分離技術シリーズ 32

物質の移動と平衡から学ぶ

化学工学的分離法の基礎
相良紘

分 離 技 術 会

｢分離技術シリーズ｣ の継続刊行に当たって研究開発とは，新しい原理や現象を発見することばかりではなく，原理・現象は既知であっても新しい方法を案出するとか，あるいは新しい組み合わせを創案することによって，新しい技術，商品，品質，機能，用途，方法等々を創出することである．
本会は主に化学品の製造に関わる分離技術を包括的に扱う専門の学会である
が，研究者・技術者を糾合して正に関連分野の研究・開発の進展を目指し，急激な変化に対応しようと心がけている．
すでに何冊か刊行された本シリーズのなかには，本会会誌 ｢分離技術｣ 誌に掲載された論文によっているものもある．しかし，論文に記載された技術を取捨選択し，それらの組み合わせを考えて執筆されたものであるから，上述の視点から成書としての価値は高いといえるであろう．
さて，最近あらたな構想のもとに，本委員会よりいろいろな分野の権威者に執筆を依頼し，本シリーズに書き下ろしの著作物が加えられることになったのは誠に慶賀に堪えない次第である．分離技術の益々の発展に寄与することは勿論，読者諸兄姉に研鑽のお役に立つものと信じている．
分離技術シリーズ出版委員会
委員長

白

石

浩

は じ め に分離という操作は，私たちの日常生活(調理など)や社会生活(医療など)の裏方として機能する一方，化学産業やエネルギー産業など多くの産業を支える柱になっている．このような産業の中核技術に位置づけられる比較的大規模かつ汎用的な分離技術を「化学工学的分離」と呼ぶことにするが，それらの技術の根幹をなす基礎と原理はいつの時代でも何ら変わるものではない．したがってその基礎と原理を知ってはじめて，産業社会ひいては人類社会に役立つ技術の改良と革新が可能になるし，さまざまなトラブルにも縦横に対応できる．
化学工学的分離の基礎と原理を理解するには，扱う物質の化学的性質から出発する場合と物理的挙動に軸足を置く場合が考えられるが，工業装置を開発して設計し製作・建設するという視点に立つならば，後者によるアプローチ，すなわち物質の移動と平衡から，学んでいくのがより実際的なように思われる．
本書は，学部学生や院生のための教科書・参考書として，また若手研究者や技術者の入門書として活用されることを企図し，公益社団法人化学工学会の会
誌「化学工学」(2015 年 1 月～ 4 月)に掲載された小特集『分離の基礎を数学力で学び直そう』を大幅に改変したものである．改変の骨子は，①学ぶべきポ
イントが何かを明確にし，②ポイントになる事象解明の手順と数学力の必要性を理解するとともに，③理解を深耕すべく演習にチャレンジすること，にある．
なお本書では，演習の解答はヒントと略解のみを記載するにとどめたが，数式の誘導など難解な演習も含まれていることから，詳しい解答は「詳細解答編」として分離技術会のホームページにアップロードした．関心あれば下記ア
ドレスにアクセスして閲読されるか，ダウンロードして利用されたい(無償)．
http://www.sspej.gr.jp/publications/related_books.html(分離技術会の販売する書籍一覧)
2016年

陽春
相

良

紘

目

第１講

次

どんな混合物が分離の対象になり，どのような方法で分離されるか····························································································

1

1.1

分離を専門分野別に大別する ·················································

1

1.2

混合物を混ざり方で分類する ·················································

11.3

化学工学的分離法を整理し分類する ········································

2

1.3.1

機械的分離法 ·································································

3

1.3.2

平衡型拡散的分離法 ························································

3

1.3.3

速度型拡散的分離法 ························································

5

第２講

粒子は重力場と遠心力場でどのような動きをして分離されるか····························································································

82.1

粒子の運動による抵抗力 ·······················································

2.2

流体中の粒子の抵抗係数 ·······················································

82.3

粒子の終末速度 ···································································

10

2.4

遠心力と遠心効果 ································································

13

第３講

粒子と液体はさえぎり場でどのような動きをして分離されるか····························································································

8

18

3.1

ろ過操作の基礎方程式 ··························································

18

3.2

精密ろ過と中空糸膜 ·····························································

21

3.3

限外ろ過と分画分子量 ··························································

22

3.4

膜面での濃度分極現象 ··························································

24

第４講

物質は一つの相を形成する流体中をどのように移動するか ········

27

4.1

拡散による流束 ···································································

27

4.2

流れの影響を考慮した流束 ····················································

29

4.3

境膜と境膜内での物質移動 ····················································

31

4.4

界面をはさむ二重境膜 ··························································

33

4.5

等モル相互拡散と一方拡散 ····················································

35

4.5.1

等モル相互拡散の場合 ·····················································

35

4.5.2

一方拡散の場合 ······························································

35

第５講

二相間で達成される物質の平衡状態はどんな熱力学量で表されるか····························································································
5.1

純物質の相平衡と熱力学的条件 ··············································

37
37

5.1.1

化学ポテンシャルで表す ··················································

38

5.1.2

フガシティーで表す ························································

39

混合物の相平衡と熱力学量 ····················································

40

5.2

5.2.1

活量と活量係数 ······························································

40

5.2.2

フガシティーとフガシティー係数 ······································

41

混合物の相平衡を表現する基礎式 ···········································

42

5.3

5.3.1

気液平衡 ·······································································

42

5.3.2

液液平衡 ·······································································

43

5.3.3

固液平衡 ·······································································

44

第６講

溶媒と溶質は二つの相の接する界面でどのような挙動をするか····························································································
6.1

液体の表面張力 ···································································

48
48

6.1.1

純粋液体の場合 ······························································

49

6.1.2

溶液の場合 ····································································

49

界面の熱力学 ······································································

51

6.2

6.2.1
6.3

表面吸着量と泡立ち現象の関係 ·········································

53

液液界面と界面張力 ·····························································

55

6.3.1

純粋な液体間の界面張力 ··················································

55

6.3.2

純粋液体と溶液間の界面張力 ············································

56

6.3.3

液滴の生成と拡がり ························································

57

第７講

物質は固体面にどのように吸着して流体相と平衡状態になるか····························································································

59

7.1

吸着現象 ············································································

59

7.2

吸着等温式 ·········································································

60

7.2.1

ヘンリー型 ····································································

60

7.2.2

ラングミュア型 ······························································

61

7.2.3

フロインドリッヒ型 ························································

62

7.2.4

BET型 ··········································································

62

第８講

気体分子は膜の中へどのように入り込んで移動していくか ········

68

8.1

気体分子の平均速度 ·····························································

68

8.2

気体分子の衝突回数と平均自由行程 ········································

69

8.3

ファン・デル・ワールス径 ····················································

71

8.4

クヌーセン数とクヌーセン流れ ··············································

72

8.5

気体分子の膜透過 ································································

73

第９講

分子は吸着剤の細孔内へどのように入り込んで，どんな動きをするか····························································································

79

9.1

吸着分子の吸着過程 ·····························································

79

9.2

吸着剤粒子内の拡散 ·····························································

80

9.2.1

粒子内の吸着量分布 ························································

80

9.2.2

粒子内の吸着速度式 ························································

84

9.2.3

線形推進力近似モデル ·····················································

85

9.3

吸着剤粒子の細孔構造と有効拡散係数 ·····································

87

第10講

溶媒と溶質は膜の中へどのように溶け込んで相互に分離されるか····························································································

90

10.1

透析と溶解拡散モデル ·························································

90

10.2

半透膜と浸透圧 ··································································

93

10.3

逆浸透と不可逆過程の熱力学 ················································

96

第11講

微分型のガス吸収塔と液液抽出塔の高さはどのように決めるか···························································································· 10011.1

平衡型拡散的分離装置の設計手順 ·········································· 100

11.2

微分型ガス吸収塔 ······························································· 101

11.2.1

微小高さ部分における溶質の物質収支······························· 102

11.2.2

移動単位数，移動単位高さ，塔高····································· 103

11.2.3

ガス吸収塔の操作線······················································· 10611.3

微分型液液抽出塔 ······························································· 109

11.3.1

微小高さ部分における溶質の物質収支······························· 109

11.3.2

移動単位数，移動単位高さ，塔高····································· 110

11.3.3

液液抽出塔の操作線······················································· 111

第12講

微分型の連続蒸留塔と連続晶析塔の高さはどのように決めるか···························································································· 113
12.1

微分型連続蒸留塔 ······························································· 113

12.1.1

移動単位数と移動単位高さ·············································· 114

12.1.2連続蒸留塔の操作線と q 線·············································· 115

12.2

微分型連続晶析塔 ······························································· 118

12.2.1

結晶化成分の物質収支と移動単位数·································· 120

12.2.2連続晶析塔の操作線と平衡線··········································· 120

第13講

固定層吸着塔の高さはどのように決めるか ····························· 122

13.1

吸着質の固定層内濃度分布 ··················································· 122

13.2

吸着帯の高さと固定層の高さ ················································ 123

13.2.1

吸着帯の高さ································································ 124

13.2.2固定層の高さと破過時間················································· 126

第14講

向流接触塔の理論要素はどんな場合に数式で表すことができるか···························································································· 131
14.1

棚段型ガス吸収塔の理論段数 ················································ 131

14.2

微分型ガス吸収塔の移動単位数 ············································· 134

14.3

棚段塔の理論段数と充てん塔の層高 ······································· 138

第15講

棚段塔の効率は理論的な解析から決めることができるだろうか···························································································· 140
15.1

効率の表現法と相互関係 ······················································ 140

15.1.1

ガス相基準の段効率と液相基準の段効率の関係··················· 142

15.1.2

塔効率とマーフリー段効率の関係····································· 142

15.1.3マーフリー段効率と点効率の関係····································· 14415.2

効率と物質移動の関わり ······················································ 147

演習のヒントと略解 ······································································· 150
参考図書など ················································································ 155
索引 ···························································································· 156