Modeling of Linear and Non-linear Compression Processes of Sunﬂower Bulk Oilseeds

: The present study aimed at describing the experimental and theoretical force-deformation curves of sunﬂower bulk oilseeds at varying initial pressing heights and vessel diameters as well as determining the theoretical pressure and energy along the screw press FL 200 pressing chambers. The design of e ﬃ cient oil expression systems for industry and small-scale application remains a major challenge to engineers and researchers. In attempting to solve the problem, it is important to understand the linear compression process and to transfer the knowledge to the industry involving mechanical screw presses. The universal compression testing machine at a preset load of 200 kN and a speed of 5 mm · min − 1 , tangent curve model and the screw press FL 200 geometry parameters were applied. The obtained results of pressure and energy along the screw pressing chambers (1–7) ranged from 0.31 to 101.653 MPa and 12.616 to 1231.228 J. Applying the tangent model at n = 1 and n = 2, the cumulative pressure decreased with increasing vessel diameters while energy increased. The study provides useful information for the analysis of other bulk oilseeds and optimizing the processing parameters of screw press FL 200 and the design and development of new oil presses.


Introduction
There is the concern with the environmental preservation, which is structured both in efforts to optimize energy efficiency and investments in research, development and application of renewable resources, and cleaner technologies [1][2][3][4]. Vegetable oil from oilseeds such as sunflower seeds, rapeseeds among others is one of the renewable sources worldwide for application in internal combustion engines [5,6]. However, the design of efficient oil expression systems for industry and small-scale or rural-based operations has been the main challenge to engineers and scientists [7,8].
Mechanical pressing (using a screw or hydraulic presses) and solvent extraction with n-hexane are commonly used commercial oil extraction methods [9][10][11][12][13]. Although the mechanical pressing gives a lower yield compared to the solvent extraction method, it has several advantages including the lower cost of equipment and higher oil quality [14][15][16][17]. In the literature, the oil yield using the mechanical pressing process is dependent on particle size, moisture content, heating temperature, heating time, applied pressure and pressing time [18][19][20][21]. The press and screw configurations are also factors affecting mechanical oil expression [22]. Generally, mechanical expression of oil requires the application of pressure on the operating conditions, pretreatment and raw material. In addition, for a given pressure, deformation and compression of particles begin to release the oil from the capillaries of particles.
The pressing or compression process can be understood as the process of capillary filtration where the volume of the separated liquid passing through the capillaries is dependent on the applied pressure, diameter of the capillary channel, dynamic viscosity, length of capillary channel and time of applied pressure. The compression process can also be influenced positively if the pressure, diameter and time increase while the dynamic viscosity and length also decrease. The oil expression efficiency, on the other hand, is influenced by the porosity of the cake, yield stress of the solid phase, the compressive force and viscosity of the expressed oil. The general theoretical description of oil expression has been based on the theories of consolidation originally developed for soil mechanics [22,23]. Several studies have been reported on the modeling of oilseed expression resulting in the development of empirical models, Terzaghi-type models and models based on the cell structure of the oilseeds [23][24][25][26][27][28].
Despite the significant efforts in the modeling development, press design and automation, optimizing the oil expression processing parameters along the screw chambers or lamella positions remain a problem due to the complexity of the mechanisms involved in the continuous dynamic process of the mechanical pressing of oilseeds [29]. In order to design and develop new efficient systems, it is important to understand the linear compression process of oilseeds and the transformation of the results to the non-linear compression process involving mechanical screw presses. This scope of research is limited in the literature. Therefore, the aim of this study was to describe the experimental and theoretical force-deformation curves of sunflower bulk oilseeds, determine the experimental and theoretical deformation energy as well as to determine the theoretical pressure (screw pressure) and energy (screw energy) along the screw pressing chambers of screw press FL 200.

Materials and Methods
The sunflower bulk oilseeds sample (bulk sample) was used for the linear compression test experiment. Before the experiment, impurities including leaves and pieces of stalks were removed from the bulk sample which has been kept under laboratory conditions. The moisture content of the bulk sample was determined to be 10.14 (% w.b.) using the standard procedure [30] and the relation given by [31] as described in Equation (1) as follows: where MC is the moisture content in wet basis (% w.b.), m a and m b are the weights of the bulk sample before and after oven drying at a temperature of 105 • C and a drying time of 17 hours. The universal compression-testing machine (Tempos, Model ZDM 50, Czech Republic) was used to describe the relationship between the compressive force and deformation curve patterns of the bulk sample initial pressing heights at a maximum force of 200 kN and a speed of 5 mm·min −1 (Figure 1). The initial bulk sample heights at 40, 60 and 80 mm were measured and compressed in each pressing vessel of diameter 60, 80 and 100 mm. The compression test was repeated twice. The deformation values were obtained directly from the compression test. The oil yield and experimental deformation energy [32][33][34] were calculated using Equation (2) and Equation (3) as follows: where OY is the oil yield (%), O w is the weight of oil (g) and O m is the initial weight of the bulk sample (g).
where U is the experimental deformation energy (J), F n+1 + F n and x n+1 − x n are the compressive force (kN) and deformation (mm), n is the number of data points and i is the number of sections in which the axis deformation was divided (step measurement was 0.01).

88
(c) Experimental and fitted dependency between compressive force and deformation curves of 89 sunflower bulk oilseeds at initial heights of 40, 60 and 80 mm (Equation (5)).

90
The theoretical deformation energy from the compression test was calculated based on the 91 tangent curve mathematical model [35][36][37][38], as described in Equations (4)-(6) as follows: where F is the force (kN), x is deformation (mm), A is the force coefficient of mechanical behavior 93 (kN), B is the deformation coefficient of mechanical behavior (mm −1 ), n is the fitting curve function  The theoretical deformation energy from the compression test was calculated based on the tangent curve mathematical model [35][36][37][38], as described in Equations (4)-(6) as follows: where F is the force (kN), x is deformation (mm), A is the force coefficient of mechanical behavior (kN), B is the deformation coefficient of mechanical behavior (mm −1 ), n is the fitting curve function exponent. Equation (4) describes the theoretical deformation energy of the bulk sample at a specific pressing height where the force is a function of the deformation. Equation (5) and Equation (6) explain the integral of Equation (4) for which n = 1 and n = 2 respectively. For describing the theoretical deformation energy of the bulk sample where the force is a function of different variables such as deformation, pressing height and vessel diameter [32,34], Equation (7) was applied. Equation (8) and Equation (9) explain the integral of Equation (7) for which n = 1 and n = 2.
T E n=1 : where C is the stress coefficient of mechanical behavior (N·mm −2 ), which is the ratio of the force coefficient of mechanical behavior A (kN) to that of the square of pressing vessel diameter D (mm), and G is the compression coefficient defined as the product of the coefficient of deformation behavior B (mm −1 ) and initial pressing height H (mm) [35]. For the non-linear compression process, the screw press FL 200 pressing chambers or lamella positions ( Figure 2) were analyzed theoretically in terms of the initial compression height, deformation, compression ratio and volume of the bulk sample. The screw press geometry parameters for bulk jatropha oilseeds were used for the theoretical analysis of the bulk sample [39]. press geometry with seven pressing sections along the lamellas [38][39][40].

111
The theoretical volume of the bulk sample and the screw cross-sectional area were calculated 112 using Equation (10) and Equation (11) as follows: where is the theoretical volume of the bulk sample (m 3 ), is the screw shaft diameter (mm), is the screw inner diameter (mm), is the screw outer diameter (mm), is the screw pitch diameter (mm) and is the screw thickness (mm), is the cross-sectional area of the screw press 116 geometry (m 2 ). The theoretical pressure and energy at the screw lamella positions (from 0-7) were 117 determined using Equations (8)- (11). Both the experimental and theoretical data were statistically 118 analyzed using MathCAD software, version 15 and STATISITCA, version 13 [41,42]. The theoretical volume of the bulk sample and the screw cross-sectional area were calculated using Equation (10) and Equation (11) as follows: where V V is the theoretical volume of the bulk sample (m 3 ), D O is the screw shaft diameter (mm), D 1 is the screw inner diameter (mm), D 2 is the screw outer diameter (mm), P T is the screw pitch diameter (mm) and P k is the screw thickness (mm), A A is the cross-sectional area of the screw press geometry (m 2 ). The theoretical pressure and energy at the screw lamella positions (from 0-7) were determined using Equations (8)- (11). Both the experimental and theoretical data were statistically analyzed using MathCAD software, version 15 and STATISITCA, version 13 [41,42].

Results
The amounts of deformation, oil yield, experimental deformation energy and theoretical deformation energy of the bulk sample in relation to the varying vessel diameters and initial pressing heights are presented in Table 1. From Table 1, it can be seen that the mean total of deformation, oil yield, experimental deformation energy, and theoretical deformation energy at initial pressing heights in relation to the vessel diameters ranged from 44 It was observed that the determined or calculated amounts except oil yield increased along with the increase in initial pressing height and vessel diameter. The oil yield, however, decreased with the increase in vessel diameter. The coefficient of variation of the mean values of the above-mentioned parameters in relation to the vessel diameters also ranged from 0.98 to 11.09, 1.51 to 4.41 and 1.02 to 8.26% respectively. Particularly, the percentage difference or error values of the experimental deformation energy against the theoretical deformation energy (Equation (8)) at the various vessel diameters ranged from 5.24 to 23.43%. The lower values of the coefficient of variation greatly show the precision of the obtained results. In addition, the approximately 5% difference or error of the measured and theoretical energy values obtained with vessel diameter 80 mm showed high accuracy of the tangent model (Equation (8)) in comparison with the vessel diameters 60 and 100. The regression coefficients and the whole model with the corresponding statistical evaluation of the compression test data are presented in Tables 2 and 3.   The ANOVA statistical analysis of the determined tangent curve coefficients of A and B from Equation (4) or Equation (7) for a level of significance of 5% using the Mathcad 14 software [40] are given in Tables 4 and 5. At varying initial pressing heights and vessel diameters, the force coefficient A values applying Equation (5) (  (5) were observed. From the determined coefficients, it was observed that Equation (5) showed high suitability for fitting the linear compression data compared to Equation (6) with respect to the higher coefficient of determination values. The experimental and fitted data of the force and deformation curves of the bulk sample for vessel diameter 100 mm in relation to initial pressing heights are illustrated in Figure 1. The fitted data of vessel diameters of 60 and 80 mm showed a similar curve characteristic.   (kN), B is the deformation coefficient of mechanical behavior (mm −1 ), F-Ratio is the value of the F-test, F-Critical is the critical value that compares a pair of models, P-Value is the significance level used for testing a statistical hypothesis, R 2 is the coefficient of determination.
The calculated stress and compression coefficients of the tangent curve model applying Equations (8) and (9) are given in Table 6. For Equation (8), the mean stress coefficient C ranged from 2.44 ± 0.10 to 1.64 ± 0.08 N·mm −2 while the compression coefficient G ranged from 2.03 ± 0.03 to 2.17 ± 0.03. In comparison to Equation (9), the mean stress coefficient C ranged from 0.69 ± 0.04 to 0.99 ± 0.14 N·mm −2 while the compression coefficient G ranged from 1.97 ± 0.02 to 2.03 ± 0.03. Using both Equations (8) and (9), the stress coefficients decreased along with the increase in initial pressing heights and vessel diameters. However, the mean total of the stress coefficients (Equation (8)) in relation to the initial pressing heights decreased along with the increase in vessel diameter while for Equation (9), the stress coefficients increased. On the other hand, the compression coefficients did not show either a positive or negative linear dependency in relation to the initial pressing heights and vessel diameters. But, the mean total of the compression coefficients increased linearly with regards to the vessel diameters while that of Equation (9), both increasing and decreasing amounts were observed. Therefore, it can be said that the bulk sample initial pressing heights and vessel diameters have an effect on the stress and compression coefficients of the tangent curve model. The coefficient of variation of the mean values of the stress and compression coefficients using Equations (8) and (9) in relation to the vessel diameters also ranged from 1.02 to 5.79, 1.48 to 3.95 and 1.38 to 14.14%, respectively. The mean total values of the stress and compression coefficients obtained from Equations (8) and (9) in relation to the initial pressing heights and vessel diameters were further used to determine the amounts of screw force, pressure and energy along the screw press FL 200 pressing chambers. The data on the theoretical screw pressure and energy is indicated in Tables 7 and 8. The complete data on the screw force is not presented here since the pressure was calculated as the ratio of the screw force to the screw cross-sectional area [31,39]. Using Equation (8) (8) in comparison to Equation (9) for all vessel diameters. In addition, for both Equations (8) and (9), the cumulative amounts of pressure decreased with increasing vessel diameters while energy increased. The regression coefficients and the whole model with the corresponding statistical evaluation of the theoretical pressure and energy are presented in Tables 9 and 10. Table 7. Theoretical pressure at the screw press lamella positions.

Discussion
The parameters determined from the linear compression test were deformation, oil yield, experimental deformation energy and theoretical deformation energy. Based on the whole model of the multiple regression analysis, the vessel diameter and bulk sample initial pressing height had a significant effect (P-Value < 0.05) or (F-Ratio > F-Critical) ( Table 3) on the above mentioned determined parameters. The independent variables (vessel diameter and pressing height) would contribute significantly (P-Value < 0.05) to the prediction of the dependent variables (deformation, experimental deformation energy and theoretical deformation energy). However, for oil yield, the initial pressing height would not contribute significantly (P-Value > 0.05). This means that the coefficient of the initial pressing height will not be used in the regression model to predict the oil yield of sunflower bulk oilseeds. The force coefficient of mechanical behavior A (kN) and deformation coefficient of mechanical behavior B (mm −1 ) of the tangent curve model were statistically significant (P-Value > 0.05) or (F-Critical > F-Ratio) according to the ANOVA analysis using MathCAD, version 15 [41]. The determined coefficients can be used to describe the force-deformation curves of sunflower bulk oilseeds at a maximum force of 200 kN and speed of 5 mm min −1 . Theoretically, the area under the force-deformation curves is the deformation energy [32,34]. The tangent curve model with the corresponding fitting value of n = 1 (Equation (8)) showed higher suitability for describing the linear compression curves compared to the fitting value of n = 2 (Equation (9)) based on the coefficient of determination (R 2 ) values.
From the multiple regression results of the non-linear compression process, the screw lamella position showed statistically significant (P-Value < 0.05) ( Table 9) for predicting the screw pressure. However, the vessel diameter and tangent model fitting value were not statistically significant (P-Value > 0.05). On the other hand, the screw lamella position and model fitting value were statistically significant (P-Value < 0.05) ( Table 9) for predicting the screw energy in comparison to the vessel diameter which was not statistically significant (P-Value > 0.05). Based on the whole model statistical values (Table 10), the vessel diameter, screw lamella position and tangent model fitting value had significant influence (P-Value < 0.05) or (F-Ratio > F-Critical) on the theoretical amounts of screw pressure and energy respectively. Comparing the results of the current study (using Equation (8)) to the previously published study [39,40], it was found that the bulk oil palm kernels had higher amounts of the theoretical pressure along the screw lamella positions from (0-6) for all vessel diameters followed by sunflower bulk oilseeds and then jatropha bulk oilseeds. However, at pressing chamber positions 6 and 7, higher amounts of pressure were obtained for sunflower bulk oilseeds followed by bulk oil palm kernels and then jatropha bulk oilseeds. This trend was similar to the amounts of the theoretical energy with the exception of vessel diameter of 100 mm, where sunflower bulk oilseeds produced higher amounts of the theoretical energy along the screw lamellas. Actually, the experimental processing parameters (maximum force of 200 kN and speed of 5 mm·min −1 ) for sunflower bulk oilseeds and oil palm bulk kernels were similar compared to jatropha bulk oilseeds where the maximum force and speed were 100 kN and 1 mm·s −1 [39]. In the previous study [39], Equation (9) was only examined for the jatropha bulk oilseeds. However, for sunflower bulk oilseeds (present study) and oil palm bulk kernels (previous study) [39], both Equations (8) and (9) were investigated, and similar trend of the results was obtained as already described above. Based on these comparisons, it can be concluded that more energy would be required for recovering the oil from oil palm bulk kernels than sunflower bulk oilseeds when using the screw press FL 200. This conclusion, however, cannot be stated for jatropha bulk oilseeds for now until similar processing parameters are studied. Furthermore, based on the multiple linear regression results, the screw lamella position and fitting curve value of the tangent model (Equations (8) and (9)) were found to significantly (P-Value < 0.05) influence the amount of the theoretical energy of both sunflower bulk oilseeds and oil palm bulk kernels while the vessel diameter had no significant effect (P-Value > 0.05). The screw lamella position also had a significant effect on the theoretical amounts of force and pressure while the vessel diameter and fitting curve value of the tangent model did not show significant influence. Most importantly, the strain or compression ratio which is the ratio of deformation to the initial pressing height is influenced by the pressing factors including moisture content and friction [35]. Therefore, the compression ratio variable in Equation (8) and Equation (9) was divided by the coefficient of the pressing factors which was estimated for each vessel diameter (60, 80 and 100 mm) in relation to the processing parameters. For jatropha bulk oilseeds at a maximum force of 100 kN [38], the estimated pressing factors coefficients values of 1.42, 1.55 and 1.74 in increasing order of the vessel diameter were reported. In the case of sunflower bulk oilseeds at a maximum force of 200 kN, the coefficient values of 1.226, 1.384 and 1.537 were observed for Equation (8) and 1.208, 1.328 and 1.436 for Equation (9). For oil palm bulk kernels, the values of the pressing coefficients were 1.637, 2.14 and 2.89 for Equation (8) and 1.59, 1.88 and 2.42 for Equation (9). The tangent curve models (Equations (8) and (9)) suggest that the coefficients of the pressing factors should be determined experimentally to obtain adequate knowledge on the optimum processing parameters of the screw press FL 200.
In the literature, it is obvious that many models have been applied extensively on the modeling of oilseeds or food processing engineering aimed at understanding the aerodynamics and biophysical or physical properties as well as optimizing the processing parameters. Some of these models include response surface methodology, artificial neural network, adaptive neuro-fuzzy inference system, fuzzy logic design [43][44][45][46][47][48][49]. However, the tangent curve mathematical model applied in this present study and previously published studies show reliability for describing the linear and non-linear compression processes of bulk oilseeds based on the experimental or model boundary conditions [35][36][37]. Future studies would consider examining the above-mentioned models in the linear and non-linear compression processes of selected bulk oilseeds.

Conclusions
Based on the results presented and discussed, it was revealed that the coefficients of the independent variables (vessel diameter and initial pressing height) in the determined regression model would contribute significantly to the prediction of the dependent variables (deformation, experimental deformation energy and theoretical deformation energy of sunflower bulk oilseeds in the linear compression process. The initial pressing height coefficient in the regression model had no significant effect on the oil yield in comparison to the vessel diameter which had a significant effect. The tangent curve model with the corresponding fitting value of n = 1 (Equation (8)) showed high suitability for describing theoretically the experimental force-deformation curves as well as the deformation energy of sunflower bulk oilseeds. Using (Equation (8)), the screw pressure amounts along the screw press FL 200 pressing chamber positions (1-7) ranged from 1.438 to 48.412 MPa, 1.808 to 39.466 MPa and 2.179 to 33.816 MPa for vessel diameters 60, 80 and 100 mm while the screw energy values ranged from 90.699 to 166.074 J, 102.158 to 161.088 J and 112.451 to 155.926 J. The coefficients of the screw lamella position and tangent curve model fitting value in the determined regression model showed statistical significance for predicting the theoretical screw energy. The cumulative amounts of the theoretical screw pressure along the screw press FL 200 pressing chamber positions (1-7) decreased with increasing vessel diameters while the screw energy increased. The lower values of the coefficient of variation and percentage difference or error of the measured and theoretical data obtained in the linear compression process proved high precision and accuracy for determining the non-linear compression parameters (screw energy and pressure). The modeling processes described in this study would be applied on other commonly used bulk oilseeds such as soybean, sesame, rapeseeds to fully understand their mechanical behaviors in both the linear and non-linear pressing conditions and also to determine the optimal processing parameters of the mechanical screw FL 200 using response surface methodology.