ПОВЫШЕНИЕ ЧИСТОТЫ ПРОДУКТА ЗА СЧЕТ ЭНЕРГИИ

ȼȿɋɌɇ. ɆɈɋɄ. ɍɇ-ɌȺ. ɋȿɊ. 2. ɏɂɆɂə. 2007. Ɍ. 48. ʋ 3
167
ɍȾɄ 541.183+66.071.7+621.694.2
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(À¶Ê»ºÆ¶ ˾¾ͻÇÀÄ¿ È»ËÃÄÁĹ¾¾ ¾ ÃĸÑË Â¶È»Æ¾¶Áĸ; e-mail: heifets@tech.chem.msu.ru)
d ÇȶÈÒ» ö ÄÇÃĸ» ƶ¸Ãĸ»ÇÃÄ¿ Âĺ»Á¾ Åƾ»þȻÁÒÃÄ À ÅÆÄÌ»ÇÇÉ lxb ÅÄÀ¶½¶ÃÄ, ÍÈÄ Ç
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ÅƾÃ̾ž¶ÁÒöµ Ç˻¶ ÅÆÄÌ»ÇǶ lxb Ç Ó¼»ÀÈÄÆÄÂ.
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Ɉɬɥɢɱɢɬɟɥɶɧɨɣ ɱɟɪɬɨɣ ɦɟɬɨɞɚ ɤɨɪɨɬɤɨɰɢɤɥɨɜɨɣ
ɚɞɫɨɪɛɰɢɢ (ɄɐȺ) ɩɪɢ ɜɫɟɦ ɦɧɨɝɨɨɨɛɪɚɡɢɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɪɟɲɟɧɢɣ ɹɜɥɹɟɬɫɹ ɪɚɡɥɢɱɢɟ ɞɚɜɥɟɧɢɣ, ɩɪɢ ɤɨɬɨɪɵɯ ɩɪɨɢɫɯɨɞɢɬ ɢɡɛɢɪɚɬɟɥɶɧɚɹ ɚɞɫɨɪɛɰɢɹ, ɬ.ɟ. ɪɚɡɞɟɥɟɧɢɟ ɤɨɦɩɨɧɟɧɬɨɜ ɝɚɡɨɜɨɣ ɫɦɟɫɢ, ɢ ɞɟɫɨɪɛɰɢɹ ɨɫɬɚɜɲɟɝɨɫɹ ɤɨɦɩɨɧɟɧɬɚ, ɩɪɢɜɨɞɹɳɚɹ ɤ ɪɟɝɟɧɟɪɚɰɢɢ
ɚɞɫɨɪɛɟɧɬɚ [1]. ȼ ɨɫɧɨɜɟ ɦɟɬɨɞɚ ɥɟɠɢɬ ɬɟɪɦɨɞɢɧɚɦɢɱɟɫɤɢɣ ɰɢɤɥ, ɨɫɧɨɜɧɵɦɢ ɫɨɫɬɚɜɥɹɸɳɢɦɢ ɤɨɬɨɪɨɝɨ
ɹɜɥɹɸɬɫɹ ɫɬɚɞɢɹ ɢɡɛɢɪɚɬɟɥɶɧɨɣ ɚɞɫɨɪɛɰɢɢ ɨɞɧɨɝɨ ɢɡ
ɤɨɦɩɨɧɟɧɬɨɜ ɢɫɯɨɞɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ, ɨɫɭɳɟɫɬɜɥɹɟɦɚɹ
ɩɪɢ ɞɚɜɥɟɧɢɢ pa, ɢ ɫɬɚɞɢɹ ɪɟɝɟɧɟɪɚɰɢɢ ɚɞɫɨɪɛɰɢɨɧɧɨɝɨ ɫɥɨɹ, ɜɵɩɨɥɧɹɟɦɚɹ ɩɭɬɟɦ ɫɛɪɨɫɚ ɷɬɨɝɨ ɤɨɦɩɨɧɟɧɬɚ
ɩɪɢ ɦɟɧɶɲɟɦ ɞɚɜɥɟɧɢɢ p0 [1, 2]. Ȼɥɚɝɨɞɚɪɹ ɦɚɥɨɣ
ɢɧɟɪɰɢɨɧɧɨɫɬɢ ɪɟɝɟɧɟɪɚɰɢɢ ɚɞɫɨɪɛɟɧɬɚ ɦɟɬɨɞ ɄɐȺ
ɧɚɯɨɞɢɬ ɜɟɫɶɦɚ ɲɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɬɟɯɧɨɥɨɝɢɢ [3,
4]. ɇɟɞɨɫɬɚɬɤɨɦ ɦɟɬɨɞɚ ɄɐȺ ɹɜɥɹɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɧɟɜɵɫɨɤɚɹ ɱɢɫɬɨɬɚ ɩɪɨɞɭɤɰɢɨɧɧɨɝɨ ɝɚɡɚ. ɇɚɩɪɢɦɟɪ,
ɩɪɢ ɩɨɥɭɱɟɧɢɢ ɤɢɫɥɨɪɨɞɚ ɢɡ ɜɨɡɞɭɯɚ ɜ ɫɨɜɪɟɦɟɧɧɵɯ
ɭɫɬɚɧɨɜɤɚɯ ɄɐȺ ɫɨɞɟɪɠɚɧɢɟ ɚɡɨɬɚ ɜ ɩɪɨɞɭɤɬɨɜɨɦ
ɝɚɡɟ, ɤɚɤ ɩɪɚɜɢɥɨ, ɧɟ ɦɟɧɶɲɟ 2,5%, ɢ ɞɥɹ ɩɨɥɭɱɟɧɢɹ
ɛɨɥɟɟ ɱɢɫɬɨɝɨ ɩɪɨɞɭɤɬɚ ɩɪɢɯɨɞɢɬɫɹ ɩɪɨɩɭɫɤɚɬɶ ɩɨɥɭɱɟɧɧɭɸ ɝɚɡɨɜɭɸ ɫɦɟɫɶ ɱɟɪɟɡ ɞɨɩɨɥɧɢɬɟɥɶɧɭɸ ɭɫɬɚɧɨɜɤɭ ɄɐȺ, ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɫɧɢɠɟɧɢɸ ɷɮɮɟɤɬɢɜɧɨɫɬɢ
ɫɨɫɬɚɜɧɨɝɨ ɰɢɤɥɚ. ɉɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɢɫɫɥɟɞɨɜɚɧɢɟ ɬɚɤɢɯ ɮɨɪɦ ɨɪɝɚɧɢɡɚɰɢɢ ɄɐȺ, ɩɪɢ ɤɨɬɨɪɵɯ ɛɭɞɟɬ
ɩɨɜɵɲɚɬɶɫɹ ɱɢcɬɨɬɚ ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ ɛɟɡ ɫɭɳɟɫɬɜɟɧɧɵɯ ɞɨɥɧɢɬɟɥɶɧɵɯ ɡɚɬɪɚɬ ɷɧɟɪɝɢɢ.
dÁ¾µÃ¾» ÄÈÃÄǾȻÁÒÃÄ¹Ä Å»Æ»Å¶º¶
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Ɉɫɧɨɜɧɵɦɢ ɫɬɚɞɢɹɦɢ ɛɟɡɧɚɝɪɟɜɧɨɣ ɄɐȺ ɹɜɥɹɸɬɫɹ: ɚɞɫɨɪɛɰɢɹ, ɞɟɫɨɪɛɰɢɹ ɢ ɡɚɩɨɥɧɟɧɢɟ ɚɞɫɨɪɛɟɪɚ
12 ȼɆɍ, ɯɢɦɢɹ, ʋ 3
ɩɪɨɞɭɤɬɨɜɵɦ ɝɚɡɨɦ, ɢɧɨɝɞɚ ɫɯɟɦɭ ɄɐȺ ɞɨɩɨɥɧɹɸɬ
ɫɬɚɞɢɟɣ ɩɪɨɞɭɜɤɢ ɚɞɫɨɪɛɟɪɚ ɩɪɨɞɭɤɬɨɜɵɦ ɝɚɡɨɦ [1].
ɇɚ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ ɢɫɯɨɞɧɚɹ ɝɚɡɨɜɚɹ ɫɦɟɫɶ ɩɨɫɬɭɩɚɟɬ ɜ ɚɞɫɨɪɛɟɪ, ɩɟɪɜɨɧɚɱɚɥɶɧɨ ɡɚɩɨɥɧɟɧɧɵɣ ɩɪɨɞɭɤɬɨɜɵɦ ɝɚɡɨɦ ɞɨ ɞɚɜɥɟɧɢɹ p0. Ⱥɞɫɨɪɛɰɢɹ ɩɪɨɬɟɤɚɟɬ
ɩɪɢ ɩɪɚɤɬɢɱɟɫɤɢ ɩɨɫɬɨɹɧɧɨɦ ɞɚɜɥɟɧɢɢ p0 ɢ ɫɨɩɪɨɜɨɠɞɚɟɬɫɹ ɨɛɪɚɡɨɜɚɧɢɟɦ “ɨɫɬɪɨɝɨ” ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɮɪɨɧɬɚ,
ɲɢɪɢɧɚ ɤɨɬɨɪɨɝɨ l << L, ɝɞɟ L – ɞɥɢɧɚ ɚɞɫɨɪɛɟɪɚ.
ȼɥɢɹɧɢɟ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɯ ɢ ɪɟɠɢɦɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɧɚ
ɞɥɢɧɭ ɮɪɨɧɬɚ, ɚ ɬɚɤɠɟ ɤɨɧɜɟɤɬɢɜɧɚɹ ɧɟɭɫɬɨɣɱɢɜɨɫɬɶ
ɮɪɨɧɬɚ ɢɫɫɥɟɞɨɜɚɧɵ ɜ ɪɚɛɨɬɚɯ [5, 6]. ȼ ɪɚɛɨɬɚɯ [7, 8]
ɪɚɫɫɱɢɬɚɧɨ ɩɪɨɢɡɜɨɞɫɬɜɨ ɷɧɬɪɨɩɢɢ ɜ ɨɛɥɚɫɬɢ ɮɪɨɧɬɚ
ɚɞɫɨɪɛɰɢɢ.
Ɏɪɨɧɬ ɚɞɫɨɪɛɰɢɢ ɪɚɡɞɟɥɹɟɬ ɨɛɴɟɦ ɚɞɫɨɪɛɟɪɚ ɧɚ
ɞɜɟ ɨɛɥɚɫɬɢ. ɉɟɪɟɞ ɮɪɨɧɬɨɦ ɫɨɫɬɚɜ ɝɚɡɚ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɨɫɬɚɜɭ ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ, ɩɨɡɚɞɢ ɮɪɨɧɬɚ ɫɨɫɬɚɜ ɝɚɡɚ ɫɨɜɩɚɞɚɟɬ ɫ ɫɨɫɬɚɜɨɦ ɢɫɯɨɞɧɨɣ ɝɚɡɨɜɨɣ
ɫɦɟɫɢ. ɋɥɟɞɨɜɚɬɟɥɶɧɨ, ɜ ɤɨɧɰɟ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ ɩɚɪɰɢɚɥɶɧɨɟ ɞɚɜɥɟɧɢɟ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ (i = 1, 2) ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ p0i = RTc 0i , ɝɞɟ R = 8,314 ɤȾɠ/ɦɨɥɶ.Ʉ, t –
ɬɟɦɩɟɪɚɬɭɪɚ (Ʉ), c0i – ɦɨɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ (i = 1, 2) ɜ ɢɫɯɨɞɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ. ɉɨɥɧɨɟ
ɞɚɜɥɟɧɢɟ ɝɚɡɚ ɜ ɚɞɫɨɪɛɟɪɟ ɧɚ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ p0 =
p01 + p02. Ⱦɟɫɨɪɛɰɢɹ ɩɪɨɜɨɞɢɬɫɹ ɩɪɢ ɞɚɜɥɟɧɢɢ p1,
ɦɟɧɶɲɟɦ, ɱɟɦ p0. ȼɚɠɧɵɦ ɩɚɪɚɦɟɬɪɨɦ, ɯɚɪɚɤɬɟɪɢɡɭɸɳɢɦ ɄɐȺ, ɹɜɥɹɟɬɫɹ ɨɬɧɨɲɟɧɢɟ
α
p1
1 .
p0
Ⱦɥɹ ɬɨɝɨ ɱɬɨɛɵ ɧɚɣɬɢ ɡɚɜɢɫɢɦɨɫɬɶ β( α), ɝɞɟ β –
ɦɨɥɶɧɚɹ ɞɨɥɹ ɩɟɪɜɨɝɨ (ɩɪɢɦɟɫɧɨɝɨ) ɤɨɦɩɨɧɟɧɬɚ ɜ
ɩɪɨɞɭɤɬɨɜɨɦ ɝɚɡɟ, ɪɚɫɫɦɨɬɪɢɦ ɢɡɨɬɟɪɦɢɱɟɫɤɢɣ ɩɪɨɰɟɫɫ. Ɉɩɪɟɞɟɥɢɦ ɦɨɥɶɧɭɸ ɤɨɧɰɟɧɬɪɚɰɢɸ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ c1i ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ ɚɞɫɨɪɛɟɪɚ ɨɛɴɟɦɚ V0 ɩɨɫɥɟ
ȼȿɋɌɇ. ɆɈɋɄ. ɍɇ-ɌȺ. ɋȿɊ. 2. ɏɂɆɂə. 2007. Ɍ. 48. ʋ 3
168
ɡɚɜɟɪɲɟɧɢɹ ɫɬɚɞɢɢ ɞɟɫɨɪɛɰɢɢ, ɩɪɟɞɩɨɥɚɝɚɹ, ɱɬɨ ɚɞɫɨɪɛɟɧɬ ɧɚɯɨɞɢɬɫɹ ɜ ɪɚɜɧɨɜɟɫɢɢ ɫ ɝɚɡɨɦ, ɜɵɬɟɤɲɢɦ
ɢɡ ɚɞɫɨɪɛɟɪɚ ɜɨ ɜɧɟɲɧɢɣ ɨɛɴɟɦ V1 ɩɪɢ ɞɚɜɥɟɧɢɢ p1.
ɉɪɢ ɪɚɫɫɦɨɬɪɟɧɢɢ ɥɢɧɟɣɧɨɣ ɚɞɫɨɪɛɰɢɢ ɦɨɠɧɨ ɫɨɫɬɚɜɢɬɶ ɦɚɬɟɪɢɚɥɶɧɵɣ ɛɚɥɚɧɫ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ:
(ε χ i (1 ε))V0c0i (ε χ i (1 ε))V0c1i V1c1i ,
i = 1, 2,
(1)
ɝɞɟ ε – ɩɨɪɨɡɧɨɫɬɶ ɫɥɨɹ, χi – ɤɨɧɫɬɚɧɬɚ Ƚɟɧɪɢ i-ɝɨ
ɤɨɦɩɨɧɟɧɬɚ.
ɉɨ ɨɩɪɟɞɟɥɟɧɢɸ α ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
c11 c12
α.
c01 c02
(2)
Ɋɟɲɚɹ ɥɢɧɟɣɧɭɸ ɫɢɫɬɟɦɭ ɚɥɝɟɛɪɚɢɱɟɫɤɢɯ ɭɪɚɜɧɟɧɢɣ (1) – (2) ɨɬɧɨɫɢɬɟɥɶɧɨ Ç11, Ç12, V1, ɩɨɥɭɱɚɟɦ
ɝɞɟ d 1 γ
αc 01
c11 ,
γ
(3)
k
k
α
, k 2 , k i ε χ i (1 ε ),
γ (1 k ) γ
k1
c 01
.
c 01 c 02
ɑɢɫɥɨ ɦɨɥɟɣ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ m1i, ɤɨɬɨɪɵɟ ɛɭɞɭɬ ɧɚɯɨɞɢɬɶɫɹ ɜ ɚɞɫɨɪɛɟɪɟ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɫɬɚɞɢɢ ɞɟɫɨɪɛɰɢɢ, ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɜ ɜɢɞɟ m1i V0 k i c1i . ȼ
ɫɥɭɱɚɟ α << 1 ɩɨɫɥɟ ɥɢɧɟɚɪɢɡɚɰɢɢ ɫɨɨɬɧɨɲɟɧɢɣ (3)
ɩɨ α ɩɨɥɭɱɚɟɦ:
m11 V0 c01 k1α
,
γ (1 k ) k
V c k k 2 (1 γ ) α
m12 0 01 1
.
γ ( γ (1 k ) k )
( γ (1 γ )) α
1β
1 ,
x (β )
γ ( γ (1 k ) k )
k
γ
(5)
ɝɞɟ x M /( k1V0 c 01 ) . ȼɬɨɪɨɟ ɭɪɚɜɧɟɧɢɟ ɹɜɥɹɟɬɫɹ
ɫɥɟɞɫɬɜɢɟɦ ɭɫɥɨɜɢɹ ɫɨɜɩɚɞɟɧɢɹ ɫɨɫɬɚɜɨɜ ɝɚɡɚ ɜ ɚɞɫɨɪɛɟɪɟ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɫɬɚɞɢɢ ɡɚɩɨɥɧɟɧɢɹ ɢ ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ, ɬ.ɟ. Ç21 = β (c01 + c02) , ɱɬɨ ɦɨɠɧɨ
ɩɪɟɞɫɬɚɜɢɬɶ ɤɚɤ
β .
α
βx γ (1 k ) k
γ
(6)
Ⱦɥɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɝɨ ɫɥɭɱɚɹ ɦɚɥɵɯ α ɢ β ɢɡ (5)
ɢ (6) ɫɥɟɞɭɟɬ ɢɬɨɝɨɜɚɹ ɮɨɪɦɭɥɚ
c
4α
),
c11 01 ¸ d ¸ (1 1 2
γ (1 k ) d 2
c12 Ⱦɥɹ ɨɩɪɟɞɟɥɟɧɢɹ β ɢ M ɧɟɨɛɯɨɞɢɦɨ ɫɨɫɬɚɜɢɬɶ ɞɜɚ
ɭɪɚɜɧɟɧɢɹ. ɉɟɪɜɨɟ ɭɪɚɜɧɟɧɢɟ ɹɜɥɹɟɬɫɹ ɫɥɟɞɫɬɜɢɟɦ
ɭɫɥɨɜɢɹ, ɱɬɨ ɞɚɜɥɟɧɢɟ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɫɬɚɞɢɢ ɡɚɩɨɥɧɟɧɢɹ ɪɚɜɧɨ ɞɚɜɥɟɧɢɸ ɢɫɯɨɞɧɨɣ ɝɚɡɨɜɨɣ ɫɦɟɫɢ,
ɩɨɫɬɭɩɚɸɳɟɣ ɜ ɚɞɫɨɪɛɟɪ ɧɚ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ, ɬ.ɟ.
Ç21 + c22 = c01 + c02, ɱɬɨ ɦɨɠɧɨ ɩɪɟɞɫɬɚɜɢɬɶ, ɜɨɫɩɨɥɶɡɨɜɚɜɲɢɫɶ (4), ɤɚɤ
(4)
ɇɚ ɫɬɚɞɢɢ ɡɚɩɨɥɧɟɧɢɹ ɚɞɫɨɪɛɟɪɚ ɞɨ ɢɫɯɨɞɧɨɝɨ ɞɚɜɥɟɧɢɹ p0 ɜ ɚɞɫɨɪɛɟɪ ɩɨɞɚɟɬɫɹ M ɦɨɥɟɣ ɩɪɨɞɭɤɬɨɜɨɝɨ
ɝɚɡɚ, ɜ ɤɨɬɨɪɨɦ ɦɨɥɶɧɚɹ ɞɨɥɹ ɩɪɢɦɟɫɧɨɝɨ ɤɨɦɩɨɧɟɧɬɚ
ɪɚɜɧɚ β. Ɉɛɨɡɧɚɱɢɜ ɱɟɪɟɡ m2i ɱɢɫɥɨ ɦɨɥɟɣ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ, ɫɨɞɟɪɠɚɳɟɝɨɫɹ ɜ ɚɞɫɨɪɛɟɪɟ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɫɬɚɞɢɢ ɡɚɩɨɥɧɟɧɢɹ, ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ
m2i = m11 + βΜ, m22 = m12 + (1 – β)Μ.
ɋ ɞɪɭɝɨɣ ɫɬɨɪɨɧɵ, m2i = ki c2i V0,
ɝɞɟ c2i – ɦɨɥɶɧɚɹ ɤɨɧɰɟɧɬɪɚɰɢɹ i-ɝɨ ɤɨɦɩɨɧɟɧɬɚ ɜ ɝɚɡɨɜɨɣ ɮɚɡɟ ɚɞɫɨɪɛɟɪɚ ɩɨɫɥɟ ɡɚɜɟɪɲɟɧɢɹ ɫɬɚɞɢɢ ɡɚɩɨɥɧɟɧɢɹ.
β
αγ
.
(1 k )( k γ (1 k ))
(7)
ȼɢɞɧɨ, ɱɬɨ ɫ ɭɦɟɧɶɲɟɧɢɟɦ α ɥɢɧɟɣɧɨ ɭɦɟɧɶɲɚɟɬɫɹ β, ɬ.ɟ. ɡɚɝɪɹɡɧɟɧɧɨɫɬɶ ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ. ɉɪɢ
ɪɚɡɞɟɥɟɧɢɢ ɝɚɡɨɜ ɫ ɛɥɢɡɤɢɦɢ ɚɞɫɨɪɛɰɢɨɧɧɵɦɢ ɫɜɨɣɫɬɜɚɦɢ (k ≈ 1), ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ [6], ɜɨɡɪɚɫɬɚɟɬ ɬɨɥɳɢɧɚ ɮɪɨɧɬɚ, ɢ ɞɥɹ ɞɨɫɬɢɠɟɧɢɹ ɬɪɟɛɭɟɦɨɣ ɱɢɫɬɨɬɵ
ɩɪɨɞɭɤɬɚ ɜɦɟɫɬɟ ɫ ɭɦɟɧɶɲɟɧɢɟɦ ɜɟɥɢɱɢɧɵ α ɧɟɨɛɯɨɞɢɦɨ ɭɜɟɥɢɱɢɜɚɬɶ ɞɥɢɧɭ ɚɞɫɨɪɛɟɪɚ ɞɥɹ ɬɨɝɨ, ɱɬɨɛɵ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ ɮɪɨɧɬ ɛɵɥ ɞɨɫɬɚɬɨɱɧɨ ɬɨɧɤɢɦ.
ɋɥɟɞɭɟɬ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɧɚ ɩɪɚɤɬɢɤɟ ɡɚɝɪɹɡɧɟɧɨɫɬɶ
ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ ɧɢɠɟ, ɱɟɦ ɪɚɫɫɱɢɬɚɧɧɚɹ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ (7). ɗɬɨ ɫɜɹɡɚɧɨ ɫ ɬɟɦ, ɱɬɨ ɜ ɩɪɨɰɟɫɫɟ
ɜɵɩɨɥɧɟɧɢɹ ɫɬɚɞɢɢ ɡɚɩɨɥɧɟɧɢɹ ɜ ɚɞɫɨɪɛɟɪɟ ɪɟɚɥɢɡɭɟɬɫɹ ɧɟɪɚɜɧɨɦɟɪɧɨɟ ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɩɪɢɦɟɫɧɨɝɨ ɤɨɦɩɨɧɟɧɬɚ ɩɨ ɞɥɢɧɟ ɫɥɨɹ ɚɞɫɨɪɛɟɧɬɚ. ɉɨɷɬɨɦɭ ɜ ɧɚɱɚɥɟ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ ɱɢɫɬɨɬɚ ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ
ɜɵɲɟ, ɱɟɦ ɜ ɫɪɟɞɧɟɦ, ɜɫɥɟɞɫɬɜɢɟ ɱɟɝɨ ɛɨɥɟɟ ɪɚɧɧɟɟ ɜɤɥɸɱɟɧɢɟ ɫɬɚɞɢɢ ɚɞɫɨɪɛɰɢɢ ɩɪɢɜɨɞɢɬ ɤ ɩɨɥɭɱɟɧɢɸ ɛɨɥɟɟ ɱɢɫɬɨɝɨ ɩɪɨɞɭɤɬɚ, ɨɞɧɚɤɨ ɩɪɢ ɷɬɨɦ
ɭɦɟɧɶɲɚɟɬɫɹ ɚɤɬɢɜɧɵɣ ɨɛɴɟɦ ɚɞɫɨɪɛɟɪɚ ɢ ɫɧɢɠɚɟɬɫɹ ɷɮɮɟɤɬɢɜɧɨɫɬɶ. ɉɪɨɞɭɜɤɚ ɚɞɫɨɪɛɟɪɚ ɩɪɨɞɭɤɬɨɜɵɦ ɝɚɡɨɦ ɬɚɤɠɟ ɩɪɢɜɨɞɢɬ ɤ ɧɟɤɨɬɨɪɨɦɭ ɩɨɜɵɲɟɧɢɸ ɱɢɫɬɨɬɵ ɩɪɨɞɭɤɬɚ, ɧɨ ɩɪɢ ɷɬɨɦ ɨɞɧɨɜɪɟɦɟɧɧɨ
ɫɧɢɠɚɟɬɫɹ ɩɪɨɢɡɜɨɞɢɬɟɥɶɧɨɫɬɶ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɫɨɨɬɧɨɲɟɧɢɟ (7) ɦɨɠɧɨ ɪɚɫɫɦɚɬɪɢɜɚɬɶ ɤɚɤ ɜɟɪɯɧɸɸ
ɨɰɟɧɤɭ ɡɚɝɪɹɡɧɟɧɧɨɫɬɢ ɩɪɨɞɭɤɬɚ.
ȼȿɋɌɇ. ɆɈɋɄ. ɍɇ-ɌȺ. ɋȿɊ. 2. ɏɂɆɂə. 2007. Ɍ. 48. ʋ 3
s˻¶ lxb Ç ¹¶½Ä¸Ñ Ӽ»ÀÈÄÆÄÂ
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɞɥɹ ɩɨɧɢɠɟɧɢɹ ɞɚɜɥɟɧɢɹ ɧɚ ɫɬɚɞɢɢ
ɞɟɫɨɪɛɰɢɢ ɜ ɫɯɟɦɚɯ ɄɐȺ ɢɫɩɨɥɶɡɭɸɬ ɜɚɤɭɭɦɧɵɟ ɧɚɫɨɫɵ [9], ɱɬɨ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ
ɡɚɬɪɚɬ. Ⱦɥɹ ɫɧɢɠɟɧɢɹ ɜɟɥɢɱɢɧɵ ɩɚɪɚɦɟɬɪɚ α ɦɨɠɧɨ
ɢɫɩɨɥɶɡɨɜɚɬɶ ɷɧɟɪɝɢɸ ɫɬɪɭɢ ɫɛɪɚɫɵɜɚɟɦɨɝɨ ɝɚɡɚ, ɧɚɩɪɚɜɥɹɹ ɟɟ ɜ ɝɚɡɨɜɵɣ ɷɠɟɤɬɨɪ, ɤɨɬɨɪɵɣ, ɛɭɞɭɱɢ ɩɨɞɤɥɸɱɟɧ ɤ ɚɞɫɨɪɛɟɪɭ ɧɚ ɫɬɚɞɢɢ ɞɟɫɨɪɛɰɢɢ, ɨɛɟɫɩɟɱɢɬ
ɫɧɢɠɟɧɢɟ ɞɚɜɥɟɧɢɹ. ɇɚ ɪɢɫɭɧɤɟ ɩɪɟɞɫɬɚɜɥɟɧɚ ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɄɐȺ, ɫɨɫɬɨɹɳɟɝɨ ɢɡ ɬɪɟɯ ɚɞɫɨɪɛɟɪɨɜ
ɢ ɷɠɟɤɬɨɪɚ, ɩɪɢ ɭɫɥɨɜɢɢ p0 > 2 ɚɬ. ɉɪɢ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɞɨɡɜɭɤɨɜɨɝɨ ɷɠɟɤɬɨɪɚ ɞɚɜɥɟɧɢɟ ɧɚ ɜɯɨɞɟ ɜ ɷɠɟɤɬɨɪ ɪɚɜɧɨ 2 ɚɬ [10]. ɋɬɚɞɢɹ ɞɟɫɨɪɛɰɢɢ ɜɵɩɨɥɧɹɟɬɫɹ
ɜ ɬɪɢ ɷɬɚɩɚ. ȼ ɧɚɱɚɥɟ ɫɬɚɞɢɢ ɞɟɫɨɪɛɰɢɢ ɜ ɨɛɥɚɫɬɢ
ɞɚɜɥɟɧɢɣ 2 < p < p0 ɚɬ ɫɛɪɚɫɵɜɚɟɦɵɣ ɝɚɡ ɧɚɩɪɚɜɥɹɟɬɫɹ ɜ ɪɟɡɟɪɜɭɚɪ ɧɚɤɨɩɢɬɟɥɶ (ɝɚɡɨɜɵɣ ɤɨɥɥɟɤɬɨɪ) ɫ
ɞɚɜɥɟɧɢɟɦ ~2 ɚɬ. Ʉɨɥɥɟɤɬɨɪ ɫɥɭɠɢɬ ɢɫɬɨɱɧɢɤɨɦ ɝɚɡɚ
ɞɥɹ ɷɠɟɤɬɨɪɚ. ȼ ɫɟɪɟɞɢɧɟ ɫɬɚɞɢɢ ɞɟɫɨɪɛɰɢɢ ɜ ɨɛɥɚɫɬɢ ɞɚɜɥɟɧɢɣ 1 < p < 2 ɚɬ ɝɚɡ ɫɛɪɚɫɵɜɚɟɬɫɹ ɜ ɨɤɪɭɠɚɸɳɭɸ ɫɪɟɞɭ, ɦɢɧɭɹ ɥɢɧɢɸ ɷɠɟɤɬɨɪɚ. ɂ, ɧɚɤɨɧɟɰ, ɩɪɢ
p < 1 ɚɬ ɚɞɫɨɪɛɟɪ ɩɨɞɤɥɸɱɚɟɬɫɹ ɤ ɷɠɟɤɬɨɪɭ, ɫɨɡɞɚɸɳɟɦɭ ɜɭɤɭɭɦ ɩɨɪɹɞɤɚ 10–2 ɚɬ, ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɭɦɟɧɶ-
169
–3
ɲɢɬɶ ɜɟɥɢɱɢɧɭ ɩɚɪɚɦɟɬɪɚ α ɞɨ ~10 ɢ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɦɟɧɶɲɢɬɶ ɡɚɝɪɹɡɧɟɧɨɫɬɶ β ɞɨ ~10–2.
ȼ ɩɪɟɞɫɬɚɜɥɟɧɧɨɣ ɧɚ ɪɢɫɭɧɤɟ ɫɯɟɦɟ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ ɄɐȺ ɫɛɪɨɫ ɝɚɡɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɫ ɬɨɪɰɚ
ɚɞɫɨɪɛɟɪɚ. ȼɪɟɦɹ ɪɟɝɟɧɟɪɚɰɢɢ ɩɪɢ ɬɚɤɨɣ ɨɪɝɚɧɢɡɚɰɢɢ ɫɛɪɨɫɚ ɝɚɡɚ ɦɨɠɟɬ ɨɤɚɡɚɬɶɫɹ ɧɟɩɪɢɟɦɥɟɦɨ
ɛɨɥɶɲɢɦ ɜɫɥɟɞɫɬɜɢɟ ɡɧɚɱɢɬɟɥɶɧɨɝɨ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɫɥɨɹ ɜɞɨɥɶ ɨɫɢ ɚɞɫɨɪɛɟɪɚ. ɗɬɨ ɜɪɟɦɹ
ɦɨɠɧɨ ɭɦɟɧɶɲɢɬɶ ɩɭɬɟɦ ɨɪɝɚɧɢɡɚɰɢɢ ɫɛɪɨɫɚ ɝɚɡɚ
ɱɟɪɟɡ ɛɨɤɨɜɭɸ ɩɨɜɟɪɯɧɨɫɬɶ. ȼɵɛɨɪ ɤɨɧɤɪɟɬɧɨɣ ɫɯɟɦɵ ɨɪɝɚɧɢɡɚɰɢɢ ɫɛɪɨɫɚ ɝɚɡɚ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɪɟɛɭɟɦɨɣ ɩɪɨɞɨɥɠɢɬɟɥɶɧɨɫɬɶɸ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ, ɤɨɬɨɪɚɹ ɞɨɥɠɧɚ ɛɵɬɶ ɫɨɝɥɚɫɨɜɚɧɚ ɫ ɜɪɟɦɟɧɟɦ ɪɚɛɨɱɟɝɨ
ɰɢɤɥɚ ɄɐȺ. ȼ ɩɪɢɛɥɢɠɟɧɢɢ ɩɨɥɭɛɟɫɤɨɧɟɱɧɨɝɨ ɚɞɫɨɪɛɟɪɚ ɜ ɪɚɛɨɬɟ [11] ɩɨɥɭɱɟɧɚ ɮɨɪɦɭɥɚ ɡɚɜɢɫɢɦɨɫɬɢ ɜɪɟɦɟɧɢ ɪɟɝɟɧɟɪɚɰɢɢ ɨɬ ɪɟɠɢɦɧɵɯ ɢ ɤɨɧɫɬɪɭɤɰɢɨɧɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɄɐȺ
t L 45, 3 ¸
11 αα 2
¸
(1 ε ) 2
ε3
¸
χ μ L2
+p ¸d p2
×
p 2  p ¬ 2 ¯ 2
žž 0 ­­­ °° ,
× ¡¡
Ÿ+p ® °
+
p
¢¡
±
ɋɬɚɞɢɹ ɪɟɝɟɧɟɪɚɰɢɢ ɩɪɨɯɨɞɢɬ ɜ 3 ɷɬɚɩɚ: ɫɛɪɨɫ ɱɚɫɬɢ ɝɚɡɚ ɜ ɝɚɡɨɜɵɣ ɤɨɥɥɟɤɬɨɪ Ʉ ɞɨ ɞɚɜɥɟɧɢɹ, ɪɚɜɧɨɝɨ
ɞɚɜɥɟɧɢɸ ɜ ɤɨɥɥɟɤɬɨɪɟ (2 ɚɬ); ɫɛɪɨɫ ɝɚɡɚ ɜ ɚɬɦɨɫɮɟɪɭ (ɞɨ ɚɬɦɨɫɮɟɪɧɨɝɨ ɞɚɜɥɟɧɢɹ); ɫɛɪɨɫ ɝɚɡɚ ɩɪɢ
ɧɢɡɤɨɦ ɞɚɜɥɟɧɢɢ, ɫɨɡɞɚɜɚɟɦɨɦ ɷɠɟɤɬɨɪɨɦ, ɩɢɬɚɸɳɢɦɫɹ ɝɚɡɨɦ ɢɡ ɤɨɥɥɟɤɬɨɪɚ; Ⱥ1, Ⱥ2, Ⱥ3 – ɚɞɫɨɪɛɟɪɵ
13 ȼɆɍ, ɯɢɦɢɹ, ʋ 3
(8)
ȼȿɋɌɇ. ɆɈɋɄ. ɍɇ-ɌȺ. ɋȿɊ. 2. ɏɂɆɂə. 2007. Ɍ. 48. ʋ 3
170
ɝɞɟ tL – ɜɪɟɦɹ, ɜ ɬɟɱɟɧɢɟ ɤɨɬɨɪɨɝɨ ɞɚɜɥɟɧɢɟ ɜ ɫɟɱɟɧɢɢ ɫɥɨɹ ɚɞɫɨɪɛɟɧɬɚ, ɪɚɫɩɨɥɨɠɟɧɧɨɝɨ ɧɚ ɪɚɫɫɬɨɹɧɢɢ L
ɨɬ ɫɟɱɟɧɢɹ ɜɵɯɨɞɚ ɝɚɡɚ, ɭɦɟɧɶɲɢɬɫɹ ɞɨ ɧɟɤɨɬɨɪɨɣ
ɜɟɥɢɱɢɧɵ p, ε – ɩɨɪɨɡɧɨɫɬɶ ɫɥɨɹ, dp – ɞɢɚɦɟɬɪ ɡɟɪɧɚ
ɚɞɫɨɪɛɟɧɬɚ, Δp – ɪɚɡɧɢɰɚ ɦɟɠɞɭ ɞɚɜɥɟɧɢɟɦ ɜ ɧɚɱɚɥɟ
ɪɟɝɟɧɟɪɚɰɢɢ ɢ ɞɚɜɥɟɧɢɟɦ ɜɨ ɜɧɟɲɧɟɣ ɫɪɟɞɟ. ȼɟɥɢɱɢɧɚ
L ɡɚɜɢɫɢɬ ɨɬ ɫɩɨɫɨɛɚ ɨɪɝɚɧɢɡɚɰɢɢ ɫɛɪɨɫɚ ɝɚɡɚ: ɟɫɥɢ
ɫɛɪɨɫ ɝɚɡɚ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɬɨɪɰɟɜɨɟ ɫɟɱɟɧɢɟ, ɬɨ
L ɛɥɢɡɤɨ ɤ ɩɨɥɨɜɢɧɟ ɞɥɢɧɵ ɫɥɨɹ ɚɞɫɨɪɛɟɧɬɚ; ɟɫɥɢ
ɫɛɪɨɫ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɱɟɪɟɡ ɛɨɤɨɜɭɸ ɩɨɜɟɪɯɧɨɫɬɶ
ɚɞɫɨɪɛɟɪɚ, ɬɨ L ɛɥɢɡɤɨ ɤ ɪɚɞɢɭɫɭ ɫɥɨɹ.
dѸĺÑ
1. ɇɚ ɨɫɧɨɜɟ ɪɚɜɧɨɜɟɫɧɨɣ ɦɨɞɟɥɢ ɩɪɢɦɟɧɢɬɟɥɶɧɨ ɤ ɩɪɨɰɟɫɫɭ ɄɐȺ ɩɨɤɚɡɚɧɨ, ɱɬɨ ɫ ɭɦɟɧɶɲɟɧɢɟɦ
ɞɚɜɥɟɧɢɹ ɧɚ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ ɥɢɧɟɣɧɨ ɭɛɵɜɚɟɬ
ɡɚɝɪɹɡɧɟɧɨɫɬɶ ɩɪɨɞɭɤɬɨɜɨɝɨ ɝɚɡɚ.
2. ɋ ɰɟɥɶɸ ɭɦɟɧɶɲɟɧɢɹ ɞɚɜɥɟɧɢɹ ɧɚ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ ɩɨɫɥɟɞɧɸɸ ɪɟɤɨɦɟɧɞɭɟɬɫɹ ɩɪɨɜɨɞɢɬɶ ɜ 3 ɷɬɚɩɚ.
Ⱦɥɹ ɫɧɢɠɟɧɢɹ ɞɚɜɥɟɧɢɹ ɧɚ 3-ɦ ɷɬɚɩɟ ɫɬɚɞɢɢ ɪɟɝɟɧɟɪɚɰɢɢ ɩɪɟɞɥɨɠɟɧɨ ɢɫɩɨɥɶɡɨɜɚɬɶ ɝɚɡɨɜɵɣ ɷɠɟɤɬɨɪ, ɱɟɪɟɡ
ɤɨɬɨɪɵɣ ɩɪɨɩɭɫɤɚɟɬɫɹ ɫɛɪɨɫɨɜɵɣ ɝɚɡ. ɉɪɟɞɫɬɚɜɥɟɧɚ
ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ ɩɪɨɰɟɫɫɚ ɄɐȺ ɫ ɷɠɟɤɬɨɪɨɦ.
ɋɉɂɋɈɄ ɅɂɌȿɊȺɌɍɊɕ
1. Ruthven D.M., Farooq S., Knaebel K. Pressure Swing
Adsorption. N.Y., 1994.
2. White D.H., Barkley P.G. // Chem. Eng. Progr. 1989. 85. Ɋ. 25.
3. Banerjee R., Narayankhedkar K.G., Sukhatme S.P. // Chem.
Eng. Sci. 1990. 45. Ɋ. 467.
4. Sircar S., Golden T.C., Rao M.B. // Carbon. 1996. 34. Ɋ. 1.
5. z¶¿ e. Ɍɟɨɪɟɬɢɱɟɫɤɢɟ ɨɫɧɨɜɵ ɯɪɨɦɚɬɨɝɪɚɮɢɢ ɝɚɡɨɜ. Ɇ.,
1963.
6. i»Á»ÃÀÄ d.m., n¶À»»¸ g.b., w»¿Ê»Ì m.j. // ɂɡɜ. ɊȺɇ. Ɇɟɯɚɧɢɤɚ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ. 2006. ʋ 3. ɋ. 77.
7. i»Á»ÃÀÄ d.m., w»¿Ê»Ì m.j. // Ⱦɨɤɥ. ɊȺɇ. ɋɟɪ. ɏɢɦɢɹ. 2005.
400. ʋ 2. ɋ. 11.
8. i»Á»ÃÀÄ d.m., w»¿Ê»Ì m.j. // ȼɟɫɬɧ. Ɇɨɫɤ. ɭɧ-ɬɚ. ɋɟɪ. 2. ɏɢɦɢɹ. 2005. 46. ɋ. 37.
9. http://www.criotech.ru/linde_ksa_1.shtml.
10 b·Æ¶Âĸ¾Í e.o. ɉɪɢɤɥɚɞɧɚɹ ɝɚɡɨɜɚɹ ɞɢɧɚɦɢɤɚ. Ɇ., 1976.
11. n¶À»»¸ g.b., i»Á»ÃÀÄ d.m., w»¿Ê»Ì m.j. ɇɚɭɱɧ. ɤɨɧɮɟɪ.
«Ʌɨɦɨɧɨɫɨɜɫɤɢɟ ɱɬɟɧɢɹ». ɋɟɤɰɢɹ ɏɢɦɢɹ, 18–25 ɚɩɪɟɥɹ
2006 ɝ. Ɍɟɡ. ɞɨɤɥ. Ɇ., 2006. ɋ. 24.
ɉɨɫɬɭɩɢɥɚ ɜ ɪɟɞɚɤɰɢɸ 05.10.06
PRODUCT PURITY INCREASE AT THE EXPENSE OF ENERGY OF
THE EXHAUST GAS IN THE PRESSURE SWING ADSORPTION
PROCESS
Ye.A. Makeyev, V.L. Zelenko, L.I. Heifets
(Division of Chemical Technology and New Materials)
It has been shown that purity of the product gas increases while ratio of gas pressure during the
gas-vent step to gas pressure during the adsorption step, decreases. As applied to a series of the
adsorbers operated in-parallel, this ratio is proposed to be reduced by means of the adsorber
vacuumization during the gas-vent step with the help of ejection by using the exhaust gas flow,
discharging from other adsorbers.