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Environ Eng Res > Volume 28(5); 2023 > Article
Rasouli, Dini, and Ataeiyan: Anaerobic co-digestion of sewage sludge and Cladophora green algae: Investigation of synergistic effects and Optimization of substrate composition ratio

Abstract

Anaerobic co-digestion of primary and secondary sewage sludge and Cladophora green algae was investigated under mesophilic temperature conditions. The design of experiment method and the optimal mixture design were used to systematically optimize the substrate composition ratios and elucidate the possible synergistic effects for an anaerobic digestion system. A reduced cubic model was created by Design-Expert software as a function of substrate composition ratios. The model was validated by ANOVA experimentally. Also, the substrate composition ratio's effects on variations in biogas production were studied. All linear impacts on changes in biogas production were significantly observed, and interactions between substrates in combined digestion had synergistic impacts on biogas production rate. The highest amount of biogas (235.17–296.03 ml/g VS) was obtained with ratios of equal to 70-60%, B equal to 0–17%, and C equal to 18–30%. Eventually, the model optimization was performed to predict the optimal conditions to achieve the maximum biogas production rate. It was seen that the predicted and actual values of produced biogas in favorable conditions with an error of about 1.3% are well consistent. The authors conclude that the optimal mixture design can be utilized to assess the optimal composition of substrates in an anaerobic digestion system.

1. Introduction

In wastewater treatment plants (WWTP), a significant quantity of solid particles are collected from the settling process (the first stage of treatment) and the activated sludge process (the second stage of treatment), which is called sewage sludge. To protect the environment, it must be treated before landfilling. Sludge management can account for up to 60% of total municipal costs of wastewater treatment. So, much effort is being made to minimize sludge production and optimize sludge processing. There are several options available for wastewater sludge treatment which anaerobic digestion biotechnology is the most widely used. The importance of energy supply and safety, environmental impacts, and increasing energy costs for wastewater treatment have made the anaerobic digestion process the leading technology for renewable energy production [1]. The process of anaerobic digestion converts sludge into a stable product and leads to energy recovery by producing biogas [2].
Usually, sewage sludge is specified by a high buffer capacity and small C/N ratio. Hence, they can be used as a co-substrate with a large amount of easily degradable organic materials and materials with low alkalinity. In addition, in many cases, anaerobic digestion of sewage sludge can lead to dilution of some undesirable compounds in the sewage sludge, like pathogens and heavy metals [3].
Algae is essential as the most promising potential source of green fuel worldwide. The third generation of biofuels is algal masses. Algae has certain advantages over herbs. It grows 5 to 10 times faster under suitable conditions and also has a higher biomass production ratio compared to the biomass of herbs [4, 5].
To investigate the anaerobic digestion process, parameters such as process stability, methane production, and organic matter removal efficiency are usually measured. In anaerobic digestion, pH is a crucial factor and can serve as the index of anaerobic digestion performance. Process stability is mainly controlled by several parameters, including pH and concentration of intermediate products (volatile fatty acids (VFAs) and ammonia (ammonium-N)) [6, 7]. Substrate compositions are essential to achieve a sustainable process. A meager C/N ratio leads to high ammonia levels and thus stops methane production [2, 8]. While the C/N ratio is less than 20, a disbalance occurs between the carbon and nitrogen required by the microbial population. This disbalance leads to the release of nitrogen (ammonia) during digestion, which can be an inhibitory factor for metanogenic bacteria, resulting in the accumulation of VFAs in the reactor [9, 10]. Another factor that reduces methane production is the unavailability of sufficient substrate for microorganisms, caused by the large particle size or hard cell wall [2]. An alternative approach to overcome these problems is the use of anaerobic co-digestion. The advantages of anaerobic co-digestion include the following [3, 11, 12]:
  • C/N ratio correction

  • Compensation of the rare nutrients for microorganisms

  • Reducing the potential of toxic substances

  • Stimulation of synergistic effects on microorganisms

Recent investigations have shown that anaerobic co-digestion of sludge with algae increases methane production.[13, 14] Mahdy, Mendez [15] by anaerobic co-digestion of the primary sludge (75% COD) and Chlorella Vulgaris microalgae (25% COD), increased the efficiency of microalgae methane production by 17% compared to the theoretical value.
Anaerobic co-digestion of Chlorella sp. and activated sludge residue mixture modified the reduction of volatile solids, which increased the efficiency of hydrolysis and microalgae biogas efficiency by 10% [16]. Similarly, anaerobic co-digestion of the Chlorella sp. and sewage sludge (63% VS) mixture with Scenedesmus sp. (37% VS) increased methane production by 23% compared to the mono-digestion of sewage sludge [8].
It seems, reuse of digested materials of composed microalgae and sewage sludge from anaerobic co-digestion in agriculture to be a promising method to reach zero waste production in the systems of microalgae-based wastewater treatment [17]. Digested materials of anaerobic co-digestion are high in organic matter, organic carbon, and organic nitrogen which can be reused as a modifier of soil physicochemical or biological properties in agriculture, they also have a high potential to use as a fertilizer for plants due to their essential minerals [17, 18]. Digested materials are rich in ammoniacal nitrogen, which is readily existing for plants, and are also rich in other nutrients such as phosphorus and potassium [17, 19].
The highest amount of produced methane by the process of anaerobic co-digestion of sludge, algae, and carbon-rich materials was reported between 190–270 mlCH4/g VS. The maximum methane production by algae is reported between 140–270 mlCH4/g VS, which is similar to the amount of methane production in the case of sludge [20]. The amount of methane produced depends on the type of the algae for digestion and the operational conditions of the digester.
Wickham, Galway [21] used algae as a co-substrate in the anaerobic co-digestion of sewage sludge. The concentration of the used algae was ranged from 0.25 to 9% of the mass fraction. They found that adding algae up to 6% (wt/wt) to sewage sludge increases cumulative methane production. By adding 6% or fewer algae, the acids made have enough time to digest, but adding more algae than the optimum point (6%) causes volatile fatty acids to accumulate. Reviewing the various studies show that the combined anaerobic digestion of urban wastewater sludge with algal biomass and appropriate organic matter can effectively increase methane production and decomposition and also stabilize the process.
However, when conducting anaerobic co-digestion tests to confirm the feasibility of mixing different waste streams for the production of biogas and waste stabilization, it is vital not to overestimate the amplifying impacts of the waste interaction. For example, the increase in biogas production may not result from a synergistic effect of waste but simply due to the introduction of more organic matter into the bioreactor. Therefore, to properly investigate the synergistic interaction of various wastes, digestion experiments should be controlled and performed in a systematic method [22]. Rahman, Saha [23] used the mixture design method to investigate the synergistic effects of mixed substrates in experiments and create the optimal mixture composition. They showed that statistical techniques are available to optimize nutritional composition.
The mixture method is a response surface methodology (RSM) design that allows us to investigate the effect of ratio variation between variables. In the mixture design method, a domain is a regular polygon with an equal number of components and vertices, and this domain is in the space of similar size to the number of components minus one [24]. A mixed design consisting of three elements is an equilateral triangle whose vertices correspond to compounds containing 100% of a single element. Each of the three edges represents a mixture that does not have one of the three components and is called binary mixtures. In addition, the interior points correspond to triple mixtures. To study the impact of mixture components on the response variable, simplex designs are used, and a simple network design or a simple central design can be selected from them. Fig. [1] shows a simple center design for the three components. These designs are usually reinforced with additional points in the experimental area. The used models in mixture designs are different from the polynomials were used at the response surface for independent variables. These models are famous Scheffé polynomials that can be a linear, quadratic, perfect cube, and particular cube [25]. In most researches, the proportions of the components are randomly selected, and there is little data on optimizing the waste ratios to maximize digestion efficiency in a controlled and systematic manner. The aims of this study are performance analysis of the anaerobic co-digestion process of sewage sludge as an organic waste with Cladophora green algae, analysis of the synergy effects, and optimization of the response variable using a mixture design.

2. Materials and Methods

2.1. Preparation of Substrate

2.1.1. Primary and secondary sludge

Primary (A) and secondary (B) sludges were prepared from the Sarkan city wastewater treatment plant in Tuyserkan, Iran. Then, the samples were filled into the sterilized containers, and to maintain the actual condition, the sample containers were kept at a temperature range of 0–4 °C until transfer to the laboratory.

2.1.2. Cladophora algae

The source of Cladophora algae (C) was microalgae powder which was provided by Arian Gostar Co.

2.1.3. Insemination material

The output substrate of the semi-industrial reactors of the Renewable Energy Laboratory in Bu-Ali Sina University was used as the insemination material. The output of the semi-industrial reactors was cow dung, which was fully digested in the reactor for about 6 months.

2.2. Reactors Start-Up Procedure

The feeding was intermittent (batch). The substrates were filled into the reactors according to the mixing method in specific proportions, and water was added to them until the desired TS was reached. 20 CC of insemination material was added to the reactors. Then, the reactor door was immediately closed. The hydraulic retention time for the experiments was considered 21 days.

2.3. Biogas Production and Measurement System

BMP system was employed to measure the content of the produced gas. The produced biogas was directed through the outlet pipe into a 1-liter water bottle. Thus, the pressure of the produced biogas caused the water inside the bottle to discharge into a scaled cylinder by a hose which one end was the bottom of the water bottle, and the other end was outside the water bottle. Thus, the amount of discharged water indicates the volume of the produced gas [26] (Fig. [2]). Digestion was conducted at mesophilic temperature (38 °C).

2.4. Methods of Analysis

The methods and instructions in the Standard Method [27] for examining water and wastewater were used to perform physical and chemical experiments on sludge samples. Metrohm pH meter made in Germany was used to measure the pH of the substrate inside the reactors.

2.5. Design of Experiments By the Optimal Mixture Design Method

The Design of experiments (DOEs) method provides an impressive tool for optimization of the processes and determining the optimal formula for a particular mixture. To evaluate the effect of anaerobic co-digestion on the production of biogas as a response variable under 3 independent factors, the optimal mixture design was used. These factors represent the fraction of each feedstock in the mixture, which varies from zero to one without limitation in the design space. If “q” indicates the number of ingredients in the system and “xi” indicates the “i” ratio of ingredients in the mixture, then [25]:
(1)
i=1qxi=x1+x2++xq=1.0;         xi>0;         i=1,2,3,q
In a mixture design, the measured response depends only on the relative proportions of the materials or components in the mixture and not on the volume of the mixture. In most mixture designs, there are constraints on the component ratio that limit the possible space of the variables between a lower limit (Lj) and an upper limit (Uj). The general form of the constrained mixture problems is defined as Eq. (2):
(2)
fXf=1         and         LfXfUf
In mixture design, the response variable (Y) is optimized based on the experimental values of the independent factors (Xj) as shown by Eq. (3):
(3)
Y=f(X1,X2,X3,X4,,Xn)
Independent, continuous, and controllable variables are assumed by the experiments with insignificant errors. Detection of the proper estimation is required for the functional relationship between the independent variables and the response. The response was utilized to expand an experimental model that linked the response (produced methane) to the independent variables, which are a fraction of primary sludge, secondary sludge, and Cladophora microalgae.
Usually, the mixture design included the following steps [28]:
  1. Choosing the right mixture design: several mixture design techniques such as Optimal Mixture Designs, Simplex-Centroid Design, and Simplex Lattice Design, where a suitable technique must be selected based on the range of independent variables or boundary constraints. When the scope of the independent variables is the same, a simple mixture design is used. On the other hand, an optimal strategy is a good choice when the boundary constraints are non-simple and have non-uniform sizes. Three types of optimal strategies, which are called D-optimal, A-optimal, and I-optimal, are available in Design-Expert software. Optimization of D is favorable for factorial and screening designs to recognize the essential variables. The algorithm selects points that minimize the size of the confidence interval of the coefficients. The A-optimal strategy reduces the mean of polynomial coefficients variance. The I-optimal strategy uses an integrated variance criterion which leads to minimizing the mean-variance of responses in a particular interest area.

  2. Selecting the name, unit, and boundary constraints of the components

  3. Selecting the name and unit of answers

  4. Suggest a suitable plan for finding the relationship between the answers and the components of the mixture

  5. Performing all experiments proposed by the plan one by one similar to the numbers

  6. Recording the obtained answers from the experimental results in the answers column of the Office-Word software

2.6. Statistical Analysis

The subsequent phase in the mixture test design is to fit the experimental model, investigation the competency of the fitted model, display the 2D contours and the 3D response surface, and make adjustments to optimize the ratio of the mixture components. Design-Expert V.13 Software of the statistical software package (Stat-Ease, Inc., US) was employed to analyze the regression of experimental data and plot the response surface. Also, the ANOVA method was utilized for the estimation of the statistical parameters.

3. Results and Discussion

The used Lagoon sludge has 681 mg/L phosphorus, 58% of carbon, and 135mg/L of nitrogen with C/N ratio of 5. Also, the sludge has the moisture, volatile organic matter, and pH of 97.4%, 86%, and 6.3, respectively.

3.1. Design of Experiments

Because I-optimal designs provide lower mean predictive variance across the experimental area, I-optimal was the optimal design type. So a desirable prediction was made about the input range. Table [1] shows the design summary. By adjusting the number and range of components, the I-optimal design algorithm selects points that minimize the predictive integral of variance across the design space [29].
In this study, the model selected 24 points. 12 points were for modeling, 5 points for estimating the non-fit, 5 points for repeating the test, and 2 of them were central. Therefore, 24 run conditions were given by the proposed model. Response values were obtained by performing the considered experiments by the model and then entered in the answer column of the software. The conditions of the 24 experiments proposed by the model and values of the experimental response are presented in Table [2].
A third-degree model (cubic) model was fitted to the experimental data by Design-Expert software. The final model obtained for predicting the production biogas concerning the components of the mixture can be expressed as Eq. (4):
(4)
Biogas=162.20A+79.23B+94.43C+376.81AC+798.79AC(A-C)
By default, high levels of mixed components are coded as +1 and low levels as 0. The coded equation helps recognize the relative effects of the parameters by comparing the parameter coefficients. Fig. 3 shows the response values predicted by the used model versus the actual response values (obtained from the experiment). Also, Fig. [3] shows the model in recording the correlation between mixture components with R-Sq. equal to 98.22% have been successful. The predicted R² of 0.9694 is in suitable agreement with the adjusted R² of 0.9784; i.e., the difference is less than 20%.
Sufficient precision evaluates the signal-to-noise ratio and compares the range of predicted values at design points with the average prediction error. Ratios greater than four represent the appropriate model [25]. The deal of adequate precision in the proposed model was 50.496, which shows the right signal and indicates the competency of the used model to move in the design space.
To evaluate the consistency and significance of the model, ANOVA was performed by Design-Expert software. Also, ANOVA indicates the effect of independent factors and the interaction of variables on the produced biogas in the mixture. The results of ANOVA are shown in Table [3]. The impacts of parameters of AB, BC, ABC, AB (A-B), and BC (B-C) in the third-degree model (Cubic) were not significant and were removed from the model and the model was modified to a reduced Cubic model.
The F-value compares the variances of difference between the mean responses at the design points and estimated responses corresponding to the linear model with the expected observed changes as calculated from the duplicate design points (pure error). F-value equal to 261.81 indicates the significance of the model. P-value is the possibility of achieving the F-value. The values less than 0.5 indicate that there is a statistically considerable difference between the means. The values greater than 0.1 indicate that there is not any difference between the means. Therefore, the overall value of P (error value probability) which is less than 10−4 confirms that the model is significant. Also, the ANOVA chart shows that the mixture components, including A, B, C, AC, and AC (A-C), are substantial terms of the model because their P-value is less than 0.05.

3.2. Diagnostics

The first goal of a diagnostic test is a graphical analysis of the model. The primary diagnostic tool is the residuals normal plot. Following the points of 45° line represents that the residual distribution is normal and no data transfer is required. The standard probability diagram shows how the residues follow a normal distribution. Even with typical data, some moderate dispersions are expected. Specific curved patterns such as “S-shapes” that is recognizable at a glance indicate that a better analysis can be performed by performing a transfer function on the dependent variable or model response [25]. This benchmark is confirmed in the second diagnostic tool that is the Box-Cox diagram. The Box-Cox chart is a tool to help to recognize the proper power transfer function for apply to a response. The lowest point in the Box-Cox diagram indicates the best value of lambda, where the least total of residues squares in the converted model is generated. When the maximum to minimum ratio of response value is greater than 3, there will be a more remarkable ability to modify the model by the power function. Also, this chart shows a confidence interval of 95%. According to the Box-Cox diagram and the lambda values in the defined range, there was no need to apply the transfer function.

3.3. Effects of Mixture Components and Optimization

According to the table of ANOVA, all linear parameters of the equation are considered essential and can strongly affect biogas. Among the interactions, only the AC interaction was significant. However, when all parameters change simultaneously, only the 3-D surface diagram of the model can indicate the effect. The 3-D surface diagram shows the amount of produced biogas as a function of the fractions of Primary sludge (A), Secondary sludge (B), and Cladophora algae (C) in Fig. [4a]. The sum of fractions of A, B, and C is 100, and there is the highest and lowest amount of biogas in the study area. Also, Fig. [4b] Shows the contour diagram a 2-D representation of the response. This 2-D diagram is shown in the form of a triangular graph, in which the contour lines show the amount of biogas in each composition. When the other two factors remain constant, it provides information about the impact of all 3 independent parameters on biogas production. Biogas production in experiments of 3, 5, 14, 15, and 21 was more than 250 ml/g VS. In the experiments of 3, 5, and 15, the amount of secondary sludge in the composition is zero and in the investigations of 14 and 21 is less than 20% of the total substrate composition. Also, in these experiments, the amount of primary sludge is almost more than 50% of the substrate composition. Therefore, it can be concluded that the presence of primary sludge in the substrate composition improves the performance of biogas production, and secondary sludge reduces its performance. On the other hand, in all these experiments except the experiment of 15, the amount of algae was less than 40% of the composition. This reflects that increasing the ratio of algae in the composition to above 40% reduces biogas production. Meanwhile, in the experiments of 17 and 22, biogas production has reached less than 70 ml/g VS, which is a minimal amount. In these experiments, the proportion of algae in the composition is 70 and 100% of the total composition, respectively. These results are consistent with the results of other scholars [13, 14]. In one study, Sole-Bundo, Cucina [17] showed that anaerobic co-digestion of sewage sludge and microalgae (75%-25% VS) reduces the potential of biotoxicity in the digested feed. Anaerobic co-digestion dilutes the effect of inhibitory compounds. Dilution of potentially toxic compounds, modification in nutrient balance, microorganisms synergistic effects, increased load of biodegradable organic matter, and more stable digestion are the reasons for better biogas efficiency [12, 30, 31].

3.4. Response Prediction and Confirmation Experiments

Predicting and confirming the response (Table [4]) is the final phase in any experiment, and it allows you to add levels for each element or component into the current model. Based on the anticipation equation presented in the ANOVA output, the software estimates the predicted responses and associated confidence intervals. The 95 percent prediction interval (PI) is the range in which any individual value was predicted to fall 95 percent of the time, whereas the 95 percent confidence interval (CI) is the range in which the process average was expected to fall 95 percent of the time.
Because there is more scatter in individual values than in averages, the PI is higher (a wider spread) than the CI, as seen in Table [4]. The standard deviation associated with SE mean in this table denotes the prediction of an average value at the selected component levels, whereas the standard deviation associated with SE pred. denotes the prediction of a single observation at the selected factor or component levels. An experiment was carried out with the parameters proposed by the model to assess the validity of the response provided by the model. The findings show that the experimental values are quite near to the anticipated values, indicating that the model predicts the responses correctly.

4. Conclusion

Using the design of experiment and optimal mixture design, 24 experiments were considered by Design-Expert software and, a reduced cubic model was fitted to the laboratory results. The model was confirmed statistically. The ANOVA showed that both the model and the model parameters are significant. The 3-D surface diagram of the model explicitly indicates the presence of maximum biogas in the investigated range of factors. The highest amount of biogas in the reactor feed (235.17–296.03 ml/g VS) was obtained with the ratios of Primary sludge (A) 60–70%, Secondary sludge (B) 0–17%, and Cladophora algae (C) 18–30%. The model was numerically optimized, and the optimal composition for the highest amount of biogas production (290.86 mg/L) was determined as 74.34% of feed A and 25.66% of feed B without the presence of feed C. The amount of produced biogas under the optimal laboratory conditions was 296.03mg/L, which is very close to the predicted value by the model. Therefore, the optimal mixture design can be utilized as an alternative optimization tool and method in optimizing the composition of substrates in an anaerobic digestion system.

Nomenclature

Abbreviations

ANOVA

Analysis of Variance

BMP

Biochemical Methane Potential

C

Carbon

COD

Chemical Oxygen Demand

DOE

Design of Experiment

N

Nitrogen

RSM

Response Surface Methodology

VFA

Volatile Fatty Acid

VS

Volatile Solid

WWTP

Wastewater Treatment Plant

Symbols

Lj

Lower Limit

q

Number of ingredients in the system

Uj

Upper Limit

xi

The "i" ratio of ingredients in the mixture

Xj

Independent Factor

Y

Response Variable

Notes

Conflicts of interest

The authors have declared no conflicts of interest for this article.

Author contributions

M.R. (Assistant Professor) conceived of the presented idea, carried out the experiment, designed and performed the experiments, derived the models, analyzed the data, and wrote and revised the manuscript, M.D. (Graduated M.Sc. Student) conceived of the presented idea, carried out the experiment, designed and performed the experiments, derived the models, analyzed the data, and wrote the manuscript, B.A. (Graduated M.Sc. Student) conceived of the presented idea, carried out the experiment, and wrote the manuscript.

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31. Sreekrishnan TR, Kohli S, Rana V. Enhancement of biogas production from solid substrates using different techniques––a review. Bioresour. Technol. 2004;95:1–10. https://doi.org/10.1016/j.biortech.2004.02.010
crossref pmid

Fig. 1
Schematic of a simple central mixing method for three components
/upload/thumbnails/eer-2021-516f1.gif
Fig. 2
Biochemical methane potential testing system (BMP)
/upload/thumbnails/eer-2021-516f2.gif
Fig. 3
Response values predicted by the model vs. laboratory response values
/upload/thumbnails/eer-2021-516f3.gif
Fig. 4
a) 3D surface graph, and b) contour graph of the amount of produced biogas as a function of fractions of A, B, and C.
/upload/thumbnails/eer-2021-516f4.gif
Table 1
Summary of design
Study type: Mixture
Design type: I-optimal
Design model: cubic
Runs: 24

Component Name Units Type Minimum Maximum Coded Low Coded High Mean Std. Dev.

A Primary sludge % Mixture 0 100 +0 ↔ 0 +1 ↔ 100 34.09 29.26
B Secondary sludge % Mixture 0 100 +0 ↔ 0 +1 ↔ 100 33.54 29.71
C Cladophora algae % Mixture 0 100 +0 ↔ 0 +1 ↔ 100 32.37 27.42
Response Name Units Observations Minimum Maximum ratio Analysis Mean Std. Dev.

Y1 Biogas ml/g VS 24 59.42 309.48 5.21 Polynomial 150.82 72.93
Table 2
Conditions of 24 experiments and experimental response values of the proposed model
Run Build Type Space Type Component 1
A: Primary sludge
%
Component 2
B: Secondary sludge
%
Component 3
C: Cladophora algae
%
Response
Biogas
ml/g VS added
1 Center Center 33.3333 33.3333 33.3333 90.88
2 Model Vertex 100 0 0 154.19
3 Replicate Edge 70.8773 0 29.1227 296.03
4 Model Edge 0 71.4431 28.5569 114.56
5 Model Edge 70.8773 0 29.1227 287.04
6 Model Interior 17.3689 18.5206 64.1105 94.65
7 Model Edge 29.7685 70.2315 0 169.29
8 Model Edge 72.3022 27.6978 0 173.8
9 Center Center 33.3333 33.3333 33.3333 132.92
10 Replicate Edge 0 71.4431 28.5569 127.89
11 Model Vertex 0 100 0 73.86
12 Model Edge 28.4759 0 71.5241 87.54
13 Replicate Center 33.3333 33.3333 33.3333 120.43
14 Model Interior 64.1432 17.3312 18.5256 309.48
15 Lack of Fit Edge 44.5515 0 55.4485 264.1
16 Replicate Edge 72.3022 27.6978 0 189.55
17 Model Edge 0 29.9939 70.0061 63.71
18 Lack of Fit Interior 47.5373 45.4189 7.04384 170.12
19 Lack of Fit Interior 2 50.2303 47.7697 98.3
20 Replicate Interior 17.3689 18.5206 64.1105 102.04
21 Lack of Fit Interior 51.263 11.4634 37.2736 205.88
22 Model Vertex 0 0 100 59.42
23 Model Interior 17.7999 63.2151 18.985 133.9
24 Lack of Fit Interior 11.462 81.8257 6.71224 89.37
Table 3
ANOVA for Reduced Cubic model, Response: Biogas
Source Sum of Squares df Mean Square F-value p-value
Model 86821.97 4 21705.49 261.81 < 0.0001 significant
Linear Mixture* 52957.68 2 26478.84 319.39 < 0.0001
AC 13897.66 1 13897.66 167.63 < 0.0001
AC(A-C) 15858.94 1 15858.94 191.29 < 0.0001
Residual 1575.18 19 82.90
Lack of Fit 1262.17 13 97.09 1.86 0.2290 not significant
Pure Error 313.01 6 52.17
Cor Total 88397.15 23

Inference for linear mixtures uses Type I sums of squares

Mixture Component coding is L_Pseudo.

The Sum of squares is Type III – Partial.

Table 4
Point prediction and Confirmation
Run 1 Response Predicted Mean Predicted Median Observed Std Dev n SE Pred 95% PI low Data Mean 95% PI high
Biogas 153.82 153.82 165.55 9.10518 3 5.67069 141.951 144.89 165.688
Two-sided Confidence = 95%
Confirmation Location: Center Point in 3 repetitions
Primary sludge Secondary sludge Cladophora algae
33.3333 33.3333 33.3333
Biogas
154.12
139.88
140.67 Mean= 144.89
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