## Introduction

Most combustion boilers that produce steam or electricity have various stages of extracting the enthalpy from flue gases produced by combusting fossil fuels. These include, waterwall tubes, Superheat and Reheat tubes, economizer and air preheaters. Air preheaters are typically the last stage in the combustion process where useful enthalpy is extracted from the flue gas to preheat combustion air. These air preheaters can be classified in two broad categories, namely tubular and regenerative air preheaters.

Tubular preheaters consist of straight tube bundles, where energy is transferred from the hot flue gas flowing inside many thin walled tubes to the cold combustion air flowing outside the tubes. Regenerative or rotating type air preheaters consist of baskets of regenerative heat absorbing materials that transfer heat from the flue gasses to the combustion air.

## Air Preheater Heat Transfer

By design, regenerative air preheaters have cold heat transfer surfaces as the air preheater gives up its enthalpy to heat up the combustion air as it rotates from the air duct to the flue gas duct. The heat transfer surfaces then absorb heat from the flue gas as it rotates within the flue gas duct. This creates a 3-dimensional temperature pattern within the heat transfer element that radiates from the gas inlet to the gas outlet and from the air side ducting to the outer edge of the flue gas duct.

Figure 2 below shows the temperature gradient from the Hot End to the Cold End through the Air preheater as the air and gas pass through.

Figure 3 below shows the temperature gradient across the face of the air preheater within the heat transfer baskets directly at the cold end of the Air preheater.

## TherMap – A thermodynamic model of the regenerative Air Preheater (APH)

The TherMap model was developed by Lehigh University under funding and guidance from EPRI and licensed by Breen worldwide. The model comprises of critical mechanical design parameters of the air preheater and information on the fluid temperature and flow properties for the air and flue gas. Some of the critical design parameters include:

- Layer/Depth configuration
- Diameter
- Heat Transfer Element profile
- Material Selection

Element profiles for regenerative APHs can be characterized in two general types: closed and open (See Figure below). Commercial regenerative heat transfer elements are composed of a pair of element sheets appropriately spaced to provide a flow passage between them. An example of a closed element profile is the Notched Flat 6-mm element (NF6), is shown below. The element pair is formed by a series of notches which rest on an adjacent flat sheet with contact along the total flow length. They provide the necessary spacing and form discrete individual flow channels of fixed cross-sectional area along the flow length or element depth. There is no flow communication from one channel to the adjacent one.

The Double Undulated (DU) element is an example of an open-channel element where the notches, which provide the required spacing, rest on a series of point contacts on the adjacent sheet. Flow can move across the element pair since there are openings between the two sheets along the flow length between point contacts.

Other variations of these basic types exist and vary among manufacturers, such as Corrugated Undulated (CU), Flat Notched Crossed (FNC) or Notched Plate (NP). New advanced surface types such as UNU and DNF suggest improved performance over older types.

While the choice of element profile for a given APH design is driven by many factors (e.g., heat transfer and pressure drop), from the standpoint of sootblowing effectiveness, closed-element profiles are preferred, because they contain the flow energy from the sootblower and thereby offer better fly ash removal than open-element profiles. In an open-channel element, the sootblower energy can deflect to the sides and flow around the deposit.

The Layer/Depth configuration in a regenerative APH is typically a 3-layer (traditional) or a 2-layer (AbS tolerant) design. In the more traditional 3 layer design, the cold end layer is typically 12 to 18 inches deep. There are two additional layers, namely the intermediate layer and the hot end. In a two layer, AbS tolerant design, the cold end is 36 to 42 inches deep and there is no intermediate layer. In some refinery boilers, there may be only one layer.

Finally, the Air Preheater may have a primary air section resulting in a tri-sector design or the primary air preheater may be separate resulting in a bi-sector design.

### The Thermodynamic Heat Transfer Model

The TherMap model performs numerical simulations of the heat transfer processes within the APH metal matrix. Specifically, the model is a two-dimensional, finite-difference model that describes the heat transfer processes within the metal matrix of the APH at some radial distance from the center of rotation. An order-of-magnitude analysis showed that heat conduction in the radial direction between adjacent heat transfer passages in the metal matrix is not important. This allowed the reduction of the three-dimensional problem to two dimensions.

Figure 5 below illustrates the geometry and coordinate system used in the analysis. To convert this time-dependent problem to steady- state conditions, a coordinate system, which is fixed in space, was chosen where r, θ and y denote the radial, circumferential and axial coordinates. The equations that need to be solved to compute the fluid and metal temperature distributions and thermal performance of the APH are the conservation of energy equations for the combustion air, flue gas and metal. Since, at any instant, the control volume is partially occupied by the metal matrix and partially by flue gas or combustion air, it is convenient to define the following quantities:

- Volumetric porosity: εv = Volume of Metal/Total Volume
- Surface porosities: εi = Cross Sectional Area of Metal Matrix in i-direction/Total Cross Sectional Area in i- direction, where i = r, θ, y
- Specific heat transfer area: AS = Total Heat Transfer Area/Total Volume

After performing the coordinate transformation x = rθ, the governing equations can be written as:

Energy Conservation for Metal Matrix:

Energy Conservation for Flue Gas/Combustion Air:

where:

### Model Output

Based on the information and modeling process described above, it is possible to model the actual heat transfer between the heat exchange surfaces and the fluid media, be it the air extracting heat from the heat transfer surfaces or the heat transfer surfaces extracting heat from the flue gas. The actual temperature gradients within the air preheater are likely somewhat radial due to the mechanical design of the air preheater, for all practical purposes, one can assume the gradients to the linear from the hot end to the cold end on one axis and from the air-side to the gas-side rotation boundary to the gas-side to the air-side rotation boundary. Therefore this may be represented on a graph as shown in Figure 6 below.

The model takes operating data such as air side inlet temperature, gas side flue gas inlet temperature, air preheater rotational speed, inlet air flow and gas flow rates, leakage coefficients for air-side, gas-side and radial leakage and the composition of flue gas and air as inputs. The result is a matrix of data points representing the fluid temperatures, air and gas, and the metal matrix temperature throughout the air preheater baskets, at each increment in the two dimensional matrix representing distance across the duct in one dimension and cold end to hot end in the other dimension.

The blue graph represents the minimum metal matrix temperature as it rotates from the air side to the gas side at each incremental distance from the cold end to the hot end. The red line similarly represents the maximum metal temperature of the metal matrix temperature as it rotates from the gas side to the air side at each incremental distance from the cold end to the hot end.

When the model is developed for an air preheater, the model fidelity is tested against the predicted air and has outlet temperatures. The model parameters are tuned until the predicted temperatures closely match the actual measured air and gas outlet temperatures at various loads.

## Model Implementation

At the basic level, the model is a windows executable that takes as input a data file comprising of the physical properties, heat transfer coefficients and operating data inputs. The resultant output is a data file comprising the two dimensional matrix of metal and fluid temperatures. EPRI has developed a Microsoft Excel front end to this engine which is used as an offline tool to conduct data analysis, model tuning and general process analysis.

Breen has implemented a shell around the windows executable and wrapped it into a Windows Human Machine Interface program that can communicate with plant DCS or data historians such as OSI-PI and run the model in real time and provide the relevant outputs back to the DCS or data historian.

Breen has further developed a technique to run a box factorial design on the operating conditions within the plant operations and generate a set of polynomial equations that represent a statistically valid approximation of the model. These polynomials can then be implemented in a DCS or other system and executed in real time to generate relevant data outputs for process monitoring and optimization.