain the real time temperature value as controlled variable, carry out multivariable prediction control configuration and enforcement.

Realize the coordination control of weight product ratio, cat head column bottom temperature, this three classes controlled variable of reflux ratio, need on control strategy, treat respectively each class variable.

For weight product ratio, calculate given control target to optimize, provide the percentage that departs from and limit as control.The span that departs from the percentage proportional limit is 0～10%, and the value increase helps to improve control stability, but has reduced control accuracy.For temperature and reflux ratio, adopt Region control, on the Distributed Control System operation interface, revise the bound of control according to Rectification Tower Design parameter and operating experience by the operative employee.Keeping reflux ratio is in order to guarantee that rectifying column has both economical separating degree in certain zone.

According to Analysis on Mechanism, each variable in stable operation, guarantee the ability difference of product on qualified, thereby different soft priority just should be set, when variable transfinites, regulate according to soft priority.Soft priority level initializing is as follows:

Reflux ratio＞temperature＞weight product ratio

The control target is the amount of the transfiniting weighted calculation value minimum of each variable.Promptly

J _c＝w _η|Δη|+w _Ttop|ΔT _top|+w _Tbot|ΔT _bot|+w _r|Δr|，

J wherein _cBe the control object function;

Δ η, Δ T _Top, Δ T _Bot, Δ r is respectively controlled variable η, T _Top, T _Bot, r exceeds the value of control limit, poor for corresponding control limit when each controlled variable value transfinites is 0 when not transfiniting;

w _η, w _Ttop, w _Tbot, w _rBe respectively controlled variable η, T _Top, T _Bot, r actual weights.

Weight computation method has continuity, both can guarantee that a certain variable transfinites it mainly to be regulated when very big, can realize all transfinite coordination control when little of several variablees again.Weights are big more, illustrate that the amount of transfiniting that this Variable Control reaches is more little, and promptly the soft priority of this variable is big more.According to the standardization weights of the different sizes of each variable of soft priority level initializing,, instead push away the actual weights that should be provided with again according to the variance size of this variable:

$w_{\mathrm{\η}}=w_{\mathrm{\η}}^o/{\mathrm{\σ}}_{v,\mathrm{\η}},w_{\mathrm{Ttop}}=w_{\mathrm{Ttop}}^o/{\mathrm{\σ}}_{v,\mathrm{Ttop}},w_{\mathrm{Tbot}}=w_{\mathrm{Tbot}}^o/{\mathrm{\σ}}_{v,\mathrm{Tbot}},w_r=w_r^o/{\mathrm{\σ}}_{v,r},$

W wherein _η ^o, w _Ttop ^o, w _Tbot ^o, w _r ^oBe respectively controlled variable η, T _Top, T _Bot, r the standardization weights;

σ _{V, η}, σ _{V, ltop}, σ _{V, lbot}, σ _{V, r}Be respectively controlled variable η, T _Top, T _Bot, r standard deviation.

The actual weights that are provided with that will instead push away gained by the engineer interface carry out online modification.

Agent model operation optimization (optimization module) based on the product quality analysis data

In the actual production, common 4～8 hours of raw material and product sampling chemical examination is (better if any in-line analyzer, that sampling period of much shorter can be arranged) once.After obtaining analysis data, according to agent model,, reduce reflux ratio to guarantee product quality, reducing the reboiler thermic load is target, uses intelligent optimization algorithms such as genetic algorithm, searches for more excellent controlled variable, performance variable desired value.

Colony of initialization, getting individual number is n=30～150.Each individual b _iBe to be designated as { D/B, T _Top, T _Bot, R/F, the data group of Q/F}, wherein each variable all in the even value (comprising the border) in 5～10% up and down of current operating value, finally is combined into the data group individuality that has nothing in common with each other.

Get fitness function

Fit＝Const-(w _CtopC _top+w _CbotC _bot+w _QQ)，

Wherein Const is a constant, act as to make J guarantee to be positive number;

w _Ctop, w _Cbot, w _QBe respectively variable C _Top, C _Bot, Q weights.

Calculate each individual fitness according to neural network model and following formula, wherein neural network model is a forward calculation.

Select computing: according to

$\mathrm{Num}\left(b_i\right)=\mathrm{Fit}\left(b_i\right)/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{Fit}\left(b_j\right)*n,i=\mathrm{1,2},...,n$

Determine to select each individual number of times, generate new colony.Like this, the individuality that fitness is big remains, and the individuality that fitness is little may be eliminated.

Crossing operation: from new colony, select p at random _c* n is to (p _c=0.05～0.1), in every pair of individuality, selects certain variable in the data group at random, do interpolation and calculate

b _i，new{k}＝Rand*b _i，old{k}+(1-Rand)*b _j，old{k}，

b _j，new{k}＝(1-Rand)*b _i，old{k}+Rand*b _j，old{k}，

Wherein Rand is [1,2] interval interior equally distributed random number.Newly be worth the old value of replacement with calculating gained, form new individuality.

Variation computing: in new colony, select p at random _v* n (p _v=0.02～0.05), each individuality is selected certain variable in the data group at random, increases or reduce a percentage (1～5%) at random.

Afterwards, suitably remove the repeating data of selecting in the operation, remain unchanged to guarantee the individual in population number.New colony iteration is carried out fitness calculating and the computing of selecting, intersect, make a variation, till the fitness of individual in population maximum is tending towards a stationary value or iterations and reaches a certain numerical value (100～150), take out the optimal solution of the individuality of this maximum adaptation degree as optimization calculating, and with the control target of this optimal solution as each controlled variable of control computing.

The present invention is from the control and the optimization demand of rectifying column, according to the high characteristics of rectifying column product quality required precision, the give chapter and verse material balance relationship and the component balanced relation of rectifying principle and rectifying column, adopt weight product ratio to carry out operation optimization as the control method and the use agent model of main controlled variable, reach the edge optimization of product, guaranteeing to increase the yield of high-value product under the qualified prerequisite of product quality, and the energy-saving and cost-reducing optimization method of implement device.This invention, by solving the setting and the optimization problem of weight product ratio reasonable value, realized this control of observational variable of the following fluctuation of reflection product quality fast of weight product ratio, create maintenance product quality condition stably, be able to utilize the analysis data in long sampling chemical examination cycle to be optimized fine tuning with product quality.The present invention does not rely on soft measurement, has overcome many shortcomings that the soft certainty of measurement of relative rectifying column high purity product index request is difficult to meet the demands and brings.

Fig. 1 is a rectifying column principle process chart.Among the figure, D is that overhead product amount, B are bottom product amount, T _TopBe tower top temperature, T _BotFor column bottom temperature, R are that capacity of returns, Q are that thermic load amount, F are inlet amount.

Data acquisition among the present invention, processing and control and optimization are calculated, are realized and can realize by host computer.Fig. 2 is a kind of scheme that realizes in host computer.Control program is by real-time data base or by OPC (OLE for Process Control) mode retrieve processed data, and main data processed result is calculated and finished the back and show or send into the Distributed Control System demonstration at host computer.Display control interface is used for controlling parameter adjustment on host computer and Distributed Control System.

Fig. 3 is the block diagram of off-line training modeling, and a is the training step of the neural network model of optimization, and b is the step response model identification step of control.

Fig. 4 is the program flow diagram of rectifying column on-line optimization control.

The present invention will be further described below in conjunction with the example of a propylene propane rectifying column.

Use HYSYS flowsheeting software, set up the flowsheeting of propylene propane rectifying column, and the flow process analog parameter is adjusted, to obtain and actual approaching analog result according to the Distributed Control System real data.

Foundation optimization is acted on behalf of the input variable of neural network model and chooses cat head bottom product amount than D/B, tower top temperature T _Top, column bottom temperature T _Bot, capacity of returns charge ratio R/F, thermic load amount charge ratio Q/F, so the data that actual needs obtains comprise overhead product amount D, bottom product amount B, tower top temperature T _Top, column bottom temperature T _Bot, capacity of returns R, thermic load amount Q, inlet amount F.Output variable is respectively overhead product impurity branch rate C simultaneously _Top, bottom product impurity divides rate C _Bot, i.e. cat head bottom product quality.

Change operating condition, obtain product quality and process data under the different operating modes.It is defective that operating mode has contained product quality, and performance variable, controlled variable and design conditions depart from situations such as bigger.500 groups of data samples of final acquisition.These inputoutput datas are carried out standardization.Afterwards, therefrom choose 400 groups of data as training sample, other 100 groups of data are as test sample book.Use training sample to carry out the training of neutral net iteration, and to the neutral net of per step training gained with training sample calculation training error, calculate predicated error with test sample book, when predicated error increases or training error when no longer obviously reducing by reducing to become, this neural metwork training finishes.Use the method to train a plurality of neutral nets, select final training error and predicated error all minimum as training result.

With capacity of returns and reboiler thermic load as performance variable, with weight product ratio, tower top temperature, column bottom temperature, reflux ratio as controlled variable, as the multivariable prediction control scheme of rectifying column.At first carry out test modeling, set up the step response model of capacity of returns, reboiler thermic load and overhead product flow, bottom product flow, tower top temperature, column bottom temperature.Calculate by Analysis on Mechanism then, set up the hybrid prediction model of process.

Based on above-mentioned hybrid prediction model, calculate weight product ratio, reflux ratio in real time and obtain the real time temperature value as controlled variable, carry out multivariable prediction control Distributed Control System configuration and enforcement.

Use the communication interface program process data on the Yokogawa Distributed Control System to be collected in the real-time data base of host computer by the control network.Director demon is the required data of obtaining from real-time data base, then product flow, weight product ratio, the reflux ratio after the line computation compensation.Each flow was got currency or the arithmetic mean of instantaneous value in 5 minutes before this when wherein weight product ratio calculated.

Weight product ratio is adopted adaptively correcting, and promptly when using for the first time, cat head, the bottom product flow historical data arithmetic mean of instantaneous value got after the compensation in 2 hours before this calculate weight product ratio initial set value.

Weight product ratio calculates given control target to optimize, and provides the percentage that departs from and limits as control, departs from percentage range and is set to 5%.Temperature and reflux ratio adopt Region control, on the Distributed Control System operation interface, revise the bound of control according to Rectification Tower Design parameter and operating experience by the operative employee, tower top temperature is limited to 47～49 ℃, and column bottom temperature is limited to 57～60 ℃, and reflux ratio is limited to 12～20.

According to Analysis on Mechanism, each variable in stable operation, guarantee the ability difference of product on qualified, thereby different soft priority just should be set, when variable transfinites, regulate according to soft priority.Soft priority level initializing is as follows:

Reflux ratio＞temperature＞weight product ratio

It is 1.5,1,0.5 that the setting of standardization weights sets gradually, and the actual weights that are provided with are 0.15,1,5.The actual weights that are provided with that will instead push away gained by the engineer interface carry out online modification.

In this example, raw material was chemically examined once in 4 hours, and overhead product was chemically examined once in 2 hours, and bottom product chemical examination in 4 hours once.After obtaining analysis data, according to agent model,, reduce reflux ratio to guarantee product quality, reducing the reboiler thermic load is target, uses intelligent optimization algorithms such as genetic algorithm, searches for more excellent controlled variable, performance variable desired value.

Colony of initialization, getting individual number is n=100.Each individual bi is designated as { D/B, T _Top, T _Bot, R/F, the data group of Q/F}, wherein each variable all in the even value (comprising the border) in 10% up and down of current operating value, finally is combined into the data group individuality that has nothing in common with each other.

Calculate each individual fitness, and the computing of selecting, intersect, make a variation.P wherein _c=0.1, p _v=0.03, iteration is 120 by number of times.

Take out the optimal solution of the individuality of maximum adaptation degree as optimization calculating, and with the control target of this optimal solution as each controlled variable of control computing.

Behind this scheme implementation, the operation of tower is more steady, the cat head propylene content is increased to 99.3% by 98.85%, at the bottom of the tower in the propane propylene content be generally 0%, propene yield is increased to 30.5% by 28.8%, device energy consumption is reduced to 23.7 kilograms of mark oil by 29.53 kilograms of mark oil, and has guaranteed the more high separation under the fractionation operation condition and same operation expense stably to greatest extent, surpassing in the device long-time running under 30% the situation of design load, device is steadily produced.

Claims (2)

1. a kind of automatic control and the optimization method of rectifying column is characterized in that this method contains following off-line training and 2 stages of on-line implement successively:

Off-line training step contains following steps:

Steps A 1: use the rectifying column of HYSYS flowsheeting software simulation reality, and act on behalf of neural network model according to process data and product quality data foundation optimization that this simulation softward produces; This steps in sequence is undertaken by following substep:

Steps A 1.1: use HYSYS flowsheeting software simulation rectifying column, and model parameter is adjusted, to obtain and actual approaching analog result according to the on-the-spot real data that collects by Distributed Control System;

Steps A 1.2: process data and product quality data sample that above-mentioned flowsheeting software is produced carry out standardization by following formula:

x ^o＝(x-m _x)/σ _x，

Wherein x is an initial data, x ^oStandardized data for correspondence;

m _x, σ _xArithmetic mean of instantaneous value and the standard deviation of representing this data sample respectively;

Described data sample obtains by following steps: changes operating condition, obtains process data and product quality data under the different operating modes, thus the multi-group data that obtains;

Steps A 1.3: set up final neural network model according to the multi-group data sample that steps A 1.2 obtains, this model is that final training error and predicated error are a minimum model in a plurality of neutral nets:

$C_{\mathrm{top}}^o={\mathrm{NN}}_{\mathrm{top}}({(D/B)}^o,T_{\mathrm{top}}^o,T_{\mathrm{bot}}^o,{(R/F)}^o,{(Q/F)}^o),$

$C_{\mathrm{bot}}^o={\mathrm{NN}}_{\mathrm{bot}}({(D/B)}^o,T_{\mathrm{top}}^o,T_{\mathrm{bot}}^o,{(R/F)}^o,{(Q/F)}^o),$

NN wherein _Top, NN _BotThe expression neural network model, actual is 5 * 10 * 1 RBF network;

Steps A 2: actual rectifying column is carried out test modeling, set up the following step response model of capacity of returns, reboiler thermic load and overhead product flow, bottom product flow, tower top temperature, column bottom temperature:

$\left[\begin{array}{c}{D}_c\\ B_c\\ T_{\mathrm{top}}\\ T_{\mathrm{bot}}\end{array}\right]=f(G,\left[\begin{array}{c}R\\ Q\end{array}\right]),$

Wherein f is a convolution algorithm;

G is the step response model that test modeling is set up;

The on-line implement stage comprises following steps:

Step B1: host computer initialization:

Be provided with: the timer cycle;

Overhead product impurity divides rate C _TopWeight w _Ctop

Bottom product impurity divides rate C _BotWeight w _Cbot

The weight w of thermic load amount Q _Q

The weight w of the actual weight product ratio amount of transfiniting Δ η _η

The tower top temperature amount of transfiniting Δ T _TopWeight w _Ttop

The column bottom temperature amount of transfiniting Δ T _BotWeight w _Tbot

The weight w of the reflux ratio amount of transfiniting Δ r _r

Making fitness function J is the constant C onst that positive number is set;

Step B2: be carved into when judging control not:

If be carved into during control, then carry out next step; Otherwise, wait for;

Step B3: host computer through the OPC communication interface by the rectifying column field data below the Distributed Control System collection and deposit real-time data base in: overhead product amount D, bottom product amount B, tower top temperature T _Top, column bottom temperature T _Bot, capacity of returns R, thermic load amount Q and inlet amount F; Be calculated as follows cat head, bottom product flow behind the liquid level dynamic compensation simultaneously, change the product flow measured deviation that causes with the product savings of avoiding producing because of level fluctuation at the bottom of cat head, the tower:

D _c＝D+(h _top(L _top，new)-h _top(L _top，old))/t，

B _c＝B+(h _bot(L _bot，new)-h _bot(L _bot，old))/t，

H wherein _Top, h _BotBe the function that liquid level is converted to the quality amount of savings based on the container Mathematical Modeling;

L _{Top, new}, L _{Top, old}Be respectively current and a period of time return tank of top of the tower liquid level detected value before, its numerical value is got percentage;

L _{Bot, new}, L _{Bot, old}Be respectively still liquid level detected value at the bottom of the tower before current and a period of time, its numerical value is got percentage;

T is that the time interval of being got is calculated in compensation;

Actual weight product ratio:

η＝D _c/B _c；

Step B4: host computer judges whether to obtain new product quality analysis data:

If obtain new product quality analysis data, then execution in step B5; Otherwise, change step B6 over to;

Step B5: based on the product quality analysis data described neural network model of genetic algorithm optimization, with the more excellent controlled variable of search, reach the assurance product quality, reduce capacity of returns, reduce the purpose of these two performance variable values of reboiler thermic load, described controlled variable is meant weight product ratio, tower top temperature, column bottom temperature and reflux ratio; This steps in sequence contains following each substep:

Step B5.1: colony of initialization:

Set the value of individual in population number n, each individual b _iBe to be designated as { D/B, T _Top, T _Bot, R/F, the data group of Q/F}, wherein each variable is all evenly got a plurality of values in 5～10% the closed interval about of current operating value, finally is combined into the data group individuality that has nothing in common with each other;

Step B5.2: read neural network model, calculate each individual fitness according to neural network model and following formula, described fitness is

Fit＝Const-(w _CtopC _top+w _CbotC _bot+w _QQ)；

Step B5.3: determine to select each individual number of times according to following formula,, eliminate the little individuality of fitness, generate new colony to keep the big individuality of fitness:

$\mathrm{Num}\left(b_i\right)=\mathrm{Fit}\left(b_i\right)/\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\mathrm{Fit}\left(b_i\right)*n,i=\mathrm{1,2},...,n;$

Step B5.4: from the colony that step B5.3 obtains, select p at random _c* n is right, p _c=0.05～0.1, at every couple of individuality { b _i, b _jIn select k variable in the data group at random, be calculated as follows new value, and replace old value, form new individuality:

b _i，new{k}＝Rand*b _i，old{k}+(1-Rand)*b _j，old{k}，

b _j，new{k}＝(1-Rand)*b _i，old{k}+Rand*b _j，old{k}，

Wherein Rand is [1,2] interval interior equally distributed random number;

Step B5.5: from the colony that step B5.4 obtains, select p at random _v* n, p _v=0.02～0.05, each individuality is selected certain variable in the data group at random, increases or reduce a percentage 1～5% at random;

Step B5.6: in the colony that step B5.5 is obtained, suitably remove the repeating data of selecting in the operation, remain unchanged to guarantee the individual in population number;

Step B5.7: in the colony that step B5.6 is obtained, repeating step B5.2～B5.6 is tending towards a stationary value until the fitness of individual in population maximum, though perhaps do not reach till the iterations that stationary value reached setting; Take out the optimal solution of the individuality of this maximum adaptation degree, and this is separated as the target of controlling described each controlled variable as optimization calculating;

Step B6: as performance variable, as controlled variable, rectifying column is carried out multivariable prediction control with weight product ratio, tower top temperature, column bottom temperature and reflux ratio with capacity of returns and reboiler thermic load; This steps in sequence contains following each substep:

Step B6.1: judge whether off-duty mistake of above-mentioned optimization: if the off-duty mistake, then weight product ratio with the mean value of 1～2 hour actual value before as target, tower top temperature, column bottom temperature and reflux ratio with the center line of control bound as target; If moved, then the optimal solution that step B5.7 is obtained is as the target of described each controlled variable;

Step B6.2: read step response model, and press step response model, the computing formula of weight product ratio η and the hybrid prediction model of following formula generative process:

Reflux ratio r:

r＝R/D _c；

Step B6.3:, realize the multivariable prediction control of rectifying column according to the hybrid prediction model of process:

At first, set the control bound: the control limit of weight product ratio is based on the control target, the permission percentage that setting departs from, get 0～10%, the control limit of tower top temperature, column bottom temperature and reflux ratio is revised on the Distributed Control System operation interface according to Rectification Tower Design parameter and operating experience by the operative employee.

Secondly, set soft priority: reflux ratio＞temperature＞weight product ratio; Wherein, temperature comprises tower top temperature and column bottom temperature;

Once more, the control goal-setting is the amount of the transfiniting weighted calculation value minimum of each variable:

J _c＝wη|Δη|+w _Ttop|ΔT _top|+w _Tbot|ΔT _bot|+w _r|Δr|，

J wherein _cBe the control object function;

Δ η, Δ T _Top, Δ T _Bot, Δ r is respectively controlled variable η, T _Top, T _Bot, r exceeds the value of control limit, poor for corresponding control limit when each controlled variable value transfinites is 0 when not transfiniting;

w _η, w _Ttop, w _Tbot, w _rBe respectively controlled variable η, T _Top, T _Bot, r actual weights, determine by following formula:

$w_{\mathrm{\η}}=w_{\mathrm{\η}}^o/{\mathrm{\σ}}_{v,\mathrm{\η}},w_{\mathrm{Ttop}}=w_{\mathrm{Ttop}}^o/{\mathrm{\σ}}_{v,\mathrm{Ttop}},w_{\mathrm{Tbop}}=w_{\mathrm{Tbot}}^o/{\mathrm{\σ}}_{v,\mathrm{Tbot}},w_r=w_r^o/{\mathrm{\σ}}_{v,r},$

W wherein _η ^o, w _Ttop ^o, w _Tbot ^o, w _r ^oBe respectively controlled variable η, T _Top, T _Bot, r the standardization weights, according to above-mentioned soft priority level initializing;

σ _{V, η}, σ _{V, Ttop}, σ _{V, Tbot}, σ _{V, r}Be respectively controlled variable η, T _Top, T _{Bot, r}Standard deviation;

Step B7: the value of the controlling value of capacity of returns and reboiler thermic load and each controlled variable of response, this control cycle finishes, and gets back to step B2 and waits for following one-period.

2. a kind of automatic control and the optimization method of rectifying column according to claim 1 is characterized in that: described h _Top, h _BotObtain by following formula respectively:

For the common horizontal return tank of cat head:

$h_{\mathrm{top}}\left(L_{\mathrm{top},\mathrm{new}}\right)={\mathrm{\ρ}}_{\mathrm{top}}{\mathrm{Len}}_{\mathrm{top}}*(\arccos \left(\frac{(0.5-L_{\mathrm{top},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{top}}}{R_{\mathrm{top}}}\right)*R_{\mathrm{top}}^2$

$-(0.5-L_{\mathrm{top},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{top}}\sqrt{R_{\mathrm{top}}^2-{\left((0.5-L_{\mathrm{top},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{top}}\right)}^2}),$

$h_{\mathrm{top}}\left(L_{\mathrm{top},\mathrm{old}}\right)={\mathrm{\ρ}}_{\mathrm{top}}{\mathrm{Len}}_{\mathrm{top}}*(\arccos \left(\frac{(0.5-L_{\mathrm{top},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{top}}}{R_{\mathrm{top}}}\right)*R_{\mathrm{top}}^2$

$-(0.5-L_{\mathrm{top},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{top}}\sqrt{R_{\mathrm{top}}^2-{\left((0.5-L_{\mathrm{top},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{top}}\right)}^2}),$

For vertical tower still at the bottom of the tower:

$h_{\mathrm{bot}}\left(L_{\mathrm{bot},\mathrm{new}}\right)={\mathrm{\ρ}}_{\mathrm{bot}}*\mathrm{\π}{R}_{\mathrm{bot}}^2*(0.5-L_{\mathrm{bot},\mathrm{new}}){\mathrm{Hs}}_{\mathrm{bot}},$

$h_{\mathrm{bot}}\left(L_{\mathrm{bot},\mathrm{old}}\right)={\mathrm{\ρ}}_{\mathrm{bot}}*\mathrm{\π}{R}_{\mathrm{bot}}^2*(0.5-L_{\mathrm{bot},\mathrm{old}}){\mathrm{Hs}}_{\mathrm{bot}},$

ρ wherein _Top, ρ _BotBe respectively density of liquid at the bottom of cat head, the tower;

R _Top, R _BotBe respectively the radius of still at the bottom of return tank of top of the tower, the cylindrical tower;

Hs _Top, Hs _BotBe respectively the detection height of liquid level instrument at the bottom of cat head, the tower;

Len _TopLength for return tank of top of the tower.

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