分子分离过程中的膜操作_膜科学与工程大全_9787030345011

分子分离过程中的膜操作

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　　膜技术在许多领域发挥着主导作用，如海水淡化、废水处理与回用、人造器官等。《膜科学与工程大全：分子分离过程中的膜操作》阐述和讨论了最具有重大作用的膜操作的基本原理及其应用，包括液相（MF、UF、NF和RO）和气相（气体分离和蒸汽渗透）压力驱动系统以及其他分离过程，如渗析、渗透汽化、电化学膜系统等。

引言
20世纪被描绘成一个众多资源密集型工业迅猛发展的时期，尤其是在一些亚洲国家，其特征还表现在全球人口增长、寿命延长以及生活质量水准的全面提高。伴随近代史的上述正面评价指标的还有水危机、环境污染和大气中CO。排放量增加等负面评价指标。描述我们最新进展的改革的这些负面评价指标很大程度上取决于改革自身或针对改革的推动力是否缺少创新和既能控制又能减小世界范围工业发展中相对明显的负面指标的新策略。废水处理策略就是一个明确的例子，如图1所示，自1556年至今，相同理念基本上出现在各种废水处理系统中。
今天人们都意识到需要致力于知识密集型工业技术的发展，这将使得工业系统实现从基于数量基准向基于质量基准的转变成为可能。人类资本正在逐步成为这种社会经济改革的推动力，可持续发展的机遇来自于先进技术的应用。膜技术已在许多领域被认为是能致力于实现可持续发展的最有效技术之一（图2）。
过程工程是解决当今及未来世界所面临的新问题的技术创新中最密切的学科之一。最近，从逻辑学上过程强化已被认为是上述问题的最好的过程工程答案。过程强化包括装置、设计以及过程开发方法的创新等，这些创新可望在化学和任何其他制造及加工过程中诸如生产成本、装置尺寸、能量消耗及废物产生的降低与遥控、信息流及过程灵活性的改进等方面获得实质性进展（图3）。
然而如何有效实现上述策略并非显而易见。一个有趣和重要的情形是现代膜工程的持续发展，它的基本特征满足了过程强化的需要。膜操作的固有特性包括高效和操作简便、特定组分传递过程的高选择性和渗透性、集成系统中不同膜操作的相互兼容性、低能耗需求、操作过程中的良好稳定性和环境协同性、易于控制和放大以及大的操作弹性等，因此成为使得化学和其他工业生产过程合理化的令人关注的手段。许多膜操作实际上基于相同硬件（膜材料）区分于不同软件（方法）。传统的膜分离操作（反渗透（RO）、微滤（MF）、超滤（UF）、纳滤（NF）、电渗析、渗透汽化等）已经大量用于许多不同用途，并由此引导出一些诸如催化膜反应器和膜接触器等新的膜系统。

2.01 Fundamentals in Reverse Osmosis
G Jonsson, Technical University of Denmark, Lyngby, Denmark F Macedonio, University of Calabria, Arcavacata di Rende (CS), Italy a2010 Elsevier B.V. All rights reserved.
2.01.1 Introduction 2
2.01.2 Phenomenological Transport Models 3
2.01.2.1 Irreversible Thermodynamics-Phenomenological Transport Model 3
2.01.2.2 IT-Kedem?Spiegler Model 4
2.01.3 Nonporous Transport Models 4
2.01.3.1 Solution?Diffusion Model 4
2.01.3.2 Extended Solution?Diffusion Model 5
2.01.3.3 Solution?Diffusion-Imperfection Model 5
2.01.4 Porous Transport Models 5
2.01.4.1 Friction Model 5
2.01.4.2 Finely Porous Model 6
2.01.5 Comparison and Summary of Membrane Transport Models 7
2.01.6 Influence from Operating Conditions on Transport 7
2.01.6.1 Effect of Pressure 7
2.01.6.2 Effect of Concentration 8
2.01.6.3 Effect of Feed Flow 8
2.01.6.4 Effect of Temperature 8
2.01.6.5 Effect of pH 9
2.01.7 Experimental Verification of Solute Transport 10
2.01.7.1 Single-Salt Solutions 12
2.01.7.2 Mixed-Salt Solutions 13
2.01.7.3 Organic Solutes and Nonaqueous Solutions 16
2.01.7.4 Mixed Organic Solutes 18
2.01.7.5 Membrane Charge 18
2.01.7.6 Membrane Fouling and Concentration Polarization Phenomena: Limits of Membrane
Processes 19
References 20

2 Reverse Osmosis and Nanofiltration

2.01.1 Introduction
Several models on reverse osmosis (RO) transport mechanisms and models have been developed to describe solute and solvent fluxes through RO mem-branes. The general purpose of a membrane mass transfer model is to relate the fluxes to the operating conditions. The power of a transfer model is its ability to predict the performance of the membrane over a wide range of operating conditions. To realize this objective, the model has to be integrated with some transport coefficients often determined based on some experimental results.
When theories are proposed to describe mem-brane transport, either the membrane can be treated as a black box in which a purely thermodynamic description is used, or a physical model of the mem-brane can be introduced. The general description obtained in the first case gives no information on the flow and separation mechanisms. On the other hand, the correctness of data on the flow and separation mechanisms obtained in the second case depends on the chosen model.
The transport models can be divided into three categories:
1.
phenomenological transport models which are inde-pendent of the mechanism of transport and are based on the theory of irreversible thermodynamics (irreversible thermodynamics ? phenomenological transport and irreversible thermodynamics ? Kedem?Spiegler models);

2.
nonporous transport models, in which the membrane is supposed to be nonporous or homogeneous (solution?diffusion, extended solution?diffusion, and solution?diffusion-imperfection models (SDIMs)); and

3.
porous transport models, in which the membrane is supposed to be porous (preferential sorption-capillary flow, Kimura?Sourirajan analysis, finely porous and surface force-pore flow, and friction models).

Fundamentals in Reverse Osmosis 3
Most models for RO membranes assume diffusion or pore flow through the membrane while charged-membrane theories include electrostatic effects. For example, Donnan exclusion models can be used to determine solute fluxes in the often negatively charged nanofiltration membranes.
Moreover, RO membranes have, in general, an asymmetric or a thin-film composite structure where a porous and thin top layer acts as selective layer and determines the resistance to transport. Macroscopically, these membranes are homoge-neous. However, on the microscopic level, they are systems with two phases in which the transport of water and solutes takes place. Figure 1 provides a schematic presentation of a thin-film composite membrane structure with (1) the highly selective skin layer which acts as a barrier, (2) the intermediate porous layer where the selectivity decreases to zero, and (3) the nonselective porous sublayer.
The porous sublayer influences the total hydrau-lic permeability (Lp) from Reference 1:
111 1
Lp .Lp sl tLp il tLp pl e1T
But it has almost no influence on the solute rejection properties of the membranes. Therefore, most trans-port and rejection models of RO membranes have been derived for single-layer membranes focusing almost only on the surface thin layer.
Transport models can help in identifying the most important membrane structural parameters and showing how membrane performance can be improved by varying some specific parameters. One of the main membrane intrinsic parameters is the reflection coefficient, s, introduced by Staverman
[2] and defined as
? lp P
X lp .Jv .0 e2T

Figure 1 Schematic presentation of thin-film composite membrane structure.
where s describes the effect of the pressure driving force on the flux of solute and represents the relative permeability of the membrane to the solute:
1.
s .1 for a high-separation membrane and

2.
s .0 for a low-separation membrane in which the solute is significantly carried through the mem-brane by solvent flux.

In RO, the intrinsic retention Rmax is related to sand normally sRmax (as reported in Reference 3). Pusch
[4] derived the following relationship between Rmax csmax
and :Rmax 1 ?1 ?
.eT? c9
s
where csmax is the mean salt concentration at infinite Jv.

2.01.2 Phenomenological Transport Models
2.01.2.1 Irreversible Thermodynamics-Phenomenological Transport Model
The membrane is treated as a black box when nothing on the transport mechanism and membrane structure is known. In this case, the thermodynamics of irreversible thermodynamics (IT) processes can be applied to membrane systems. According to the IT theory, the flow of each component in a solution is related to the flows of other components. Then, different relation-ships between the flux through the membrane and the forces acting on the system can be formulated.
Onsager [5] suggests that fluxes Ji are related to the forces Fj through the phenomenological coeffi-cient Lij:
X
Ji .LiiFi tLijFj for i .1;...;n e3Ti.j
6
For systems close to equilibrium, the cross-coefficients are equal:
Lij .Lji for i .6j e4T
Kedem and Katchalsky [6] used the linear phe-nomenological relationships (Equations (3) and (4)) to derive the phenomenological transport:
Jv P ?
.lpeTe5TJs .!te1 ? TJvecsTln e6T
where parameters lp, !, and sare simple functions of the original phenomenological coefficient Lij.
Usually RO systems are far from equilibrium; therefore, Equation (4) may not be correct. Moreover,
4 Reverse Osmosis and Nanofiltration
phenomenological transport equations (5) and (6) have been rarely applied for describing RO membrane transport both because the often large concentration difference across the membranes invalidates the linear laws and because this analysis does not give much information regarding the transport mechanism.

2.01.2.2 IT-Kedem?Spiegler Model
Spiegler and Kedem [13] bypassed the problem of linearity by rewriting the original IT equations for solvent and solute flux in differential form:
dP d
Jv .pv ?e7T
dx dx
dcs
Js1 ?csJv
.p dx teTe8Twhere pv is the water permeability, x the coordinate direction perpendicular to the membrane, and ps the solute permeability. Integrating Equations (7) and (8) over the thickness of the membrane by assuming pv, ps, and sconstant, the following equations for the solvent flux Jv and retention R are achieved:
pv
Jv .x eP ?Te9T
f1 ? exp.?Jve1 ? Tx=psge10TR .1 ?exp.?Jve1 ? Tx=ps
where x is the membrane thickness. Equation (10) can be rearranged as follows:
c9s1 x
c0s .1 ? ? 1 ? exp ?Jve1 ? Tps e11T
However, similar to phenomenological transport equations, Spiegler and Kedem relationships also do not give information on the membrane transport mechanism.

2.01.3 Nonporous Transport Models
2.01.3.1 Solution?Diffusion Model
The solution?diffusion model assumes that (1) mem-brane surface layer is homogenous and nonporous and (2) both solute and solvent dissolve in the surface layer and then they diffuse across it independently. Water and solute fluxes are proportional to their chemical potential gradient. The latter is expressed as the pressure and concentration difference across the membrane for the solvent, whereas it is assumed to be equal to the solute concentration difference across the membrane for the solute:
Jv .AeP ?Te12T
DvcvVv
A .e13T
R T x
Js .Bces -?cs0Te14T
Dsk
B .e15T
x
where A is the hydraulic permeability constant lp, B is the salt permeability constant, cs -and cs0are, respec-tively, the salt concentrations on the feed and permeate sides of the membrane. Dv and Ds are the diffusivities of the solvent and the solute in the membrane, respectively; cv is the concentration of water in the membrane; Vv is the partial molar volume of water; R is the universal gas constant; T is the temperature; k is the partition or distribution coefficient of solute defined as follows:
kg solute m ? 3 membrane K .kg solute m ? 3 solution e16T
k measures the solute affinity to (k > 1) or repulsion from (k < 1) the membrane material.
Following Equations (12)?(15), differences in solubilities and diffusivities of the solute and solvent in the membrane phase are important in this model since these differences strongly influence the fluxes through the membrane. Moreover, these equations prove that the solute flux through the membrane is independent of water flux.
Because the concentration of salt in the permeate solution c0s is usually much smaller than cs -, Equation
(14) can be simplified as follows:
Js .Bcs -e17T
Equations (12) and (17) show that the water flux is proportional to the applied pressure, whereas the solute flux is independent of pressure. This means that the membrane selectivity increases with increasing pressure. The membrane selectivity can be measured as solute rejection R given by
c0s
R .1 ? c-s 100% e18T
By combining Equations (12)?(18) with the rela-tionship (19) between c0s, Jv, and Js, the membrane rejection can be expressed as follows:
Js
c0s .Jv v e19T
Fundamentals in Reverse Osmosis 5
v B
R .1 ? 100% e20T
A P ?
eT
where v is the density of water.
The main advantage of the solution?diffusion model is its simplicity. One of its restriction is that it foresees rejection equal to 1 at infinite flux eP !1T,a limit not reachable for many solutes. Therefore, this model is appropriate for solvent?solute-membrane systems where the separation is close to 1. Moreover, it can be noted that Equation (5) is reduced to the solution? diffusion model when s .1.

2.01.3.2 Extended Solution?Diffusion
and solvent and solute can flow through them without any change in concentration. Therefore, SDIM includes pore flow as well as diffusion of solute and solvent through the membrane and it can be considered a compromise between solution?diffusion and porous models. Moreover, Jonsson and Boesen [10] proved that SDIM can be used to determine a parameter identified with the reflection coefficient. According to themodel,water and solutefluxes can be writtenas
Jv .k1eP ?TtK3P
|...........{z...........}|..{z..}
diffusion pore flow contribution to water flux
k3
.ek1 tk3TP ?k1 tk3 e23T

Model Js .k2tK3Pc
9
s
|....{z....}
pore flow of solute through the membrane
e24T
In the solution?diffusion model, the effect of pressure on solute transport is neglected [8, 19]. In order to where K3P is the term proportional to the pressure-

include the pressure term, the salt chemical potential driving force; k1 and k2 are the transport parameters gradient has to be written as for diffusive water and solute flux, respectively; and
k3 is the transport parameter for the pore flow.

c
s
s
P e21T
.RT ln
tVs
Equations (23) and (24) can be rearranged to give
s
where s is the solute chemical potential difference
0
c
990
the reduction factor [3]:
s csJv s
eP ?Ttk3 P
k1
k3

the membrane and Vs is the solute partial c
across
e25T..
k2
Js
molar volume.
P
c
t
k1 c9s k1
For sodium chloride?water separation, Burghoff

VsP and comparing Equation (23) with Equation (5), set al. [8] suggest ignoring the pressure term can be obtained:
RT
1

c
s ? 6P.
.k3 e26T
when ln
>>8:0 10
c
0s
Including pressure, particularly for organic-water
where the ratio k3 =k1 is
1 t
k1
a measure of the relative systems, the solute flux is given by contribution of pore flow compared to diffusive flow.
Dsk
0-
s ? sTtlsp
where lsp is the pressure-induced transport parameter.
Equation (22) has been proved to be accurate for different organic solutes with cellulose acetate mem-branes [8].

2.01.3.3 Solution?Diffusion-Imperfection Model
The solution?diffusion model is one of the most referred membrane models. It presupposes that the membrane surface is homogenous/nonporous and it has the limitation that the intrinsic value of retention is always unity.
The SDIM developed by Sherwood et al. [9] considers that small imperfections exist on the mem-brane surface due to the membrane-making process,
P e22T
Js
.x e
cc
This model has been successfully applied for the
performance description of several solutes and
membranes [10], particularly it is proper for those membranes exhibiting lower separation than that cal-culated from solubility and diffusivity measurements.

2.01.4 Porous Transport Models
Among the transport models in which the membrane is supposed to be porous, friction and finely porous models are described in this section.
2.01.4.1 Friction Model
Friction model considers that the transport through porous membrane occurs both by viscous and diffu-sion flow. Therefore, the pore sizes are considered so
6 Reverse Osmosis and Nanofiltration
small that the solutes cannot pass freely through the pores but friction between solute-pore wall and sol-vent-pore wall and solvent?solute occurs. The frictional force F is linearly proportional to the velo-city difference through a proportional factor X called friction coefficient indicating the interaction between solute and pore wall:
F23 .?X23 eu2 ?u3T.?X23u2 e27T
F13 .?X13 eu1 ?u3T.?X13u1 e28T
F21 .?X21eu2 ?u1Te29T
F12 .?X12eu1 ?u2Te30T
Equations (27)?(30) are derived considering the membrane as reference (u3 .0). Considering that the frictional force per mole of solute F23 is given by
J2p
F23 .?X23u2 .?X23 e31T
c2p
Equation (27) can be written as
J2p
F23 .?X23 e32T
c2p
Jonsson and Boesen [10] have presented a detailed description of this model and they have shown that, as F21 is the effective force for diffusion of solute in the center of mass system, the solute flux per unit pore area J2p is given by
1 J2p .X21 c2pe?F21Ttc2p ?u e33T
A balance of applied and frictional forces is equal to
F2 .? eF21 tF23Te34TNeglecting the pressure term and in the case of dilute solution behavior, F2 is equal to
RT dc2p
F2 .? c2p dx e35T
Defining b as the term that relates the frictional coefficients X23 (between solute and membrane) and X21 (between solute and water)
b .X21 tX23 e36TX21
and inserting in Equations (29), (32), and (34)?(36), J2p can be written as
RT dc2p c2p?u J2p .? X21?b dx tb e37T
The coefficient for distribution K of solute between bulk solution and pore fluid is given by
K .c2p =c2 e38T
with Jv ."?u, Ji .J2?", and .?x, using the pro-duct condition
c02 .Ju 2p e39T
and integrating Equation (37) with the boundary conditions x .0: c2p .Kc92; x .?: c2p .Kc0 the following equation for the ratio c2 9 =c2 0 is obtained:
c9b exp u"?X21 ? 1
X21
c022 .1 tk exp u""?"RTRT e40T
In this derivation K, b, and X21 are assumed to be independent from the solute concentration.

2.01.4.2 Finely Porous Model
The finely porous model was developed by Merten
[11] using a balance of applied and frictional forces proposed by Spiegler [12]. It is a combination between viscous flow and frictional model presented in detail by Jonsson and Boesen [10]. The premise of the model is to describe, reasonably, the transport of water and solutes in the intermediate region between solution?diffusion model and Poiseuille flow:
1.
the first is reasonable when applied to very dense membranes and solutes which are almost totally rejected, whereas

2.
Poiseuille flow can be used to describe the trans-port through porous membranes consisting of parallel pores.

Jonsson and Boesen [10] showed that the following equation can be used to determine Rmax from RO experiments:
c92 bb ?Jv
c02 .K t1 ? K exp ? "? D2 e41T
where D2 is the solute diffusion coefficient. From Equation (41), the maximum rejection Rmax (at Jv !1) is given by K 1
Rmax ..1 ? b .1 ? K e42T
X231 tX21
Equation (42) shows how rejection is related to a kinetic term (the friction factor b) and to a thermo-dynamic equilibrium term (K). Spiegler and Kedem
[13] derived the following corresponding expression:
1 X23u2
.1 ? K 1 tX21 1 tX21u1 e43T
X23
Equations(42)and(43)areidenticalapartthecorrection term X13u2 =X21u1 whichismuchsmaller than 1for

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