Chemical Engineering Journal90(2002)
253–266
Simulation of industrial catalytic-distillation process for production of methyl tert-butyl ether by developing user’s model
on Aspen plus platform
Jie Bao a,*,Buliang Gao b,Xiaoqun Wu c,Makoto Yoshimoto a,Katsumi Nakao a
a Department of Applied Chemistry and Chemical Engineering,Faculty of Engineering,Yamaguchi University,
Tokiwadai2-16-1,Ube,Yamaguchi755-8611,Japan
b Qilu Petrochemical Research Institute of Sinopec,Zibo,Shandong255400,China
c Department of Chemical Engineering,Zhejiang University,Hangzhou,Zhejiang310071,China
Received30October2001;accepted26March2002
Abstract
The industrial catalytic-distillation process for the production of methyl tert-butyl ether(MTBE)from methanol and isobutylene was simulated by developing the process model as a user modular on Aspen plus platform.The model utilizes the Aspen plus system and retains the characteristics of the self-designed model,which has been veri?ed in various scale-up processes.The experimentally determined reaction kinetics was applied in the model.NRTL and Redlick–Kwong–Soave equations were selected for the vapor–liquid equilibrium calculation. The NRTL binary interaction parameters were estimated from the experimental data of the two-component vapor–liquid equilibrium.Two typical industrial plants for the MTBE production,one using the loose-stack-type package technology and the other using the bale-type package technology in the catalytic-distillation column,were chosen as the sample processes to demonstrate the validity of the model.The ?owsheet simulations of the two industrial plants were done on Aspen plus platform,in which the simulation of the catalytic-distillation column used the developed user modular.The results show that fair agreements between the calculated and operating data were obtained.?2002Elsevier Science B.V.All rights reserved.
Keywords:Industrial simulation;Catalytic-distillation process;Methyl tert-butyl ether;Aspen plus;User modular
1.Introduction
Catalytic-distillation technology for the production of methyl tert-butyl ether(MTBE)has been commercialized to the scale of annual productivity more than100,000t in many countries[1–4].To meet the needs of the de-sign for the new plants and optimization of the existing ones,an accurate mathematical model for simulating the industrial-scale catalytic-distillation process is needed.On the other hand,very few industrial cases were reported, although many studies were devoted to the modeling of catalytic-distillation process[5].A practical model should have at least the following capacities:(1)it describes the structural characteristics of catalyst packages used in in-dustrial processes,(2)the fundamental parameters such ?Corresponding author.Present address:Department of Bioscience and Biotechnology,Faculty of Engineering,Okayama University,Tsushi-manaka3-1-1,Okayama700-8530,Japan.Tel.:+81-86-251-8202;fax: +81-86-231-0257.
E-mail address:baojie@biotech.okayama-u.ac.jp(J.Bao).as reaction kinetics and vapor–liquid equilibrium data are supported by either experimental data or reliable database, (3)it is veri?ed by industrial operation data,and(4)the industrial?owsheet can be simulated,not merely in a single catalytic-distillation unit.
In our previous reports,the model for the catalytic-distillation process in the MTBE production was success-fully applied in various scales from bench tests,pilot tests, and in a semi-industrial plant with the annual productivity of2000t MTBE[3,6].With the rapid industrialization rate of the process,some shortages in the model appeared.First, the model was a self-designed Fortran program used to simulate a single catalytic-distillation unit.Thus,the whole ?owsheet composed of different unit operations could not be simulated.Second,only?ve components were used in the model instead of the12main components in the real case.The eight main hydrocarbon components were repre-sented by only three key components,isobutylene,1-butane and1-butylene.This certainly created the inaccuracy in the real industrial operation with massive productivity.Third, the database and calculation functions in the previous model
1385-8947/02/$–see front matter?2002Elsevier Science B.V.All rights reserved. PII:S1385-8947(02)00041-4
254J.Bao et al./Chemical Engineering Journal90(2002)253–266
Nomenclature
A,B,C,D coef?cients of tridiagonal matrix
A1Arrhenius frequency factor of rate
constant k1
A2Arrhenius frequency factor of rate
constant k2
b NRTL binary interaction parameter
c component number
C molar concentration(mol/m3)
E1activation energy of rate
constant k1(J/mol)
E2activation energy of rate constant
k2(J/mol)
FI1molar?owrate of the mixed
C4/methanol feedstock(mol/s)
FI2molar?owrate of the methanol
feedstock(mol/s)
h enthalpy of liquid stream(J/mol)
H enthalpy of vapor stream(J/mol)
H heat of reaction(J/mol)
HI enthalpy of feedstock(J/mol)
k1?rst-order rate constant of the
forward reaction of reaction(1)(s?1) k2?rst-order rate constant of the reverse
reaction for reaction(1)(s?1)
L liquid molar?owrate(mol/s)
N number of equilibrium stages
NC1start stage of catalyst packing
NC2end stage of catalyst packing
NF1stage of the mixed C4/methanol
feedstock
NF2stage of the methanol feedstock
P pressure of the system(MPa)
P0vapor Antoine pressure(MPa)
Q total heat of reaction(J)
r reaction rate(mol/m3s)
R gas constant(J/mol K)
R reacted moles of components(mol) t time(s)
T temperature(K)
v molar volume(m3)
V vapor molar?owrate(mol/s)
V C catalyst volume(m3)
V L liquid volumetric?owrate(m3/s)
V T catalyst space velocity(s?1)
x molar fraction of liquid
X B conversion of isobutylene
y molar fraction of vapor
ZI molar fraction of feedstock
Greek letters
αNRTL binary interaction parameters α,δempirical coef?cients of catalyst
package
γliquid activity coef?cient
ρliquid molar density(mol/m3)
φvapor fugacity
Subscripts
B isobutylene
i component(1≤i≤c)
j equilibrium stage(1≤j≤N)
M methyl tert-butyl ether
Superscripts
k reaction section in the small reactor at
each stage(1≤k≤KS)
KS number of package layers at each stage
were limited and it was dif?cult to carry out the detailed optimization calculations.
Aspen plus system is one of the standard software for ?owsheet simulation in the processing industries.It is supported by strong databases,complete sets of modules, and?exible simulation tools.The system provides many built-in modules for simulating various processes,and the modular for simulating the reactive-distillation process is also one of them.An important assumption is given in this reactive-distillation modular,that is,both reaction and separation are assumed to take place in the liquid phase in the column trays or packings.Therefore,the liquid residue time or liquid holdup is required[7,8].In the heterogeneous catalytic-distillation process,however,the solid catalyst particles are packed into many catalyst envelopes,instead of the homogeneous dispersion in the liquid phase in the trays or packings.The reactions occur inside the catalyst packages when the liquid contacts the catalyst particles. Then,the products?ow out of the packages,and the sep-aration takes place on the trays or packings through the count-current vapor–liquid contact.This fact indicates a major difference between homogeneous and heterogeneous processes:the reaction and separation actually take place in the different locations of the column in the heterogeneous process,i.e.reaction in the catalyst packages and separation in the trays or packings.Therefore,the parameters of liquid residue time or the liquid holdup on the trays or packings in the heterogeneous process can only be used in the separa-tion calculation,whereas the reaction calculation needs the parameters of contacting time of liquid with catalyst in the catalyst packages.Hence,we may conclude that the built-in reactive-distillation modular in Aspen system is not suit-able for simulating the heterogeneous catalytic-distillation process for the above reason.
To overcome the above problems,an effort was made in this study to develop a self-de?ned model for simulating heterogeneous catalytic-distillation,and then to connect the model with Aspen plus as a user modular.In the new model,
J.Bao et al./Chemical Engineering Journal90(2002)253–266255 the contacting time of liquid with catalyst is represented by
the catalyst space velocity V T appearing in the reaction equa-
tions.In this way,not only the user modular takes advan-
tages of strong database,?exible simulation functions and
optimization tools of Aspen plus system,but it also keeps
the characteristics of the model that had been veri?ed in the
previous scale-up experiments.
The purpose of this study is(1)to establish a mathemati-
cal model oriented to the heterogeneous catalytic-distillation
structure,(2)to build the mathematical model in the user
modular provided by Aspen plus and compile it into an avail-
able modular on Aspen plus platform,(3)to connect the
database and calculation functions of Aspen plus with the
user model,and(4)to apply the model into the industrial
applications.
2.Reaction kinetics and thermodynamics
2.1.Reaction kinetics
The synthesis of MTBE from methanol and isobuty-
lene catalyzed by Amberlyst-15or similar sulphonic
ion-exchange resin catalysts[3]is a reversible etheri?cation
as shown in Eq.(1):
CH3C(CH3)=CH2(B)+CH3OH k1
k2
CH3C(CH3)2OCH3(M)
(1)
According to Yang et al.[9],the forward reaction of reaction
(1)is?rst-order with respect to the isobutylene concentra-
tion and zero-order with respect to the methanol concentra-
tion,respectively,and the reverse reaction is?rst-order with
respect to the MTBE concentration as shown in Eq.(2):?r B=k1C B?k2C M(2) where k1=A1exp(?E1/RT)and k2=A2exp(?E2/RT) are the?rst-order rate constants for the forward and reverse
reactions,respectively.The values of Arrhenius frequency
factors A1,A2and activation energy E1,E2for the sul-
phonic ion-exchange resin catalyzed reaction are listed in
Table1[9].The reaction kinetic data had been veri?ed in
several industrial applications of the MTBE production,
in which the?xed-bed reactor packing of the same catalyst
was used.
The main side reactions are the dimerization of isobuty-
lene to diisobutylene(2,4,4-trimethyl-1-pentene),and the
hydration of isobutylene to tert-butyl-alcohol(TBA)as
Table1
Arrhenius parameters of rate constant k1and k2for MTBE synthesis catalyzed by sulphonic ion-exchange acidic resin catalysts
A1A2E1(J/mol)E2(J/mol) 6.50×105 1.36×108 4.74×1047.04×104shown in Eqs.(3)and(4),respectively:
2CH3C(CH3)=CH2→CH2=C(CH3)CH2C(CH3)2CH3
(3) CH3C(CH3)=CH2+H2O→CH3C(CH3)2OH(4) The kinetic study shows that reaction(3)can only take place when the addition of methanol is insuf?cient(the molar ra-tio of methanol to isobutylene is lower than0.8)[9].Since the methanol addition is carefully arranged to allow the mo-lar ratio of methanol to isobutylene to be higher than0.8 at each stage of the catalytic-distillation column,reaction (3)can be reasonably neglected in the catalytic-distillation unit.For reaction(4),the minor water in hydrocarbon and methanol feedstocks is consumed in the pre-reactor before it is fed into the catalytic-distillation column.Therefore,re-action(4)can also be neglected in the catalytic-distillation unit.The products of the two side reactions are considered in the vapor–liquid equilibrium calculation,whereas the re-action kinetics are not included in the calculation.
2.2.Vapor–liquid equilibrium
A typical industrial process for the MTBE produc-tion involves at least12components:propylene,isobu-tane,1-butane,1-butylene,isobutylene,cis-2-butylene, trans-2-butylene,methanol,MTBE,diisobutylene,TBA, and water.Since methanol associates almost all hydrocar-bon components into azeotropic pairs,the system shows the strong non-ideal properties.The vapor–liquid equilibrium constant K i for component i is expressed in Eq.(5):
K i=γi
φ0i
φi
P0i
P exp
v i(P?P0i)
RT
(5)
whereγi is the liquid activity coef?cient,φ0i andφi the vapor fugacity in pure and mixture state,respectively,P0i the vapor Antoine pressure,v i the molar volume and P is the total pressure of the system.The NRTL equation and Redlick–Kwong–Soave equation are selected to calculate liquid activity coef?cientγi and the vapor fugacityφi(and φ0i),respectively.The NRTL activity coef?cient equation is expressed in Eq.(6):
lnγi=
j
x jτji G ji
k
x k G ki
+
j
x j G ij
k
x k G kj
τij?
m
x mτmj G mj
k
x k G kj
(6) where G ij=exp(?αijτij),τij=b ij/T andαij=αji.The NRTL binary interaction parameters b ij,b ji andαij were estimated from the experimental data of two-component vapor–liquid equilibrium using data regression system (DRS)in the Aspen plus system,followed by the thermo-dynamics consistence check.The estimated NRTL binary
256J.Bao et al./Chemical Engineering Journal90(2002)253–266
Table2
Values of NRTL binary interaction parameters for components involved
in MTBE synthesis
Components i–j b ij b jiαij Propylene–methanol b617.96258.780.30
Propylene–MTBE b204.97?114.110.30
Propylene–tert-butyl alcohol b617.96258.780.30
Isobutane–methanol a663.40505.940.47
Isobutane–MTBE a204.96?114.110.30
Isobutane–tert-butyl alcohol a663.40505.940.47
1-Butane–methanol a672.37516.540.47
1-Butane–MTBE a230.71?117.970.47
1-Butane–tert-butyl alcohol a672.37516.540.47
1-Butylene–methanol a695.79440.170.47
1-Butylene–MTBE a?288.49440.510.30 1-Butylene–tert-butyl alcohol a695.79440.170.47
Isobutylene–methanol a790.53435.530.47
Isobutylene–MTBE a?141.72225.700.30 Isobutylene–tert-butyl alcohol a790.53435.530.47 Trans-2-butylene–methanol a695.79440.170.47 Trans-2-butylene–MTBE a?288.49440.510.30 Trans-2-butylene–tert-butyl alcohol a695.79440.170.47 Cis-2-butylene–methanol a190.02237.430.30 Cis-2-butylene–MTBE a440.17695.790.47 Cis-2-butylene–tert-butyl alcohol a?162.1746.980.30 Methanol–MTBE a663.40505.940.47 Methanol–diisobutylene b204.96?114.110.30 Methanol–tert-butyl alcohol b663.40505.940.47 Methanol–water b828.39?1329.540.30 MTBE–diisobutylene b440.51?288.490.30 MTBE–tert-butyl alcohol b489.67?240.510.30 MTBE–water b682.051108.820.30 Diisobutylene–tert-butyl alcohol b695.79440.170.47 Tert-butyl alcohol–water b217.51?1395.020.30
a Parameters estimated from experimental VLE data.
b Parameters from Aspen database DIPPR[8].
interaction parameters b ij,b ji andαij are shown in Table2. The other fundamental properties such as molar volume, heat capacity,vapor capacity and density,etc.were called from DIPPR database in the Aspen plus system.
3.Model development on Aspen plus platform
3.1.Model con?guration of catalytic-distillation column
For developing a practical catalytic-distillation process, the design of an ef?cient catalyst package poses considerable challenges[5].For the MTBE production process,the?ne sulphonic ion-exchange resin particles with its size less than 1.0mm have to be enveloped in various conceivable shapes [5,10–12].Among them,two typical structures had been applied to an industrial scale of more than100,000t annually, one being the bale-type package[13–16]and the other the loose-stack package[6,3,17].
Two considerations are taken as the most important factors for the catalyst packages:one being the contact ef?ciency of liquid with catalyst,and the other being the reaction ef?ciency of catalyst.Correspondingly,the model development should re?ect the characteristics of the cat-
alyst packages.Two empirical coef?cientsαandδwere
introduced in the model:αrepresents the ratio of the liquid
?owrate entering the catalyst package to the total liquid
?owrate,re?ecting the contact ef?ciency of liquid to cat-
alyst(liquid?ows into the passby ways in many kinds of
packages).δrepresents the ratio of the real reaction rate to
the kinetic reaction rate under the same conditions(liquid
?oods through catalyst in non-plug?ow in many packages).
The value ofαwas determined by measuring the cross-area
occupied by catalyst to the total cross-area in the reactive
section.The value ofδwas determined separately in a spe-
cially designed small reactor.The detailed procedure:put a
single catalyst package in the small reactor under the same
reaction and hydrodynamic conditions(same count-current
vapor–liquid?owrates),then determine its reaction rate and
compare with the kinetic rate.The two coef?cients were
used to model various types of catalyst packages during the
process development from bench tests,and different scales
of pilot tests[3,6].The value ofαwas between0.5and1.0,
the value ofδwas between0.6and1.0.
On the other hand,the catalyst package had shown contin-
uous improvement in both the aspects.In the?nal type used
in the commercial plant,the design of the loose-stack pack-
age let all the liquid enter the catalyst envelope,and then
?ood smoothly through the catalyst container.As the result,αwas1.0by its de?nition.The experimental determination ofδwas also close to the unity value of1.0,because of the
perfect contacting of liquid with catalyst in the packages,
and because the?ow is close to the plug-?ow pattern inside
the packages.The trial-and-error method was used to search
the most suitable value ofαandδfor the bale-type package
[3,6,17].We found that the calculation results gave the best
?tness to the operating ones using the unity value of1.0to
both of the parameters.This fact indicates that the industrial
packages of the bale-type package are also under the condi-
tions of perfect contacting of liquid with catalyst and stable
plug?ow inside the packages.In other words,the two co-
ef?cients in the current model for the industrial simulations
can be ignored.This is why we keep the coef?cients in the
model for consistency with the previous model[3,6],and to
give them the value of1.0in the current industrial cases.
The equilibrium stage model based on the bale-type and
loose-stack-type packages in the reactive section is shown
in Fig.1.Fig.1(a)indicates the whole catalytic-distillation
column,and Fig.1(b)indicates the detailed structure of a
typical equilibrium stage in the reactive section.There are
N equilibrium stages in the column.The catalyst packages
are installed from stages NC1to NC2,forming the reactive
section.The catalyst packages at each stage of the reactive
section are represented by a corresponding small reactor.
This small reactor is divided into several layers from1to
KS corresponding to the real arrangement of the catalyst
packages.The mixed C4stream FI1and pure methanol
stream FI2are fed into the column at stages NF1and NF2,
respectively.The radial gradients of composition and heat
J.Bao et al./Chemical Engineering Journal90(2002)253–266
257
Fig.1.Schematic diagram and con?guration of catalytic-distillation column:(a)whole column model;(b)equilibrium stage model. transfer are neglected at the equilibrium stage.The reaction
is considered taking place in the liquid phase.
3.2.Model equations
The model equations based on the typical equilibrium
stage j are shown as follows:
(1)Mass balance equation:
d(E j x j,i)
d t =L j?1x j?1,i+V j+1,i y j+1,i?L j x j,i
?V j y j,i+FI j ZI j,i+ R j,i(7)
where FI j and ZI j are the feedstock?owrate and compo-sition at stage j(NF1or NF2),respectively. R j,i is the consumption rate for component i at stage j.The terms of R j,i>0, R j,i<0and R j,i=0correspond
to the reactants,the products,and the unreacted compo-nents,respectively.
(2)Reaction equations:
The reaction kinetics equation(2)is rearranged regarding to isobutylene conversion X B for the merit of application convenience as shown in Eq.(8):
X B=
k1
k1+k2
1?exp
?(k1+k2)
V C
V L
=
k1
12
1?exp
?
k1+k2
T
(8)
where V C is the catalyst volume,V L the liquid vol-umetric?owrate?owing through the catalyst and V T (=V L/V C)is the catalyst space velocity,meaning the liquid volumetric rate?owing through per volume unit of solid catalyst.The swelling of the catalyst is taken into
258J.Bao et al./Chemical Engineering Journal90(2002)253–266 account in the volume calculation(20%increase in
volume after the dry resin catalyst particles are bathed
in liquid).V T is decided by the catalyst amount and
the liquid?owrate of the column.The reciprocal of
V T,1/V T,indicates the contacting time of liquid with
catalyst,corresponding to the liquid residue time in
the homogeneous reactive-distillation process.The dif-
ference between the two parameters is that the liquid
residue time in the homogeneous process is a parameter
used for both reaction and separation,while the space
velocity V T is only used to describe the reaction behav-
iors in the heterogeneous process.The liquid residue
time in the heterogeneous process is also calculated at
each equilibrium stage but it has no direct relations to
the reaction behaviors,since the reaction and separation
occurs at different locations of the catalytic-distillation
column(reaction in the catalyst package,and separation
in the trays or packings).
The consumption rate R j,i on stage j is calculated
in Eq.(9).The catalyst space velocity on each catalyst
package is calculated to give the conversion yield of
isobutylene at each package:
R j,i=
KS
k=1
αL k j?1
k1
k1+k2
×
1?exp
?
δ(k1+k2)V C
(NC2?NC1+1)·KS·αL k j?1ρj
(9)
whereρj is the liquid molar density,k the layer of cat-alyst package at stage j(1≤k≤KS),αthe contacting ef?ciency of liquid to catalyst,andδis the reaction ef?-ciency in the catalyst package.The value forαandδin the two industrial cases was taken to be unity,because of the reasons described in Section3.1.
(3)Vapor–liquid equilibrium equation:
y j,i=K j,i x j,i(10) where K j,i is the vapor–liquid equilibrium coef?cient for component i at stage j,calculated from Eqs.(5)and
(6).
(4)Component summation equations:
c
i=1
x j,i=1(11) c
i=1
y j,i=1(12) (5)Enthalpy balance equations:
L j?1h j?1+V j+1H j+1?L j h j?V j H j
+FI j HI j+ Q j=0(13) Q j= H j R j,i(14) where HI j is the molar enthalpy of feedstock,and H j and Q j are the molar heat of reaction and total heat of reaction at stage j,respectively.
The model equations(Eqs.(7)–(14))are rearranged into the form of tridiagonal matrix as shown in Eq.(15):
A j x t+1
j?1,i
+B j x t+1
j,i
+C j x t+1
j+1,i
=D j(15) where the matrix coef?cients A j,B j,C j,D j take different values at the different section of the column from N=1,2 to NC1?1;NC1,NC1+1to NC2?1;NC2,NC2+1to N?1 and N.The independent variables in the catalytic-distillation column include the number of equilibrium stages N,the number of package layers at each stage KS,the locations of the methanol and mixed C4feedstock streams NF1and NF2,the start and end stages of catalyst packing NC1and NC2,the pressure on the top stage,the pressure drop of the column(or the pressure on the bottom),the catalyst volume packed in the column V C,the re?ux ratio,the re?ux tem-perature,distillate?owrate,and the feedstock?owrate and composition variables.The model equations(Eqs.(7)–(14)) are simultaneously solved using the relaxation algorithm af-ter the independent variables,and the relaxation coef?cient and the initial values of the parameters are given.The dia-gram of the detailed calculation?owsheet is shown in Fig.2.
3.3.Design of catalytic-distillation user modular on Aspen plus platform
(1)The program is written into the user modular using the
built-in Fortran language following the grammar and communication rules issued by Aspen plus system,and then compiled it into an executive?le using NDP Fortran compiler.
(2)The reaction kinetic model is developed as a subroutine
of the user modular.
(3)The vapor–liquid equilibrium model is developed by
calling NRTL equation for liquid activity coef?cient calculations and Redlick–Kwong–Soave equation for vapor fugacity calculations.The NRTL binary inter-action parameters b ij,b ji andαij estimated from the experimental data are applied to replace the data from UNIFAC model in Aspen plus.
(4)Other general thermodynamic properties are calculated
by calling DIPPR database through the subroutines such as VTHRM for vapor pure substance proper-ties,LTHRM for liquid pure substance properties, VMTHMY for vapor mixture properties,LMTHMY for liquid mixture properties,ENTHV for vapor mixture enthalpy,ENTHL for liquid mixture enthalpy,VOLV for vapor mixture molar volume,VOLL for liquid mix-ture molar volume,FUGV for vapor mixture fugacity, FUGLY for liquid mixture fugacity,etc.
J.Bao et al./Chemical Engineering Journal90(2002)253–266
259
Fig.2.Calculation?owsheet of user model USROPT developed for simulating catalytic-distillation column.
(5)The communication between the user modular and
other system modules,database,function tools and monitor systems are realized through the connection of material streams,enthalpy and entropy streams as well as information streams according to the rules and formats of Aspen plus system.
(6)Writing the input parameters,calculation results and
calculation information into the report?les by calling common subroutines.
The detailed communication and calling processes are also shown in Fig.2.The user program USROPT includes one main program and13self-de?ned subroutines.4.Results and discussion
4.1.Simulation of Plant A using loose-stack package technology
Fig.3(a)shows the industrial?owsheet of Plant A using the loose-stack package technology in the catalytic-distillation column with the annual MTBE pro-duction of20,000t.The mixed C4hydrocarbons containing about32%(wt.)isobutylene is mixed with methanol in the static mixer V-2and then pumped into the pre-reactor R-1, in which about90%isobutylene is converted.The products
260J.Bao et al./Chemical Engineering Journal 90(2002)
253–266
Fig.3.Diagrams of (a)industrial and (b)Aspen plus ?owsheets of Plant A.
from R-1are fed into the catalytic-distillation column CD-1after the heat exchanger E-1.The methanol feedstock is split into two streams by the splitter V-1;one is mixed with the mixed C4in the static mixer V-2as described above,the other is fed into CD-1directly at the upper location of the column.The sulphonic ion-exchange resin catalysts packing in the loose-stack envelopes are installed in the reactive section of CD-1.The MTBE product is obtained as the bottom products of CD-1.The distillate containing the unreacted C4hydrocarbons and methanol are fed into the water stripper column D-1.The hydrocarbons are recovered from the top of D-1,and the methanol/water mixture from the bottom of D-1is fed into the methanol distillation col-umn D-2after another heat exchanger E-2.The methanol is recovered as the distillate of D-2(the recycling of methanol is not included in the ?owsheet).Water from the bottom of D-2is also fed back to D-1for recycling.Fresh water is added to D-2to compensate the loss in D-1and D-2.
J.Bao et al./Chemical Engineering Journal 90(2002)253–266261
The Aspen plus ?owsheet of Plant A is shown in Fig.3(b).The splitter V-1and static mixer V-2are represented by MIXER modules,the pre-reactor R-1by RSTOIC modu-lar,the heat exchangers E-1and E-2by HEATER modules,the catalytic-distillation column CD-1by USER modular USROPT,the water stripper D-1by SEP modular,and the methanol distillation column D-2by RADFRAC modular.The NRTL equation and Redlick–Kwong–Soave equation are applied for the whole ?owsheet except the water stripper D-1.In D-1,the UNIF-LL equation is applied because of the existence of the liquid–liquid equilibrium inside D-1.There are 14streams,8unit operation blocks,1tear stream and 1design-spec block included in the Aspen plus ?owsheet.The catalytic-distillation column CD-1is the key equip-ment of the Plant A.The recti?cation section is packed with structured packings,with 4m in height and 1m in diameter.The reactive section is packed with 10layers of the catalyst packages and 10layers of the valve trays,with 23m in height and 1.4m in diameter.The stripping section is packed with 30layers of the valve trays,with 14.5m in height and 1.4m in diameter.Before the catalytic-distillation technology was put into application,MTBE was commercially produced in the ?xed-bed reactor using the same catalysts [3].The sepa-ration of the MTBE products was carried out in a distillation column using the same kind of the valve trays and structured packings.The ef?ciency of the valve trays and the HETP height of the structured packings were determined in the
Table 3
Comparison between calculated and operating results in Plant A Operating conditions
Case 1Case 2Case 3Number of equilibrium stage
(excluding condenser and reboiler)323232Recti?cation section 777Reactive section 101010Stripping section
151515Mixed C4/methanol feedstock (kg/h)809098608170Methanol feedstock (kg/h)130150130Feedstock temperature (?C)66.768.677.2Isobutylene in feedstock (wt.%) 2.45 2.45 2.32Methanol in feedstock (wt.%)0.61 2.03 1.54Catalyst weight (kg)350035003500Re?ux ?owrate (kg/h)468059205021Re?ux temperature (?C)46.076.456.9Pressure at top (MPa)0.800.800.80Pressure at bottom (MPa)0.850.850.85Results
Case 1
Case 2
Case 3
Operating data
Calculated data Operating data Calculated data Operating data Calculated data Composition (wt.%)
Isobutylene in distillate 0.060.0480.070.0540.080.037MTBE in bottom 99.5499.6899.3699.6299.3399.45TBA in bottom 0.790.0480.410.0820.420.06Methanol in bottom 0.050.250.060.240.050.36C4in bottom
0.110.070.170.060.090.13Conversion yield of isobutylene (%)CD-1
98.1798.8698.0499.7097.6699.08Total process
99.85
99.90
99.83
99.88
99.83
99.92
rating experiments of the industrial distillation column.The ef?ciency or HETP data obtained were used to calculate the number of the equilibrium stages in the current industrial catalytic-distillation column.The data are shown in Table 3.Three operating cases with different ?owrates of the mixed C4and methanol were simulated as shown in Table 3.The conversion yields of isobutylene in R-1were 91.81,92.52and 92.76%in Cases 1–3,respectively.Table 3shows that the calculated compositions in both distillate and bottom streams of CD-1agree well with the operating data.The calculated isobutylene conversion in each case is also close to the operating data.The axial distributions of isobutylene,methanol,MTBE,and temperature pro?les are shown in Fig.4.The ?gure indicates that the calculated temperature pro?les are in good agreements with the oper-ating data.It can be concluded that the user modular can be used in the ?owsheet simulation of the catalytic-distillation process with the loose-stack-type catalyst package.
The kinetic study shows that the molar ratio of methanol to isobutylene should be no less than 0.8to prevent the dimerization of isobutylene.The molar ratios of methanol to isobutylene in the feedstock to CD-1are 1.58,2.54and 2.36for Cases 1–3,respectively.Fig.4(a)shows an axial distri-bution of low methanol concentration,particularly in the re-active section.This fact indicates that Case 1might be under the risk of isobutylene dimerization due to the de?ciency of methanol in the feedstock.On the other hand,Case 2gives
262J.Bao et al./Chemical Engineering Journal 90(2002)
253–266
Fig.4.Axial distributions of component concentrations and temperature along column height for Plant A ((a)Case 1;(b)Case 2;(c)Case 3):(?, ,?)calculated molar fractions of MTBE,isobutylene and methanol,respectively;(?,?)calculated and observed stage temperatures,respectively.
an opposite tendency of the axial methanol distribution as shown in Fig.4(b),in which the axial ratio of methanol to isobutylene is too high due to the higher methanol feed-stock.This leads to a high methanol concentration in the distillate,and consequently,the high methanol concentra-tion in the distillate increases the operating cost of the water stripper D-1and methanol distillation column D-2.Case 3gives a reasonable axial methanol distribution as shown in Fig.4(c),indicating that the optimal molar ratio of methanol to isobutylene in the feedstock might be around 2.36.
It is also found from Fig.4that the peak value of the isobutylene and methanol concentrations appears in the
stripping section.This might indicate that the present feed-stock location at stage 17is too low to take advantage of higher reactant concentrations as the driving forces of reaction.
4.2.Simulation of Plant B using bale-type package technology
Another industrial application is for Plant B using the bale-type package technology in the catalytic-distillation column with the MTBE production of 40,000t annually as shown in Fig.5(a).The catalytic-distillation column DA-301
J.Bao et al./Chemical Engineering Journal90(2002)253–266
263
Fig.5.Diagrams of(a)industrial and(b)Aspen plus?owsheets of Plant B.
is composed of two columns,the combination of the recti?-cation and reactive sections as the upper column,with36m in height and0.95m in diameter,and the stripping section as the down column.The upper column is56m in height and 2.2m in diameter.The down column is15m in height and 1.05m in diameter.The recti?cation section is packed with 10layers of the valve trays.The reactive section is packed with9layers of the catalyst packages.The stripping section is packed with25layers of the valve trays.The numbers of the equilibrium stages in each section of the column DA-301 were obtained in the industrial rating tests,carried out soon after Plant B was operated to its optimal conditions.The data obtained are shown in Table4.
Plant B is more complicated than Plant A because the methanol recycling is taken into account.The mixed C4 hydrocarbons containing about40wt.%isobutylene is mixed
264J.Bao et al./Chemical Engineering Journal90(2002)253–266
Table4
Comparison between calculated and operating results in Plant B
Operation conditions Value
Number of equilibrium stage(excluding condenser and reboiler)29
Recti?cation section7
Reactive section9
Stripping section13
Mixed C4/methanol feedstock to DA-301(kg/h)10596
Methanol feedstock to DA-301(kg/h)280
Feedstock temperature to DA-301(?C)60.0
Isobutylene concentration to DA-301(wt.%) 3.23
Methanol concentration to DA-301(wt.%) 2.29
Catalyst weight in DA-301(kg)1473
Re?ux?owrate in DA-301(kg/h)2759.4
Re?ux temperature in DA-301(?C)40.0
Pressure at top of DA-301(MPa)0.784
Pressure at bottom of DA-301(MPa)0.945
Results Distillate Bottom stream
Operating data Calculated data Operating data Calculated data Compositions(wt.%)
Propylene 1.14 1.130.000.00 Isobutene 1.03 1.030.000.00
1-Butane 3.11 3.090.020.00
1-Butylene57.1356.720.090.00 Isobutylene0.240.440.000.00 Trans-2-butylene20.3420.370.170.00
Cis-2-butylene12.3812.500.190.00 Methanol 4.61 4.710.020.80 Methyl tert-butyl ether0.000.0098.6498.66 Diisobutylene0.000.000.680.43
Tert-butyl alcohol0.000.000.190.10 Water0.000.000.000.01 Operating parameters Operating data Calculated data Distillate?owrate(kg/h)5494.005494.00
Bottom?owrate(kg/h)5428.435428.43
Distillate temperature(?C)63.0062.00
Bottom temperature(?C)144142.39 Isobutylene conversion(%)96.3092.96
Total isobutylene conversion(%)99.6299.30
with methanol in static mixer V-202B and then pumped into the protective reactor R-201to remove the harmful heavy metal ions.The stream enters the pre-reactor R-202conse-quently after a heat exchanger E-201in which about90% isobutylene is converted.The product stream from R-202is fed into the main catalytic-distillation column DA-301after another heat exchanger V-203.The methanol feedstock is split into two streams by the splitter V-202A;one is mixed with the mixed C4in the static mixer V-202B as described above,and the other is fed into DA-301directly.The cat-alyst particles packed into the bale-type envelopes are in-stalled in the middle section of DA-301.MTBE is obtained as the bottom products of DA-301.The unreacted C4hydro-carbons and methanol from the distillate of DA-301are fed into the water stripper column T-201.The hydrocarbons are recovered from the top stream of T-201.The methanol/water mixture from the bottom of T-201after a heat exchanger E-205is fed into the methanol distillation column T-202for the recovery of methanol.The unreacted methanol is recov-ered as the distillate and recycled back to V-202A as the methanol feedstock again.Part of the recovered methanol is removed to tank reservoir in the splitter V-205.Water is recovered as the bottom stream of T-202,and then fed back to T-201.Fresh water is added to T-202to compensate the loss in T-201and T-202.
The Aspen plus?owsheet for Plant B is shown in Fig.5(b).The splitter V-202A is represented by MIXER modular,the static mixer V-202B,the splitter V-205and water stripper T-201by SEP modules,the protective reac-tor R-201and main reactor R-202by RSTOIC modules, the heat exchangers E-201and E-205by HEATER mod-ules,the heat exchanger V-203by MIXER modular,the catalytic-distillation column DA-301by USER modular USROPT,and the methanol distillation column T-202by RADFRAC modular.Similar to the simulation of Plant A, the modi?ed NRTL equation and Redlick–Kwong–Soave
J.Bao et al./Chemical Engineering Journal90(2002)253–266
265
Fig.6.Axial distribution of component concentrations and temperature along column height for Plant B:(?, ,?)calculated molar fractions of MTBE, isobutylene and methanol,respectively;(?,?)calculated and observed stage temperatures,respectively.
equation of state are applied in the whole?owsheet except D-1in which the UNIF-LL equation is applied.There are 11unit operation blocks,19streams,2tear streams,1 design-spec block,2convergence blocks and1on-line For-tran block in the Aspen plus?owsheet as shown in Fig.5(b). Table4shows that the calculated component concen-trations in both distillate and bottom stream of DA-301 agree well with the operating data.The axial distributions of isobutylene,methanol,MTBE,and temperature pro?les are shown in Fig.6.The calculated temperature pro?les are in good agreement with the operating data.It indicates that the user modular can be used in the?owsheet simulation of catalytic-distillation process with the bale-type catalyst package.
The calculated conversion of isobutylene is3.34%lower than the observed one although the total conversion of isobutylene is very close.A possible explanation is given. In the real operation,a small portion of catalyst particles was gradually ground into powder in the strikes with the upward vapor streams and downward liquid streams in the long-term operation.The powders slowly moved out of the catalyst bales and settled down in the bottom reboiler. The accumulation of the catalyst powders in the reboiler caused MTBE to decompose,and let the MTBE concen-tration below the product standard98wt.%with higher methanol concentration in the product.Therefore,the cat-alyst powders had to be removed from the reboiler during the periodic maintenance of the equipment.However,the catalyst amount used in the calculation was measured af-ter2years’operation in the maintenance.Obviously,the real catalyst amount should be larger than the measured data,because the catalyst loss could not be included. This loss of catalyst might be responsible for the isobuty-lene conversion decrease.Different from Plant B,Plant A was a new equipment.The catalyst weight was measured before the operation started.The operating data were also obtained several days after the start-up of the plant.So there is no signi?cant difference in the conversion yield of isobutylene between the calculated and operating data for Plant A.
The molar ratio of methanol to isobutylene in the feed-stock to DA-301is2.67.This ratio is even much higher than that of Plant A in Case2.So it is not surprising to?nd that the axial methanol concentration shows an unreason-able distribution.A big peak of the methanol concentration is found near the bottom besides the one in the reactive section.To improve the present situation,the following measures should be taken:(1)to increase the feeding location of mixed C4stream;(2)to decrease methanol in the feedstock to the ratio of methanol to isobutylene of2.36.
5.Conclusion
(1)The industrial catalytic-distillation process for the
MTBE production was simulated by developing the catalytic-distillation model as a user modular on the Aspen plus platform,taking advantage of the strong database,?exible simulation functions and optimiza-tion tools of the Aspen plus system,while retaining the characteristics of the previous veri?ed model.
(2)The experimentally determined reaction kinetics was
applied in the model.NRTL and Redlick–Kwong–Soave equations were selected for the vapor–liquid equilib-rium calculation.The NRTL binary interaction param-eters were estimated from the experimental data of the two-component vapor–liquid equilibrium.
(3)The?owsheet simulations of the two industrial plants,
using the loose-stack-type package and the bale-type
266J.Bao et al./Chemical Engineering Journal90(2002)253–266
package technologies in the catalytic-distillation column,were simulated on the Aspen plus platform.
The results show that fair agreements between the calculated and operating data were obtained. References
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高考文科数学模拟试卷 一、选择题：本大题共10小题，每小题5分，共50分．在每小题给出的四个选项中，只有一项是符合题目要求的． 1．已知复数z满足（2﹣i）2?z=1，则z的虚部为（） A．B．C．D． 2．已知集合A={x|x2=a}，B={﹣1，0，1}，则a=1是A?B的（） A．充分不必要条件B．必要不充分条 C．充要条件D．既不充分也不必要条件 3．设单位向量的夹角为120°，，则|=（） A．3 B． C．7 D． 4．已知等差数列{a n}满足a6+a10=20，则下列选项错误的是（） A．S15=150 B．a8=10 C．a16=20 D．a4+a12=20 5．一几何体的三视图如图所示，则该几何体的体积为（） A．B．C．4﹣πD． 6．双曲线=1的顶点到其渐近线的距离为（） A． B．C． D． 7．周期为4的奇函数f（x）在[0，2]上的解析式为f（x）=，则 f（2014）+f（2015）=（） A．0 B．1 C．2 D．3
8．已知x，y满足约束条件，则z=2x+y的最大值为（） A．2 B． C．4 D． 9．在△ABC中，内角A、B、C的对边分别是a、b、c，若c2=（a﹣b）2+6，△ABC的面积为，则C=（） A．B．C．D． 10．设f′（x）为函数f（x）的导函数，已知x2f′（x）+xf（x）=lnx，f（1）=，则 下列结论正确的是（） A．xf（x）在（0，+∞）单调递增B．xf（x）在（1，+∞）单调递减 C．xf（x）在（0，+∞）上有极大值 D．xf（x）在（0，+∞）上有极小值 二、填空题：本大题共5小题，每小题5分，共25分. 11．右面的程序框图输出的S的值为． 12．在区间[﹣2，4]上随机取一个点x，若x满足x2≤m的概率为，则m= ．13．若点（a，9）在函数的图象上，则a= ． 14．已知x＞0，y＞0且2x+y=2，则的最小值为．
第 1 页 共 10 页 图 1 图2 圆梦2015·高三数学（理）仿真模拟三 一、选择题：本大题共8小题，每小题5分，满分40分．在每小题给出的四个选项中，只有一项是符合题目要求的． 1．已知函数lg y x =的定义域为A ,{} 01B x x =≤≤,则A B =（ ） A ．()0,+∞ B ．[]0,1 C ．(]0,1 D ．[)0,1 2．设i 为虚数单位,若复数() ()2231i z m m m =+-+-是纯虚数,则实数m =（ ） A ．3- B ．3-或1 C ．3或1- D ．1 3 ．设函数sin 2y x x =的最小正周期为T ,最大值为A ，则（ ） A ．T π= ,A = B . T π=,2A = C ．2T π= ,A = D ．2T π=,2A = 4．某由圆柱切割获得的几何体的三视图如图1所示,其中俯视图是 中心角为60?的扇形,则该几何体的体积为（ ） A ． 3 π B ．23π C ．π D ．2π 5．给定命题p ：若20x ≥，则0x ≥； 命题q :：已知非零向量,,a b 则 “⊥a b ”是“-+=a b a b ”的充要条件. 则下列各命题中,假命题的是（ ） A ．p q ∨ B ． ()p q ?∨ C ．()p q ?∧ D ．()()p q ?∧? 6．已知函数()222,02,0 x x x f x x x x ?+≥=?-）的比值a b ,称这些比值中的最小值为这个 数表的“特征值”.当2n =时, 数表的所有可能的“特征值”最 大值为（ ） A ．3 B ． 43 C ．2 D ．32
绝密★启 用前2020 年普通高等学校招生全国统一考试 理科综合能力测试试题卷 ( 银川一中第一次模拟考试) 注意事项： 1.答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。 2.作答时，务必将答案写在答题卡上。写在本试卷及草稿纸上无效。 3.考试结束后，将本试卷和答题卡一并交回。 可能用到的相对原子质量：H-1 C-12 N-14 O-16 P-31 S-32 Cl-35.5 Ca-40 V-51 Fe-56 Cu-64 Zn-65 一、选择题：本题共13 小题，每小题6 分，在每小题给出的四个选项中，只有一项是符合题目要求的。 1.下列关于生物大分子的叙述中，正确的是 A．肺炎双球菌、烟草花叶病毒都含有核糖体和核 酸B．生物体内参与信息传递的信息分子都是蛋白 质 C.细胞质中的核酸只含核糖，细胞核中的核酸只含脱氧核糖 D.人的吞噬细胞和浆细胞结构和功能不同，根本原因是遗传信息执行情况不同 2.某农作物细胞间隙的浓度为a，细胞液的浓度为b，细胞质基质的浓度为c，在对农 作物施肥过多造成“烧苗”过程中，三者之间的关系是 A．a>b>c B．b>c>a C．a>c>b D．b>a>c 3．下列关于变异和进化的说法，正确的是 A.用秋水仙素处理单倍体植株后得到的一定是纯合子 B.在三倍体无子西瓜的培育过程中，用四倍体西瓜作母本，用二倍体西瓜作父本，得到 的种子胚细胞中含有三个染色体组 C.两个种群间的隔离一旦形成，这两个不同种群的个体之间就不能进行交配，或者即使 能交配，也不能产生可育后代 D.突变能为生物进化提供原材料，但不包括染色体数目的变异，因为该过程并没有新的 基因产生
黑池中学2018级高三数学期末模拟试题理科（四） 一、选择题：本大题共12小题，每小题5分，共60分. 1.已知集合{}2,101，， -=A ，{} 2≥=x x B ，则A B =I A ．{}2,1,1- B.{ }2,1 C.{}2,1- D. {}2 2.复数1z i =-,则z 对应的点所在的象限为 A ．第一象限 B.第二象限 C.第三象限 D.第四象限 3 .下列函数中,是偶函数且在区间(0,+∞)上单调递减的函数是 A ．2x y = B ．y x = C ．y x = D ．2 1y x =-+ 4.函数 y=cos 2(x + π4 )－sin 2(x + π4 )的最小正周期为 A. 2π B. π C. π2 D. π 4 5. 以下说法错误的是 （ ） A ．命题“若x 2 -3x+2=0,则x=1”的逆否命题为“若x≠1,则x 2 -3x+2≠0” B ．“x=2”是“x 2 -3x+2=0”的充分不必要条件 C ．若命题p:存在x 0∈R,使得2 0x -x 0+1<0,则﹁p:对任意x∈R,都有x 2 -x+1≥0 D ．若p 且q 为假命题,则p,q 均为假命题 6.在等差数列{}n a 中, 1516a a +=,则5S = A ．80 B ．40 C ．31 D ．-31 7.如图为某几何体的三视图，则该几何体的体积为 A ．π16+ B ．π416+ C ．π8+ D ．π48+ 8.二项式6 21()x x +的展开式中，常数项为 A ．64 B ．30 C ． 15 D ．1 9.函数3 ()ln f x x x =-的零点所在的区间是 A ．(1,2) B ．(2,)e C ． (,3)e D ．(3,)+∞ 10.执行右边的程序框图，若0.9p =，则输出的n 为 A. 6 B. 5 C. 4 D. 3 开始 10n S ==， S p
高考文科数学模拟题 一、选择题: 1．已知集合{}{} 12,03A x x B x x =-<=<<，则A B =（） A ．{} 13x x -<”是“0< 高考数学模拟试题 （第一卷） 一、选择题：（每小题5分，满分60分） 1、已知集合A={x|x 2+2ax+1=0}的真子集只有一个，则a 值的集合是 A ．（﹣1，1）； B ．(﹣∞,﹣1)∪[1，+∞]； C ．{﹣1，1}； D ．{0} 2、若函数y=f(x)的反函数y=f －1(x)满足f －1(3)=0，则函数y=f(x+1)的图象必过点： A ．（0，3）； B ．（－1，3）； C ．（3，－1）； D ．（1，3） 3、已知复数z 1,z 2分别满足| z 1+i|=2，|z 2－3－3i|=3则| z 1－z 2|的最大值为： A ．5； B ．10； C ．5+13； D ．13 4、数列 ,4 3211,3211,211++++++ ……的前n 项和为： A ．12+n n ； B ．1+n n ； C ．222++n n ； D ．2+n n ； 5、极坐标方程ρsin θ=sin2θ表示的曲线是： A ．圆； B ．直线； C ．两线直线 D ．一条直线和一个圆。 6、已知一个复数的立方恰好等于它的共轭复数，则这样的复数共有： A ．3个； B ．4个； C ．5个； D ．6个。 7、如图，在正方体ABCD —A 1B 1C 1D 1中，E 、F 是异面直 线AC ，A 1D 的公垂线，则EF 和ED 1的关系是： A ． 异面； B ．平行； C ．垂直； D ．相交。 8、设(2－X)5=a 0+a 1x+a 2x+…+a 5x 5, 则a 1+a 3+a 5的值为： A ．－120； B ．－121； C ．－122； D ．－243。 9、要从一块斜边长为定值a 的直角三角形纸片剪出一块圆形纸片，圆形纸片的最大面积为： A ．2 πa 2； B ．24223a π-； C ．2πa 2； D ．2)223(a π- 10、过点（1，4）的直线在x,y 轴上的截距分别为a 和b(a,b ∈R +)，则a+b 的最小值是： A ．9； B ．8； C ．7； D ．6； 11、三人互相传球，由甲开始发球并作为第一次传球。经过5次传球后，球仍回到甲手中，则不同的传球方式共有： A ．6种； B ．8种； C ．10种； D ．16种。 12、定义在R 上的偶函数f(x)满足f(x+2)=f(x －2)，若f(x)在[﹣2，0]上递增，则 A ．f(1)>f(5.5) ; B ．f(1) 银川一中2019届高三年级第一次月考 理科综合试卷 命题人：本试卷分第I卷（选择题）和第II卷（非选择题）两部分。其中第II卷第33?38题为选考题, 其它题为必考题。考生作答时，将答案写在答题卡上，在本试卷上答题无效。 第I卷（共126分） 可能用到的相对原子质量（原子量）：H—1 0—16 Na—23 K—39 Mn—55 Cu—64 Ni—59 一、选择题：本题包括13小题。每小题6分，共78分，每小题只有一个选项符合题意。 1.下列有关病毒、原核生物和真核生物的描述，正确的是 A.病毒、原核生物和真核生物的共同点是遗传物质都是DM B.原核牛物和真核生物都具有完整的生物膜系统 C.病毒进入原核细胞后，细胞内的溶酶体会将其“消化” D.病毒能够借助原核生物或真核生物的核糖体来合成自身的蛋白质 2.玉米种子的萌发是种子的胚从相对静止状态变为生理活跃状态，并长成营自养生活的幼苗的过 程。下列关于该过程的叙述，正确的是 A.在萌发过程中，主要以被动运输的方式从外界吸收水和无机盐 B.在萌发过程中，细胞呼吸加强，导致细胞内有机物的总量一直减少 C.萌发过程中，各细胞的形态、结构和功能发生稳定性差异，但遗传物质没有发生变化 D.种子萌发初期增加的主要元素为C元素 3.结构与功能相统一是生物学的基本观点之一。下列叙述不能说明这一观点的是 A.叶绿体内类囊体膜堆叠使膜面积增大，利于光能充分利用 B.神经细胞轴突末梢有大量突起，有利于附着更多的神经递质受体蛋白 C.细胞骨架能维持真核细胞的形态，它与细胞的物质运输等活动有关 D.线粒体内膜向内突起形成悄，有利于附着更多的有氧呼吸有关的酶 4.自噬作用是普遍存在于大部分真核细胞屮的一种现象，是溶酶体对自身结构的吞噬降解，它是 细胞内的再循环系统。下列哪一项不属于自噬作用 A.为细胞内新细胞器的构建提供原料，即细胞结构的再循环 B.吞噬细胞吞噬受病每感染的细胞 C.衰老的细胞进入编程死亡过程屮的细胞内的吞噬 D.清除降解细胞内受损伤的细胞结构、衰老的细胞器 5.与物质跨膜运输相关的叙述正确的是 2020高考理科数学模拟试题精编 (考试用时：120分钟 试卷满分：150分) 注意事项： 1．作答选择题时，选出每小题答案后，用2B 铅笔在答题卡上对应题目选项的答案信息点涂黑；如需要改动，用橡皮擦干净后，再选涂其他答案。答案不能答在试卷上。 2．非选择题必须用黑色字迹的钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内相应位置上；如需改动，先划掉原来的答案，然后再写上新答案；不准使用铅笔和涂改液。不按以上要求作答无效。 3．考生必须保证答题卡的整洁。考试结束后，将试卷和答题卡一并交回。 第Ⅰ卷 一、选择题(本大题共12小题，每小题5分，共60分．在每小题给出的四个选项中，只有一项是符合题目要求的．) 1．设全集Q ＝{x |2x 2－5x ≤0，x ∈N}，且P ?Q ，则满足条件的集合P 的个数是( ) A ．3 B ．4 C ．7 D ．8 2．若复数z ＝m (m －1)＋(m －1)i 是纯虚数，其中m 是实数，则1z ＝( ) A ．i B ．－i C ．2i D ．－2i 3．已知等差数列{a n }的公差为5，前n 项和为S n ，且a 1，a 2，a 5成等比数列，则S 6＝( ) A ．80 B ．85 C ．90 D ．95 4．小明每天上学都需要经过一个有交通信号灯的十字路口．已知十字路口的交通信号灯绿灯亮的时间为40秒，黄灯5秒，红灯45秒．如果小明每天到路口的时间是随机的，则小明上学时到十字路口需要等待的时间不少于20秒的概率是( ) A.34 B.23 C.12 D.13 5．已知以下三视图中有三个同时表示某一个三棱锥，则不是．． 该三棱锥的三视图的是( ) 6．已知p ：a ＝±1，q ：函数f (x )＝ln(x ＋a 2＋x 2)为奇函数，则p 是q 成立的( ) 2020年高考文科数学模拟试卷及答案（共三套） 2020年高考文科数学模拟试卷及答案（一） 一、选择题：(本大题共12小题，每小题5分，在每小题给出的四个选项中，只有一项符合题目的要求) 1、设集合{}1 2 3 4U =，，，，集合{}2540A x x x =∈-+ 高三上期第二次周练 数学（理科） 第Ⅰ卷（选择题， 共60分） 一、选择题：本大题共12个小题,每小题5分,共60分.在每小题给出的四个选项中， 只有一项是符合题目要求的. 1．设集合{}=0123A ，，，， {}=21B x x a a A =-∈，， 则=( )A B ? A. {}12， B. {}13， C. {}01 ， D. {}13-， 2．已知i 是虚数单位， 复数z 满足()12i z i +=， 则z 的虚部是（ ） A. i - B. i C. 1- D. 1 3．在等比数列{}n a 中， 13521a a a ++=， 24642a a a ++=， 则数列{}n a 的前9项的和9S =（ ） A. 255 B. 256 C. 511 D. 512 4．如图所示的阴影部分是由x 轴， 直线1x =以及曲线1x y e =-围成， 现向矩形区域OABC 内随机投掷一点， 则该点落在阴影区域的概率是（ ） A. 1e B. 21 e e -- C. 11e - D. 11e - 5．在 52)(y x x ++ 的展开式中， 含 2 5y x 的项的系数是（ ） A. 10 B. 20 C. 30 D. 60 6．已知一个简单几何体的三视图如右图所示， 则该几何体的 体积为 ( ) A. 36π+ B. 66π+ C. 312π+ D. 12 7．已知函数 ())2log(x a x f -= 在 )1,(-∞上单调递减， 则a 的取值范围是( ) A. 11<< 2018高考文科数学模拟试题 一、选择题： 1．已知命题，，则是成立的（ ）条件． A ．充分不必要 B ．必要不充分 C ．既不充分有不必要 D ．充要 2．已知复数，，，是虚数单位，若是实数，则（ ） A ． B ． C ． D ． 3．下列函数中既是偶函数又在上单调递增的函数是（ ） A ． B ． C ． D ． 4．已知变量，之间满足线性相关关系 ，且，之间的相关数据如下表所示：则（ ） A ．0.8 B ．1.8 C ．0.6 D ．1.6 5．若变量，满足约束条件，则的最大值是（ ） A ．0 B ．2 C ．5 D ．6 6．已知等差数列的公差和首项都不为，且成等比数列，则（ ） A ． B ． C ． D ． 7．我国古代数学名著《孙子算经》中有如下问题：“今有三女，长女五日一归，中女四日一归，少女三日一归．问：三女何日相会？”意思是：“一家出嫁的三个女儿中，大女儿每五天回一次娘家，二女儿每四天回一次娘家，小女儿每三天回一次娘家．三个女儿从娘家同一天走后，至少再隔多少天三人再次相会？”假如回娘家当天均回夫家，若当地风俗正月初二都要回娘家，则从正月初三算起的 :12p x -<<2:log 1q x 2019年高考数学仿真模拟试题 本试卷共6页。考试结束后，将本试卷和答题卡一并交回。 注意事项： 1．答题前，考生先将自己的姓名、准考证号码填写清楚，将条形码准 确粘贴在考生信息条形码粘贴区。 2．选择题必须使用2B 铅笔填涂；非选择题必须使用0.5毫米黑色字迹的 签字笔书写，字体工整、笔迹清楚。 3．请按照题号顺序在答题卡各题目的答题区域内作答，超出答题区域 书写的答案无效；在草稿纸、试卷上答题无效。 4．作图可先使用铅笔画出，确定后必须用黑色字迹的签字笔描黑。 5．保持卡面清洁，不要折叠，不要弄破、弄皱。不准使用涂改液、修正带、 刮纸刀。 一、选择题：本题共12小题,每小题5分,共60分。在每小题给出的四个选 项中,只有一项是符合题目要求的。 1.已知集合{}3,2,1=A ，{} Z x x x x B ∈<--= ,0322 ,则=B A Y A ．{}2,1 B ．{}3,2,1,0 C ．[]2,1 D ．[]3,0 2.复数 i i 212-+的共轭复数的虚部是 A ．53- B ．53 C ．1- D ．1 3.下列结论正确的是 A ．若直线⊥l 平面α，直线⊥l 平面β，且βα,不共面，则βα// B ．若直线//l 平面α，直线//l 平面β，则βα// C ．若两直线21l l 、与平面α所成的角相等，则21//l l D ．若直线l 上两个不同的点B A 、到平面α的距离相等，则α//l 4.已知34cos sin = -αα，则=?? ? ??-απ4cos 2 A. 91 B. 92 C. 94 D. 9 5 5.设直线l 过双曲线C 的一个焦点，且与C 的一条对称轴垂直，l 与C 交于B A 、两点， 绝密★启用前 2017年普通高等学校招生全国统一考试 理科综合能力测试-生物部分 （银川一中第一次模拟考试） 本试卷分第I卷（选择题）和第II卷（非选择题）两部分，其中第II卷第33?40题为选考题，其它题为必考题。考生作答时，将答案答在答题卡上，在本试卷上答题无效。考试结束后，将本试卷和答题卡一并交回。 注意事项： 1. 答题前，考生务必先将自己的姓名、准考证号填写在答题卡上，认真核对条形码上的姓名、准考证号，并将条形码粘贴在答题卡的指定位置上。 2. 选择题答案使用2B铅笔填涂，如需改动，用橡皮擦干净后，再选涂其他答案的标号; 非选择题答案使用0. 5毫米的黑色中性（签字）笔或碳素笔书写，字体工整、笔迹清楚。 3. 考生必须按照题号在答题卡各题号相对应的答题区域（黑色线框）内作答，写出草稿纸上、超出答题区域或非题号对应的答题区域的答案一律无效。 4. 保持卡面清洁，不折叠，不破损。 5. 做选考题时，考生按照题目要求作答，并用2B铅笔在答题卡上把所选题目对应的题目涂黑。 可能用到的相对原子质量：H-l C-12 N-14 0-16 S-32 Fe-56 Cu-64 Ba-137 第I卷 一、选择题：本题共13小题，每小题6分，在每小题给出的四个选项中，只有一项是符合题 目要求的。 1. 破伤风杆菌一般在较深伤口内繁殖，可产生外毒素使机体发病，而外毒素的毒性可被胰蛋 白酶解除。下列有关分析错误的是 A. 破伤风杆菌的呼吸方式为无氧呼吸 B. 破伤风杆菌分泌的外毒素是在内质网上的核糖体合成的 C. 破伤风杆菌分泌的外毒素不能直接作为疫苗进行预防接种 D. 破伤风杆菌生命活动所需的能量来源于有机物的氧化分解 2. 科研人员研究小鼠癌变与基因突变的关系。如图为小鼠结肠癌发生过程中细胞形态和部分 凹凸教育高考文科数学模拟题 本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分，满分150分，考试时间120分钟. 第Ⅰ卷 一、选择题：本大题共12小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题目要求的. 1．已知全集,U R =且{}{} 2|12,|680, A x x B x x x =->=-+<则()U C A B I 等于 （A ）[1,4)- （B ）(2,3] （C ）(2,3) （D ）(1,4)- 2．已知i z i 32)33(-=?+（i 是虚数单位），那么复数z 对应的点位于复平面内的 （A ）第一象限 （B ）第二象限 （C ）第三象限 （D ）第四象限 3．下列有关命题的说法正确的是 （A ）命题“若21x =，则1=x ”的否命题为：“若21x =，则1x ≠”． （B ）“1x =-”是“2560x x --=”的必要不充分条件． （C ）命题“x R ?∈，使得210x x ++<”的否定是：“x R ?∈， 均有210x x ++<”． （D ）命题“若x y =，则sin sin x y =”的逆否命题为真命题． 4．某人骑自行车沿直线匀速旅行，先前进了a 千米，休息了一段时间，又沿原路返回b 千米（)a b <，再前进c 千米，则此人离起点的距离s 与时间t 的关系示意图是 （A ） （B ） （C ） （D ） 5．已知(31)4,1()log ,1a a x a x f x x x -+ F D C B A 2019年高考数学模拟试题（理科） 注意事项： 1．本试卷分第Ⅰ卷（选择题）和第Ⅱ卷（非选择题）两部分。答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。 2．回答第Ⅰ卷时，选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。如需改动，用橡皮擦干净后，再选涂其他答案标号。写在本试卷上无效。 3．回答第Ⅱ卷时，将答案写在答题卡上。写在本试卷上无效。 4．考试结束后，将本试卷和答题卡一并收回。 一．选择题：本大题共12个小题，每小题5分，共60分。在每小题给出的四个选项中只有一项是符合题目要求的 1．已知集合}032{2>--=x x x A ，}4,3,2{=B ，则B A C R ?)(= A ．}3,2{ B ．}4,3,2{ C ．}2{ D ．φ 2．已知i 是虚数单位，i z += 31 ，则z z ?= A ．5 B ．10 C ． 10 1 D ． 5 1 3．执行如图所示的程序框图，若输入的点为(1,1)P ，则输出的n 值为 A ．3 B ．4 C ．5 D ．6 （第3题） （第4题） 4．如图，ABCD 是边长为8的正方形，若1 3 DE EC =，且F 为BC 的中点，则EA EF ?= A ．10 B ．12 C ．16 D ．20 5．若实数y x ,满足?? ???≥≤-≤+012y x y y x ，则y x z 82?=的最大值是 A ．4 B ．8 C ．16 D ．32 6.一个棱锥的三视图如右图，则该棱锥的表面积为 A ．3228516++ B ．32532+ C ．32216+ D ．32216516++ 7. 5张卡片上分别写有0，1，2，3，4，若从这5张卡片中随机取出2张，则取出的2张卡片上的数字之和大于5的概率是 A ． 101 B ．51 C ．103 D ．5 4 8．设n S 是数列}{n a 的前n 项和，且11-=a ，11++?=n n n S S a ，则5a = A ． 301 B ．031- C ．021 D ．20 1 - 9. 函数()1ln 1x f x x -=+的大致图像为 10. 底面为矩形的四棱锥ABCD P -的体积为8，若⊥PA 平面ABCD ,且3=PA ，则四棱锥 ABCD P -的外接球体积最小值是 银川一中2021届高三年级第四次月考 理科综合能力测试-生物 命题教师：注意事项： 1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。 2．作答时，务必将答案写在答题卡上。写在本试卷及草稿纸上无效。 3．考试结束后，将本试卷和答题卡一并交回。 可能用到的相对原子质量：H-1 C-12 O-16 Ni-59 Cu-64 Mg-24 I-127 一、选择题：本题包括13小题。每小题6分，共78分，在每小题给出的四个选项中，只有一个选项符合题意。 1．脂肽是一种高效环保材料，在化妆品、洗涤工业等领域得到广泛应用,脂肽是由枯草芽孢杆菌分泌的生物表面活性剂，其结构如下图所示，下列叙述正确的是 A．该化合物的空间结构主要由氨基酸的空间结构决定 B．该化合物加热变性后仍能与双缩脲试剂产生紫色反应 C．枯草芽孢杆菌分泌脂肽需要经过内质网、高尔基体等结构 D．该化合物的合成至少要经过7次氨基酸之间的脱水缩合反应 2．2020年10月5日，诺贝尔生理学或医学奖授予哈维·阿尔特、迈克尔·霍顿和查尔斯·M·赖斯三位科学家，以表彰他们在发现“丙型肝炎病毒”（即HCV）方面作出的贡献。该病毒体呈球形，为单股正链RNA病毒（中心法则：+RNA→蛋白质；+RNA→-RNA→大量+RNA），其衣壳外包绕含脂质的囊膜，囊膜上有刺突。下列关于该病毒的说法正确的是 A．HCV的预防只需要切断传播途径和注射疫苗即可加以防控 B．HCV与HIV都可使人类染病，可通过无丝分裂延续子代 C．HCV的增殖离不开宿主细胞提供氨基酸、核苷酸和核糖体等 D．若要培养该病毒用于研究疫苗，需要提供相应的营养物质和活的大肠杆菌 3．下列有关“基本骨架”或“骨架”的叙述，错误的是 A．真核细胞中由纤维素组成细胞骨架，与细胞运动、分裂和分化有关 B．DNA分子中的脱氧核糖和磷酸交替连接排在外侧构成基本骨架 高考理科数学模拟试卷（含答案） 本试卷分选择题和非选择题两部分. 第Ⅰ卷(选择题)1至2页,第Ⅱ卷 (非选择题)3至4页,共4页,满分150分,考试时间120分钟. 注意事项： 1.答题前,务必将自己的姓名、考籍号填写在答题卡规定的位置上. 2.答选择题时,必须使用2B 铅笔将答题卡上对应题目的答案标号涂黑,如需改动,用橡皮擦擦干净后,再选涂其它答案标号. 3.答非选择题时,必须使用0.5毫米黑色签字笔,将答案书写在答题卡规定位置上. 4.所有题目必须在答题卡上作答,在试题卷上答题无效. 5.考试结束后,只将答题卡交回. 第Ⅰ卷 (选择题,共60分) 一、选择题：本大题共12小题,每小题5分,共60分.在每小题给出的四个选项中,只有一项是符合题目要求的. 1. 已知集合2 {1,0,1,2,3,4},{|,}A B y y x x A =-==∈,则A B =I (A){0,1,2} (B){0,1,4} (C){1,0,1,2}- (D){1,0,1,4}- 2. 已知复数1 1i z = +,则||z = (A) 2 (B)1 (D)2 3. 设函数()f x 为奇函数,当0x >时,2 ()2,f x x =-则((1))f f = (A)1- (B)2- (C)1 (D)2 4. 已知单位向量12,e e 的夹角为 2π 3 ,则122e e -= (A)3 (B)7 5. 已知双曲线22 221(0,0)x y a b a b -=>>的渐近线方程为3y x =±,则双曲线的离心率是 (B) 3 (C)10 (D)10 9 6. 在等比数列{}n a 中,10,a >则“41a a <”是“53a a <”的 作业指导书 密接式钩缓装置检修 密接式钩缓装置检修岗位作业要领 标准化密接式钩缓检修岗位安全风险提示 1.工作时必须穿戴防砸皮鞋，防止车轮碾伤或铁屑扎伤； 2.必须戴安全帽、防护眼镜，防止异物溅入眼睛； 3.检修时要轻拿轻放，检修、搬运、存放时均不得落地； 4.使用升降小车取钩时，注意安装牢固后再分解车钩。 目次 1.工前准备 (1) 2.密接式车钩装置与车体分离 (2) 3.分解钩缓装置 (3) 4.零部件检修 (7) 5.密接钩装置组装及试验 (14) 6.密接钩装车 (18) 7.钩高调整 (20) 8.完工清理 (22) 钩缓装置检修作业指导书类别：A2、A3级检修系统：车钩缓冲装置部件：密接式钩缓装置 密接式钩缓装置检修作业指导书适用车型：25T 作业人员：车辆钳工3-4名（岗位合格证）作业时间：6小时/个 工装工具：1.钢卷尺； 2.钩缓升降车； 3.活动扳手、手锤、钩引、力矩扳手； 4.托盘。作业材料：砂轮片、护目镜、扫帚、簸箕、拖布、平板调整垫 作业场所：辅库 环境要求：通风、自然采光良好 操作规程：钩缓升降车技术操作规程 参考资料： 1.《铁路客车段修规程（试行）》.（铁总运〔2014〕349号）. 2.《车辆钳工》.中国铁道出版社.2011 3.《车辆处转发中国铁路总公司运输局关于印发客车常见故障专项整治方案的通知》（辆函〔2015〕240号） 4.《中国铁路总公司运输局关于印发客车检修规程勘误的通知》（运辆客车函〔2016〕137号） 安全防护及注意事项： 1.——徒手搬运配件时，防止掉落，避免伤及人员； 2.——打磨配件时，注意力集中，避免伤及人员。 基本技术要求： 1.车钩缓冲装置整体分解下车，清除锈垢，可见部位外观检查须良好，探伤部件须露出金属本色。回转机构、连 挂系统分解检修，缓冲器、钩体、安装座状态检查，表面无裂纹。橡胶件A2修状态不良时更新，A3修时更新。 2.探伤件经热处理、调修后或经过焊修、机械加工的探伤部位须复探。 3.有力矩要求的防松螺母均须按表一标准用扭力扳手检查，其余螺母、螺栓可参考执行。 4.所有组装配件须是合格品。 2019高考文科数学模拟试卷 一、选择题 1. 已知集合{ } 2 230A x N x x =∈+-≤，则集合A 的真子集个数为 （A ）31 （B ）32 （C ）3 （D ）4 2. 若复数()()21z ai i =-+的实部为1，则其虚部为 （A ）3 （B ）3i （C ） 1 （D ）i 3.设实数2log 3a =，12 13b ??= ??? ，13 log 2c =，则有 （A ）a b c >> （B ）a c b >> （C ）b a c >> （D ）b c a >> 4.已知1 cos()43 π α+ =，则sin2α= （A ）79- （B ）79 （C ）22± （D ）79 ± 5. 宋元时期数学名著《算学启蒙》中有关于“松竹并生”的问题：松长五尺，竹长两尺，松日自半，竹日自倍，松竹何日而长等，右图是源于其思想的一个程序框图，若输入的,a b 分别为5,2，则输出的n 等于 （A ）2 （B ）3 （C ）4 （D ）5 6.如图，AB 为圆O 的一条弦，且4AB =，则OA AB =u u u r u u u r g （A ）4 （B ）-4 （C ）8 （D ）-8 7.以下命题正确的个数是 ①函数()f x 在0x x =处导数存在，若0:()0p f x '=；0:q x x =是()f x 的极值点， 则p 是q 的必要不充分条件 ②实数G 为实数a ，b 的等比中项，则G ab =± ③两个非零向量a r 与b r ，若夹角0a b 银川一中2021届高三年级返校测试 理科综合能力试卷-生物部分 命题教师：注意事项： 1．答卷前，考生务必将自己的姓名、准考证号填写在答题卡上。 2．作答时，务必将答案写在答题卡上。写在本试卷及草稿纸上无效。 3．考试结束后，将本试卷和答题卡一并交回。 可能用到的相对原子质量：H-1 N-14 O-16 Na-23 S-32 Mn-55 一、选择题：本题包括13小题。每小题6分，共78分，在每小题给出的四个选项中，只 有一个选项符合题意。 1．用驴皮熬成的阿胶已有两千多年的应用历史。其滋补作用体现为：加快新陈代谢，促进组织细胞再生和增强免疫力。下列说法正确的是 A．阿胶具有滋补作用的原因是含有对人体有益的Zn、Fe、Ca等微量元素 B．驴皮细胞的脂肪含量较低，其主要储能物质是葡萄糖 C．食用阿胶能减少人体对糖类的摄入，因为阿胶中含有的多糖主要是纤维素 D．用驴皮熬成的阿胶为人体提供的主要营养物质之一可能是必需氨基酸 2．科学家使用相同的完全培养液分别培 养水稻和番茄，一段时间后，检测培 养液中的离子浓度，如图所示。 下列说法错误的是 A．水稻和番茄对离子吸收具选择性的 直接原因与膜上载体有关 B．定期向培养液中通入空气有助于促进根细胞对离子的吸收 C．Mg和Ca等矿质元素在细胞中主要以离子形式存在 D．水稻对Mg2+和Ca2+的吸收量比水多，番茄吸收水比吸收SiO2+的量多 3．无丝分裂又叫核粒纽丝分裂，是最早被发现的一种细胞分裂方式，细胞不经过有丝分裂各时期分裂为大致相等的两部分的细胞分裂方式。下列叙述正确的是 A．无丝分裂不进行DNA分子的复制 B．蛙的红细胞和细菌都能进行无丝分裂 C．无丝分裂中，核膜和核仁不消失，没有染色体的变化 D．秋水仙素可抑制无丝分裂中细胞的分裂，从而使细胞体积增大 4．达尔文的自然选择学说，揭示了生物进化的机制，解释了适应性的形成和物种形成的原因；但其理论并不完善，现代生物进化理论极大地丰富和发展了达尔文的自然选择学说。 下列有关生物进化的描述错误的是 A．自然选择学说指出可遗传变异是生物进化的原材料，包括突变和基因重组 B．适应的形成是由于具有有利变异的个体更容易生存并留下后代，是自然选择的结果C．现代生物进化理论在分子水平和种群水平对达尔文自然选择学说进行了补充与丰富D．中性突变学说认为决定生物进化方向的是中性突变的逐渐积累，而不是自然选择5．对照实验是生物科学探究中常用的实验方法之一，设置对照实验的方法也多种多样。下列关于对照实验的说法，错误的是 A．“低温诱导染色体加倍”的实验中，作为对照的常温组也要用卡诺氏液处理 B．“探究生长素类似物促进扦插枝条生根”的预实验中，不需要设置对照实验 C．“探究血浆维持pH相对稳定”的实验中，清水组和缓冲液组都作为对照组 D．沃泰默探究狗胰液分泌调节的实验中，将稀盐酸注入狗的血液能起对照作用 6．下列说法中不属于负反馈调节的是 A．胰岛素的分泌量增加会降低血糖浓度，血糖浓度反过来影响胰岛素的分泌 B．甲状旁腺激素引起血钙含量升高，高血钙又抑制了甲状旁腺的分泌 C．一片草原的兔子数量增多，导致青草减少的同时兔的天敌数量增多，会导致兔子的数量减少 D．促甲状腺激素释放激素会促进垂体分泌促甲状腺激素，促甲状腺激素会促进甲状腺分泌甲状腺激素 29．（12分） 某研究小组利用某植物进行下列关于光合作用有关的实验： 第一步：将一植株保留一叶片a和一幼嫩果实c，b为叶片和果实连接的茎； 第二步：把处理好的植株放入一透明小室，并放到光合作用最适的温度和光照强度下培养； 第三步：向小室充入一定量14CO2，密封小室，立即用仪器测定a、b、c三处的放射性物质含量并记录； 2017年普通高等学校招生全国统一模拟考试 文科数学 考场：___________座位号：___________ 本试卷分第I 卷（选择题）和第II 卷（非选择题）两部分。满分150分，考试时间120分 钟. 第I 卷（选择题共60分） 选择题：本大题共12小题，每小题5分，共60分.在每小题给出的四个选项中，只有一项是符合题目要求的。 (1)设集合A=｛4，5，7，9｝，B=｛3，4，7，8，9｝，全集U A B =，则集合 () U A B 中的元素共有( ) (A) 3个 （B ） 4个 （C ）5个 （D ）6个 （2）（2） 复数 3223i i +=-( ) （A ）1 （B ）1- （C ）i (D)i - （3）已知()()3,2,1,0a b =-=-，向量a b λ+与2a b -垂直，则实数λ的值为（ ） （A ）17- （B ）17 （C ）1 6 - （D ）16 （4）已知tan a =4,cot β=1 3 ,则tan(a+β)=( ) (A)711 (B)711- (C) 713 (D) 713 - （5）已知双曲线)0(13 2 22>=- a y a x 的离心率为2，则=a （ ） A. 2 B. 26 C. 2 5 D. 1 （6）已知函数()f x 的反函数为()()10g x x ＝＋2lgx ＞，则=+)1()1(g f ( ) （A ）0 （B ）1 （C ）2 （D ）4 （7）在函数①|2|cos x y =，②|cos |x y = ，③)62cos(π + =x y ,④)4 2tan(π -=x y 中，最小正周期为π的所有函数为（ ) A.①②③ B. ①③④ C. ②④ D. ①③ （8）如图，网格纸的各小格都是正方形，粗实线画出的事一个几何体的三视图，则这个几 何体是（ ） A.三棱锥 B.三棱柱 C.四棱锥 D.四棱柱 （9）若0tan >α，则( ) A. 0sin >α B. 0cos >α C. 02sin >α D. 02cos >α (10) 如果函数3cos(2)y x φ=+的图像关于点4(,0)3 π 中心对称，那么φ的最小值为( ) (A) 6π (B) 4π (C) 3π (D) 2 π （11）设,x y 满足24, 1,22,x y x y x y +≥?? 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