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A scheme that optimizes the converter of an ammonia synthesis plant to determine optimal inlet temperatures of the catalyst beds has been developed. The optimizer maximizes an objective function—The fractional conversion of nitrogen on the four catalyst beds of the converter subject to variation of the inlet temperature to each catalyst bed. An iterative procedure was used to update the initial values of inlet temperature thus ensuring accurate results and quick convergence. Converter model results obtained with optimized operating conditions showed significant increase in fractional conversion of 42.38% (from 0.1949 to 0.2586), increased rate of reaction evident in a 13.18% (0.5317 to 0.4616) and 23.84% (0.1946 to 0.1482) reduction in reactants (hydrogen and nitrogen) concentration respectively and a 56.48% increase (from 0.1181 to 0.1838) in ammonia concentration at the end of the fourth catalyst bed compared to results obtained with industrial operating conditions.

The need to operate process equipments at optimal conditions that ensures efficient performance and economic competitiveness of products of similar industries is a growing challenge to process designers and entrepreneurs of industries. An optimal set of design and operating parameters ensures that the industry/system functions in the most efficient way. One way of achieving this is through optimization. Optimization is a widely used engineer- ing tool for enhancing efficiency and performance of systems. It is the process of determining the operating conditions of a process/system’s parameters that ensures the most efficient operation of the system/process by adjusting the process parameters so as to maximize some specified set of parameters or one or more of the pro- cess specifications while keeping all others within their constraints. The improved efficiency/performance can be measured by the reduction in production cost, increase in profit or increase in the quantity of products pro- duced. Operating parameters usually optimized include process variables such as flow rates, pressures, tempera- tures or equipment size such as volume, length and catalyst volume.

Optimization involves minimizing or maximizing an objective function; in most optimization problems, the objective function could be an economic return or term based on some parameters of the system, minimizing a cost function or maximizing a profit function; Optimizing the efficiency of the system by minimizing or max- imizing parameters that indicates performance of the system viz: minimize specific energy consumption [

The ammonia synthesis converter is a major component of the ammonia synthesis loop. Steady state one di- mensional pseudo-homogeneous models of an axial flow four catalyst bed ammonia synthesis converter were successfully developed by Akpa and Raphael [

In this work, a parameter that indicates directly the efficiency of the converter—the fractional conversion of the reactants to products is optimized. The model equation that predicts the fractional conversion of reactants to products is used as the objective function to be maximized.

In an earlier work by Akpa and Rapheal [

However in this optimization; an optimum inlet temperature of each bed which will result in the highest frac- tional conversion, lowest reactant concentration and highest product concentration was determined.

A constrained non-linear optimization procedure was used to determine the optimum inlet temperatures of the four catalyst beds which maximize the objective function (model equation that predicts the fractional conversion of the ammonia converter).

The objective function to be maximized is:

Subject to the values of the inlet Temperature:

where A = cross-sectional area of the bed (m^{2}); X = fractional conversion of Nitrogen; _{3}); _{ind}_{.} = industrial plant inlet temperature; T_{Design} = design inlet temperature; T_{inlet} = inlet temperature of bed.

Where the reaction rate expression of Temkin-Pyzhez expressed in terms of activities by Dyson and Simon [

Other parameters in this equation can be obtained following the methods outlined in Akpa and Raphael [

The industrial values of the inlet temperature of each bed were used as starting guesses, with maximum possi- ble value being the maximum value of the design temperature for the reactor and catalyst (823 K) above which the catalyst would begin to sinter [

where:

An algorithm developed to solve this optimization problem is shown below:

Process Optimization algorithmStep 1: Guess initial inlet temperature of bed (industrial inlet temperature of each bed)

Step 2: Optimize converter bed j (j = 1, 2, 3, 4)

Determine converter performance:

Solve objective function to obtain fractional conversion of reactants in Bed j: equation (1)

using the program “CONVERTER SIMULATOR” [

The converter simulation program [

Equation (4) gives the outlet temperature of each bed.

Step 3: Update value of the inlet temperature using the bisection method

Step 4: Optimize converter Bed j using present inlet temperature value

Solve objective function to obtain fractional conversion of reactants in Bed j: equation (1)

using the program “CONVERTER SIMULATOR” [

The converter simulation program [

Step 5: Check if objective function has been maximized:

Compare present

Step 6: If answer to Step 5 is “YES”:

Optimum inlet of Bed j has been obtained.

If answer to Step 5 is “NO”:

Repeat Steps 3, 4, 5 and 6.

The steps above were followed to develop the optimization algorithm flow chart shown in

Having obtained the optimum input/quench temperatures to Bed 1, 2, 3 and 4, these values (optimum temper- atures) were then used to run the converter simulator program [_{2}, hydrogen H_{2}) and product (ammonia NH_{3}) at any point in the converter. The maximum conversion recorded at the end of Bed 4 is now taken as the optimum for the converter.

The result of optimization of the four catalyst beds of the converter by solving the objective function at varying inlet bed temperatures to obtain outlet fractional conversion for each catalyst bed is shown in

Having obtained the optimum inlet temperatures for each catalyst bed, the simulation program earlier developed by Akpa and Raphael [

A comparison of the model prediction of converter performance using values of inlet bed temperatures from optimization results and industrial plant values [

Bed | Bed Length (m) | Conversion | Inlet Temperature (K) | Outlet Temperature (K) | |||
---|---|---|---|---|---|---|---|

Model | Optimization | Model | Optimization | Model | Optimization | ||

1 | 1.3 | 0.0427 | 0.057 | 712 | 740 | 727.96 | 757.22 |

2 | 1.8 | 0.1034 | 0.1175 | 721 | 750 | 743.50 | 773.66 |

3 | 2.6 | 0.1493 | 0.1766 | 685 | 720 | 702.48 | 739.52 |

4 | 3.7 | 0.1949 | 0.2586 | 726 | 700 | 742.88 | 716.60 |

Bed | Concentration (mole %) | |||||
---|---|---|---|---|---|---|

Hydrogen | Nitrogen | Ammonia | ||||

Model | Optimization | Model | Optimization | Model | Optimization | |

1 | 0.6395 | 0.5789 | 0.2314 | 0.1884 | 0.0445 | 0.1006 |

2 | 0.5967 | 0.5336 | 0.2167 | 0.1729 | 0.0748 | 0.1381 |

3 | 0.5621 | 0.4936 | 0.2056 | 0.1596 | 0.0978 | 0.1935 |

4 | 0.5317 | 0.4616 | 0.1946 | 0.1482 | 0.1181 | 0.1848 |

These results (increase in fractional conversion, reduction in reactants concentration and increase in product concentration) show improvements in converter efficiency when operated at optimized conditions.

One dimensional model was used for the optimization of the optimizations of an ammonia converter was per- formed to determine optimal inlet temperatures of the catalyst bed that will maximize an objective func- tion—model equation that predicts the fractional conversion of the catalyst beds of the converter. The optimum inlet temperatures of the catalyst beds obtained were used as operating conditions for the converter. The conver- ter model equations using these new optimum inlet temperatures predicted improved efficiency (42.38% in- crease in fractional conversion and 56.48% increase in ammonia concentration) compared with results obtained using industrial inlet catalyst bed temperature values.

An unsteady state and or two dimensional model of the ammonia converter are proposed for future study and simulation of the converter. The optimization procedure developed in this work can also be used for optimiza- tion of processes/systems.

A: Cross sectional area (m^{2})

K: Rate constant for the reverse reaction

K_{a}: Equilibrium constant

L: Length of converter bed (m)

M: Total mass flow rate (KJ/kmol)

P: Operating pressure (Bar)

R_{i}: Rate of reaction with respect to component i

T: Temperature (K)

X: Fractional conversion of nitrogen

Y_{i}: Mole fraction of component i