Experimental Modeling and Optimization of CO2 Absorption into Piperazine Solutions Using RSM-CCD Methodology.

The present work evaluates and optimizes CO2 absorption in a bubble column for the Pz-H2O-CO2 system. We analyzed the impact of the different operating conditions on the hydrodynamic and mass-transfer performance. For the optimization of the process, variable conditions were used in the multivariate statistical method of response surface methodology. The central composite design is used to characterize the operating condition to fit the models by the least-squares method. The experimental data were fitted to quadratic equations using multiple regressions and analyzed using analysis of variance (ANOVA). An approved experiment was carried out to analyze the correctness of the optimization method, and a maximum CO2 removal efficiency of 97.9%, an absorption rate of 3.12 g/min, an N CO2 of 0.0164 mol/m2·s, and a CO2 loading of 0.258 mol/mol were obtained under the optimized conditions. Our results suggest that Pz concentration, solution flow rate, CO2 flow rate, and speed of stirrer were obtained to be 0.162 M, 0.502 l/h, 2.199 l/min, and 68.89 rpm, respectively, based on the optimal conditions. The p-value for all dependent variables was less than 0.05, and that points that all three models were remarkable. In addition, the experiment values acquired for the CO2 capture were found to agree satisfactorily with the model values (R 2 = 0.944-0.999).

Introduction

Control and mitigation of the emission of carbon dioxide, the most significant contributor to the increasing greenhouse effect, have been the aim of extensive research to avoid permanent damage to the climate system. The combustion of fossil fuel for energy generation is recognized as the dominant source of anthropogenic CO2 emission. CO2 removal and storage is a practical option that has the possibility to decrease CO2 emission from large fixed industrial stations.[1,2] Among different techniques suggested for CO2 capture including chemical and physical absorption, adsorption, membrane, and cryogenic processes, amine scrubbing is a robust, matured, appropriate, and popular technology that is in use from 1930 and could apply to conventional power plants.[3] Nevertheless, it has some issues such as corrosion, amine losses, and high energy requirement for solvent regeneration.[4] Consequently, more research is required to improve the process and solvents. Compared to amines, Pz has been presented to have many beneficial qualities containing low thermal and oxidative degradation rates,[5,6] the low regeneration energy,[7,8] the fast CO2 absorption rate, and low corrosivity relative to widely used monoethanolamine (MEA), diethanolamine, and other amines.[9] Furthermore, Pz displays a relatively high absorption rate.[10] In recent research, the stirrer bubble column is applied to the amine-based CO2 absorption processes.[11−14] A bubble column is used in diverse industrial processes owing to the simple design, great heat- and mass-transfer performance, and intricate hydrodynamic attribute. However, the scale-up and design of this equipment are very laborious due to its complicated hydrodynamic. The absorption performance of the system is a complex dependent on layout, scheme, and operating parameters such as column construction, sparger characteristic, type and speed of stirrer, the flow rate of liquid and gas, CO2 partial pressure, and amine loading. Therefore, a good understanding of the complex relationship between the effective factors is essential to optimize the process. In light of these concerns, a systematic approach is particularly significant to evaluate the true potential of this technology and indicate the influence of key parameters on its performance.

Response surface methodology (RSM) is a time-consuming and powerful statistical technique that could be applied to optimize and model a wide range of engineering systems.[15] This method includes experimental design, which systematically reduces the number of tests, and numerous regression assessment to attain the conditions that resulted in the best answer about the studied empirical range.[16] RSM is an effective tool for simultaneous consideration independent variables and their interactions that affect the objective function where a reply of profits is impressed by numerous factors.[17] The target response is approximated with a polynomial equation in which its coefficients describe the effect of corresponding variables, and also this mathematical model is a guide to optimization search.[18]

Newly, several articles published about the usage of RSM regarding the preparation of CO2 solid sorbents,[19−22] and the other studies are focused on optimizing the CO2 absorption process. The performance of commercial active carbon for CO2 removal from simulated shifted-syngas flow was studied using full factorial and central composite designs (CCDs).[16] Nuchitprasittichai and Cremaschi[18] applied RSM to the simulation of the CO2 capture process in amine-based process to identify the design variables and optimal operating conditions which yield the least costly of the process. Also, to evaluate the quality of RSM results, they compared it with an artificial neural network (ANN) and concluded that the RSM models could predict the optimal solutions which are close to the ones obtained by ANN.[23] Morero et al.[24] used RSM to evaluate the performance of the different solvents in the absorption–desorption biogas upgrading process. The effects of temperature, total pressure, amount of CO2, circulation rate, and their interactions on use energy, recovery of CH4, and CO2 capture were determined. Babamohammadi et al.[25] employed a CCD to present a quadratic model for CO2 solubility in a blended solution based on MEA amount, temperature, concentration of glycerol, and gas flow rate. The obtained results revealed that amine concentration is the most effective parameter on the objective function. Table demonstrates the recent studies on using RSM to optimize the CO2 capture process.

Table 1

Some Studies on the CO2 Absorption Performance Using RSM Techniquesa

sorbent	variables	response	design	model	R2, Adj-R2	refs.
TEPA-DEA, MSU-F	CTEPA, CDEA, CMECH	qCO2	full factorial, CCD	Y = 5.62192 + 0.0830368X1 – 0.0345798X2 – 0.0208987X3 – 0.156328X12 – 0.619369X22 – 0.140422X32 – 0.295X1X2 – 0.215X1X3 – 0.1375X2X3	0.953	(19)
activated carbon	T, PCO2	qCO2, tb	full factorial	Q = 2.146 – 0.048T + 2.128PCO2 – 0.0109T × PCO2 + 0.0003T2 – 0.106PCO22	0.999, 0.998	(26)
				tb = 5.394 – 0.056T + 0.981PCO2 – 0.017T × PCO2 + 0.0003T2 + 0.516PCO22	0.990, 0.984
activated carbon	Tactivation, Dburn-off	qCO2	full factorial	Y = −20.4159 + 0.0668T + 0.2134B – 0.0002T × B – 0.00004T2 – 0.0016B2	0.970, 0.949	(20)
activated carbon	T, PCO2	qCO2, tb	full factorial	capture capacity = 3.1210 – 0.0779T + 0.8067PCO2 + 0.0006T2	0.982, 0.969	(16)
				tb = 8.0421 – 0.2394T + 2.4067PCO2 + 0.0020T2	0.991, 0.984	(16)
activated carbon	Tdes, Pdes, P/F ratiodes	qCO2	CCD	qCO2 = 2.6474 + 0.0008Tdes + 0.2684P/F ratio – 0.1394(P/F ratio)2	0.879, 0.746	(27)
				CO2 recovery = 93.3768 + 0.0292Tdes + 9.4468P/F ratio – 4.8908(P/F ratio)2	0.880, 0.746
				productivity = 7.9418 + 0.0025Tdes + 0.8038P/F ratio – 0.4159(P/F ratio)2	0.880, 0.746
				H2 purity = 97.2066 + 0.0123Tdes + 4.0052P/F ratio – 2.0771(P/F ratio)2	0.878, 0.742
				CO2 purity = 90.7025 – 0.0949Tdes + 1.4473Pdes – 12.9794P/F ratio	0.867, 0.720
				rmaxdes = 29.0996 + 0.2078Tdes – 3.4356Pdes – 11.9295P/F ratio	0.804, 0.586
TEPA, b-CHT	αTEPA,CCO2, T, W/F ratio	qCO2	face-CCD, full factorial	Y = 5.65 – 0.37A + 0.23B + 0.23C + 0.47D – 0.17B × C – 0.26B × D – 1.3D2	n.d, 0.917	(28)
HMPD, AEEA	PCO2, CHMPD, CAEEA	αCO2, absorption rate	n.d.	(CO2 loading)1.78 = 9.52686 – 0.65341A – 0.15605B – 0.042155C + 1.72213 × 103D + 0.035598A × B + 7.89927 × 10–4A × C – 2.30339 × 106C × D + 0.042381A2 + 5.04678 × 10–5C2 – 2.88343 × 10–7D2	0.962, 0.949	(29)
				Ln(RA) = −5.73021 + 0.63342A + 1.84441B + 5.19352 × 10–3C + 5.5474 × 10–4D – 0.12781A × B + 5.24926 × 10–5A × D – 0.16195A2 – 0.53105B2 – 1.62696 × 10–7D2	0.969, 0.967
MEA, glycerol	CMEA,CglycerolT, Qg	αCO2	CCD	CO2 solubility = −56.73729 + 15.15341A12.24614B + 0.37652C – 0.066545D – 1.74354A × B + 7.69107 × 10–3B × D + 2.21104A2 + 1.19621B2	0.953, 0.935	(25)
DGA, DEPG	P, T, PCO2	qCO2, Qreb, Qcooling	CCD	power requirement = +76783.34 + 49159.26A + 33009.96B + 25702.65AB	0.999, 0.998	(24)
				cooling duty = +80574.82 + 50957.43A + 32256.25B – 4235.73C + 25293.69AB	0.997, 0.995
				recovered CH4 = +97.40 −3.87B +2.32C −0.35D + 2.10BC + 0.65CD	0.977, 0.944
				captured CO2 = +89.62 + 13.58A + 27.14B – 9.11C – 3.28B2	0.961, 0.907
MEA, DGA DEA, MDEA, TEA	ns, absorber, Camine, ns,stripper, Tstripper, Qreb	CO2 capture	full factorial, Box–Behnken	n.d.	n.d.	(18)
aminated activated carbons	Tamination	qCO2,qCO2,des	CCD	YS = 27.12 + 2.96x1 + 0.57x2 + 0.79x3 – 1.24x12 – 1.49x22 – 0.29x1x2 + 0.8x1x3	0.976, 0.964	(22)
				YD = 93.7 – 2.6x1 – 0.48x2 – 0.25x3 + 1.36x12 + 0.86x22 + 0.19x1x2 – 0.33x1x3	0.988, 0.982

n.d. = not defined.

In the present research, the principal objective was to investigate the effect of the modification parameters, Pz concentration, liquid flow rate, CO2 flow rate, and speed of stirrer, on the CO2 absorption performance such as CO2 loading, CO2 removal efficiency, absorption rate, and NCO of the modified absorption in a stirrer bubble column. Because the design and evaluation of statistical tests can be used for process modeling and optimization,[30−33] the RSM based on the CCD was used to design experiments and also developing the quadratic equation models that would predict the optimum conditions for desirable responses. Up to now, no analysis has been done on the optimization of absorption performance by Pz–H2O–CO2 in the stirrer bubble column using the RSM approach. The main feature of the bubble column is its absorption performance which is strongly affected by the operating conditions. For the analysis of the optimization for the operating condition of the Pz–H2O–CO2 system, the method of experimental design was applied. To comprehend the interactions between the variables, the statistical model has been developed.[34] To discover the optimum condition and the processes optimization under which the finest conceivable response has been investigated, RSM is the best-fitted statistical method[20] and the experiment numbers needed are decreased due to the use of it.

Materials and Method

Materials

In this research, the aqueous Pz solution was used as an absorbent to study of the CO2 absorption performance. The liquid chemical solvent was acquired from Merk Co., Germany with the >99% purity, and the solvent without extra purification was applied. To prepare the desirable aqueous solutions (0.1, 0.2, 0.3, 0.4, and 0.5 M), double-distilled water was used. The Testo 327-1, Germany gas analyzer, was applied to analyze the value of CO2 gases in the outlet of the column. The CO2 gas cylinder (99.999% purity) was prepared from Hor Mehr Tab Gas Co. and was used a compressor (300 l capacity, AP-301, Mahak) to the preparation of the air. Two flow meters were used to measure carbon dioxide and air in the entrance in term of l/min. The CO2 concentration was revolving from 12 to 44% by volume.

Apparatus and Procedure

Figure displays the schematic diagram of 10 cm ID and 38 cm height bubble column equipped with a mixer, a distributor of 30 mm height and 75 mm OD, and a manometer to set the liquid volume. The distributor holes were 1.0 mm ID and inclusive of six holes. The fresh Pz solution is fed into a feed tank. Then, the feed is fed into the upper column. The fresh solution was passed through the flow meter and the appropriate amount of liquid has been set to 3.0 l with a manometer in all experiments. The flow rate of solution and concentration of Pz solution ranges were 0.5 to 2.5 l/h and 0.1 to 0.5 M, respectively. The mixer was applied to improve the absorption time and contact area of bubbles and liquid in the far away areas of the column. For this purpose, a dimmer was used to set and control the stirrer speed. CO2 and air were released from the compressor and high purity cylinder, respectively, and carried to the bubble column with a separate flow meter. The individual regulator has been used to regulate CO2 and air pressure. The CO2 and mixed gas flow rate ranges were 0.6–2.2 and 5.0 l/min, respectively. Also, the electrical heating was applied to prohibit the hydrate formation in the gas pipeline. All tests were performed at ambient temperature, and atmospheric pressure. The CO2 unabsorbed was measured continuously by an analyzer in the treated discharge column.

Figure 1

Experimental system for absorption of carbon dioxide study.

Experiments Design

One of the suitable tools for analysis, assessment, and modeling of the result of different operating variables on the interaction is RSM. RSM was developed by Box and Behnken.[35,36] This expression was emanated of the graphical point of view created since the adaptability with the mathematical model, and its application has been extensively expressed in chemo-metrics contexts. RSM includes statistical methods and mathematical groups that are obtained from experimental models to fit the empirical data in communication to the experimental setup. To this end, the functions of quadratic polynomial were employed to explain the work studied.[37] Several steps in the RSM usage such as an optimization method (Figure ) are as follows: (1) the experimental design selection and carrying out the experiments due to the choice of the empirical matrix;[38] (2) the election of independent variables from the large results on the process via the empirical region definition and screening studies, according to the study purpose and the researcher experience;[33] (3) the statistical–mathematic processing of the experimental data created via the appropriate polynomial model;[39] (4) the model’s fitness assessment to experimental data;[40] (5) the urgent confirmation and replacement feasibility a substitution in orientation to the optimal; and (6) optimizing the value of each studied variables.

Figure 2

The scheme of study for RSM.

In the current work, to specify the optimum levels, the CCD of RSM was applied. CCD can be used to extend response models of second-order with finite factor numbers n (2 < n < 6). According to the CCD, the design of experiments was applied to extend an RSM by quadratic approximation model. In this work, the RSM together with the CCD was applied to simulate the CO2 absorption process. The four major independent variables, namely, liquid and CO2 flow rate, concentration of Pz, and speed of stirrer were considered. The all four independent variables parameter were considered at five various levels (−α, −1, 0, +1, +α). These factors were selected on the basis of our previous literature[12,41,42] and operated in the range of 0.1 to 0.5 M, 0.5 to 2.5 l/h, 1 to 2.2 l/min, and 0 to 400 rpm, respectively. According to available studies on CO2 absorption, the operating conditions and the levels of the considered variable for the CCD runs were selected and are introduced in Table .

Table 2

Range and Level of Independent Variables for CCD Runsa

				level
factors	tag	symbol	units	+α1	–1	0	+1	+α1
Pz concentration	CPz	X1	M	0.1	0.2	0.3	0.4	0.5
liquid flow rate	Ql	X2	l/h	0.5	1.0	1.5	2.0	2.5
gas flow rate	QCO2	X3	l/min	0.6	1.0	1.4	1.8	2.2
stirrer speed	w	X4	rpm	0	100	200	300	400

α = 2 (axial point or star for orthogonal CCD about four independent variables).

Therefore, the following quadratic equation was used with four independent variables:[18,43]where Y is the response function that is predicted (i.e., CO2 removal efficiency), β0 represents the constant term (offset), β and β express the coefficient of the linear and quadratic result, respectively, X and X represent the coded value of variable i, j, and β express the interaction coefficient effect, and ε represents the unanticipated parameters related to the experiments.[20,39]

The analysis of multiple regressions of the experimental data to fit eq was used by the applying the least-squares method, which it causes to generate the β coefficients with the least possible residual. The model acquired explains the response behavior in the empirical area as an independent variable agent. The CO2 capture based on the modified Solvay method was optimized using RSM. Numerical optimization was followed by analyzing the critical factors and their interactions. The design of runs was in accordance with CCD. The reaction time was considered in a screening survey and set to be 2 h because maximum CO2 capture was not at this time. The optimal liquid and gas flow rate, Pz concentration, and speed of stirrer speed for CO2 capture have been found by the response optimizer.

After obtaining information about each empirical level of the selected plan, it is essential to explain the response treatment similar to the values points study to fit a mathematical equation. That’s mean; there must be estimates the parameters b from the eq . Therefore, in the notation of matrix, eq can be express as[44]where X is the chosen experimental design matrix, e is the residual, y and b are the response and the model parameter vectors, respectively, and m and n indicate the lines and columns numbers from the matrices, respectively. Equation is solved by utilizing a statistical method named the method of least square.[45] The least-square method is a regression analysis skill exploited to fit a model to a set of empirical data producing the best residual feasible. In the following, because mathematical alteration in eq , a vector b can be calculated as[23]

The mathematical model can sometimes rarely examine the experimental domain after fitting the performance with the data. The further reliable method to appraise the model quality is using of analysis of variance (ANOVA). The ANOVA main mentality is to contrast the change because of the variation of the variable amount combined with the change because of accidental errors intrinsic to the generated errors as a result of the response computations. From this analogy, it is practicable to consider the regression importance applied to anticipate answers to evaluate the empirical variance origins. In the ANOVA, the diversity of the datasets is evaluated with a scattered study. An estimate of the deflection (d) that every seeing (y) or its repeats (y) here in connection to the media (y̅), or, further clarification, the quadratic of this deflection is introduced in eq

The all sum of the square seeing deflections in communication with the media is named the total sum of the square (SStot); it may be differentiated in the sum of the square because of the coordinated model, in this way, because of the regression (SSreg) and the residuals produced with the model (SSres), as demonstrated below[39]

As the central point repeats are created, it can be feasible to assess the net error related to replication. Afterward, the residuals sum of the square can be divided into two parts: the pure error sum of the square (SSpe) and the lack of fit sum of the square (SSlof), as demonstrated below[39]

During the sum of the square division for all variation, origin (residual, regression, pure, total, and lack of fit error) is created with its degrees of freedom (d.f.)-related numbers; the “media of the square” (MS) are acquired. The degree of freedom numbers for these variation origins are computed by the statements demonstrated in Table , where p is the number of the mathematical model coefficients and m and n show the number of levels used and total observations in the research, respectively. Equations relevant to the variation origin for the computing of MSs and SSs are also provided in Table .[36,37]

Table 3

Variance Analysis for a Fitted Mathematical Model to an Empirical Data Set Using Multiple Regressionsa

variation source	sum of the square	degree of freedom
regression		p–1
residuals		n–p
lack of fit		m–p
pure error		n–m
total		n–1

m, total levels number in the plan; n, observations number; p, number of model parameter; y̅, overall media; ŷ, estimated value for the level i by the model; ®, repeats media carried out in the same set of empirical conditions. y, repeats performed in each single levels.

To determine if a parameter is important, a p-value test with at least a 95% confidence level has been used for empirical consequences. The determination coefficient corrected with the absolute average deviation (AAD) and variables number (Adj-R2) was deliberated in order to survey the model correctness. Adj-R2 should be near to 1.0 and the AAD should be as small as feasible between the observed and predicted. Adj-R2 indicates the ratio of data variables defined by the model. The AAD represents the deviations between the calculated and empirical values and it is calculated by the following equation means[45]where n is the experiment numbers and y and y are the experimental and calculated responses, respectively.

Occasionally, a small subset of the data has a disproportionate effect on the regression model. In other words, predicting or estimating parameters probably depends more on the influential subset than the majority data. Some parameters are used to influence diagnostics through the following equations.where, y, , and e are the measured response data, the predicted value from the model, and error value, respectively. Leverage (h) is the ability of a design point to impression the model coefficients fit, given their position in the design space. Leverage is a point that varies from 0 to 1 and shows how much a design point influences the model’s values. A leverage of 1 means that the predicted and experiments value are exactly equal, that is, the residual will be 0.where X and H are the model matrix of n rows and p columns and an n × n symmetric matrix, respectively. The diagonal elements of the H matrix are the leverages. Leverage indicates the fraction of the error variance, along with the point approximated, and carried into the model. The numbers of estimated standard deviations separating the actual and predicted values named internally studentized residual as

The externally studentized residual was computed by leaving each run, out of the analysis, one at a time and estimating the response from the remaining runs.where n and p are the number of runs minus the one being left out and the number of terms in the model including the intercept, respectively. The t-value was defined as the number of standard deviations difference between the actual response and predicted value. A value associated with the t-distribution that measures the number of standard deviations separating the parameter estimates from zero.

DFFITS is the studentized difference between the predicted value without observation i and the predicted value with observation i that defined aswhere

DFBETAS is a statistical measure of impression based on the different in coefficients of model (betas) that occurs when a run is removed and displays the impression the ith seeing has on each regression coefficient. The DFBETAS is the standard errors number that the jth model coefficient alters if the ith observation is deleted. A great value of DFBETAS infers that the ith seeing has further effect on the jth coefficient.

Cook’s distance (D) is a square yield of a monotonic function of the leverage and the ith internally studentized residual[22]

The equation above represents that D contains the squared studentized residual, which indicates how well the model fits the ith observation yi and a component that measures how far that point is from the rest of the data. If the value of D is significantly less than 1, omitting the ith case cannot change the regression coefficients estimated very well.

Theoretical Basis

CO2 removal efficiency determined as the mole of CO2 captured per moles of CO2 loaded to the column is as follows[46,47]where yCO and yCO are CO2 removal efficiency, mole fraction of CO2 in inlet and outlet columns, respectively, and R is the CO2 removal efficiency. The bubbles were supposed to be oblate-ellipsoidal and specified by the minor axis (e) and major axis (E). The dimensions a bubble relevant with a diameter equivalent to a sphere with the same ellipsoid volume was calculated as follows[48,49]

The volume surface mean diameter or Sauter mean diameter (d32) was determined with the data computed to get an adequate diameter by means of eq .[50]where n is the bubbles number which have an equivalent diameter d. The changing the volume in the column was specified by the seeing of the fluid level and the alteration generated when the gas phase is existing. The gas holdup (εG) was computed by the expansion method of volume (eq ).[12]where Vl is the volume of liquid before the gas entrance and ΔV is the solution volume expansion after the gas is blown through the liquid, computed from the liquid level change. The volume variation of gas–liquid dispersion was observed with respect to the seeing changes in the liquid level and its increase after entering the gas. Thus, the specific interfacial area was calculated by using the gas holdup and the Sauter mean diameters as eq .[48]

The gaseous mixture (air–carbon dioxide) was blown through the sparger disc into the liquid phase, and the liquid is conducted through the counter-currently. In all experiments, the absorption performance was done in 1 h, and it was assumed that the liquid phase does not enter the gases, and the air was not solved in the solution. The CO2 absorption rate (ΔG) can be easily calculated as the competition in CO2 concentration through the column at the pressure and temperature constant with the following equationwhereρg,in and Qg,in are the density of inlet gases and inlet gas flow rate, respectively. Also, yCO and yCO are the CO2 mole fraction in the inlet and outlet of the column, respectively. In each test, different points of data are prepared in a steady-state flux with different partial pressures of the gas phase. Because it is hard to obtain the concentration of CO2 in the gas–liquid interface, overall mass transfer coefficient (KG) and equilibrium CO2 partial pressure of the liquid phase (pCO*) were used. The CO2 mass-transfer flux (NCO) into the aqueous Pz solution at the bubble column is given by the expression[51]where pCO and pCO* are the partial pressure of CO2 in the gas phase and solution bulk, respectively. And also, KG is the overall mass-transfer coefficient. At the above equation, the pressure difference term can be expressed using the log mean average CO2 partial pressure at the inlet and outlet columns[52]

Because the solution or equilibrium CO2 partial pressure is unknown, the amount of pCO* term in the case of CO2 unloaded absorbent can be omitted. Therefore, the log mean average CO2 partial pressure will be equal pCO. Thus, the overall mass transfer coefficient, KG, can be calculated by the following expression

Reaction Kinetics

According to our previous studies,[11] numerous chemical reactions happen in a bubble column. The possible reactions are summarized in Table .

Table 4

Reaction Kinetics of CO2 in the Pz Solution

For kinetic evaluation of the system, the understanding of all species concentration in the solution is required. The details and calculation method are in our previous work.[42] The CO2 loading (αCO) is used to compare the amount of CO2 absorption in the solution and this parameter is determined as follows[5]

Result and Discussion

Design of Experiment and Statistical Analysis Method

The RSM was used to analyze the effect of several parameters on the CO2 absorption performance. The independent level variables are the different values that should be determined by the experiments. All these independent variables were examined at five levels. Before applying the RSM, an experimental plan was selected that specified what tests must be done in the experimental area under survey as a set of various combinations of the independent variable levels. In this study, the effect of the four variables [Pz concentration (X1), liquid flow rate (X2), CO2 flow rate (X3), and stirrer speed (X4)] on the CO2 absorption process was appraised in terms of CO2 loading, CO2 removal efficiency, and NCO. This includes 30 tests, which are demonstrated in Table , consisting of 24 factorial points and 6 additional repeats at the design center in which it was conceivable to approximate the experimental error related by the replications.

Table 5

Coded and Actual Values of the Variables Used to Design the Experiment

run	variables				response			run	variables				response
no.	X1	X2	X3	X4	% R	α	NCO2a103	no.	X1	X2	X3	X4	% R	α	NCO2a103
1	0	0	0	0	73.6	0.053	9.52	16	–1	–1	1	–1	76.8	0.072	12.30
2	0	0	0	0	73.7	0.056	9.43	17	2	0	0	0	78.4	0.041	12.42
3	–1	–1	–1	1	72.6	0.970	6.34	18	1	–1	–1	1	75.9	0.082	10.18
4	0	0	0	0	73.8	0.054	9.53	19	1	–1	–1	–1	76.2	0.080	10.09
5	1	–1	1	1	76.2	0.870	11.70	20	–1	1	1	1	77.6	0.099	11.82
6	0	0	0	0	73.8	0.054	9.46	21	0	2	0	0	80.4	0.078	12.56
7	–1	–1	–1	–1	73.6	0.530	9.24	22	1	1	–1	1	81.2	0.056	13.11
8	0	0	0	2	73.1	0.520	9.13	23	0	–2	0	0	73.8	0.052	9.93
9	–1	1	–1	–1	74.5	0.580	9.27	24	1	1	–1	–1	78.1	0.048	11.61
10	0	0	0	0	73.7	0.055	9.44	25	0	0	0	–2	73.1	0.049	9.22
11	1	1	1	1	76.7	0.048	11.80	26	–2	0	0	0	70.2	0.152	8.84
12	1	–1	1	–1	78.6	0.069	14.20	27	1	1	1	–1	80.2	0.047	12.86
13	0	0	0	0	73.8	0.055	9.45	28	0	0	2	0	77.2	0.056	10.22
14	–1	–1	1	1	77.4	0.054	13.70	29	–1	1	1	–1	80.9	0.072	14.20
15	0	0	–2	0	70.5	0.041	6.80	30	–1	1	–1	1	79.6	0.680	13.70

The unit of α, and NCO are mol/mol, and mol/m2·s, respectively.

The RSM suggested a quadratic model that relates for four CO2 absorption processes to the independent variables (eqs –31 in Table ). The CO2 removal efficiency, CO2 loading, CO2 absorption rate, and NCO are the response, and X1, X2, X3, and X4 are the coded terms of the investigated parameters. The value and sign of each correlation phrase coefficient display the decreasing and increasing effects of the response parameters. Given the proposed correlation for CO2 removal efficiency, the relative significance of the independent agents are as follows: X1 (i.e., Pz concentration) with value of −1.31 for the coefficient, X2 (i.e., liquid flow rate) with value of −5.03 for the coefficient, X3 (i.e., CO2 flow rate) with value of +3.11 for the coefficient, and X4 (stirrer speed) with value of +2.12 for the coefficient. The maximum increasing impact of the dependent factor is +2.06 that is related to the interaction between X1 and X2 parameters. The coded factors in the quadratic model can be applied to forecast the response levels given by each agent. By default, the low levels and upper levels of the factors are coded as −2 and +2, respectively. The equations of coded were beneficial for knowing the relative effect of the parameters by comparing the coefficient of factors. The equation of regression for the response variables in coded terms acquired from the empirical data based on the interaction influences between the factors is shown in Table .

Table 7

Equations in Terms of Coded Factors

parameter	correlation
CO2 removal efficiency	28
CO2 loading (mol/mol)	29
absorption rate	30
mass transfer flux (mol/m2·s)	31

Table 6

Estimated Coefficients in Terms of Coded Factors

	% R	loading, mol/mol	ΔG, g/min	NCO2, mol/m2·s
constant	+78.86	+0.0678	1.86	+0.0110
X1	–1.31	–0.0792	–0.0435	+0.0002
X2	–5.03	–0.0149	–0.1363	–0.0005
X3	+3.11	+0.0208	0.8288	+0.0044
X4	+2.12	+0.0053	0.0572	+0.0002
X1X2	+2.06	+0.0003	0.0529	–0.0001
X1X3	+0.1150	–0.0083	0.0250	+0.0002
X1X4	–1.01	–0.0030	–0.0281	–0.0003
X2X3	+0.0000	+0.0000	0.0000	+0.0000
X2X4	–2.96	–0.0015	–0.0787	–0.0002
X3X4	+0.0000	+0.0000	0.0000	+0.0000
X12	+1.35	+0.0522	0.0389	+0.0000
X22	+4.71	+0.0136	0.1291	+0.0007
X32	–0.4716	+0.0012	0.0608	+0.0000
X42	–2.24	–0.0008	–0.0599

Analysis of Variance (ANOVA)

ANOVA and the statistical parameters for the CO2 removal efficiency, CO2 loading and NCO from the CCD are presented in Table . Analysis of the model fitness was done by applying a lack of fit and an ANOVA test. An experimental data will fit the model well if it shows a considerable regression and a no considerable lack of fit. The statistical importance was appraised applying the interactions, factors, and p-value of the model. As can be seen from Table , the model p-value for CO2 removal efficiency is 0.0003 and the model p-value for both CO2 loading and NCO is less than 0.0001, which shows the model parameters are considerable. It must be mentioned that a p-value less than 0.050 indicates that the model is significant in the response, and the value lower than 0.001 demonstrates that the model is highly significant in the response. p-values > 0.1 indicate that the model is insignificant.[20,53,54] Moreover, the model terms have a considerable result on the response because of the large F-value. The F-value for three CO2 removal efficiency, CO2 loading, and NCO were obtained to be 12.8, 1193.38, and 96.62, respectively.[55] The model F-value for CO2 removal efficiency, CO2 loading, and NCO were 12.80, 1193.38, and 96.62, respectively, which points that the models are meaningful. There is only less than 0.01% probability that this large amount of F-value may occur because of noise.

Table 8

ANOVA Results and Statistical Parameters of the Developed Quadratic Correlation Versus; Concentration of Pz (X1), Solution Flow Rate (X2), CO2 Flow Rate (X3), and Speed of Stirrer (X4)

	CO2 removal efficiency					CO2 loading, mol/mol					NCO2, mol/m2·s
source	sum of squares	degree of freedom	mean square	F-value	p-value	sum of squares	degree of freedom	mean square	F-value	p-value	sum of squares	degree of freedom	mean square	F-value	p-value
model	159.36	12	13.28	12.8	0.0003	0.0435	12	0.0036	1193.3	<0.0001	0.0001	12	8.786 × 10–6	96.6	<0.0001
X1	1.68	1	1.68	1.6	0.2345	0.0062	1	0.0062	2036.3	<0.0001	4.198 × 10–8	1	4.198 × 10–8	0.461	0.5139
X2	5.01	1	5.01	4.8	0.0556	0.0000	1	0.0000	14.5	0.0041	4.718 × 10–8	1	4.718 × 10–8	0.518	0.4896
X3	21.82	1	21.82	21.0	0.0013	0.0010	1	0.0010	320.8	<0.0001	0.0000	1	0.0000	480.6	<0.0001
X4	8.24	1	8.24	7.9	0.0201	0.0001	1	0.0001	16.9	0.0026	6.620 × 10–8	1	6.620 × 10–8	0.728	0.4156
X1X2	0.8166	1	0.8166	0.787	0.3981	1.594 × 10–8	1	1.594 × 10–8	0.005	0.9438	7.077E-10	1	7.077 × 10–10	0.007	0.9316
X1X3	0.0150	1	0.0150	0.014	0.9070	0.0001	1	0.0001	25.7	0.0007	5.509 × 10–8	1	5.509 × 10–8	0.605	0.4563
X1X4	1.87	1	1.87	1.8	0.2124	0.0000	1	0.0000	5.3	0.0468	1.829 × 10–7	1	1.829 × 10–7	2.0	0.1898
X2X3	0.0000	0				0.0000	0				0.0000	0
X2X4	5.13	1	5.13	4.9	0.0533	1.332 × 10–6	1	1.332 × 10–6	0.438	0.5244	2.674 × 10–8	1	2.674 × 10–8	0.294	0.6008
X3X4	0.0000	0				0.0000	0				0.0000	0
X12	3.72	1	3.72	3.6	0.0907	0.0056	1	0.0056	1841.8	<0.0001	3.575 × 10–9	1	3.575 × 10–9	0.039	0.8472
X22	4.94	1	4.94	4.8	0.0571	0.0000	1	0.0000	13.5	0.0051	1.247 × 10–7	1	1.247 × 10–7	1.4	0.2717
X32	0.3643	1	0.3643	0.351	0.5681	2.403 × 10–6	1	2.403 × 10–6	0.791	0.3968	1.530 × 10–9	1	1.530 × 10–9	0.017	0.8996
X42	12.91	1	12.91	12.4	0.0064	1.450 × 10–6	1	1.450 × 10–6	0.477	0.5069	1.917 × 10–8	1	1.917 × 10–8	0.211	0.6570
residual	9.34	9	1.04			0.0000	9	3.036 × 10–6			8.183 × 10–7	9	9.093 × 10–8
lack of fit	5.69	8	0.7116	0.195	0.9466	0.0000	8	3.166 × 10–6	1.5	0.5504	6.190 × 10–8	8	7.737 × 10–9	0.010	1.0000
pure error	3.64	1	3.64			2.000 × 10–6	1	2.000 × 10–6			7.565 × 10–7	1	7.565 × 10–7
cor total	168.69	21				0.0435	21				0.0001	21

Fit Statistics

It can be derived from the determination coefficient (R2 = 0.945, 0.999, and 0.992 for CO2 removal efficiency, CO2 loading and NCO, respectively), which indicates that the data fit the model very well. Namely, 94.5, 99.9, and 99.2% of the total variation of CO2 removal efficiency, CO2 loading, and NCO, respectively, were justified in reply to the offered quadratic correlation (Table ). As remarked by Joglekar and May,[56] for the data fit the model very well, the correlation coefficient must be at least 0.8. The high value of R2 indicates good compatibility between the actual and calculated results within the wide range of the experiments (see Figure ). In this work, the regression equation of the determination coefficient (R2) was above 0.94 for all three response variables, indicating that the polynomial can properly explain the communication between the interactions, factors, and response. The actual against predicted value plot for CO2 removal efficiency rise is shown in Figure a. As seen in this figure, the residuals were generally placed on a straight line and normally distributed. The actual value and predicted value for all responses were close to each other (not shown). Therefore, this observation shows that these models were suitable for the empirical data, and they can be applied to the analysis and prediction of the absorption performance. The adequate precision (adeq Precision) of this correlation for CO2 removal efficiency, CO2 loading, and NCO were 14.40, 129.49, and 41.30, respectively (adeq precision >4) that represents that the model noise ratio is located in the favorable range.[31] A ratio or adequate precision greater than 4 is favorable. Because of the ANOVA analysis results and Figure a, the offered model for all three systems is valid.

Table 9

ANOVA for Response Surface Quadratic Model

factors	% R	CO2 loading, mol/mol	NCO2, mol/m2·s
R2	0.945	0.999	0.992
adjusted R2	0.871	0.999	0.982
predicted R2	NAa	NAa	NAa
adeq precision	14.403	129.488	41.305
std. dev.	1.0200	0.0017	0.0003
mean	77.2200	0.0653	0.0120
C.V. %	1.32	2.67	2.51

Case(s) with 1.0000 leverage: PRESS statistic and pred R2 not defined. The deviation error for R2, adjusted R2, adeq precision are 0.0001 and deviation error for std. dev., mean, and C.V. % are 0.00001, 0.00001, and 0.001, respectively.

Figure 3

The CCD Predicted value of CO2 removal efficiency vs; (a) actual absorption, and (b) externally studentized residuals, and externally studentized residuals vs; (c) normal probability, and (d) number of run.

As known, the residuals from the least-squares are a significant instrument for the investigation of the adequacy of the models. The hypothesis of constant variance at distinct levels was considered at Figure b by drawing the predicted response values versus residual as acquired from the model. As seen in these figures, there was a random distribution of points up and down the x-axis between +4.594 and −4.594 without any trends. This conclusion surveys the reliability and adequacy of the models, and a constant variance was seen through the response range. As an additional tool to check the adequacy of the final model, the normal probability chart of the studentized residuals has been shown in Figure c. If the model is sufficient, the points on the normal probability charts versus the residuals must form a straight line. On the other hand, as an extra useful tool to examine the suitability of the ultimate model, the normal distribution probability charts of the studentized residuals were shown in Figure c. If the model is sufficient, the points on the normal probability charts versus the residuals must form a straight line. In these charts, the points pursue a direct line and approving that the errors were distributed normally with mean constant and zero but unclear variance as the fundamental hypothesis of the studies. And also, the charts of different variables versus residuals such as run order, predicted values, and factors were analyzed (not shown). There was no reason to doubt any independence contravention or hypothesis of constant variance, as all plots represented a closely permanent variance over the response ranges. Therefore, all charts seemed to be favorable and there was no reason to deny the results. Meanwhile, the residual plots for CO2 removal efficiency is shown in Figure d. Figure d is corresponding to the removal efficiency, which reveals that there was no predictable pattern observed because all the run residues lay on or between the levels of −4.594 to 4.594.

Interaction of Factors

In this work, the version 11.0 of Design Expert was applied to represent three-dimensional (3-D) response surfaces and partition the dataset draws in Table . The 3-D curves of response surface to understand the interaction of the variable parameters (i.e., concentration of Pz, solution flow rate, CO2 flow rate, and the speed of stirrer) and to locate the best level of each variable for maximum response in CO2 removal efficiency, CO2 loading, and NCO were drawn in Figures –6. And also in these figures, the plots were applied to the detection of the best range of each four variable factor. The label lines on the plot, also the various colors of the plots and response surfaces, represented a degrees variety of interaction based on the CO2 removal efficiency, CO2 loading, and NCO [see eqs , 29 and 31]. The mutual influence of the two variable parameters on the removal efficiency was more considerable than that of the two another one showed in Figure . The mutual influence of the liquid flow rate and CO2 concentration was similar to that of the Pz concentration and solution flow rate. Anyhow, the curved slope on the three-dimensional response surface (see Figure a,d) displayed that the concentration level of CO2 and Pz a higher effect on the removal efficiency compared with the speed of stirrer and gas flow rate level of setup. As a result, these two parameters played an important task in impressing the CO2 removal, which became known to be compatible with the outcomes acquired from the regression model ANOVA. In the circumstances of this research, the main reason for increasing the removal efficiency with the CO2 flow rate comes from the increase in the number of CO2 molecules and causes to increase the reaction between the CO2 and free Pz molecules and leads to an increase in the CO2 removal efficiency. On the contrary, as seen from Figure c, the removal efficiency was increased to an optimum value and then decreased with the increase in the speed of the stirrer. By increasing the speed of stirrer, the CO2 bubbles were broken to the small ones and cause to increase the contact area between CO2 and Pz molecules. But, by further increasing the stirrer speed (>200 rpm), the removal efficiency decreases due to the phenomenon of coagulation. Furthermore, according to the RSM, the removal efficiency decreased favorably (blue area in Figure d) when the liquid flow rate increased to a given level, which proposes that Pz concentration remaining the main parameter in controlling the CO2 removal efficiency. According to the 3-D response surface displayed in Figures and 6, Figure c displayed that there was a considerable relationship between the CO2 and liquid flow rate. As seen from this figure, the mass-transfer flux was improved with increases in the CO2 flow rate but decreases with the liquid flow rate. And also, the mass transfer flux attained the maximum value (approximately 0.01599 mol/m2·s) when the gas flow rate was at their maxima within the experiment boundaries. Furthermore, the interaction importance between the liquid flow rate and stirrer speed was the same as that between liquid flow rate and Pz concentration (see Figure a), and the mass transfer flux increased weak with continual increases in both variable parameters.

Figure 4

Response surface plots of CO2 removal efficiency as a function of (a) solution flow rate and Pz concentration, (b) CO2 flow rate and Pz concentration, (c) stirrer speed and Pz concentration, (d) solution flow rate and CO2 flow rate, (e) solution flow rate and stirrer speed, and (f) stirrer speed and CO2 flow rate.

Figure 6

Response surfaces plots of CO2 loading as a function of (a) solution flow rate and Pz concentration, (b) CO2 flow rate and Pz concentration, (c) stirrer speed and Pz concentration, (d) CO2 flow rate and solution flow rate, (e) stirrer speed and solution flow rate, and (f) stirrer speed and CO2 flow rate.

Figure 5

Response surfaces plots of mass transfer flux as a function of (a) solution flow rate and Pz concentration, (b) CO2 flow rate and Pz concentration, (c) CO2 flow rate and solution flow rate, and (d) stirrer speed and CO2 flow rate.

Figure a indicates that the loading increased and decreased with continual increases in the solution flow rate and concentration of Pz, respectively. However, it was obvious from this figure that there is the weak interaction between the CO2 loading and liquid flow rate. Figure d indicates that interaction importance of CO2 flow rate on the loading was great. By increasing the flow rate of the CO2 because of the increase in the number of the empty CO2 molecules in the solution, the chemical reaction rate between the CO2 and Pz increased and caused to increase the loading. It can be found from Figure e that the loading increased with the increase of the speed of stirrer because of broken bubbles to small ones and caused to increase in the contact area.

Best Absorption Operating Parameters

One of the purposes of this work was to observe independent variable (i.e., CPz, Ql, QCO, and w) combination somehow to get the maximum absorption performance. Because of the performed tests, the RSM optimization proposed various combinations of the variables to get over 95% absorption performances. In this way, an optimization run with 97.6% of CO2 removal efficiency was selected. This optimal point can be obtained in the following conditions: 0.162 M of Pz concentration, 0.502 l/h of liquid flow rate, 2.199 l/min of CO2 flow rate, and 68.898 rpm of stirrer speed. At optimal points, the absorption rate, CO2 loading, and NCO were obtained 2.980 g/min, 0.198 mol/mol, and 0.0164 mol/m2·s, respectively. Three repeat experiments were carried out under the suggested optimal conditions. As seen in Table , the average experimental was in near assent with the anticipated. On the other hands, the validity of the proposed model is confirmed again.

Table 10

Repeatability and Validation Test for the Experimental Absorption Performance Carried Out under Optimal conditionsa

	experimental				predicted
	% R	G, g/min	CO2 loading, mol/mol	NCO2, mol/m2·s	% R	G, g/min	CO2 loading, mol/mol	NCO2, mol/m2·s
RUN 1	96.8	2.968	0.197	0.0164	97.6	2.980	0.198	0.016
RUN 2	97.7	2.972	0.196	0.0164
RUN 3	97.6	2.974	0.197	0.0164

The deviation error for % R, G, CO2 loading, and mass transfer flux are 0.01, 0.0001, 0.0001, and 0.00001, respectively.

Using numerical optimization, a favorable value for each input parameter and response can be chosen. Here, the feasible input optimizations that can be chosen contain the minimum, maximum, range, none (for responses), target, and set so as to appoint an optimized output value for a given set of conditions. In this work, the variables of input data were given to determine ranged values because the response was planned to gain a maximum. with these conditions, the maximum achieved CO2 removal efficiency, absorption rate, loading, and mass transfer flux were 97.93%, 3.129 g/min, 0.258 mol/mol, and 0.016447 mol/m2·s, respectively (see Table ) at above-mentioned conditions.

Table 11

Optimization of the CO2 Adsorption by RSM-CCD

parameter and response	constrain	low	high	optimum condition
CPz (mol/l)	in range	0.1	0.5	0.152
Ql (l/h)	in range	0.5	2	0.63
QCO2 (l/min)	in range	1	2.2	2.16
W (rpm)	in range	0	300	247.9
CO2 loading (mol/mol)	maximize	0.024	0.198	0.258
NCO2 (mol/m2·s)	maximize	0.00636	0.01599	0.01645
CO2 removal efficiency (%)	maximize	70.64	82.26	97.93

Deviation Plots

The deviation plot indicates the overall influence of all process parameters on the response function, and the center point (0) was the middle point of the operating range. A perturbation plot to compare the effect of all four operating parameters (Pz concentration, CO2 and liquid flow rate and stirrer speed) at the reference points is demonstrated in Figure . It was observed from Figure a that the CO2 loading decreases with the increase of the Pz concentration (A) and liquid flow rate (B) due to the increase of Pz in the solution. However, the reduction rate of loading was further for Pz concentration in comparison to the liquid flow rate. It is also clear that the CO2 loading rises with an increase in the CO2 flow rate (C) due to increase CO2 agents in the interface and then in solution. It can be noticed that from this plot, the stirrer speed (D) has also the same effect due to the increase of the contact area because of the bubbles broken into small bubbles. It is also evident from the Figure b that the NCO rises with the increase of the CO2 flow rate (C) and stirrer speed (D), but the effect of the CO2 flow rate was significant. And also, the increase of the flow rate had a negative effect and the effect of Pz concentration was low. It can be observed from Figure c that the effect of parameters on the CO2 removal was the same CO2 loading.

Figure 7

Deviation curves for responses with coded factors; (a) CO2 loading, (b) mass transfer flux, and (c) CO2 removal efficiency.

Conclusions

In this work, the influence of numerous important operating parameters such as Pz concentration, liquid flow rate, CO2 flow rate, and speed of stirrer on CO2 loading, CO2 removal efficiency, and NCO has been investigated. We optimized the piperazine-based CO2 capture process to maximize the absorption performance using simulation–optimization RSM. The RSM with CCD was used to the development of appropriate model by the least-squares method. The deviation errors obtained for all absorption performance less than 0.0001 and the results were the following:

From the regression analysis of variables, it has been found that the models were successfully tested and all verified with empirical data and determined the values of the optimum variables to maximize absorption performance.

The model p-value for CO2 removal efficiency, CO2 loading, and NCO were less than 0.05 and that points all three models are significant. And also, the model F-value for these three absorption performances were 12.80, 1193.38, and 96.62, respectively, and it indicates only less than 0.01% probability that this large amount of F-value may occur because of noise.

The process optimization was performed and the empirical values acquired for the CO2 capture were found to agree satisfactorily with the model values. The optimal absorption conditions were obtained at the Pz concentration of 0.1 M, solution flow rate of 0.56 l/h, mixed gas flow rate of 2.16 l/min, and stirrer speed of 298 rpm. In these conditions, the experimental yield of CO2 removal efficiency, CO2 loading, and NCO were 97.9%, 0.258 mol/mol, and 0.0164 mol/m2·s, respectively. The results of the comparison of predictions with experimental data (% AARD = 3.78–18.14, MSE = 0–6.784 and R2 = 0.855–0.953) determined that the Buckingham π theory has the potential to properly predict of reactive absorption performance over a wide range of experimental conditions.