**1. Introduction**

Solid oxide fuel cells (SOFCs) have recently received attention as an alternative power source since they have especially high electrical efficiency, low emission and fuel flexibility. Challenging issues for SOFC commercialization are having long-term durability and enhancing economic efficiency. Due to the long operation time of a SOFC, it is mainly utilized as a stationary power plant. Therefore, achieving high system efficiency and fuel utilization becomes important because it is directly linked to economic efficiency [1,2]. To improve system efficiency, designing an appropriate system configuration is necessary in addition to applying highly efficient components. The overall system efficiency varies according to the layout of the system components.

Generally, thermal energy from stack off-gas and system exhaust gas are utilized in order to improve system efficiency. The heat is recovered at heat recovery heat exchangers (HR-HEs) and often supplied to the fuel/air preheater and reformer or used to generate steam necessary for the reforming reaction [3,4]. The SOFC combined heat and power (CHP) system has also been widely suggested for efficient SOFC systems [5–9]. In utilizing exhaust heat from the stack and system, the system composition and its configuration highly affect the system's overall efficiency. Therefore, many studies on designing system configurations have been conducted [6,7].

In order to improve system efficiency, anode off-gas recirculation (AOGR) can be adopted for the SOFC system. Anode off-gas (AOG) contains unreacted hydrocarbons and a high content of steam. The recirculated AOG reacts as fuel inside a fuel cell, leading to an

**Citation:** Choi, E.-J.; Yu, S.; Kim, J.-M.; Lee, S.-M. Model-Based System Performance Analysis of a Solid Oxide Fuel Cell System with Anode Off-Gas Recirculation. *Energies* **2021**, *14*, 3607. https://doi.org/10.3390/ en14123607

Academic Editor: Bahman Shabani

Received: 23 May 2021 Accepted: 14 June 2021 Published: 17 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

increase in the fuel utilization efficiency. The efficiency of the steam methane reforming (SMR) reaction is also promoted by additionally supplied steam from AOG [10,11].

In the study of Powell et al. [12], a 2 kW class SOFC system with AOGR was experimentally verified. Heat and steam from AOG were delivered to an adiabatic steam reformer. As a result, the overall fuel utilization efficiency was increased up to 93%, and the system achieved a maximum net LHV efficiency of 57% at 1.7 kW. Additionally, a parametric study of the SOFC system with AOGR was conducted by Lee et al. [10]. In this study, a turbocharger and an ejector were suggested to supply air and recirculated AOG. The effects of the external reforming (ER) ratio, fuel utilization and steam to carbon (S/C) ratio were examined. The suggested system showed electrical efficiency of 64.6% when the ER ratio, fuel utilization and S/C ratio were 0.4, 0.75 and 2.5, respectively. Through the sensitivity analysis, it was revealed that fuel utilization was the most influential factor in the system efficiency. Table 1 presents a literature summary of the SOFC system with AOGR analyzed by many researchers.

**Table 1.** A literature summary of the SOFC system with AOGR.


Additionally, the method that can generate additional electricity by utilizing SOFC exhaust gas has been widely studied. SOFC hybridization with other power generation systems allows the system efficiency to be effectively improved [7,18,19]. Kuchonthara et al. [19] evaluated a combined power generation system with a SOFC and various gas turbine (GT) cycles. The results indicated that the humid air turbine promoted the thermal efficiency of the overall system. The effectiveness of a SOFC-engine hybrid system was experimentally demonstrated by Kim et al. [18]. A 5 kW class SOFC stack and internal combustion engine were combined, and the electrical efficiency of the hybrid system increased by up to 26%.

In this paper, two SOFC system configurations with AOGR were developed. The differences between the first AOGR system (AOGR #1) and the second AOGR system (AOGR #2) were the heat flows of AOG, cathode off-gas (COG) and catalytic combustor off-gas (CCOG). The details were described in Section 2. The performances of each

system were evaluated in comparison with those of a reference system. For comparison, component-level mathematical modeling was conducted. Analysis of the effect of the fuel/air utilization factor and recirculation ratio was conducted based on the simulation result. In particular, the temperature of each component, net power, and electrical and thermal efficiency were examined.

#### **2. System Configurations**

To evaluate the system efficiency of various SOFC system configurations, the reference SOFC system and the system with AOGR were analyzed. The reference system shown in Figure 1a consists of an external steam reformer (ESR), a SOFC stack, a catalytic combustor (CC), air blowers, a steam generator, an air preheater and an HR-HE. For an efficient system, a direct internal reforming (DIR) SOFC was suggested. The DIR stack enables hydrocarbons to be reformed directly inside a stack [20,21]. As the steam reforming reaction is highly endothermic, the ESR needs a large amount of heat. In the reference system, ESR thermally integrated with CC was used, in other words the heat of combustion from CC was directly provided to the ESR. This ESR is called an allothermal reformer [4]. Due to the thermal stability of CC, additional air to the CC blows when needed to keep the temperature of the CC lower than 1123.15 K [22]. Thermal energy from COG was used to generate the steam required for the steam reforming process. Cooled COG has the effect on preventing the excessive temperature increase of the CC. CCOG supplies heat to the ESR and stack air flow. The rest of the CCOG thermal energy was recovered from the HR-HE.

The first concept of the SOFC system with AOGR is suggested in Figure 1b, and it is named the AOGR #1 system. AOG flowed into the fuel preheater through a recirculation blower. The recirculation blower was generally able to withstand hot gas up to 1073.15 K, so recirculated AOG needed to be cooled at the fuel preheater. The recirculated AOG is able to warm the ESR and simultaneously provide the additional steam required for the SMR reactions. Distinctive flows of AOG and fuel are marked with blue lines in Figure 1b.

Figure 1c shows the second concept of the SOFC system with AOGR, which is called the AOGR #2 system. While the ESRs shown in Figure 1a,b were thermally integrated to the CC, the ESR shown in Figure 1c obtained the required heat only from the reactant flows, namely, the adiabatic reformer. It has been demonstrated that the SMR reaction can occur using only the sensible heat of the inlet gas [4,12]. The inlet fuel to the ESR was heated in two stages by the heat from recirculated AOG and COG. The heat of CCOG was used to warm up the stack supplied air and was recovered at the HR-HE. The differences of the AOGR #2 system compared to the AOGR #1 system are highlighted with green lines in Figure 1b.

**Figure 1.** *Cont.*

**Figure 1.** Schematic diagram of the system configuration; (**a**) reference system, (**b**) AOGR #1 system, and (**c**) AOGR #2 system.
