CC BY
27
DOI: 10.17277/amt.2017.03.pp.051-060
Optimization of Adsorption Processes with Cyclic Variable Pressure
in Gas Mixture Separation
E.I. Akulinin*, A.A. Ishin, S.A. Skvortsov, D.S. Dvoretsky, S.I. Dvoretsky
Tambov State Technical University, 106, Sovetskaya St., Tambov, 392000, Russia * Corresponding author: Tel. +7 (909) 231 40 61. E-mail: [email protected]
Abstract
The paper considers the problems of optimization of the regime variables (pressure at the adsorption stage and the time of the adsorption cycle), and automation of the adsorption separation process of the gas mixture and production of hydrogen in a 4-adsorption plant for pressure swing adsorption. Since the optimization problem belongs to the class of nonlinear programming problems, penalty methods and methods of sequential quadratic programming have been used for its solution. A two-level SCADA system for adaptive optimization and control has been developed to solve the optimization problem and automatically control the hydrogen production process. The results of simulation studies of the effectiveness of the SCADA control system with a stepwise change in the disturbances (concentration of carbon dioxide, temperature and pressure of the gas mixture) in the feed of the pressure swing adsorption plant are presented.
Keywords
Pressure swing adsorption; gas mixture separation; hydrogen; carbon dioxide; process dynamics; mathematical model; optimization; disturbances; control.
© E.I. Akulinin, A.A. Ishin, S.A. Skvortsov, D.S. Dvoretsky, S.I. Dvoretsky, 2017
Introduction
The formulation of optimization and automation problems begins with the analysis of its functioning as a control object that involves the study of the static and dynamic properties of the process, identification of input, main disturbing and control actions, output (controlled) variables, and finding acceptable ranges for their change. The analysis of the adsorption
separation of gas mixture and hydrogen production in a 4-adsorption pressure swing adsorption (PSA) plant as a control object conducted in [1, 2] made it possible to determine (Fig. 1):
- input variables x (disturbing actions) of PSA
plant (composition yin = (, y2", y™ ), temperature Tgn, consumption Gin and pressure Pin of gas
K
Pa
ads
ads
Control variables u
Fig. 1. Structural diagram of the PSA plant as a control object in hydrogen production
mixture in the plant feed, pressure on the production PH"2 and discharge Pqo2 outlets of the PSA plant
-pout\ ; ^ v — <T,in fin fin pin pout pout 1 . PH2 A ie x = {y , Tg , G , P , PH2, PCO2};
- control variables u pressure Pads and cyclic
time Tads of adsorption stage ), U. u = {Pads, Tads }
- output variables y of the PSA plant
(compositions yout = (y{°ut, y2ut, y^ut), consumptions
Gout, Gp and temperature T°ut of the gas mixture at
the PSA plant outlet, plant productivity Q = y1utGp,
where Gp = Gout - Gdes, Gdes is volumetric flow rate of hydrogen-rich gas directed to the regeneration of
adsorbent, i.e. y = {yout, Gout, Gp, Tout, Q}.
Mathematical modules for the hydrogen production process in the 4-adsorption PSA plant
A mathematical description of the dynamics of the adsorption process in the PSA plant adsorbers for hydrogen production [1] can be given in the form of a block diagram of the "Adsorber" mathematical module (Fig. 2). The mathematical model differs from the known ones, as it takes into account the impact of mass and heat transfer processes and the velocity of a multicomponent gas mixture flow on the kinetics of mixed-diffusive transport of adsorbent (H2, CO2, CO), and allows calculating the profiles of component concentrations and temperatures in the gas and solid phases, pressure and velocity of the gas mixture by the adsorbent height as a function of time. The tuning parameters of the mathematical model are the mass
transfer coefficients Pk (1 - H2, 2 - CO2, 3 - CO) and
formal kinetic parameters Pk and 9 of the equation of mass transfer of adsorbent (H2, CO2, CO) from the gas phase to the solid phase of the adsorbent (through the phase interface):
d~0L = tgh(9(v g-vg)) +1) + F,
dt 2
k = H2, CO2, CO:
where F is the right-hand side of the kinetics equation
of non-stationary convective (external) mass transfer,
11 * 1 Fk =Pk (ck -ck); Pk is the mass transfer factor
referred to the concentration of adsorbent in the gas
phase, 1/s; ck is molar concentration of the k-th
component of the gas mixture, mol/m3; ak is sorption
value of the k-th component in the adsorbent, mol/m3,
c\ is the adsorption concentration at the phase interface or the equilibrium current adsorption value
3 2
ak, mol/m , Fk is the right-hand side of the kinetics equation inside the diffusion adsorption process, F-2 = $2{a*k-ak ); P2 is the kinetic coefficient, 1/s; a*k is the adsorption value, which is the equilibrium
current concentration of adsorbent
in flow of the
gas mixture on the outer surface of the granules,
3 *
mol/m ; vg is velocity of the gas mixture, m/s; vg is
the critical velocity of the gas mixture, which determines the transition from the diffusion region (external mass transfer) to the kinetic region (internal diffusion in adsorbent granules) of adsorption transfer, m/s.
A specific type of equations for determining the tuning parameters of the model is given in [2, 3]. However, the numerical values of the parameters obtained from these equations are recommended to be used as initial approximations for solving the inverse coefficient problem using the equations
of the mathematical model [3]: vg =0.022 m/s;
PH2 = 0,816 1/s; PCo2 =0.021 1/c; PCo = 0.084 1/s;
PH2 = 0.73 1/c; PCo2 =0,012 1/s; PCo = 0.059 1/s, 9 = 18.2.
The state of the valve is described by the components of the vector o that are Boolean variables taking the values 0 or 1. The specific form of the function o = o(t) is determined using the valve switching cycle of the PSA plant [1, 2]. A mathematical description of the operating mode of the valve system of the 4-adsorption PSA plant for hydrogen production can be presented in the form of a block diagram of the mathematical module "Valve system" (Fig. 3).
In Fig. 2, the following notation is adopted: s, s0 - are porosity coefficients of the adsorbent with and without the porosity of the granules, respectively, m3/m3; Dg is the effective coefficient of longitudinal
mixing of the k-th component in the gas mixture, m2/s; x is a spatial coordinate along the axis of the adsorber
(height in the adsorbent bed), m; t is time, s; eg, p -
are the specific heat and molar density of the gas mixture, respectively, J/(mol-K), mol/m3; Tg is the
temperature of the gas mixture, K; Ta is the adsorbent
temperature, K; A,g, Xa - are the coefficients of
thermal conductivity of the gas mixture and adsorbent, respectively, W/(m • K); a - is the heat transfer
c
k
ck (x ), k =1 nk
t o
T-n(t)
S
_ a dTa ^ ha da
_pacp +pa ^ hk 1 '^a 2
F dt k=1 dt ex2
auak +x 5 ^Ta
'aSu (Ta _Tg) = °
dT+ (0, t )
dt
= aSu (Ta (0, t)_ Tgn (t))
dTa (L, t)
dt
= _aSu (Ta (L, t )_ T0ut (t ))
Tout (t )
Fig. 2. The block diagram of the mathematical description of the "Adsorber" module
AM&T -
^5
AP
k 5
aP
k„
Fig. 3. Block diagram of the mathematical description of the module "Valve system":
G5 - is the flow through the control valve K5, m3/s;
kv5 - is the valve throughput, m3/(s-Pa); T5 - is the valve opening
degree K5; AP - is the pressure drop across the valve K5, Pa; G = G(ct, kv, AP) is the system of equations determining the flow of gas passing through the shut-off valves K1.1- K4.1, K1.2-K4.2, K1.3-K4.3, K12, K13, K14, K23, K24, K34 of the PSA plant [1]
Fig. 4. The block diagram of the mathematical description of the module "Receiver"
coefficient from the surface of the adsorbent granules
3
to the gas mixture flow, W/(m2-K); Su =(1 -s)— is
r
gr
the specific surface coefficient of the adsorbent granules, m2/m3, rgr is the radius of the adsorbent
granule, m; cap is the specific heat capacity of the adsorbent, J/(kg-K); pp is the density of the adsorbent, kg/m3; eg is the adsorbate specific heat, J/(mol-K); hp is the heat of adsorption of the k-th component of the gas mixture, J/mol; y is the sphericity coefficient of the adsorbent granules; ^g is the dynamic viscosity of the gas mixture, is the molar mass of
the gas mixture, kg/mol; b is the arameter vector of the Langmuir-Freundlich sorption isotherm [3].
Finally, the mathematical description of the receiver includes equations for the dynamics of pressure and concentration of the components of the gas mixture to be separated, and it can be visually represented in the form of a block diagram of the mathematical module "Receiver" (Fig. 4), where VM - is the molar volume, m3/mol; Vres is the volume of the receiver, m3; Pres is the pressure of the gas mixture in the receiver, Pa; Pout is the pressure of the
production gas mixture, Pa; GP is the consumption of production gas mixture, m3/s; Gout is the consumption of production gas mixture at the outlet of adsorbers A1 - A4, m3/s, is determined by a logical expression:
G°ut = G1,2^1,2 V G2,2ct2,2 v G3,2a3,2 v G4,2a4,2 ;
e'", res, e°u'es is the concentration of gas mixture
components at the inlet and outlet of the receiver, respectively.
Further, the concentrations of hydrogen, dioxide and carbon monoxide will be denoted by y = (y1, y2, y3), vol. %.
Statement of the task of optimizing the process variables of the PSA plant
The task of optimizing the process of hydrogen production using PSA technology can be formulated as follows: for given ranges of disturbing actions
f in rjlin f~<in r)in ryout ryout \ • i ,
x = {y , Tg , G , P , Ph2 , Pco2 }, it is required to find a vector of permissible controls u = (Pads, xads), in which the objective function is the average value of the concentration y1out of production hydrogen for a given period [0, tpr] reaching the extreme value, i.e.
I (u ) =
1 pr p { j°ut (u*)dt
Pr 0
(1)
= max
u={Pads ,tads }
1 lPr
tL f y°°ut(u)dt
Pr 0
to satisfy the connections F(x, y", y', y, u) = 0 in the form of equations of a mathematical model [1] and constraints on:
- concentration of production hydrogen y°ut
(2)
y°ut - y°ut < 0;
- productivity QH of the PSA plant
Q < Q < Q;
(3)
- the flow rate of the gas mixture G'" in the feed of the PSA plant
G" < G'n < G" ; (4)
out
- adsorption pressure Pads
P1" ^ Pads, (5)
where z, z are lower and upper limit permissible values of technological variables.
The formulated problem (1) - (5) belongs to the class of problems of nonlinear programming, and for its solution, we will use the penalty methods and sequential quadratic programming [4].
Automation of the PSA plant for hydrogen production
A 2-level SCADA system for adaptive optimization and control has been developed to solve the optimization problem (1) - (5) and control the hydrogen production process.
The process variables of the hydrogen adsorption plant are subject to random changes during the adsorption process. The disturbance values, which are represented by unregulated variables of the initial gas mixture in the feed of the PSA plant, also vary randomly during the process. In this case, it is necessary to maintain a priori an unknown maximum value of the specified optimization function, which causes the application of the adaptive optimization and control system with variable tasks to automatic regulators operating by the principle of disturbance control with a reference to the process model in the control loop.
In the SCADA system of adaptive optimization and control, the current values of disturbing actions are
continuously controlled, and when the disturbing actions deviate from the nominal values at the upper level, the optimization problem (1) - (5) is promptly solved by the personal computer, and the current optimal tasks u = (Pads, tads) are determined for the automatic control system regulators of the hydrogen production process at the lower level.
Based on the obtained value t ads, the cyclogram
U of valve operation is recalculated and the programming regulator (PR) is implemented in the 4-adsorption PSA plant for hydrogen production. The current optimum value Pads comes as a reference to the PID controller of a single-loop automatic feedback control system (Fig. 5).
Thus, the SCADA system of adaptive optimization and control of the process modes of the PSA plant provides the following functions:
- search and maintenance of the optimum value of
the purity yOut of the produced hydrogen;
- calculation of the current optimum time of adsorption step t ads;
- calculation and implementation of the optimum cyclogram of valve operation in 4-adsorption PSA plant for hydrogen production;
- calculation of the current optimum adsorption
pressure Pads;
- calculation and formation of control actions on valve drives [1].
The functional diagram of the automation system of the 4-adsorption PSA plant is shown in Fig. 6.
SCADA-system
Fig. 5. Block diagram of the control system:
Y - the valve opening degree; S - sensor, R - regulator, LG - logic gate, PR - programming regulator
Controller SCADA
Fig. 6. Functional diagram of automation (start)
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
Q C O C C >4 tu u > t > U £ u —< > 2 e* Ë of ^ o sal ■u G > L B = > O ofvalve V2i Control valve Vm Current position ofvalve V!4 Control valve Via Current position i> ■U —. > P CÖ io ol O v^lveJVu Current position £ u — > p I i of U vahjjeJVjd Current position = <U P > - ^ m > <8 Jr oj c- <1.5 b P -p 3 O M Vli <U —} CL. adsorber A2 Pressure in < = fej 2 ■E 3 of w fl} Jr CBj QH < fel -Ê o O OJO P co ; Cu 1
Devices installed in the place
Controller
SCADA
Fig. 6. Functional diagram of automation (end)
Simulation study of the control system
The results of a comparative analysis of the PSA plant operation with and without adaptive optimization in the SCADA control system are presented in Table 1.
Fig. 7 shows the results of simulation studies of the SCADA control system with a stepwise change in disturbing actions.
The analysis of transient processes in the SCADA system of adaptive optimization and control (Fig. 7 a, b, c) with a stepwise change in the proportion of CO2 in the gas mixture flow at the inlet to the PSA plant makes it possible to conclude that in the PSA plant with adaptive optimization and control, a decrease in the concentration of production hydrogen from 99 to 96 vol. % is observed, while in the PSA plant without adaptive optimization it decreases from 94 to 87 vol. % At the same time, the SCADA system maintains the concentration y™' of production
gp , m /s
Tads, s
0,0150 0,0134 0,0117 0,0100 0,0003 0,4000
0,3000
; i I GP
f A
^ 1 1 li
- i i
- i : i i ^■ads
i i /
40
43
41
30
1020 1040
y°ut ,vol. % 00 00 05 03 01 00 00 00 1020
1000
1000 a)
2000 2020
2120
2320 b)
2020
2020
Table 1
Analysis of PSA plant performance
Distrubing actions - * , .. , , „, A/, • • / , vol. % /, vol. % , '
stepwise increase: ' vol. %
y2 from 34 to 40 vol. % 00.00 00.40 0.3
Tgn from 30 to 00 °C 00.02 04.13 4.00
PHut up to 0.3 MPa H2 00.02 00.00 3.03
PCO up to 0.1 MPa 00.01 00.22 0.20
/, / are values of the objective function with and without adaptive optimization in the control system, respectively.
hydrogen at the maximum possible level for the changed characteristics of the initial gas mixture in the plant feed and ensures the constraint (3) on the permissible plant capacity.
P, MPa
1,0 1 0,0
- r—!-^ -1-1-:- -□-1-
r 1 i i i i
V ; \ \
JC i X \ ^ : / i 4 : -d/ V 1 A
~~fl \ 1 / L /1 \l /- ^^ J i K^ / :
P'n, MPa 1,00
1,000 1,00 1,040 1,03 1,010 1,0
1920 1940 1960 1980 2000 2020 2 s
c)
Fig. 7. Transient processes in the SCADA control system with a stepwise increase in the CO2 content of the starting mixture from 30 to 45 % vol.:
a - the change in the consumption GP of production hydrogen and the optimum time of the adsorption cycle T ads
as a function of time; b - the change in concentration y°u' as a function of time in the presence of adaptive optimization (1) and without adaptive optimization (2); c - pressure changes in adsorbers A1 - A4 of the PSA plant
P
2
0
Gp, m3/s
0,0150 0,0134 0,0117 0,0100 0,0083 0,0067
0,0050
i A
1 1
J ads
50
44 42 40 38 36 34
1920 1940 1960 1980 2000 2020 2040 t, s
P, MPa
a)
Pn
2 1,5 1
0,5
/ 1 ' -Y J J J- :
Srv— 1 i i i i
\\ \ r \ V - .ft 1 A1 A 'A ■ 1 A3-A 1 \ ^
\s 1 ' A 1 iC : X\ i
/1 \ 1 / l\ - / 1 \ 1 / 1 : 1 N—J i
P'n, MPa 1,59
1920 1940 1960 1980 2000 2020 2040 2s
C)
1,575
1,56
1,545
1,53
1,515
1,5
y°ut, vol. % 100 99 98 97 96 95 94 93 92
1920 2120 2320 2520 2720 t, s b)
Fig. 8. Transient processes in the SCADA control system with a stepwise increase in the temperature Tln of the initial mixture from 30 to 50 °C:
a - change in the consumption GP of production hydrogen and the optimum time of the adsorption cycle s ads as a function of time; b - the change in concentration y°ut as a function of time with adaptive optimization (1) and without adaptive optimization (2); c - pressure changes in the adsorbers A1 -A4 of the plant
Fig. 8 shows the graphs of transient processes in the SCADA system of adaptive optimization and control with a stepwise increase in the temperature
Tgn of the initial mixture from 30 to 50 °C. The analysis
shows that the SCADA system compensates for the stepwise disturbance by decreasing the duration of the adsorption stage from 42 s to 36 s (Fig. 8 a). At the same time, the SCADA system maintains the
Gp, m3/s
0,0050 0,0034 0,0H7 0,6!00 0,0033 0,0007
0,0050
i
fw- _a __ A > ~ A
r
1 t ,
1 ads
/
1 1
PHU, MPa Pads
2 1,5 1
0,5
1920
1940
1960
1980 C)
2000
2020
48 46 44 42 40 38
1920 1940 1960 1980 2000 2020 t,s a)
concentration of production hydrogen at ~ 99 % vol.
and the consumption GP of production hydrogen at the minimum acceptable level (Fig. 8 a), while in the PSA plant without adaptive optimization, the concentration of production hydrogen reaches ~ 94 % vol. (Fig. 8 b).
Fig. 9 shows the graphs of the transient processes in the SCADA system with an increase in the pressure
P-" at the production outlet of the PSA plant up to
, vol. %
100
98
96
94
92
i i i i
- i i r 7' '
I i . i - i i i i 1 i 2 1 2 i
; i . i , i i / „ _ u—-^------*—-vi i
; i . i i i i i i i i i i i
1920
2120
2320 2520 b)
2720
t, s
Fig. 9. Transient processes in the SCADA control system with a stepwise increase in the pressure P^
at the production outlet of the plant up to 0.3 MPa:
a - the change in the consumption GP of production hydrogen and the optimum time of the adsorption cycle T ads as a function of
time; b - the change in concentration y1o"t as a function of time with adaptive optimization (1) and without adaptive optimization (2); c - pressure changes in the adsorbers Aj-A4 of the plant
ads
0
G1^ ,m / s 0,0150F
0,0134 0,0117 0,0100 0,0083 0,0067 0,0050
Gp 1.
K
~jr
Ta ds 1 1 1.
/ 1 1 1"
1 1 1"
Tads,s
56 54
48 46 44 42 40
1920 1940 1960 1980 2000 2020 t,s a)
PO2, MPa Pa 2 1,5 1
0,5
/ X. I \i /
I ^ I I--I --,
0 h , i , ^^^^^......T, rrr^m 1,54
1920 1940 1960 1980 2000 2020 t,s
c)
0.3 MPa. In response to this disturbance, the SCADA system increases the adsorption pressure Pads with an insignificant reduction in the adsorption cycle time t acs (Fig. 8 c), which allows maintaining the production hydrogen flow of the PSA plant within the permissible limits (Fig. 8 b), providing the maximum
possible purity of hydrogen y™2 = 99 % for the changed conditions (Fig. 8 a). In the PSA plant, without adaptive optimization, the purity of production
hydrogen is y™2 = 95 vol. %.
Fig. 10 a, b, c show the graphs of the transient processes in the SCADA-system with a stepwise increase in pressure at the discharge outlet of the PSA plant up to 0.1 MPa. In the general case, an increase in
the discharge pressure PCo2 reduces the qualitative
indices of the adsorption process (Fig. 10 a, b); the SCADA system of adaptive optimization in this case
minimizes the reduction of purity y°ut of production hydrogen from 99 to 96 vol. % , maintaining the specified limits, while in the PSA plant without
adaptive optimization, the purity y°ut of production hydrogen reduces from 94 to 89 vol. % (Fig. 10 a). The adsorption pressure Pads and the duration of the adsorption stage t ads increase in this case, while the
consumption UP of the production hydrogen remains at the minimum acceptable level (Fig. 10 b, c).
y°ut, vol. % 100
98
96
94
92
90
88 1920
2420
2920
3,s
b)
Fig. 10. Transient processes in the SCADA control system with stepwise increase in pressure P^
at the discharge outlet of the plant to 0.1 MPa:
a - the change in the flow rate GP of the production hydrogen and the optimum time of the adsorption cycle i ads as a function
of time; b - the change in concentration y1out as a function of time with adaptive optimization (1) and without adaptive optimization (2); c - pressure changes in the adsorbers A1 -A4 of the plant
Conclusion
Using modern methods of systems analysis, mathematical modeling and control theory, new scientific results were obtained for theoretical and practical application of automated processes for adsorption separation of gas mixtures with cyclically varying pressure. We developed mathematical, informational and algorithmic support of a 2-level SCADA-system for adaptive optimization and control over the 4-adsorption PSA plant for hydrogen production with a purity of 96-99 vol. %.
The workability of the developed 2-level SCADA-system of adaptive optimization and control has been confirmed by the simulation method. The efficiency of its functioning under the influence of disturbing actions was verified (the PSA plants with adaptive optimization and without adaptive optimization were compared) for the following conditions: 1) if the proportion of CO2 in the gas mixture flow and the temperature of the gas mixture at the inlet to the PSA plant increased, the purity of production hydrogen increased by 6.3 and 4.8 %, respectively; 2) if the pressures at the production and discharge outlets of the PSA plant changed, the purity of the target product increased by 3.8 and 6.3 vol. % , respectively.
The research was conducted within the project part of the State Task No. 10.3533.2017/PCh.
References
1. Akulinin E.I., Ishin A.A., Skvortsov S.A., Dvoretsky D.S., Dvoretsky S.I. Mathematical modeling of hydrogen production process by pressure swing adsorption method. Advanced Materials and Technologies, 2017, No.1, pp. 38-49.
2. Ishin A.A. Ma'ema'icheskoe modelirovanie i upravlenie processom poluchenija vodoroda me'odom adsorbcionnogo razdelenija gazovoj smesi: dis. ...kan. tehn. nauk: 05.13.06 [Mathematical modeling and control of the
process of hydrogen production by the method of adsorption separation of a gas mixture: dis. ... Can. Tech. Sci.: 05.13.06]. Tambov: TGTU, 2017. 152 p.
3. Jeong-GeunJee, Min-Bae Kim, Chang-Ha Lee, Adsorption characteristics of hydrogen mixtures in a layered bed: binary, ternary, and five-component mixtures. Ind. Eng. Chem. Res., 2001, Vol. 40, pp.868-878
4. Reklejtis G., Rejvindran A., Rjegsdel K. Optimizacija v tehnike: v 2 kn. [Optimization in engineering: in 2 books] M.: Mir, 1986, 667 p.
Oxygen-Enriched Air Production System
Designated purpose, application area.
The system allows producing oxygen-enriched air by the pressure swing adsorption method, and simultaneous air drying and cleaning from gaseous contaminants. The oxygen-enriched air production system is intended for industrial dehumidifers, oxygen generators, medical oxygen concentrators.
Originality, uniqueness.
The oxygen-enriched air production system in which technology of pressure swing adsorption is applied, allows producing oxygen-enriched air by stepped pressure change in adsorbers without installation of additional heating elements. It provides the possibility of prolonged work (up to 30 000 hours) and reduces electrical energy consumption.
Specifcations.
The implementation of the technology allows producing oxygen-enriched air stream free from gaseous impurities, dried until the dew point of -40 °C, containing from 30 % (at a rate of 10-12 1/min output) to 90 % oxygen (at a rate of 2-3 l/ min at the output) with energy consumption 100-150 watts.
Department "Technology and Equipment for Food and Chemical Production"
Contact person: Ph.D Akulinin Evgeniy Igorevich Tel: +7 4752 63-94-42. E-mail: [email protected]
