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Experimental based approach for reduced-order models of porous media properties prediction
Materials Today: Proceedings xxx (xxxx) xxx
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Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Experimental based approach for reduced-order models of porous media properties prediction Amir N. Saud a,⇑, Aws Al-Akam a,b, Ameen Al-joboori a a b
Al-Mustaqbal University College, University Road, Al-Hillah, Babil, Iraq University of Babylon, University Road, Al-Hillah, Babil, Iraq
a r t i c l e
i n f o
Article history: Received 13 July 2019 Received in revised form 28 August 2019 Accepted 29 September 2019 Available online xxxx Keywords: Porous alumina ceramic Pore-forming method Data analysis Reduced-order model Kriging
a b s t r a c t The pore diameter, type (open or closed), physical properties of Porous alumina ceramic were controlled by varying concentration in the mixture of Polymethylmethacrylate (PMMA) with alumina powder and sintering temperature. The porous alumina ceramic was synthesis by a dry pressing method using a microspheres Polymethylmethacrylate (PMMA) as a pore-forming agent. The properties of the porous alumina were predicted using an experimental approach. Afterwards, the measured data were used to develop a Reduced-order model (Kriging) to enable a fast prediction of the properties for an extended range of parameters variation and further analysis. The experimental results showed that the High porous alumina ceramics is having an open porosity of 72.3%, and a bulk density 1.2 gm/cm3 and these could be fabricated using PMMA microspheres. Kriging model results showed an acceptable prediction of the experimental-derived data with a maximum discrepancy of 0.02% for the apparent porosity. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Materials Engineering & Science.
1. Introduction Porous alumina ceramic is excellent in heat and chemical resistance, lightweight, and therefore are used in a wide variety of fields such as filters, catalysts, separation membranes and adsorption materials [1]. For such a porous material, a pore size corresponding to each application is required. For example, various types of pore diameters in the range of 0.005 lm to 10 lm are prepared for a filter material membrane which needs to consider air permeability, fluid flow [2]. In particular, photonic crystals having a periodic change in refractive index in the same order as the wavelength of light have a structure in which uniformly sized pores having a size of 0.12 lm to 1 lm are regularly arranged threedimensionally [3]. In addition, when gas adsorption and separation are performed by a gas sensor, a separation membrane, functions are exhibited by the presence of nano-order or angstrom pores [4]. The Nano sizing of the materials particles could improve their properties such as thermal conductivity [5]. Recently, higher porosity and adsorption property have been desired to be
⇑ Corresponding author. E-mail address: [email protected] (A.N. Saud).
improved, it is necessary to control materials from nano to macroscopic structure, and bimodal porous materials are combining the order of respective pores are attracting attention [6]. Many alternative methods have been reported to synthesis porous alumina. These include the partial sintering method, gel casting, freezing casting, organic foam method and pore-forming agent method [7]. PMMA pore-forming agent was used as a template to obtain a porous alumina that is having a porous wall structure with substantially uniform shape and particle diameter and retaining the outer shell shape of the particulate material, the template is mixed with the raw material of the matrix, and then the template is burned to eliminate the pores [7] thereby. In this article, the key novelty that the mono-dispersed Polymethylmethacrylate (PMMA) micro-balls were selected as a pore-forming agent, and the porous alumina ceramics were fabricated by the semi-dry pressing. The effects of Polymethylmethacrylate on true porosity, apparent porosity and bulk density of the porous alumina ceramics were investigated. Moreover, the measured porous media properties were used to create a Reduced-Order Model (ROM) to calculate the true porosity, apparent porosity and bulk density of the porous alumina ceramics. This model can be used for future calculations of these properties in a wider range.
https://doi.org/10.1016/j.matpr.2019.09.155 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Materials Engineering & Science.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
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A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
2. Methodology 2.1. Scope of the paper This work employs an experimentally derived data to build a Reduced-order model to predict the main impact of PMMA content and sintering temperature on the porous media properties. The methodology consists of the generation of the experimental data and measures the True, apparent and bulk density. The measured data are used to establish a Reduced-order model (i.e. Kriging) and validate it using the leave-one-out cross-validation method. The new model can be used to predict the properties for a wider range of parameters. 2.2. Samples preparation Alumina powder was used with an average particle size of 3 mm, whereby the Polymethylmethacrylate (PMMA) as pore-forming agents and the sodium polyphosphate as deflocculating. Alumina powder was weighed and dry-mixed thoroughly in a mortar pestle with the required amount of PMMA and deflocculated (5 batches). Afterwards, the desired volume of the PVA solution was added, so that the final PVA content of the batch is 3%. The sugar solution was carefully blended with the previous mixture using agate mortar for 10 min. The samples were produced by semi-dry pressing in a hydraulic press (Carver Press USA) at a various load 70 MPa with soaking time of 90 s. The sample size of 20 mm U 6 mm thickness was prepared and then dried in an oven at 50 °C overnight. Then the green samples were sintered in different conditions of 1200, 1300, 1400, and 1500 °C and soaking time of 2 h as shown in Fig. 1. 2.3. Design of experiment Five batches with different concentrations of alumina powder and Polymethylmethacrylate (PMMA) were prepared to produce the porous alumina samples. The experimental population consisted of 20 samples with each sample regarded as a chromosome and each chromosome consists of two genes. These genes were characterised by the input parameters, in the current paper; two input parameters with four levels were utilized. The fitness function or regression equation was created using a python software program. 2.4. Response surface method (Kriging) The behavior of the Response surface methods (RSM) depend on the data type. Large number of accurate data produces high perfor-
mance of the RSM. RSM proposes techniques to detect the effect of the responses based on varying stages of control factors that are identified to direct physical processes. RSM based on employing the regression analysis on a set of data derived from laboratory tests or computational fluid dynamics (CFD) simulations at several levels [8]. The strength of the RSM techniques based on producing effective and smooth estimates for the data at discretized data-points in the multidimensional analysis [9]. The selection of the models to represent the behavior of any set of data has a pronounced impact on the reliability of the recently predicted data. The selected RSM model is Kriging [10] methods. The RSM was applied to a two-dimensional design space based on the PMMA % Wt. and Temperature °C. The purpose of this study is to demonstrate the capability of employed RSM approach in mapping multidimensional behavior of the porous media properties as a function of different intensities of PMMA % Wt. and the temperature °C that is identified to affect the properties. To confirm the reliability of the employed model in evaluating the properties, Cross-Validation (CV) approach was used to validate the results produced from RSM [11]. The Leave-One-Out technique (LOO) was utilized, to evaluate the error related to using a particular RSM on a set of reference data (experimental data). This technique is achieved by taking single data point (experimental results) out of the whole main data (Apparent porosity (%), True porosity (%) or Bulk Density) and reproduce the RSM based on the remains of the set of the data to predict for the missing data point. Then the model calculates the difference between the new and the original properties (Du; Dq and Dk). Kriging RSM method uses least-square estimation to minimize the inconsistency between the predicted and the reference data [12]. It depends on employing a spatial correlations between the observed data points using the Gaussian exponential function [11]. Simple Kriging was utilized in the current work, and absolute exponential correlation was selected. The regression function was selected to be ‘‘quadratic” and the nugget value of 1.0 1011. The upper and lower theta was selected to be 0.1 and 0.0001, respectively. Pearson coefficient [13] was used to assess the suitability of the employed regression model in the prediction of the pours media properties. Pearson correlation coefficient is a statistical function, (Eq. (1)) [13], assess the strength between variables and relationships. This formula is often known as the Pearson R test. When performing a statistical assessment between any two variables, it is used to calculate R-value to decide how strong that relationship is between those two variables.
P P P N xy ð xÞð yÞ ffi R ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h P h P 2 P 2 P 2 ii 2 N x ð xÞ N y ð y Þ
ð1Þ
3. Results and discussion 3.1. Experimental data
Fig. 1. Samples after Sintering.
Fig. 2 shows the variation of individual responsibility with the two parameters, i.e. PMMA content and sintering temperature. The porosity (apparent and true) for the samples without addition yeast cell was in the range (8.11–32.51%). The data was shown that the porosity increases from 43.15% to 75.21% with an increase in the PMMA content from 5 to 20 wt%, Fig. 2. this indicates that most of the addition was removed with the sintering process. Fig. 1 also shows the same behavior in increasing true porosity with a decrease in the sintering temperature [14,15]. On the other hand, the bulk density changes with the variation in the addition of
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
PMMA content. Moreover, it was affected by pore size, pore morphology, and the interconnectivity of the pores [16]. Fig. 3 shows the mean impact of the PMMA content and sintering temperature on the investigated properties. The x-axis represents the value of each process parameter and y-axis are the response value. The horizontal line indicates the mean of the
3
response. The main effects plot are used to examine the differences between level means for one or more factors based on values in Fig. 2. Fig. 4 a–b show the SEM surface micrographs of specimens prepared with various contents of PMMA. It was obvious that the microstructures were gravely affected by the amount of pore
Fig. 2. Impact of the PMMA content and sintering temperature on the porous media properties for a) True porosity, b) apparat porosity, c) Bulk density.
Fig. 3. Main effects of; a) apparent porosity, b) true porosity, c) bulk density.
Fig. 4. SEM for porous alumina with 20 wt% PMMA and sintering at 1200 °C.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
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A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
former. In Fig. 3 (a,b), the specimen prepared with 20 wt% pore formers did present a number of irregular pores and some small, close pores could be observed. The pores were mainly derived from the gaps remaining in the green body when the vitreous grains and abrasive particles agglomerated together in the process of sintering. As the content of PMMA increased, the total volume and connectivity of pores increased [17]. Also, it’s had relatively small quasi-spherical pores, and the pores formed were uniform in distribution. In general, the type of pores in the specimens were similar in shape to the pore formers themselves, indicating that the morphology of the pores was related to the shapes and sizes of the initial pore formers.
3.2. Reduced-order properties prediction model The Reduced-order models were used to predict the porous media properties based on the measured values. The performance of the employed reduced order model was evaluated by finding the change between the calculated and the measured properties. The discrepancy between the measured and the calculated datasets are presented in Fig. 5. Generally, the same behavior of the Kriging model in the prediction of the porous media properties was observed. The discrepancy increased and decreases across all range of the temperature and percentage rate of yeast. At some range the predicted values were found to be lower than the original data, and
Predicted Bulk Desity [gm/cm³]
Predicted True porosity (%)
Fig. 5. Discrepancy between the prediction and the experimental data; a) Apparent porosity, b) true porosity, c) bulk density.
Fig. 6. Correlation between the measured and the predicted data.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
increase over the original data afterwards. The results keep in this behavior across all the selected range of the parameters. In sum, the measured difference between the calculated and the measured data (Du; Dq and Dk) is very low and can be considered negligible. Two degrees of freedom (yeast percentage and apparent porosity) were selected to build a correlation between the measured data and the reduced order model data, Fig. 6. The results showed a linear correlation between the predicted and measured data with R of 0.999 of all the properties of the porous media. This prediction model can be used to evaluate the mutual impact of different parameters on the porous media over a wider range of variables.
[3] [4]
[5]
[6]
[7]
4. Conclusion [8]
High porous alumina ceramics have been successfully synthesis by a dry pressing method using a microspheres PMMA as a template. Among the porous compacts fabricated, a sample with 20 wt% and sintering temperature at 1200 °C had the most superior characteristics along with the open porosity of 72.3%, and bulk density 1.2 gm/cm3. The Reduced-order model was built on the experimentalderived porous alumina ceramic. The Reduced order model was validated using a leave-one-out cross-validation approach. Across the range of porous alumina ceramic properties, a Kriging method results showed acceptable results with an error of 0.02%. Overall, the results showed a linear correlation between the predicted and measured data with Pearson coefficient (R) close to unity of all the selected properties of the porous alumina. The validated model can be used to evaluate the combined impact of different parameters on the porous media properties over an extended range of parameters.
[9]
[10] [11] [12]
[13] [14]
[15]
[16]
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and sucrose for filter applications, Microporous Mesoporous Mater. 213 (2015) 48–58. H. Nishihara, S. Mukai, D. Yamashita, H. Tamon, Nishihara, Ordered macroporous silica by ice templating, Chem. Mater. 17 (3) (2005) 683–689. Z. Yuan, A. Govind Rajan, R.P. Misra, L.W. Drahushuk, K.V. Agrawal, M.S. Strano, D. Blankschtein, Mechanism and prediction of gas permeation through subnanometer graphene pores: comparison of theory and simulation, ACS Nano 11 (8) (2017) 7974–7987. F. Mebarek-Oudina, Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source, Heat TransferAsian Res. 48 (2019) 135–147, https://doi.org/10.1002/htj.21375. V. Malgras, Q. Ji, Y. Kamachi, T. Mori, F.K. Shieh, K.C. Wu, Y. Yamauchi, Malgras, Templated synthesis for nanoarchitectured porous materials, Bull. Chem. Soc. Jpn. 88 (9) (2015) 1171–1200. G. Xu, J. Li, H. Cui, Q. He, Z. Zhang, X. Zhan, Biotemplated fabrication of porous alumina ceramics with controllable pore size using bioactive yeast as poreforming agent, Ceram. Int. 41 (5) (2015) 7042–7047. A. Al-akam, T. Nikolaidis, D.G. Macmanus, Computational fluid dynamicsbased approach for low-order models of propelling nozzle performance, Proc. Inst. Mech. Eng., Part G: J. Aerospace Eng. (2019) 1–16, https://doi.org/ 10.1177/0954410019831852. G. Venter, R. Haftka, M. Chirehdast, G. Venter, R. Haftka, M. Chirehdast, Response surface approximations for fatigue life prediction, 38th Structures Structural Dynamics, and Materials Conference, 1997. A.I.J. Forrester, A. Sobester, A.J. Keane, Engineering Design via Surrogate Modelling: A Practical Guide, Wiley and Sons, Chichester, UK, 2008. G. Casella, S. Fienberg, I. Olkin, An Introduction to statistical learning, seventh ed., Springer, New York Heidelberg Dordrecht London, 2013. G. Palmer, Construction of CFD Solutions Using Interpolation Rather than Computation with the ADSI Code, 47th AIAA Aerosp. Sci. Meet. Incl. New Horizons Forum Aerosp. Expo., AIAA 2009-141, Orlando, USA, 2009. J. Cohen, Statistical Power Analysis for the Behavioral Sciences, second ed., Erlbaum, Hillsdale, NJ, 1988. N. Amir, Mohsin A. Aswad, Mohammed A. Ahmed Al-dujaili, Synthesis of gamma alumina for catalyst support using yeast cell as pore forming agent using regression model, J. Eng. Appl. Sci. 13 (2018) 9558–9563. A.P.D.M.A. Aswad, Amir Najah Saud, Preparation of Macro-Porous Alumina via Organic Additive and Characterizations Physical Properties by Using a Genetic Algorithm Method, Proceedings of the 2017 IEEE 1st International Conference on Recent Trends of Engineering Science and Sustainability, Baghdad, Iraq, 2017. Hasan Sh Majdi, Amir N. Saud, Safaa N. Saud, Modeling the physical properties of gamma alumina catalyst carrier based on an artificial neural network, Materials 12 (11) (2019) 1752. Feng Wang et al., Effects of pore connectivity and microstructure on mechanical performance of ZrO2 scaffolds and PMMA-infiltrated ZrO2 composites, J. Alloys .Compd. 728 (2017) 189–195.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
Contents lists available at ScienceDirect
Materials Today: Proceedings journal homepage: www.elsevier.com/locate/matpr
Experimental based approach for reduced-order models of porous media properties prediction Amir N. Saud a,⇑, Aws Al-Akam a,b, Ameen Al-joboori a a b
Al-Mustaqbal University College, University Road, Al-Hillah, Babil, Iraq University of Babylon, University Road, Al-Hillah, Babil, Iraq
a r t i c l e
i n f o
Article history: Received 13 July 2019 Received in revised form 28 August 2019 Accepted 29 September 2019 Available online xxxx Keywords: Porous alumina ceramic Pore-forming method Data analysis Reduced-order model Kriging
a b s t r a c t The pore diameter, type (open or closed), physical properties of Porous alumina ceramic were controlled by varying concentration in the mixture of Polymethylmethacrylate (PMMA) with alumina powder and sintering temperature. The porous alumina ceramic was synthesis by a dry pressing method using a microspheres Polymethylmethacrylate (PMMA) as a pore-forming agent. The properties of the porous alumina were predicted using an experimental approach. Afterwards, the measured data were used to develop a Reduced-order model (Kriging) to enable a fast prediction of the properties for an extended range of parameters variation and further analysis. The experimental results showed that the High porous alumina ceramics is having an open porosity of 72.3%, and a bulk density 1.2 gm/cm3 and these could be fabricated using PMMA microspheres. Kriging model results showed an acceptable prediction of the experimental-derived data with a maximum discrepancy of 0.02% for the apparent porosity. Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Materials Engineering & Science.
1. Introduction Porous alumina ceramic is excellent in heat and chemical resistance, lightweight, and therefore are used in a wide variety of fields such as filters, catalysts, separation membranes and adsorption materials [1]. For such a porous material, a pore size corresponding to each application is required. For example, various types of pore diameters in the range of 0.005 lm to 10 lm are prepared for a filter material membrane which needs to consider air permeability, fluid flow [2]. In particular, photonic crystals having a periodic change in refractive index in the same order as the wavelength of light have a structure in which uniformly sized pores having a size of 0.12 lm to 1 lm are regularly arranged threedimensionally [3]. In addition, when gas adsorption and separation are performed by a gas sensor, a separation membrane, functions are exhibited by the presence of nano-order or angstrom pores [4]. The Nano sizing of the materials particles could improve their properties such as thermal conductivity [5]. Recently, higher porosity and adsorption property have been desired to be
⇑ Corresponding author. E-mail address: [email protected] (A.N. Saud).
improved, it is necessary to control materials from nano to macroscopic structure, and bimodal porous materials are combining the order of respective pores are attracting attention [6]. Many alternative methods have been reported to synthesis porous alumina. These include the partial sintering method, gel casting, freezing casting, organic foam method and pore-forming agent method [7]. PMMA pore-forming agent was used as a template to obtain a porous alumina that is having a porous wall structure with substantially uniform shape and particle diameter and retaining the outer shell shape of the particulate material, the template is mixed with the raw material of the matrix, and then the template is burned to eliminate the pores [7] thereby. In this article, the key novelty that the mono-dispersed Polymethylmethacrylate (PMMA) micro-balls were selected as a pore-forming agent, and the porous alumina ceramics were fabricated by the semi-dry pressing. The effects of Polymethylmethacrylate on true porosity, apparent porosity and bulk density of the porous alumina ceramics were investigated. Moreover, the measured porous media properties were used to create a Reduced-Order Model (ROM) to calculate the true porosity, apparent porosity and bulk density of the porous alumina ceramics. This model can be used for future calculations of these properties in a wider range.
https://doi.org/10.1016/j.matpr.2019.09.155 2214-7853/Ó 2019 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Materials Engineering & Science.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
2
A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
2. Methodology 2.1. Scope of the paper This work employs an experimentally derived data to build a Reduced-order model to predict the main impact of PMMA content and sintering temperature on the porous media properties. The methodology consists of the generation of the experimental data and measures the True, apparent and bulk density. The measured data are used to establish a Reduced-order model (i.e. Kriging) and validate it using the leave-one-out cross-validation method. The new model can be used to predict the properties for a wider range of parameters. 2.2. Samples preparation Alumina powder was used with an average particle size of 3 mm, whereby the Polymethylmethacrylate (PMMA) as pore-forming agents and the sodium polyphosphate as deflocculating. Alumina powder was weighed and dry-mixed thoroughly in a mortar pestle with the required amount of PMMA and deflocculated (5 batches). Afterwards, the desired volume of the PVA solution was added, so that the final PVA content of the batch is 3%. The sugar solution was carefully blended with the previous mixture using agate mortar for 10 min. The samples were produced by semi-dry pressing in a hydraulic press (Carver Press USA) at a various load 70 MPa with soaking time of 90 s. The sample size of 20 mm U 6 mm thickness was prepared and then dried in an oven at 50 °C overnight. Then the green samples were sintered in different conditions of 1200, 1300, 1400, and 1500 °C and soaking time of 2 h as shown in Fig. 1. 2.3. Design of experiment Five batches with different concentrations of alumina powder and Polymethylmethacrylate (PMMA) were prepared to produce the porous alumina samples. The experimental population consisted of 20 samples with each sample regarded as a chromosome and each chromosome consists of two genes. These genes were characterised by the input parameters, in the current paper; two input parameters with four levels were utilized. The fitness function or regression equation was created using a python software program. 2.4. Response surface method (Kriging) The behavior of the Response surface methods (RSM) depend on the data type. Large number of accurate data produces high perfor-
mance of the RSM. RSM proposes techniques to detect the effect of the responses based on varying stages of control factors that are identified to direct physical processes. RSM based on employing the regression analysis on a set of data derived from laboratory tests or computational fluid dynamics (CFD) simulations at several levels [8]. The strength of the RSM techniques based on producing effective and smooth estimates for the data at discretized data-points in the multidimensional analysis [9]. The selection of the models to represent the behavior of any set of data has a pronounced impact on the reliability of the recently predicted data. The selected RSM model is Kriging [10] methods. The RSM was applied to a two-dimensional design space based on the PMMA % Wt. and Temperature °C. The purpose of this study is to demonstrate the capability of employed RSM approach in mapping multidimensional behavior of the porous media properties as a function of different intensities of PMMA % Wt. and the temperature °C that is identified to affect the properties. To confirm the reliability of the employed model in evaluating the properties, Cross-Validation (CV) approach was used to validate the results produced from RSM [11]. The Leave-One-Out technique (LOO) was utilized, to evaluate the error related to using a particular RSM on a set of reference data (experimental data). This technique is achieved by taking single data point (experimental results) out of the whole main data (Apparent porosity (%), True porosity (%) or Bulk Density) and reproduce the RSM based on the remains of the set of the data to predict for the missing data point. Then the model calculates the difference between the new and the original properties (Du; Dq and Dk). Kriging RSM method uses least-square estimation to minimize the inconsistency between the predicted and the reference data [12]. It depends on employing a spatial correlations between the observed data points using the Gaussian exponential function [11]. Simple Kriging was utilized in the current work, and absolute exponential correlation was selected. The regression function was selected to be ‘‘quadratic” and the nugget value of 1.0 1011. The upper and lower theta was selected to be 0.1 and 0.0001, respectively. Pearson coefficient [13] was used to assess the suitability of the employed regression model in the prediction of the pours media properties. Pearson correlation coefficient is a statistical function, (Eq. (1)) [13], assess the strength between variables and relationships. This formula is often known as the Pearson R test. When performing a statistical assessment between any two variables, it is used to calculate R-value to decide how strong that relationship is between those two variables.
P P P N xy ð xÞð yÞ ffi R ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h P h P 2 P 2 P 2 ii 2 N x ð xÞ N y ð y Þ
ð1Þ
3. Results and discussion 3.1. Experimental data
Fig. 1. Samples after Sintering.
Fig. 2 shows the variation of individual responsibility with the two parameters, i.e. PMMA content and sintering temperature. The porosity (apparent and true) for the samples without addition yeast cell was in the range (8.11–32.51%). The data was shown that the porosity increases from 43.15% to 75.21% with an increase in the PMMA content from 5 to 20 wt%, Fig. 2. this indicates that most of the addition was removed with the sintering process. Fig. 1 also shows the same behavior in increasing true porosity with a decrease in the sintering temperature [14,15]. On the other hand, the bulk density changes with the variation in the addition of
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
PMMA content. Moreover, it was affected by pore size, pore morphology, and the interconnectivity of the pores [16]. Fig. 3 shows the mean impact of the PMMA content and sintering temperature on the investigated properties. The x-axis represents the value of each process parameter and y-axis are the response value. The horizontal line indicates the mean of the
3
response. The main effects plot are used to examine the differences between level means for one or more factors based on values in Fig. 2. Fig. 4 a–b show the SEM surface micrographs of specimens prepared with various contents of PMMA. It was obvious that the microstructures were gravely affected by the amount of pore
Fig. 2. Impact of the PMMA content and sintering temperature on the porous media properties for a) True porosity, b) apparat porosity, c) Bulk density.
Fig. 3. Main effects of; a) apparent porosity, b) true porosity, c) bulk density.
Fig. 4. SEM for porous alumina with 20 wt% PMMA and sintering at 1200 °C.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
4
A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
former. In Fig. 3 (a,b), the specimen prepared with 20 wt% pore formers did present a number of irregular pores and some small, close pores could be observed. The pores were mainly derived from the gaps remaining in the green body when the vitreous grains and abrasive particles agglomerated together in the process of sintering. As the content of PMMA increased, the total volume and connectivity of pores increased [17]. Also, it’s had relatively small quasi-spherical pores, and the pores formed were uniform in distribution. In general, the type of pores in the specimens were similar in shape to the pore formers themselves, indicating that the morphology of the pores was related to the shapes and sizes of the initial pore formers.
3.2. Reduced-order properties prediction model The Reduced-order models were used to predict the porous media properties based on the measured values. The performance of the employed reduced order model was evaluated by finding the change between the calculated and the measured properties. The discrepancy between the measured and the calculated datasets are presented in Fig. 5. Generally, the same behavior of the Kriging model in the prediction of the porous media properties was observed. The discrepancy increased and decreases across all range of the temperature and percentage rate of yeast. At some range the predicted values were found to be lower than the original data, and
Predicted Bulk Desity [gm/cm³]
Predicted True porosity (%)
Fig. 5. Discrepancy between the prediction and the experimental data; a) Apparent porosity, b) true porosity, c) bulk density.
Fig. 6. Correlation between the measured and the predicted data.
Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155
A.N. Saud et al. / Materials Today: Proceedings xxx (xxxx) xxx
increase over the original data afterwards. The results keep in this behavior across all the selected range of the parameters. In sum, the measured difference between the calculated and the measured data (Du; Dq and Dk) is very low and can be considered negligible. Two degrees of freedom (yeast percentage and apparent porosity) were selected to build a correlation between the measured data and the reduced order model data, Fig. 6. The results showed a linear correlation between the predicted and measured data with R of 0.999 of all the properties of the porous media. This prediction model can be used to evaluate the mutual impact of different parameters on the porous media over a wider range of variables.
[3] [4]
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4. Conclusion [8]
High porous alumina ceramics have been successfully synthesis by a dry pressing method using a microspheres PMMA as a template. Among the porous compacts fabricated, a sample with 20 wt% and sintering temperature at 1200 °C had the most superior characteristics along with the open porosity of 72.3%, and bulk density 1.2 gm/cm3. The Reduced-order model was built on the experimentalderived porous alumina ceramic. The Reduced order model was validated using a leave-one-out cross-validation approach. Across the range of porous alumina ceramic properties, a Kriging method results showed acceptable results with an error of 0.02%. Overall, the results showed a linear correlation between the predicted and measured data with Pearson coefficient (R) close to unity of all the selected properties of the porous alumina. The validated model can be used to evaluate the combined impact of different parameters on the porous media properties over an extended range of parameters.
[9]
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Please cite this article as: A. N. Saud, A. Al-Akam and A. Al-joboori, Experimental based approach for reduced-order models of porous media properties prediction, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.09.155