In an ANN, a certain percentage of the data (typically 70%–
75%) is used for training. From the remaining data, a certain percentage of the data (typically 15% each) is issued for valida-tion and testing of the network. Sigmoid (input layer → hidden layer) and linear (hidden layer → output layer) transfer func-tions (Eq. 3) are used within the network. On this trained, vali-dated and tested network, further simulations are performed to predict outputs for various cases.
(3)S(t)= 1
1+e( )−t
Equilibrium-based models. The overall mass and energy bal-ance equations are solved using these models, and the main out-comes are the amount, composition and heating values of the product gases. These models neither take into account the tor design nor the process and hydrodynamics inside the reac-tor. The model calculates the chemical equilibrium composition (most stable composition) by minimization of Gibbs free energy.
One of the key advantages of this model is that no prior knowledge of complex reactions and hydrodynamics is re-quired. It is computationally inexpensive and can provide a guideline for process design and evaluation. An equilibrium model can be used to study the influence of various operating parameters, as it provides qualitative trends. The two general approaches for equilibrium models are stoichiometric and non-stoichiometric. While the two approaches are essentially equiv-alent, the fundamental difference is that stoichiometric models assume a clearly defined reaction mechanism that incorporates all the chemical reaction and the major species involved, while the non-stoichiometric equilibrium model is based on the mini-mization of Gibbs free energy, where no specific assumptions on the chemical reactions are made.
The elemental composition of the fuel, which can be ob-tained from the ultimate analysis and the operating conditions,
is only required as input to these models. Results of equilibrium models have shown good agreement with experimental data of certain reactors because the general assumptions of the models are in agreement with the actual conditions in the reactor. The general assumptions for the equilibrium model are that reaction rates are fast, residence time is long enough to reach equilibrium state, and the reactor is zero dimensional.
Rate-based models. These models are more realistic com-pared to the data-driven and thermodynamic models. They take into account the fluid dynamics, transport processes and chem-ical reactions inside the reactor. As shown in FIG. 1, depending on the system, modeling of the chemical reactions involves con-sideration of heterogeneous and homogenous reactions. Two types of rate-based models exist: chemical reaction engineering models (CRE) and computational fluid dynamic (CFD) mod-els. The mass and energy balances are solved in both modmod-els.
In the CRE model, the momentum equations are not solved;
instead, semi-empirical correlations are used to describe the flu-id dynamics (bubble diameter, bubble velocity, bubble voflu-idage, velocity of gas in emulsion phase, etc.). In a CFD model, the momentum equations are explicitly solved. Modeling chemical reactions (source terms) are common to both models.
Case study. Various prominent coal gasification technolo-gies3 have been developed and are used worldwide, including moving-bed, bed (bubbling and circulating fluidized-bed) and entrained-bed gasifiers. The moving bed and fluidized bed, among others, are considered more apt for handling high-ash coal.4 A fluidized bed has certain advantages over a moving bed in terms of scaling up and environmental issues. Moving-bed gasifiers generate tarry products, whereas a fluidized-Moving-bed gasifier yields only gaseous product as the volatiles are cracked, facilitating more environmentally friendly products and easier plant operation.5 The advantages of a fluidized-bed gasifier are well documented.6 Good gas-solid contact, excellent heat trans-fer characteristics, better temperature control, large heat stor-age capacity, a good degree of turbulence and high volumetric capacity are a few prominent advantages.
A schematic representation of a bubbling fluidized-bed con-tinuous gasifier (BFBG) is shown in FIG. 2. Typically, in a BFB continuous gasification of coal, the coal particles (0 mm–5 mm) are continuously fed into the BFB reactor at a point above the gas distributor. These particles react with the gasifying, and flu-idizing, agents—steam, air/oxygen, carbon dioxide (CO2)—
to produce gases that are primarily composed of syngas—i.e., carbon monoxide (CO) and hydrogen (H2)—at temperatures above 800°C.
During this operation, multiple reactions (gas-solid hetero-geneous and gas-gas homogenous) occur simultaneously in the reactor. The heterogeneous reactions consist of gas-solid reac-tions, such as pyrolysis, char combustion and char gasification, while the homogenous reactions consist of the water-gas shift reaction, H2 combustion, etc. The product gases coming out of the bed are passed through a cyclone separator for separation of elutriated solids. The product gases are further treated using a gas cleaning system. The superficial gas velocity varies between three to nine times the minimum fluidization velocity. The key challenges in the modeling of a BFBG are complex reaction
ki-Freeboard
FIG. 2. A schematic representation of a bubbling fluidized-bed gasifier.
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Process Engineering and Optimization
netics, gas-solid fluid dynamics and particle behavior. The two main output parameters that gauge the performance of a gasifier are:
Carbon conversion (X) = Inlet carbon – Outlet carbon Inlet carbon Cold gas efficiency (CGE) = Chemical energy
Coal energy
Chemical energy (MJ/kg) = yH2141.80 + yCO10.08 + yCH455.58 Coal (thermal) energy (MJ/kg) = 33.855°C + 144.9H + 10.5S Here, C, H and S = weight % content, dry basis; and y is the mass fraction of gases.
A set of 25 experimental data obtained for a high-ash Indi-an coal in a pilot-scale setup were simulated using the various modeling approaches. Apart from the operating conditions of the gasifier, the main input parameters for a gasifier model are the ultimate and the proximate analysis of the coal (C, H, N, S and O, volatile matter, fixed carbon, ash and moisture).
Regression analysis. The experimental data could not fit into any of the regression models, and the relationships between the input and output parameters were too scattered to fit any of the models. Similarly, regression-based models (multiple linear re-gression, power regression analysis) with six inputs from a da-taset of 106 experiments (fixed carbon, volatile matter, mineral matter, air feedrate/kg of coal, steam feed/kg of coal and
tem-perature and output in these cases were the rates and heating values of the product gases) were developed.7 The model results did not yield a good match with the experimental data.
Artificial neural network. An ANN model (FIG. 3) that indi-cated a good match with the experimental data was developed.
The model was later used for sensitivity analysis (effect of carbon content in coal, effect of temperature, etc.) that did not show the expected results, even qualitatively. The lack of anticipated results is due to the lack of a large set of experimental data for training the ANN model. Similarly, a neural network was created8 with eight inputs with a single hidden layer, and output of CO, CO2, H2 and methane (CH4). The network was trained and validated with 18 experimental data obtained from literature for a BFB wood gasifi-er. It indicated that the developed network showed a good match with the experimental data, although no results of sensitivity analysis using the developed model were discussed in the work.
To train an ANN model to be used for optimization stud-ies, an exhaustive set of data is required. ANNs cannot be used to study effects of parameters if they are out of the range of the training data and, therefore, are not useful for scale-up studies.
Equilibrium model. Simulation results with a non-stoichio-metric approach for calculating the equilibrium compositions were completed using a commercial process simulation software.
The results showed an error margin of between 20% and 40%
(FIG. 4) with respect to experimental CGE, while the carbon
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48 AUGUST 2016 | HydrocarbonProcessing.com
Process Engineering and Optimization
conversion calculated at equilibrium was always 100%. These results did not match with the actual experimental results, while the carbon conversion ranged between 60% and 90%. Although the model did not match the actual experimental data, it gave a fair indication of the operational limits and the qualitative change in the outlet gas composition and generation rate with changes in various operating parameters. Due to the high tem-perature at which entrained-flow gasifiers operate, they have shown gas composition nearly equal to the equilibrium com-positions.10 For a BFBG, the modified equilibrium models may prove to be useful, as shown in the results of previous studies.11
Rate-based models. A CRE model based on the two-phase theory12 showed a good match with the experimental data (FIG. 4), with < 20 % error. The two-phase theory assumes that the fluidized bed is divided into the emulsion and bubble phases. The emulsion phase consists of solids and the volume of gases required to keep the solids at minimum fluidization veloc-ity (Umf), while the bubble phase consists of extra gases flowing through the bed.
Other theories exist to model a BFBG. They estimate the fluid dynamics (bubble diameter, bubble velocity, bubble void-age, velocity of gas in emulsion phase, etc.) using different cor-relations. Nine chemical reactions (four heterogenous and five homogenous) have been considered in this model. The kinetics for these chemical reactions have been taken from data report-ed in literature.13 Experimental studies using TGA, autoclave, a fixed-bed reactor, etc., can be conducted to estimate the kinetics for a particular coal. The temperature profiles and the hydrody-namic profile inside the reactor showed a good match with the experimental results. This model was then used for sensitivity analysis (including pressure effects) and scale-up studies.
In the past decade, several CFD models for various reactors have been developed. In the case of a BFBG, based on how the solids are treated, two major CFD models exist: if the solid has been assumed as a continuum, then the Eulerian framework is applied to describe the motion of the solids; and if the solid particles are individually tracked, then the equation of motions are solved to track the motion of particles. The gas phase is de-scribed by the Eulerian framework and modeled similarly to single-phase flow, wherein interaction with the solid phase is ac-counted for by an additional term.
The two approaches are termed as Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) models.14 The source terms (kinetics) are the same in both the CRE and CFD models, but the main dis-tinction is the handling of the fluid mechanics. In the EL model, the solid phase exchanges mass, momentum and energy with the gas phase, where each individual particle is solved in a Lagrang-ian frame of reference. The discrete element/particle method in-spired by molecular dynamics is commonly applied. In a DEM/
DPM model, the collision between particles may either be based on a hard-sphere or soft-sphere approach.15 Closure relations in these models are not simple; several equations with semi-empir-ical parameters must be solved simultaneously. A comparative analysis of CFD models for a BFBG can be found in literature.14
A CFD model was not formulated due to two main reasons:
it was too computationally intensive, and it involved an extended simulation time (a BFBG involved complex gas solid hydrody-namics coupled with several chemical reactions). A CRE model proved a robust computational tool in attaining the objectives for design/scale-up/optimization studies of a BFBG. In literature, researchers have simulated a bench-scale BFBG using CFD and have shown a good match with the experimental data. The simu-lation time for CRE models is significantly less when compared to CFD models. The coupling of CRE models with CFD mod-els—wherein the insights (flow and mixing knowledge) obtained from a CFD model are utilized in quantifying flow and mixing in a CRE model—have been reported.16 Similarly, the use of ANNs to estimate the kinetics in a rate-based model has also been re-ported. A summary of the advantages and disadvantages of the various approaches to model the reactor are listed in TABLE 1.
C Hidden layer Output layer Input layer (i)
FIG. 3. ANN model structure to predict carbon conversion (x) and cold gas efficiency (CGE) from coal gasification in a BFB gasifier.
0.3
FIG. 4. A schematic parity plot comparing the errors obtained for the simulation of 25 experiments with a CRE model and the equilibrium model12 adapted for CGE.
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