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01 February 2004

Model application

Developmental approach to a dynamic plant gas system.

By Aleksandr I. Muravyev, Robert C. Kelahan, Paul C. Kowallis, and Greg L. Torgesen

Dynamic modeling is a valuable tool for evaluating plant operating conditions and control strategies. High-fidelity dynamic simulators, developed for the process industries in the last decade, are a solid basis for accurately modeling the dynamic transitions.

Nevertheless, development of custom components (for specific features of the process and measurement system) often comes into play to provide a realistic plant model.

The following describes the development and application of a dynamic model for the plant off-gas system, characterized by the complex structure and strong interaction of the production units with fast dynamics and sharp unexpected changes in the process pressure. The model came about in several phases using a Hysys dynamic simulator.

Plant performance

The plant has three electric arc furnaces, used for the production of elemental phosphorus. The reaction products coming off the furnaces are primarily phosphorus vapor and carbon monoxide gas. At the gas processing units, the phosphorus condenses and separates from the carbon monoxide in the condenser after particulate exits the stream in the electrostatic precipitator. Carbon monoxide goes to a common header and then to a rotary kiln, where it acts as the primary fuel in calcining phosphate ore in preparation for its use in the furnaces. Excess gas flares. In the near future the manufacturer will build a thermal oxidizer to process the excess carbon monoxide gas, thereby removing the flare most of the time.

The structure creates a highly interactive environment for pressure control in the system. Pressure control of the furnace off gas is critical to the safe and efficient operation of the plant. A surge of the furnace pressure propagates quickly to the common header, causing disturbances in the work of the kiln and parallel furnace units. On the other hand, the kiln load changes lead immediately to the header pressure disturbances, affecting the performance and pressure control of all parallel furnaces.

The dynamic modeling project came about to get a better understanding of this and several other plant control and performance issues. Due to the fast, interactive dynamics of the process, control system quality and speed of response are vital for plant performance. Using dynamic simulation is an easy and reliable way to test potential process control improvements (decoupling of the loops, gain scheduling, feedforwarding) before implementing them into the real plant. The other important control issue for the plant is a transition from the legacy system to the newer distributed control system (DCS). Dynamic modeling can help answer how the scan rate and speed of response of a new system will affect the quality of control.

The process redesign option for decreasing emissions is to install a thermal oxidizer, replacing the flare in the normal operational mode. Because of the strong interactions between furnaces, flares, thermal oxidizer, and kiln, design issues with the proposed thermal oxidizer and dynamics of the off-gas header are of great interest. Some of the issues to explore are how to maximize carbon monoxide use in the kiln, the maximum pressure in the system under a given set of upset conditions, and how quickly the thermal oxidizer must react to prevent flaring.

The main items for dynamic modeling in this part of the project are:

• create a dynamic model of the thermal oxidizer (TO) unit and develop its control system, providing stable TO performance under the changing input load;
• modify a control strategy for the common header pressure to take into account the TO as an additional interacting element;
• and evaluate the performance of the whole, modified process (with new strategies) under different scenarios of plant behavior, including abnormal and emergency situations.

Improving the pressure-relief system performance is a key plant safety issue. It relates to plant emissions. The pressure-relief devices of the existing system use steady state conditions, while the real values of the device-relieving pressure and capacity are dynamic in nature (depending, particularly, on the pressure impulse dynamics). Therefore, the first answer the manufacturer can get through dynamic simulation is to evaluate the real values of relieving pressure and relieving capacities for the devices and the overall system at various intensities and shapes of the pressure impulses. The subjects of interest for the vent system include what pressures would come about through the resulting deflagration if air is inadvertently introduced into the off-gas system, and how the pressure-relief devices interact during a pressure excursion. The next task is to use the dynamic model to modify the system. Particular items for modeling are (1) create the model of a new pressure-relief device and test its behavior before implementing it into the real plant; (2) using the simulation, evaluate different configurations of the vent system, consisting of new and existing devices; and (3) define an optimal relieving point for the new device.

Model development

Model developers used the general purpose Hysys process simulator. The custom components for modeling specific features of the pressure-relief devices used spreadsheet calculations and Hysys User Variables (Visual Basic programming). Developers built the model in two versions, basic and extended. The basic version is a model for the existing plant configuration in the normal operational mode, with the thermal oxidizer unit connected, which you can easily turn off to give the current process layout. The extended version contains, in addition, a vent system model, including the existing seals and new ones planned for installation.

Main features of the model

Due to complexity of the plant, the model is a multilayer dynamic flow sheet, containing up to four nested levels of sub-flow-sheets. The main flow sheet contains unit operations for the common header (piping, valves, condensate traps), a simplified model of the kiln, and sub-flow-sheets for the furnaces/processing units and thermal oxidizer. The furnace/processing unit flow sheet includes, in turn, sub-flow-sheets for its component and pressure-relief devices (seals).

This multilayer solution provides simplicity in reading and navigating through the model and flexibility in its development and modification. Particularly, the seal models can easily reposition along the process or switch on/off to analyze alternative structures of the pressure-relief system.

The plant piping system has a fundamental impact on the process dynamics. Because the simulator currently does not support dynamic unit operations for the pipe segment, it used a combination of a separator, simulating the pipe volume, and valves for the pipe resistance. The valve sizing used plant steady state data for one- (gas) or two-phase (liquid-gas) flow. To correctly calculate the pipe resistance in transition from one- to two-phase flow, the manufacturer used the variable valve opening and additional dynamic element, the lag transfer function.

The model also includes a part of the plant control system. The controllers and valves used simulator unit operations. The valve and actuator characteristics came according to plant data (design and experimental), and the tuning parameters of controllers were set equal to the real plant ones. The developers programmed the main process interlocks using the simulator Event Scheduler. The Event Scheduler was also a model for plant events, such as pressure excursions, load changes, and process equipment going down in emergency situations. A combination of these features, complemented with custom models of the plant seals, provides a highly realistic environment for studying plant behavior and testing the new control strategies and process design options.

Custom models

The existing plant seals are primarily of two types: gravity weighted and fixed cap. In the first type, the seal is broken (opened) when the lifting force, provided by the pressure under the moving bell, becomes higher than the bell weight. In the second type, the bell is not moving, and the seal is opened when the pressure under the bell is high enough to push out all liquid from the space under the bell (inner space of the seal) into the space between the outer surface of the bell and the seal tub (outer space of the seal). The new seal is a fixed-cap type with improved capability of resealing and liquid-gas separation.

The model for the gravity-weighted cap seal includes a bell-lifting model and equivalent pipes and valves. The bell-lifting model describes the motion of the seal bell resulting from the balance of the forces acting on it. You can use the calculated bell position to get the value of the seal opening and further calculate the relief flow rate through the seal. An equation for the bell velocity V(t) can be written as:

M*dV(t)/dt + K_R * V(t) = (P_In – P_Top)*S_Bell – W_Bell  (1)

or in a standard form of a first order filter

Tv*dV(t)/dt + V(t) = Kv*((P_In – P_Top)*S_Bell – W_Bell ) (2)

where

M is a mass of the bell,

K_R is a friction resistance coefficient,

P_In and P_Top  are the pressure values under the bell and on its top, respectively,

S_Bell and W_Bell  are the bell top area and bell weight, respectively,

Tv = M/K_R  is the time constant for a first order filter,

Kv = 1/K_R  is the gain for a first order filter.

The bell position H(t) is calculated by integrating V(t), taking into account a mechanical restriction H_max  on the bell lifting,

with constraints 0 ≤ H(t) ≤ Hmax (3)

The boundary conditions for the bell velocity are

V(t) = 0 IF (H(t) = 0 AND dV(t)/dt ≤ 0) (4a)

V(t) = 0 IF (H(t) = Hmax AND dV(t)/dt ≥ 0) (4b)

The term KR * V(t) in equation 1 is a friction-resistance force causing the bell to suspend finally when the main forces acting on the bell, weight and pressure difference, are equalized. K_R is the tuning parameter of the model. Because we know the mass of the bell, it is more suitable to use Tv (see equation 2) instead of K_R.

This time constant has a physical meaning of approximately one third of the time needed for the equalized system to stop. The bell position calculated according to equations 1 through 4 converts into the opening percent of the equivalent valve, sized according to the friction pressure drop of a seal assembly. Finally, the simulator calculates the flow rate through the seal using the current seal pressure difference and the valve characteristics.

The model for the fixed-cap seal includes a model for the dynamics of a liquid accumulation in the seal tank. It is implemented using simulator unit operations and the custom calculations for the seal state variables. The seal state variables define (1) the seal operating mode (open, closed, open with no liquid column), (2) opening/closing the pseudovalves controlling the gas path and liquid inlet/outlet to the seal tank, (3) pressure drop and height of gas-liquid column in the seal, (4) direction of the seal flow (pressure relief or suction).

The equations for the "seal open" conditions are given below, where formula (5a) works for opening the seal at the direct pressure relief (high process pressure), and equation (5b) is a vacuum relief condition,

((P_In – P_atm) > W_AboveSkirt /A_{_outer}) (5a)

OR

((P_atm – P_In) > W_AboveSkirt /A_{_inner}) (5b)

Here, P_In (P_atm) is a seal (atmospheric) pressure, W_AboveSkirt is a weight of liquid above the seal skirt (low edge of the bell), and A_{_outer} (A_{_inner}) is a cross-section area of the outer (inner) tub space.

The level of clear liquid H₀ in the seal is calculated as

H₀ = L_AboveSkirt + max (DH_{_outer}, DH_{_inner}) (6)

Here L_AboveSkirt is a tank liquid level above the seal skirt in equilibrium (when P_In = P_atm), and DH_{_outer} (DH_{_inner}) is the current deviation of the level from the datum line in the outer (inner) space of the seal tub. The values W_AboveSkirt, L_AboveSkirt, DH_{_outer}, and DH_{_inner} in equations 5 and 6 calculate using the current liquid balance in the seal tank, seal geometry data, and the process pressure value.

One calculates fractional liquid holdup K and Fraude number, Fr, using the superficial velocity of the gas V, a free-fall acceleration g, and H₀:

K = 1/(1 + Fr^1/2) (7)

Fr = V² /(g*H₀) (8)

The level H₀ and liquid holdup K can then help determine the height of a gas-liquid mixture in the seal tub, which controls the seal pseudovalves. The values Fr and V also go in the criterion calculations for transition between two-phase (liquid-gas) flow regimes, employed in the model of the new seal.

The models include features of abnormal seal functioning, such as incomplete closing of the seal and ignition reactions.

Incomplete closing of the moving bell, after the seal has opened, results in the intake of air into the gas system. As a result, the carbon monoxide gas may have an ignition reaction with the air that can cause a pressure and temperature rise in the piping system. One can model an ignition of the gas for both types of seals in situations where ambient air suction occurs due to insufficient resealing with liquid.

Model applications

The resulting model, providing an accurate evaluation of the dynamic transitions for the existing and modified processes, can see use developing advanced control strategies. On the process side, the model was used for reconstruction and analysis of plant emergency situations and for evaluation of the design options (location and parameters of new pressure-relief devices) to improve plant performance and safety.

Control strategies

There is pressure control on each furnace to maintain furnace back pressure, pressure control on compressor outlets to maintain compressor pressure, and pressure control in the common header. At the current process configuration, you can control the fuel supply to the kiln by varying the flare pressure set point, thus indirectly affecting carbon monoxide flow to the kiln. Unfortunately this control adjustment has the adverse affect of upsetting the upstream pressure controllers, particularly the nearest upstream controller at the compressor outlet. The model for the current process configuration demonstrated the effect of adding dynamic feedforward between the flare pressure control valve and the compressor outlet pressure control loop. In the simulation, the user performed step testing for the effects of the flare valve and the compressor outlet valve on the compressor outlet pressure. The results of the step testing set the feedforward gain and the feedforward lead/lag. The user was able to compare closed-loop pressure response for a typical flare pressure set point adjustment with and without feedforwarding. Feedforward reduced the upstream pressure excursion by 60%. The directionally nonlinear response limited additional reduction in the excursion.

In the modified process with the TO unit replacing the flare in the normal operational mode, the header pressure controller manipulates the off-gas flow to the TO. The flare pressure controller serves as a back up controller to prevent an uncontrolled pressure rise in the header under the rapid changes of process conditions. The modified control strategy has to maintain the kiln demand for the fuel, taking into account the constraints on TO pressure and capacity values.

Therefore, the overriding control scheme can calculate the header pressure controller set point. The TO pressure constraint takes part in overriding only when the TO's own resources on its pressure control become exhausted. The suggested strategy came from using Hysys unit operations, and the user tuned the controllers via simulation. The dynamic simulation revealed a significant interaction between the pressure at the TO reactor and the pressure drops at the TO scrubbing trains. A number of control system configurations and actuator locations were tested to find the appropriate scheme to give proper decoupling: a fast response to the reactor pressure changes while holding the scrubber pressure drops at the nominal levels.

In the resulting configuration, the user tuned the controllers to provide an acceptable performance in a wide range of the TO load and header pressure changes. Plant manufacturing suggested the test scenarios, which contained the typical flow variations to the TO in the normal and emergency modes.

The upset scenarios included the kiln-fuel interlock trip with three furnaces running and the kiln losing feed with three furnaces running. The normal simulated process transitions are the timed off-gas flow transitions and typical continuous gas flow variations.

The worst case scenario simulation was a kiln-fuel interlock trip with three furnaces running and the TO in a standby mode with half of its capacity available. In this case, the simulation shows the flaring cannot be avoided completely due to a very sharp drop in gas consumption—in about twenty seconds the kiln load goes from full load to zero—and time is needed for the TO to gain full capacity—the flat part of the flow curve to the TO at the time interval 1800 to 1870 seconds, when the TO starts taking a full load. At this moment the flaring flow rate goes to zero. The pressure in the common header during all the transitions, including the period of the kiln going back to full load, was within acceptable margins. In this way, the furnace pressure control disturbances were tolerable. The values of the TO reactor pressure and the scrubber pressure drops were also within normal limits.

As a result of test runs, the user was able to identify additional control problems. Particularly, the modified process has a much higher level of interaction in the common header than the existing one due to the piping shortcut at the point of TO connection. In this situation, variations of the number three furnace load will have a much higher impact on header pressure, and this can cause excessive interaction between the pressure controllers of the individual lines and the header pressure controller. This results in deterioration of the flow control to the kiln. The other problem is a variable process gain. Both the suggested and currently used strategies have the primary loop of the header pressure control receiving a set point from the kiln firing control system. Therefore, the controlled pressure value varies widely, depending on the kiln demand for off gas, and the plant gains for the pressure controllers, these being linked in the off-gas header, are variable. This can cause worsening of control. In simulations and in the real process, compressor pressure control response may become sluggish at high header pressures and oscillatory at low values (for the header pressure control the situation is reversed).

Potential advanced control strategies that might address these problems are decoupling (or multivariable predictive) control to alleviate the pressure controller interactions and gain scheduling for the header-linked controllers. This will happen at the phase of DCS system implementation for the modified process.

With pressure response in the off-gas header being very fast, of particular interest is the effect of the controller scan rate on the extent and duration of pressure excursions. Earlier dynamic simulations suggested a very fast, dedicated controller was necessary to best control the excursions. Improvements in DCS execution speed in recent years have raised the question of whether the older dedicated controllers, with spare parts issues, are still necessary, or could control move within a slower high-capacity, multiloop controller.

To test this, control execution in the simulation slowed, and the user was able to measure the response to a typical pressure excursion. For the case studied, maximum excursion was less than 0.5% higher with settling time essentially unaffected. This small difference was due to the slower controller not catching the beginning of the excursion as quickly. You can make the remainder of the control response equivalent with tuning. The simulation justified replacing the older controllers.

Process performance

The original reason to develop a dynamic model of the vent system was to analyze pressure profiles in the off-gas system after an incident that caused equipment damage. Minor alterations in the process, over the years, raised concerns that the off-gas system might not be adequately protected. Besides, they had to investigate the potential process sources for the incident. The main suspected reason was variation in composition of one of the furnace feed streams. The simulation provided an estimation of the feed inconsistencies potentially causing this effect. The maintenance improvements, based on these estimations, helped to decrease the risk of the accidents. Generally, the simulations demonstrated sufficient protection of the process in the abnormal situations. Nevertheless, the additional design step will help augment the process safety.

The dynamic model will help modify the plant venting system. The users ended up creating the model of a new pressure-relief device, and then they tested its behavior before installation. Using simulation, the users were able to evaluate the different configurations of the vent system with the new device and then determine the optimal parameters of the seal. Particularly, they estimated the optimal relieving points for the furnace/processing units depending on the furnace capacity and dynamics (volume and resistance) of the units.

By using extensive simulation, the responses of the existing and the modified vent system have undergone comparison at the most probable levels of furnace pressure excursions. Two typical magnitudes, moderate and severe, and several shapes of the pressure impulse (rates of the pressure rise), were simulated in different combinations. The plots present the pressure profiles for different points along the furnace/processing unit. The new system has shown superior performance, providing 10–12% less peak system pressure, with a more favorable (safe) sequence of the relief devices opening and higher resealing capabilities. The modified system has undergone successful implementation for one of the furnaces. The results of its functioning are close to those predicted in simulation. An implementation of the modernized vent system is currently under way for two other furnace units. CP

Behind the byline

Aleksandr I. Muravyev works at MYNAH Technologies in Chesterfield, Mo. Robert C. Kelahan works at Monsanto Co.'s St. Louis office, and Paul C. Kowallis and Greg L. Torgesen work at Monsanto's Soda Springs, Idaho offices.