Multi-Criteria Decision Analysis for Optimizing CO₂ and NH₃ Removal by Scenedesmus dimorphus Photobioreactors

Abstract

Numerous technologies have been investigated for mitigating air pollutant emissions from swine barns. Among them, algal photobioreactors (PBRs) can remove and utilize air pollutants such as CO₂ and NH₃ from barn exhaust. However, a challenge to PBR operation is that it involves multiple system input parameters and output goals. A key question is then how to determine the appropriate CO₂ and NH₃ concentrations in this case. Conventional statistical methods are inadequate for handling this complex problem. Multi-criteria decision-making (MCDM) emerges as a practical methodology for comparison and can be utilized to rank different CO₂–NH₃ interactions based on their environmental and biological performance. By employing MCDM methods, producers can effectively control the ratio of CO₂ and NH₃ concentrations, enabling them to identify the optimal range of operating parameters for various housing types, ensuring efficient pollutant mitigation. In this study, a multi-criteria decision-making (MCDM) approach was employed to support operation management. Specifically, influent CO₂ and NH₃ concentrations were optimized for three scenarios (the best biological, environmental, and overall performance), using a combination of two MCDM techniques. This study is anticipated to facilitate the system analysis and optimization of algae-based phytoremediation processes.

1. Introduction

Concentrated animal production results in significant air pollutant emissions that contribute to environmental pollution and global warming issues. Various air pollutants, such as NH₃, H₂S, CH₄, and CO₂, can originate from animal housing, manure storage, and land application [1]. There is a need to mitigate these pollutants while sustaining animal protein supplies. This mitigation will not only protect the environment but also improve indoor air quality critical for animal health and welfare, as well as the safety and health of farm workers [2,3].

Various mitigation technologies/practices have been researched, including air scrubbers, biofilters, tree barriers, diet manipulation, and improved manure management [4,5,6]. Among them, CO₂ and NH₃ fixation by microalgal photosynthesis has recently attracted significant attention due to its eco-friendliness and potential economic benefits. Microalgae have substantially higher cell growth and CO₂ fixation rates (about 10–50 times) than terrestrial plants [7]. They can be further valorised into biofuels, animal feed, nutrition additives, cosmetics, and pharmaceuticals [8].

Numerous factors play a crucial role in effectively reducing air pollutants released from animal barns using photobioreactor (PBR) systems. The concentrations of air pollutants vary depending on the livestock breed, animal age, and barn type. Similarly, the growth of microalgae in PBR systems differs in terms of their air pollutant reduction efficiency, biomass yield, and cell growth, which are influenced by the emitted CO₂ and NH₃ gas concentrations from the barn. Therefore, to achieve optimal CO₂ and NH₃ gas reduction efficiencies, it is essential to determine the gas concentrations at which microalgae exhibit the best cell growth and biomass yield. The existing literature indicates that while the highest cell growth, measured by cell counts, can occur at any CO₂ gas concentration, the maximum biomass yield may be obtained at a different gas concentration [9]. A microalga that demonstrates the highest cell growth at a specific CO₂ gas concentration might exhibit lower cell growth at another CO₂ concentration due to the presence of NH₃ gas in the PBR system, where CO₂ and NH₃ gases coexist [10]. In other words, although cell growth reaches its peak at a given CO₂ gas concentration, the maximum biomass yield may not be achieved at the same CO₂ gas concentration. Therefore, for the most effective mitigation of air pollutants released from animal barns using PBR systems, it is crucial to collectively evaluate and analyze the biological and environmental parameters that influence microalgae growth. By doing so, maximum efficiency can be obtained from all parameters influencing algal growth, and identifying the air pollutant concentrations at which the highest gas reduction efficiency can be achieved will enhance the system’s effectiveness and economic viability.

Challenges exist to effective CO₂ and NH₃ gas mitigation with microalgae due to the complexity of the relevant processes. For example, CO₂ and NH₃ fixation efficiencies can be affected by many operating parameters, such as gas loading rates, gas concentrations, pH, light intensity, and temperature. Numerous studies have been conducted to examine the effects of these parameters [8,11,12,13]. In nearly all these studies, different parameters were examined separately. However, interactions between the parameters should not be neglected. For example, Kang and Wen [14] reported that the solubility and uptake of CO₂ by algae were affected by the presence of NH₃ in PBRs. Moreover, algal PBRs for air pollutant mitigation (and other phytoremediation purposes) often involve multiple system input parameters (e.g., CO₂ concentrations, pH, and temperature) and multiple output goals (e.g., biomass yield and NH₃ removal efficiency), making it challenging to make management decisions concerning algal PBR operation. Previous studies have highlighted the challenge of CO₂ concentration when utilizing microalgae for pollutant capture. Traditional statistical methods may not be adequate for addressing the complexities associated with determining suitable CO₂ and NH₃ concentrations for algal growth. Therefore, prioritizing the options for mitigating pollutants through CO₂ and NH₃ concentration requires a multi-criteria approach. One practical methodology for comparison in this regard is multi-criteria decision-making (MCDM). In this paper, a multi-criteria assessment model is proposed which combines grey relational analysis (GRA) and criterion impact loss (CI-LOS) techniques. This model allows for the ranking of different CO₂–NH₃ interactions based on their environmental and biological performance. By applying the CI-LOS method, objective determination of weights can be achieved for parameters such as cell number, biomass yield, and others that monitor microalgae growth, as well as parameters indicating gas reduction efficiency. Subsequently, using the GRA method and considering these weights, the optimal CO₂ and NH₃ gas concentrations can be determined.

Advancements in decision-making sciences have made MCDM methods increasingly accessible and accepted recently. MCDM refers to decision-making in the presence of multiple criteria that are inconsistent or even contradictory [15]. It is particularly useful for systems with multiple criteria and alternatives. The development of MCDM methods is motivated by not only various real-life problems requiring the consideration of multiple criteria but also by advances in mathematical optimization, scientific computing, and computer technology [16]. A fundamental task of MCDM is to evaluate a set of alternatives with a set of criteria. This involves the determination of the criteria that can be organised according to the expectation of a decision to be made for possibly solving a problem and other alternatives [17].

MCDM has been used in solving various problems in social sciences such as supplier selection [18,19,20], financial performance [21,22], and cyber security [23,24], as well as in engineering and science problems such as geographic information systems [25,26], construction equipment evaluation [27,28], and machine tool selection [29,30]. This method has been applied successfully in environmental research areas, from optimising waste management systems [31] to selecting gas mitigation methods [32,33]. Only a few reports are available concerning its applications for algal research, with the majority focusing on harvesting technologies [34,35]. Others include the identification of the best microalgae strain for biodiesel production [36], the best areas for microalgal cultivation [37], and the best algal wastewater treatment systems [38]. To our knowledge, no application of MCDM for algal PBR operation has been reported.

This study presents the first such attempt to identify optimal NH₃ and CO₂ concentrations for algal PBR operation. The primary aim of using the multi-criteria analysis is to find the relative importance of the factors and the criteria that affect cultivation of S. dimorphus with gas concentrations typical of pig house exhaust air. As a restriction, the specified concentrations must be within the typical concentration range of swine barn exhaust. The optimization was conducted to maximize the (1) biological, (2) environmental, and (3) overall performance of algal PBR systems. For each of the system output goals (scenarios), multiple performance indicators were considered. Specifically, the biological performance (i.e., algal growth) was measured by algal cell concentration, dry algal biomass, maximum specific growth rate, and cell weight; the environmental performance (i.e., pollutant mitigation) was measured by CO₂ fixation rate, NH₃ fixation efficiency, CO₂ removal efficiency, and NH₃ removal efficiency; and the overall performance was measured by all the indicators stated above. Sixteen experimental data sets were analyzed with two MCDM methods (criterion impact loss (CILOS) and grey relational analysis (GRA)) following the multi-step procedure outlined in Figure 1. Such optimization cannot be performed with regular statistical tools.

2. Materials and Methods

2.1. Experimental Prodecure

Scenedesmus dimorphus (S. dimorphus) strain UTEX 1237 was cultivated in 1 L Erlenmeyer flasks containing 100 mL of Bold’s basal medium with the composition of Uguz et al. [24]. This strain was used because of its efficient CO₂ and NH₃ removal [24]. The prepared BBM was sterilised and placed in the autoclave for 20 min at 121 °C. The cultures were doubled weekly and then transferred to 5 L PBRs when they reached the 5 L working volume for testing. The PBRs were built from acrylic plastic sheets sized 35 cm (height) × 50 cm (length) × 10 cm (width). Figure 2 shows the PBR experiment in operation.

Following the cultivation, 16 experiments were conducted in the laboratory under controlled conditions. In brief, algal PBRs were filled with a 5 L cultivation medium, fed with CO2-laden air at an airflow rate of 5 L min⁻¹, and illuminated at a 60–65 µmol s⁻¹ m⁻² light density. CO₂ concentration in the influent air (

Table 1. Criteria and key performance indicators to evaluate the performance of algal PBRs.

Criteria	Key Performance Indicators (Kpis)		Definition
Biological Performance	C1	Cell count	Indicating algal cell concentrations grown with NH3 and CO2 typical of the barn exhaust air
	C2	Dry biomass	Indicating algal dry biomass concentrations grown with NH3 and CO2 typical of the barn exhaust air
	C3	Cell weight	Indicating average algal cell weight grown with NH3 and CO2 typical of the barn exhaust air
	C4	Growth rate	Indicating specific algal growth rate, i.e., a ratio of algal cell increase to the initial cell concentration.
Environmental Performance	C5	CO2 fixation rate	Indicating CO2 uptake by algae—an estimate from algal biomass and its carbon content
	C6	NH3 fixation rate	Indicating NH3 uptake by algae—an estimate from algal biomass and its nitrogen content
	C7	CO2 removal rate	Indicating the fraction of CO2 in PBR influents taken up by algae
	C8	NH3 removal rate	Indicating the fraction of NH3 in PRB influents taken up by algae
Overall Performance	C1, C2, C3, C4, C5, C6, C7 and C8

) was regulated using rotameters (Cole Parmer, Vernon, IL, USA) with needle valves. For NH₃, due to its strong adsorption along tubings and adaptors, no rotameter-dilution method was used. Instead, ammonium chloride (NH₄Cl) was added daily to the cultivation medium as an alternative NH₃ source. It was calculated that the NH₄Cl daily doses of 0, 19, 39, and 78 mg L⁻¹d⁻¹ would be equivalent to the aerial NH₃ concentrations of 0, 12, 25, and 50 ppm, respectively, in the influent air. Other parameters, such as pH, temperature, and lighting, were constant throughout the cultivation experiments. The experiments were performed in triplicate, with control PBRs (fed with no NH₃ or CO₂) available for comparison. CO₂ and NH₃ gas concentrations were monitored using an INNOVA 1314i photoacoustic multi-gas monitor 1314i (LumaSense Technologies A/S, Ballerup, Denmark).

2.2. Analytical Methods

A detailed description can be found in Uguz et al. [39]. In brief, algal samples harvested from the sixteen experiments were analyzed for cell concentration (cells L⁻¹), dry algal biomass concentration (mg L⁻¹), cell weight (mg cell⁻¹), specific growth rate (d⁻¹), CO₂ fixation efficiency (mg L⁻¹ d⁻¹), NH₃ fixation efficiency (mg L⁻¹ d⁻¹), CO₂ removal efficiency (%), and NH₃ removal efficiency (mg L⁻¹ d⁻¹). The cell concentration was measured using haemocytometers under an Olympus optical microscope. The dry algal biomass concentration was gravimetrically determined by vacuum-filtering a known volume of an algal sample and weighing the filter after being dried in a laboratory oven at 80 °C for 3 h [40,41]. The cell weight was calculated by dividing a dry algal biomass concentration by its corresponding cell concentration. The specific growth efficiency was calculated by normalizing a cell concentration increase with the initial cell concentration. The NH₃ and CO₂ fixation efficiencies of the algae were calculated by multiplying the growth rate of algal biomass by nitrogen and carbon contents (%wt) in S. dimorphus. The NH₃ and CO₂ removal efficiencies were calculated by dividing their fixation efficiencies (mg L⁻¹ d⁻¹) by their loading rates (mg L⁻¹ d⁻¹) to the PBRs.

2.3. Multi-Criteria Analyses

In the study, sixteen experiments with different combinations of CO₂ and NH₃ gas concentrations were conducted. At the end of each experiment, cell number, dry weight, cell weight, growth rate, CO₂ and NH₃ fixation and removal rates were calculated to monitor algal growth and CO₂ and NH₃ mitigation efficiencies. These parameters were chosen as criteria for the MCDM analysis of the experiments. Then, the weights of each criterion were determined using the CILOS method. Figure 1 shows the weight of each selected criterion in CILOS method. The derived weight numbers then served as input to GRA. As aforementioned, the analyses compared three scenarios/output goals, with each scenario involving multiple performance indicators (Table 1). The indicator data derived from algal cultivation experiments (sixteen batches) are summarized in

Table 2. Decision matrix for multi-criteria analyses.

Scenarios	NH3-CO2 Combinations	Overall Performance
		Biological Performance				Environmental Performance
Criteria Aspects		Max	Max	Max	Max	Max	Max	Max	Max
Criteria/Indicators		C1	C2	C3	C4	C5	C6	C7	C8
EXP1	0 ppm NH3-350 ppm CO2	0.54	0.60	0.31	3.39	0	0	0	0
EXP2	12 ppm NH3-350 ppm CO2	1.15	1.12	0.44	0.96	99.5	22.3	5.48	76.6
EXP3	25 ppm NH3-350 ppm CO2	1.27	1.20	0.6	2.08	81.8	18.3	4.5	36.1
EXP4	50 ppm NH3-350 ppm CO2	1.23	1.24	0.45	2.26	71.0	15.9	3.9	15.6
EXP5	0 ppm NH3-1200 ppm CO2	0.69	0.72	0.05	1.28	0	0	0	0
EXP6	12 ppm NH3-1200 ppm CO2	1.78	1.80	0.35	1.01	193.0	12.6	10.6	94.4
EXP7	25 ppm NH3-1200 ppm CO2	1.95	2.00	0.62	0.53	364.8	23.8	20.1	85.3
EXP8	50 ppm NH3-1200 ppm CO2	1.41	1.45	0.26	1.2	128.7	8.4	7.09	28.4
EXP9	0 ppm NH3-2350 ppm CO2	0.85	0.88	0.28	1.73	6.30	0.41	0.34	0
EXP10	12 ppm NH3-2350 ppm CO2	1.76	1.77	0.34	1.06	163.8	5.46	9.02	80.0
EXP11	25 ppm NH3-2350 ppm CO2	2.04	2.16	0.43	0.58	432.2	14.4	23.8	99.8
EXP12	50 ppm NH3-2350 ppm CO2	1.32	1.33	0.35	0.73	252.9	8.43	13.9	55.7
EXP13	0 ppm NH3-3500 ppm CO2	1.17	1.19	0.31	1.26	54.4	1.21	2.99	0
EXP14	12 ppm NH3-3500 ppm CO2	2.21	2.22	0.49	0.75	267.3	5.98	14.7	97.2
EXP15	25 ppm NH3-3500 ppm CO2	1.56	1.53	0.83	1.58	105.8	2.36	5.83	46.7
EXP16	50 ppm NH3-3500 ppm CO2	1.21	1.23	0.51	1.23	105.6	2.36	5.81	23.3

All criteria in the decision matrix were maximization-oriented criteria for all three scenarios. Each NH₃-CO₂ combination corresponded to a unique set of input and output data.

.

2.3.1. Criteria Impact Loss (CILOS)

The CILOS method, the theoretical background created by Mirkin (1974) and the detailed algorithm presented by Zavadskas and Podvezko [42] are among the most promising approaches to determining the objective weight. The CILOS method considers each criterion’s loss of importance (impact) when one of the other criteria achieves the optimal maximum or minimum value. The stages and calculation algorithm of the CILOS method are briefly described below [42,43,44,45,46]:

Step 1. Creating a decision matrix

The CILOS method starts with a decision matrix. The decision matrix of m × n size, which includes m criteria and n alternatives, is named Z and shown in Equation (1). Here, $r_{12}$ denotes the 2nd criterion value of the 1st alternative, while $r_{21}$ denotes the 1st criterion score of the 2nd alternative.

$$Z=\left(\begin{array}{cccc}{r}_{11}& r_{12}& \dots & r_{1m}\\ r_{21}& r_{22}& \dots & r_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ r_{n1}& r_{n2}& \dots & r_{nm}\end{array}\right)$$

(1)

Step 2. Converting cost criteria into benefits

Since the CILOS method only provides solutions for maximization-oriented criteria, Equation (2) is used to transform the minimization-oriented criteria into maximization-oriented (best). There is no minimization-oriented criterion for algal growth in this paper.

$${\stackrel{-}{r}}_{ij}=\frac{{min}_i{r}_{ij}}{r_{ij}}$$

(2)

where $r_{ij}$ is the cost-oriented criterion showing the i alternative value of the j criterion. On the other hand, ${\stackrel{-}{r}}_{ij}$ is the cost-oriented criterion transformed into a benefit-oriented criterion.

Step 3. Normalization

Equation (3) is applied to each criterion value for normalization. After normalization, a new matrix X is obtained.

$${\stackrel{-}{x}}_{ij}=\frac{r_{ij}}{{\sum }_{i=1}^n{r}_{ij}}$$

(3)

where, $x_i^{*}$ is the normalized criterion value

Step 4. Creating a square matrix (A)

After obtaining the normalized X matrix, a square matrix (A) is derived with Equations (4) and (5). The row containing the $\underset{i}{\max }{r}_{ij}$ element with the maximum value in each column is processed as in Equation (5) to form a square matrix. That is, the square matrix is obtained by taking the row with the maximum element in the ith column of the normalized decision matrix as the new matrix ith row.

$$a_j=\underset{i}{\max }{r}_{ij}=a_{k_{i}j}$$

(4)

$$a_{ij}=a_{k_{i}j}\mathrm{and}{a}_{jj}=a_j$$

(5)

where $a_{k_{i}j}$ specifies the maximum values of jth criteria, which are taken from the decision matrix with k_i rows to form a square matrix, $a_{ij}=a_{k_{i}j}$ and $a_{jj}=a_j$ [47].

Step 5. Calculating a relative loss of impact matrix (P)

The values in the square matrix A are processed by Equation (6) to form the relative loss of effect matrix $P=‖p_{ij}‖$.

$$p_{ij}=\frac{a_{jj}-a_{ij}}{a_{jj}},\left(p_{ii}=0;i,j=\mathrm{1,2},3,\dots ,m\right)$$

(6)

In matrix P, $p_{ij}$ represents the loss of effect in the jth criterion when the ith criterion is selected as the best.

Step 6. Determining a weight system matrix (F)

The F matrix in Equation (7) is formed by finding the sum of each column of the P matrix and writing the negative values of these sums on the diagonals of the P matrix.

$$F=\left(\begin{array}{cccc}-{\displaystyle \sum _{i=1}^m}{p}_{i1}& p_{12}& \dots & p_{1m}\\ p_{21}& -{\displaystyle \sum _{i=1}^m}{p}_{i2}& \dots & p_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ p_{m1}& p_{m2}& \dots & -{\displaystyle \sum _{i=1}^m}{p}_{im}\end{array}\right)$$

(7)

Step 7. Calculation of weight of each criterion

The final criterion weights ($q=q_1,q_2,\dots ,q_m)$ are determined by solving Equation (8) (using Excel 2016 or Matlab 9.13).

$${Fq}^T=0$$

(8)

The weights $q$ of the criteria are obtained by solving the equation ${Fq}^T=0$. Since this system of equations has infinite solutions, the weight vector is determined by normalizing the values so that ${\sum }_{i=1}^m{q}_i=1$.

2.3.2. Grey Relational Analysis (GRA)

Grey system theory, a control theory first proposed by Deng [48], has significantly impacted numerous fields of engineering and management. The theory enabled the development of grey relational analysis (GRA), a powerful tool that can effectively resolve complex relationships between multiple performance characteristics through the optimization of grey relational degrees [49].

As in almost all MCDM methods, GRA problem solving starts with a decision matrix consisting of the values of decision criteria. Since the decision matrix is created in the same way as CILOS (Equation (1)), no further explanation is given in this section. The problem solving procedure of GRA is summarized below [49,50,51,52,53]:

Step 1. Creating a comparison matrix

Equation (9) is used to calculate a reference series in the comparison matrix (for criteria comparison).

$$x_o=\left(x_0\left(1\right),x_0\left(2\right),\dots ,x_0\left(j\right)\right)j=\mathrm{1,2},\dots ,n$$

(9)

where $X_0\left(j\right)$ represents the optimal value of the jth criterion within the normalized values. This series is obtained by taking the best value of each criterion in the decision matrix.

Step 2. Normalization and creating of normalized decision matrix

Decision problems, by their nature, consist of criteria with different units and objectives. Therefore, a normalization process is adopted while solving the decision problems. There are three possible situations for normalization in the GRA method.

i.

The Larger-The-Better Case: If the criterion used is of the highest appropriateness for the purpose, normalization is performed using Equation (10).

$$x_i^{*}=\frac{x_i\left(j\right)-\underset{j}{\min }{x}_i\left(j\right)}{\underset{j}{\max }{x}_i\left(j\right)-\underset{j}{\min }{x}_i\left(j\right)}$$

(10)

ii.

The Smaller-The-Better Situation: If the criterion used is of the smallest appropriateness for the purpose, normalization is performed using Equation (11).

$$x_i^{*}=\frac{\underset{j}{\max }{x}_i\left(j\right)-x_i\left(j\right)}{\underset{j}{\max }{x}_i\left(j\right)-\underset{j}{\min }{x}_i\left(j\right)}$$

(11)

where, $x_i^{*}$ is the normalized criterion value, and $x_i\left(j\right)$ is the value of the jth criterion in the initial decision matrix.

iii.

The Closer-To-The-Desired-Value-The-Better Situation: If the criterion used is of the optimal appropriateness (the most suitable) for the purpose, normalization is performed using Equation (12).

$$x_i^{*}=\frac{\left|x_i\left(j\right)-x_{0b}\left(j\right)\right|}{\underset{j}{\max }{x}_i\left(j\right)-x_{0b}\left(j\right)}$$

(12)

where $x_{0b}\left(j\right)$ is the determined optimal value, and $j$th indicates the target value of the criterion. This optimal value can take a value in the range $\underset{j}{\min }{x}_i\left(j\right)\le x_{0b}\left(j\right)\le \underset{j}{\max }{x}_i\left(j\right)$. After completion of the normalization process, a normalized decision matrix is obtained. The normalized decision matrix ($X^{*}$) of m × n size, which includes m criteria and n alternatives, is shown in Equation (13).

$$X^{*}=\left[\begin{array}{cccc}{x}_1^{*}\left(1\right)& x_1^{*}\left(2\right)& \dots & x_1^{*}\left(n\right)\\ x_2^{*}\left(1\right)& x_2^{*}\left(2\right)& \dots & x_2^{*}\left(n\right)\\ ⋮& ⋮& \ddots & ⋮\\ x_m^{*}\left(1\right)& x_m^{*}\left(2\right)& \dots & x_m^{*}\left(n\right)\end{array}\right]$$

(13)

Step 3. Calculating an absolute value matrix

The normalized values of the decision matrix are subtracted from the normalized values of the reference series (Equation (14)) to form an absolute value matrix (Equation (15)).

$${∆}_{0i}=x_0^{*}\left(j\right)-x_i^{*}\left(j\right)$$

(14)

$${∆}_{0i}=\left[\begin{array}{cccc}{∆}_{01}\left(1\right)& {∆}_{01}\left(2\right)& \dots & {∆}_{01}\left(n\right)\\ {∆}_{02}\left(1\right)& {∆}_{02}\left(2\right)& \dots & {∆}_{02}\left(n\right)\\ ⋮& ⋮& \ddots & ⋮\\ {∆}_{0m}\left(1\right)& {∆}_{0m}\left(2\right)& \dots & {∆}_{0m}\left(n\right)\end{array}\right]$$

(15)

where ${∆}_{0i}$ represents the values of the absolute value matrix.

Step 4. Creating a grey relational coefficient matrix

Equation (16) is used to create the grey relational coefficient matrix in which ${∆}_{max}$ and ${∆}_{min}$ are calculated with Equations (17) and (18), respectively.

$${\gamma }_{0i}\left(j\right)=\frac{{∆}_{min}+\zeta .{∆}_{max}}{{∆}_{0i}\left(j\right)+\zeta .{∆}_{max}}$$

(16)

$${∆}_{max}=\underset{i}{\max }\underset{j}{\max }{∆}_{0i}\left(j\right)$$

(17)

$${∆}_{min}=\underset{i}{\min }\underset{j}{\min }{∆}_{0i}\left(j\right)$$

(18)

where ${\gamma }_{0i}\left(j\right)$ represents the values of the grey relational coefficient matrix. The “discriminant coefficient” or “contrast control coefficient” $\zeta$ in Equation (14) is a value in the range of [0, 1]. To be consistent with the literature, ζ = 0.5 was taken in this study for relevant analyses.

Step 5. Calculating grey relational degrees

The grey relational degree is a measure of the geometric similarity between the $x_i^{*}$ series in a grey system and the reference series $x_0^{*}$ and allows the series to be compared. A large grey relational degree indicates a strong relationship between the comparative and reference series. If the two series being compared are identical, the grey correlation degree is 1.

The calculation of grey relational degrees differs according to the weight status of the criteria. When criteria weights are all equal, the grey relational degrees are calculated with Equation (19), while Equation (20) is used when criterion weights differ.

$${\mathrm{\Gamma }}_{0i}=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.{\displaystyle \sum _{j=1}^n}{\gamma }_{0i}\left(j\right)$$

(19)

$${\mathrm{\Gamma }}_{0i}={\displaystyle \sum _{j=1}^n}\left[{w_i\left(j\right).\gamma }_{0i}\left(j\right)\right]$$

(20)

where ${\mathrm{\Gamma }}_{0i}$ refers to the grey relational degrees, and $w_i\left(j\right)$ is the weight of the $j$th criterion. The sum of the criterion weights must be equal to 1 (${\sum }_{j=1}^n{w}_j=1$).

3. Results and Discussion

3.1. Biological Performance

When evaluating the biological performance of the PBR systems at different NH₃ and CO₂ concentration levels (Scenario 1), four parameters were considered. Table 2 provides the criteria involved in the assessment and a description of the performance parameters. The high dry biomass concentration appeared to be the most dominant factor according to the weights and weight system matrix of the biological performance criteria calculated using the CILOS method (

Table 3. Criteria weights for all scenarios.

Criteria/Scenario	Scenario 1	Scenario 2	Scenario 3
q1	0.2687		0.1860
q2	0.2710		0.2130
q3	0.2066		0.1347
q4	0.2537		0.1318
q5		0.2885	0.0801
q6		0.1138	0.0504
q7		0.2880	0.0801
q8		0.3098	0.1238

). The second most dominant factor was cell concentration.

S. dimorphus showed the highest normalized cell number (2.21 ± 0.14, p < 0.01 compared with other test conditions) with 12 ppm NH₃ and 3500 ppm CO₂ (EXP 14). The maximum specific growth rate of S. dimorphus occurred on the second day of the experiment; the highest rate was 0.83 d⁻¹ with 25 ppm NH₃ and 3500 ppm CO₂ (EXP15). Dry biomass concentration was significantly higher (1.16 ± 0.08 g L⁻¹, p < 0.01) with 25 ppm NH₃ and 2350 ppm CO₂ (EXP 11) than that of other test conditions. The maximum values of performance parameters differed with NH₃ and CO₂ concentrations. The biological performance must stay at the optimum level to reduce the air pollutants released from pig houses. The MCDM method allows one to include different NH₃-CO₂ concentration combinations in a decision-making process and provides an opportunity to simultaneously evaluate multiple biological factors such as cell number, dry weight, cell weight, and maximum growth rate. Optimal CO₂ and NH₃ concentrations for algal growth to reduce air pollutants from animal feeding operations are the most significant factor controlling mitigation efficiencies, and thus directly affect the indoor air quality of barns and environmental pollution.

The experimental conditions that resulted in the best biological performance were those in EXP 14. EXP11 and EXP7 ranked second and third, respectively. The worst-performing experiments were found to be EXP13, EXP9 and EXP5.

Table 4. Grey Relational Coefficient Matrix and Ranks for Scenario 1 and 2.

Experiments/Criteria	Scenario 1						Scenario 2
	Grey Relational Coefficient Matrix				Criteria Weights Differ		Grey Relational Coefficient Matrix				Criteria Weights Differ
	C1	C2	C3	C4	${\mathbf{\Gamma }}_{0\mathit{i}}$	Rank	C5	C6	C7	C8	${\mathbf{\Gamma }}_{0\mathit{i}}$	Rank
EXP1	0.333	0.333	0.429	1.000	0.522	7	0.333	0.333	0.429	1.000	0.567	5
EXP2	0.441	0.424	0.500	0.370	0.431	13	0.441	0.424	0.500	0.370	0.434	12
EXP3	0.470	0.443	0.629	0.522	0.509	8	0.470	0.443	0.629	0.522	0.529	6
EXP4	0.460	0.453	0.506	0.559	0.493	9	0.460	0.453	0.506	0.559	0.503	9
EXP5	0.355	0.351	0.333	0.404	0.362	16	0.355	0.351	0.333	0.404	0.363	16
EXP6	0.660	0.659	0.448	0.375	0.544	5	0.660	0.659	0.448	0.375	0.511	7
EXP7	0.763	0.786	0.650	0.333	0.637	3	0.763	0.786	0.650	0.333	0.600	3
EXP8	0.511	0.513	0.406	0.395	0.460	10	0.511	0.513	0.406	0.395	0.445	11
EXP9	0.380	0.377	0.415	0.463	0.407	15	0.380	0.377	0.415	0.463	0.415	15
EXP10	0.650	0.643	0.443	0.380	0.537	6	0.650	0.643	0.443	0.380	0.506	8
EXP11	0.831	0.931	0.494	0.337	0.663	2	0.831	0.931	0.494	0.337	0.592	4
EXP12	0.484	0.476	0.448	0.350	0.441	12	0.484	0.476	0.448	0.350	0.431	13
EXP13	0.445	0.440	0.429	0.402	0.429	14	0.445	0.440	0.429	0.402	0.426	14
EXP14	1.000	1.000	0.534	0.351	0.739	1	1.000	1.000	0.534	0.351	0.665	1
EXP15	0.562	0.540	1.000	0.441	0.616	4	0.562	0.540	1.000	0.441	0.648	2
EXP16	0.455	0.450	0.549	0.398	0.459	11	0.455	0.450	0.549	0.398	0.464	10

presents the ranking of the sixteen experiments by biological performance, as determined using the GRA method (Equations (7)–(18)).

3.2. Environmental Performance

There are many factors affecting environmental performance, such as species-related and environmental influence on CO₂ and NH₃ fixation and the product yield of the microalgae. In the second scenario of the study, the environmental performance of microalgae grown in the PBR system at different NH₃ and CO₂ concentration levels was investigated. The environmental performance parameters were determined as CO₂ fixation, NH₃ fixation, CO₂ removal efficiency, and NH₃ removal efficiency (Table 2). NH₃ removal efficiency appears to be the most dominant factor for the environmental performance, and the second dominant factor was CO₂ fixation. The CILOS method processing steps (Equations (1)–(6)) for the weights and weight system matrix of the environmental performance criteria are shown in Table 3.

S. dimorphus showed the maximum CO₂ fixation (432.24 ± 41.09 mg L⁻¹d⁻¹) in EXP 11 (25 ppm NH₃ and 2350 ppm CO₂), while the maximum CO₂ removal efficiency (23.84 ± 2.73%) was achieved in EXP 7 (25 ppm NH₃ and 1200 ppm CO₂). This is because the amount of CO₂ supplied to the system in EXP 7 was 1200 ppm, while the amount of CO₂ supplied in EXP 11 was 2350 ppm. Similar results were observed for the NH₃ fixation and removal efficiencies. While the maximum NH₃ fixation was 23.8 ± 2.26 mg L⁻¹d⁻¹ in EXP 11 (25 ppm NH₃ and 2350 ppm CO₂), the maximum NH₃ removal efficiency (100 ± 6.95%) was achieved at 12 ppm NH₃ at all CO₂ concentrations.

The main purpose of reducing the air pollutants released from livestock farms by microalgae is to reduce both NH₃ and CO₂ gases in the barn environment most effectively. However, according to the results of the experiments conducted at 16 different NH₃-CO₂ concentrations, the reduction amounts of ammonia and carbon dioxide gases do not change proportionally in all experiments. For example, the CO₂ and NH₃ removal efficiencies vary independently for different gas concentrations. Ryu et al. [54] reported that Chlorella sp. had higher cell concentrations with increased CO₂ concentrations, but CO₂ fixation efficiency was lower at elevated CO₂ concentrations. When the results obtained in the study are analyzed statistically, the results identify the experiments in which the highest values of environmental parameters were obtained independently from each other. However, determining the optimum condition by considering all the environmental parameters together would allow more efficient reduction in the gases released from barns.

According to the results of Scenario 2, the first-ranked experiment was EXP14 which had 12 ppm NH₃ and 3500 ppm CO₂ gas concentrations. This experiment was followed by EXP15, EXP7 and EXP11. The worst-performing experiments were found to be EXP5, EXP8 and EXP13. Table 4 presents the ranking of the 16 experiments in terms of environmental performance, as determined using the GRA method (Equations (7)–(18)).

Aerial pollutants (NH₃ and CO₂) emitted from animal feeding operations affect the air quality of the environment, the neighborhood, and the health of both animals and workers. These air pollutant emissions are currently being regulated by national regulations and international protocols that aim to reduce air pollutant emissions from intensive livestock farming [55]. Reducing air pollutant concentrations to acceptable levels for human and environmental quality is the main objective of every environmental protection agency or regulatory body in developed or developing countries [56]. Microalgae can be used to remove these air pollutants and produce valuable products in bio-mitigation.

3.3. Overall Performance: Selection of the Optimal CO₂ and NH₃ Concentrations

The biological and environmental performance of the PBR system was evaluated in Scenarios 1 and 2, respectively. EXP 14 was ranked first for biological and environmental performance according to the MCDM methods. In the third scenario, the overall performance including all the biological and environmental parameters was investigated. The weights and weight system matrix of the overall performance criteria calculated using the CILOS method processing steps (Equations (1)–(6)) are shown in Table 3. Figure 3 shows the criteria weights for all scenarios.

According to the biological and environmental performance, EXP 14 was ranked one (Figure 4). However, the experiment ranking changed when all performance parameters were analyzed together. EXP11 was identified as the most optimal experiment for overall performance (Figure 4). EXP14 and EXP7 were the second and third ranked, respectively. The worst-performing experiments were found to be EXP13, EXP9 and EXP5.

Table 5. Grey Relational Coefficient Matrix and Ranks for Scenario 3.

	Grey Relational Coefficient Matrix								Criteria Weights Differ
Experiments/Criteria	C1	C2	C3	C4	C5	C6	C7	C8	${\mathbf{\Gamma }}_{0\mathit{i}}$	Rank
EXP1	0.333	0.333	0.429	1.000	0.333	0.333	0.333	0.333	0.434	13
EXP2	0.441	0.424	0.500	0.370	0.394	0.884	0.394	0.681	0.480	8
EXP3	0.470	0.443	0.629	0.522	0.381	0.683	0.381	0.439	0.485	7
EXP4	0.460	0.453	0.506	0.559	0.374	0.600	0.374	0.372	0.460	10
EXP5	0.355	0.351	0.333	0.404	0.333	0.333	0.333	0.333	0.350	16
EXP6	0.660	0.659	0.448	0.375	0.475	0.514	0.475	1.000	0.599	4
EXP7	0.763	0.786	0.650	0.333	0.762	1.000	0.762	1.000	0.737	3
EXP8	0.511	0.513	0.406	0.395	0.416	0.436	0.416	0.411	0.450	11
EXP9	0.380	0.377	0.415	0.463	0.337	0.337	0.337	0.333	0.380	15
EXP10	0.650	0.643	0.443	0.380	0.446	0.393	0.446	1.000	0.583	5
EXP11	0.831	0.931	0.494	0.337	1.000	0.558	1.000	1.000	0.776	1
EXP12	0.484	0.476	0.448	0.350	0.547	0.436	0.547	0.530	0.473	9
EXP13	0.445	0.440	0.429	0.402	0.364	0.345	0.364	0.333	0.404	14
EXP14	1.000	1.000	0.534	0.351	0.567	0.400	0.567	1.000	0.752	2
EXP15	0.562	0.540	1.000	0.441	0.398	0.357	0.398	0.484	0.554	6
EXP16	0.455	0.450	0.549	0.398	0.398	0.357	0.398	0.394	0.438	12

presents the ranking of the 16 experiments in terms of overall performance.

3.4. Sensitivity Analysis

Sensitivity analysis is a procedure performed to test the consistency and measure the power of decision problem results. In this study, sensitivity analysis was performed to test the consistency and measure the power of the results obtained with CILOS and GRA. The results of the third scenario, including all the criteria, and the results of other MCDM methods were compared. For the sensitivity analysis, Weighted Aggregated Sum Product Assessment (WASPAS), Multi-Attribute Ideal-Real Comparative Analysis (MAIRCA), Additive Ratio Assessment (ARAS), Multi-Attributive Border Approximation Area Comparison (MABAC) and The Complex Proportional Assessment (COPRAS) methods were used. The weights used in all methods were those calculated by the CILOS method. The correlations between the methods listed above and the results of the GRA method were tested with Spearman’s rho rank correlation. The results are shown in

Table 6. Spearman’s Rho correlation values between methods.

Method	WASPAS	MAIRCA	ARAS	MABAC	COPRAS
GRA	0.988 *	0.991 *	0.991 *	0.991 *	0.991 *

* A significant data difference methods.

.

When Spearman’s Rho values are examined, excellent correlations are observed between the rankings obtained by all other MCDM methods and the rankings obtained by the GRA method. These results prove that GRA is a consistent method with high-measuring power.

4. Conclusions

This study demonstrated the use of a multi-criteria analysis methodology combined with different CO₂ and NH₃ levels to improve the CO₂ and NH₃ fixation ability of S. dimorphus. The MCDM results show that for both the biological and environmental performance, the optimal combination of CO₂ and NH₃ concentrations is 12 ppm NH₃ and 3500 ppm CO₂. However, the optimal CO₂ and NH₃ concentrations for the overall performance were 25 ppm NH₃ and 2350 ppm CO₂. The results of this study allow producers to determine the maximum mitigation of CO₂ and NH₃ concentrations and optimise the operating parameters of PBRs for various housing types, such as dairy, poultry, and pig barns.

For example, in the poultry sector, air pollutants released from poultry houses vary depending on the breeding period of the chickens. While the air pollutant concentrations released from hen houses are low in the first days of the production period, they increase towards the end of production. Meanwhile, engineering options are available to adjust the CO₂ and NH₃ concentrations in the exhaust air from animal barns and the PRB’s algal growth. For the exhaust air, the CO₂ and NH₃ concentrations that feed into a PBR can be regulated by changing ventilation/heating configuration or settings, installing pre-scrubbers, and so on. For the algal broth, the concentrations can be adjusted by amending the liquid with carbonate or ammonium salts that are readily available on most farms. Therefore, knowing the gas concentrations at which the most effective CO₂ and NH₃ reductions can be achieved can facilitate the setup and operation of the PBR system. This study indicates that such information can be generated from MCDM analyses. Although still technically intimidating to most producers, the selected MCDM methods are far simpler and require less computing power than artificial intelligence methods (e.g., machine learning). Therefore, they can be translated into Web calculators or MS Excel-based tools that are easily adopted by producers, or implemented in animal barn controllers to automate the facility operation.

Overall, this study presents clear results that can guide decision-makers in choosing the best PBR operating parameters. This MCDM method will aid future algal phytoremediation research for enhancing CO₂ and NH₃ mitigation and minimizing the environmental impacts of animal feeding operations.

In light of the above conclusions, the following tasks are recommended for future research:

• Additional MCDM methods should be explored to broaden the scope of the multi-criteria decision-making process in air pollutant mitigation using PBR systems.
• The significance of the carbohydrate, protein, and fat values of microalgae as criteria should be further investigated. The analysis would facilitate a multi-criteria assessment not only regarding reducing air pollutants emitted from barns but also in evaluating the potential utilization of the obtained biomass in sectors such as animal feed, biodiesel, and others.
• It is advisable to develop an evaluation tool utilizing the MCDM methods examined in this study. Such a tool would simplify the air pollutant mitigation process and facilitate the comparison of the applicability of microalgae in various sectors.