Заканчивание / Книга_заканчивание скважин
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ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɝɨɪɢɡɨɧɬɚ.
1) ɩɨ ɫɬɟɩɟɧɢ ɜɫɤɪɵɬɢɹ ɩɥɚɫɬɚ (ɫɤɜɚɠɢɧɚ ɜɫɤɪɵɜɚɟɬ ɩɪɨɞɭɤɬɢɜɧɵɣ ɩɥɚɫɬ ɧɟ ɧɚ ɜɫɸ ɟɝɨ ɦɨɳɧɨɫɬɶ (Ɋɢɫɭɧɨɤ 2.3, ɜ);
2) ɩɨ ɯɚɪɚɤɬɟɪɭ ɜɫɤɪɵɬɢɹ ɩɥɚɫɬɚ (ɫɜɹɡɶ ɩɥɚɫɬɚ ɫɨ ɫɤɜɚɠɢɧɨɣ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɧɟ ɱɟɪɟɡ ɨɬɤɪɵɬɵɣ ɡɚɛɨɣ, ɚ ɱɟɪɟɡ ɩɟɪɮɨɪɚɰɢɨɧɧɵɟ ɤɚɧɚɥɵ (Ɋɢɫɭɧɨɤ 2.3, ɝ);
3) ɩɨ ɤɚɱɟɫɬɜɭ ɜɫɤɪɵɬɢɹ (ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɨɪɢɫɬɨɣ ɫɮɟɪɵ ɢɥɢ ɰɢɥɢɧɞɪɚ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ ɭɦɟɧɶɲɟɧɚ ɩɨ ɨɬɧɨɲɟɧɢɸ ɤ ɩɟɪɜɨɧɚɱɚɥɶɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɥɚɫɬɚ (Ɋɢɫɭɧɨɤ 2.3, ɛ).
ɂɡɜɟɫɬɧɨ, ɱɬɨ ɜ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜ ɩɥɚɫɬɟ ɜɨɤɪɭɝ ɫɤɜɚɠɢɧɵ ɨɛɪɚɡɭɸɬɫɹ ɞɜɟ ɡɨɧɵ ɫ ɢɡɦɟɧɟɧɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ – ɡɨɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ ɪɚɞɢɭɫɨɦ Rɡ.ɩ., ɦ ɢ ɡɨɧɚ ɤɨɥɦɚɬɚɰɢɢ rɤ. (Ɋɢɫɭɧɨɤ 2.4). Ɍɚɤɢɟ ɫɤɜɚɠɢɧɵ ɧɚɡɵɜɚɸɬ ɧɟɫɨɜɟɪɲɟɧɧɵɦɢ ɩɨ ɤɚɱɟɫɬɜɭ ɜɫɤɪɵɬɢɹ ɩɥɚɫɬɚ.
Ɋɢɫɭɧɨɤ 2.4 – ɋɯɟɦɵ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɵ ɩɥɚɫɬɚ ɩɨɫɥɟ ɜɫɤɪɵɬɢɹ ɟɝɨ ɛɭɪɟɧɢɟɦ.
1 – ɫɬɟɧɤɚ ɫɤɜɚɠɢɧɵ; 2 – ɝɥɢɧɢɫɬɚɹ ɤɨɪɤɚ; 3 – ɡɨɧɚ ɤɨɥɶɦɚɬɚɰɢɢ; 4 – ɡɨɧɚ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ; k, k1, k2 – ɩɪɨɧɢɰɚɟɦɨɫɬɢ, ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɧɚɱɚɥɶɧɚɹ, ɜ ɡɨɧɟ ɤɨɥɶɦɚɬɚɰɢɢ ɢ ɜ ɡɨɧɟ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ.
41
Ɉɛɨɡɧɚɱɢɦ ɞɚɜɥɟɧɢɟ ɧɚ ɪɚɞɢɭɫɟ ɩɪɨɧɢɤɧɨɜɟɧɢɹ Rɡ.ɩ. ɱɟɪɟɡ ɪ2, ɧɚ ɪɚɞɢɭɫɟ ɤɨɥɶɦɚɬɚɰɢɢ rɤ ɱɟɪɟɡ ɪ1, ɩɥɚɫɬɨɜɨɟ ɱɟɪɟɡ ɪɩɥ, ɚ ɧɚ ɜɯɨɞɟ ɜ ɫɤɜɚɠɢɧɭ ɱɟɪɟɡ ɪɫ. Ɍɨɝɞɚ, ɟɫɥɢ ɩɪɢɬɨɤ ɢɞɟɬ ɨɬ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ Rɤ ɤ ɫɤɜɚɠɢɧɟ ɫ ɜɨɨɛɪɚɠɚɟɦɵɦ
ɪɚɞɢɭɫɨɦ rɫ, ɫɨɝɥɚɫɧɨ ɮɨɪɦɭɥɟ |
(2.33) ɞɟɛɢɬ ɛɭɞɟɬ ɪɚɜɟɧ: |
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Qɩɥ |
2 S h k pɩɥ |
p2 |
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(2.38) |
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Ⱥɧɚɥɨɝɢɱɧɨ ɞɥɹ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɜ ɡɨɧɟ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ:
Qɡ.ɩ. |
2 S h k2 p2 |
p1 . |
(2.39) |
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ɂ ɞɥɹ ɞɜɢɠɟɧɢɹ ɠɢɞɤɨɫɬɢ ɱɟɪɟɡ ɡɨɧɭ ɤɨɥɶɦɚɬɚɰɢɢ:
Qɡ.ɤ. |
2 S h k1 p1 pɫ . |
(2.40) |
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ɂɫɯɨɞɹ ɢɡ ɭɫɥɨɜɢɹ ɧɟɪɚɡɪɵɜɧɨɫɬɢ ɩɨɬɨɤɚ, ɤɨɝɞɚ Qɩɥ = Qɡ.ɩ. ɫɪɚɜɧɢɜ ɢɯ, ɩɨɥɭɱɢɦ:
Qɮ |
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2 S h k pɩɥ pɫ |
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ɢɥɢ
= Qɡ.ɤ., ɢ,
(2.41)
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(2.42) |
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42
Ɉɬɧɨɲɟɧɢɹ |
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ɢ |
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ɩɨɤɚɡɵɜɚɸɬ, ɧɚɫɤɨɥɶɤɨ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɡɨɧ |
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ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ ɢ ɤɨɥɶɦɚɬɚɰɢɢ ɭɯɭɞɲɟɧɵ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɟɫɬɟɫɬɜɟɧɧɨɣ. ȼ ɧɟɮɬɟɝɚɡɨɜɨɣ ɩɪɚɤɬɢɤɟ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɡɚ ɫɱɟɬ ɢɡɦɟɧɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɪɨɞɵ ɜ ɩɪɢɡɚɛɨɣɧɨɣ ɡɨɧɟ
ɧɚɡɵɜɚɸɬ ɫɤɢɧ-ɷɮɮɟɤɬɨɦ S. |
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Ɍɨɝɞɚ ɮɨɪɦɭɥɚ (2.42) ɦɨɠɟɬ ɛɵɬɶ ɩɪɢɜɟɞɟɧɚ ɤ ɜɢɞɭ: |
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Qɮ |
2 S h k pɩɥ pɫ , |
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(2.43) |
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ɝɞɟ Sɛ = S1 + S2 – ɫɤɢɧ-ɷɮɮɟɤɬ ɡɚ ɫɱɟɬ ɛɭɪɟɧɢɹ, ɫɨɫɬɨɹɳɢɣ ɢɡ ɫɭɦɦɵ ɫɤɢɧ-ɷɮɮɟɤɬɨɜ ɜ ɨɛɟɢɯ ɡɨɧɚɯ ɫɧɢɠɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɢ – ɤɨɥɶɦɚɬɚɰɢɢ ɢ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ.
ɂɡ ɮɨɪɦɭɥ (2.42) ɢ |
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(2.43) ɩɨɥɭɱɚɟɬɫɹ, ɱɬɨ: |
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rɤ |
ln R ɡ.ɩ. . |
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ȿɫɥɢ ɡɨɧɚ ɤɨɥɶɦɚɬɚɰɢɢ ɨɬɫɭɬɫɬɜɭɟɬ, ɬ.ɟ rɤ = rc, ɬɨ ɮɨɪɦɭɥɚ ɩɪɢɧɢɦɚɟɬ ɜɢɞ:
Sɛ S2 |
E2 |
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(2.44)
(2.44)
(2.45)
ɂ ɧɚɨɛɨɪɨɬ, ɟɫɥɢ ɩɪɢɦɟɧɹɸɬ ɩɪɢɧɭɞɢɬɟɥɶɧɭɸ ɤɨɥɶɦɚɬɚɰɢɸ, ɜ ɪɟɡɭɥɶɬɚɬɟ
ɤɨɬɨɪɨɣ ɧɟɜɨɡɦɨɠɧɚ ɮɢɥɶɬɪɚɰɢɹ ɜ ɩɥɚɫɬ, ɬɨ: |
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E 1 ln |
rɤ |
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(2.46) |
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43
Ⱦɥɹ ɨɰɟɧɤɢ ɜɥɢɹɧɢɹ ɝɥɭɛɢɧɵ ɢ ɫɬɟɩɟɧɢ ɡɚɝɪɹɡɧɟɧɢɹ ɩɪɢɡɚɛɨɣɧɨɣ ɡɨɧɵ ɧɚ ɞɨɛɵɜɚɸɳɢɟ ɜɨɡɦɨɠɧɨɫɬɢ ɫɤɜɚɠɢɧɵ, ɧɟɫɨɜɟɪɲɟɧɧɨɣ ɩɨ ɤɚɱɟɫɬɜɭ ɜɫɤɪɵɬɢɹ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ ɛɭɪɟɧɢɟɦ, ɜɜɨɞɢɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɟɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ:
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ln R ɤ |
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(2.47) |
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ɝɞɟ |
ɞɟɛɢɬ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɫɨɜɟɪɲɟɧɧɨɣ ɫɤɜɚɠɢɧɵ. |
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ȼ ɷɬɨɣ ɮɨɪɦɭɥɟ ɱɢɫɥɢɬɟɥɶ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɜɟɥɢɱɢɧɭ ɨɫɧɨɜɧɵɯ ɮɢɥɶɬɪɚɰɢɨɧɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ, ɜɨɡɧɢɤɚɸɳɢɯ ɩɪɢ ɩɥɨɫɤɨɪɚɞɢɚɥɶɧɨɣ ɮɢɥɶɬɪɚɰɢɢ ɨɬ ɪɚɞɢɭɫɚ ɤɨɧɬɭɪɚ ɩɢɬɚɧɢɹ ɫɤɜɚɠɢɧɵ ɞɨ ɟɟ ɫɬɜɨɥɚ. ɉɪɢ ɪɚɜɧɨɦɟɪɧɨɣ ɫɟɬɤɟ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɤɜɚɠɢɧ ɫ ɪɚɫɫɬɨɹɧɢɟɦ ɦɟɠɞɭ ɧɢɦɢ 600 ɦ ɢ ɩɪɢ ɪɚɞɢɭɫɟ ɫɤɜɚɠɢɧɵ ɩɨ ɞɨɥɨɬɭ 0,1 ɦ ɡɧɚɱɟɧɢɟ ɱɢɫɥɢɬɟɥɹ ɪɚɜɧɨ 8. ɇɚ Ɋɢɫɭɧɨɤ 2.5 ɢ Ɋɢɫɭɧɨɤ 2.6 ɢɡɨɛɪɚɠɟɧɨ, ɤɚɤ ɢɡɦɟɧɹɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɩɚɪɚɦɟɬɪɨɜ ɡɨɧ ɤɨɥɶɦɚɬɚɰɢɢ ɢ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ ɩɪɨɦɵɜɨɱɧɨɣ ɠɢɞɤɨɫɬɢ. ɉɪɢ ɷɬɨɦ ɟɫɥɢ ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɨɪɢɫɬɨɣ ɫɪɟɞɵ ɜ ɡɨɧɟ ɤɨɥɶɦɚɬɚɰɢɢ ɪɚɡɦɟɪɨɦ 5 ɫɦ ɫɧɢɠɟɧɚ ɜ 20 ɪɚɡ, ɬɨ ɫɤɜɚɠɢɧɚ ɛɭɞɟɬ ɪɚɛɨɬɚɬɶ ɥɢɲɶ ɧɚ 51 % ɫɜɨɢɯ ɩɨɬɟɧɰɢɚɥɶɧɵɯ ɜɨɡɦɨɠɧɨɫɬɟɣ, ɚ ɟɫɥɢ ɜ 100 ɪɚɡ (ɱɬɨ ɜɨɡɦɨɠɧɨ), ɬɨ ɧɚ 18 %.
Ʉɚɤ ɛɵɥɨ ɨɬɦɟɱɟɧɨ ɪɚɧɟɟ, ɫɤɜɚɠɢɧɚ, ɢɦɟɸɳɚɹ ɩɟɪɮɨɪɢɪɨɜɚɧɧɵɣ ɡɚɛɨɣ, ɧɚɡɵɜɚɟɬɫɹ ɧɟɫɨɜɟɪɲɟɧɧɨɣ ɩɨ ɯɚɪɚɤɬɟɪɭ ɜɫɤɪɵɬɢɹ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ. ȿɫɥɢ ɩɪɨɞɭɤɬɢɜɧɵɣ ɩɥɚɫɬ ɜɫɤɪɵɬ ɛɭɪɟɧɢɟɦ ɧɟ ɧɚ ɜɫɸ ɟɝɨ ɦɨɳɧɨɫɬɶ, ɬɨ ɬɚɤɚɹ ɫɤɜɚɠɢɧɚ ɧɟɫɨɜɟɪɲɟɧɧɚ ɩɨ ɫɬɟɩɟɧɢ ɜɫɤɪɵɬɢɹ. ȼ ɨɛɨɢɯ ɫɥɭɱɚɹɯ ɮɚɤɬɢɱɟɫɤɢɣ ɞɟɛɢɬ ɩɪɢ ɨɛɳɢɯ ɨɞɢɧɚɤɨɜɵɯ ɭɫɥɨɜɢɹɯ ɛɭɞɟɬ ɦɟɧɶɲɟ ɞɟɛɢɬɚ ɫɤɜɚɠɢɧɵ ɫ ɨɬɤɪɵɬɵɦ ɡɚɛɨɟɦ ɢɡ-ɡɚ ɜɨɡɧɢɤɧɨɜɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɮɢɥɶɬɪɚɰɢɨɧɧɵɯ
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ɫɨɩɪɨɬɢɜɥɟɧɢɣ, ɜɵɡɵɜɚɟɦɵɯ ɢɫɤɪɢɜɥɟɧɢɟɦ ɢ ɫɝɭɳɟɧɢɟɦ ɥɢɧɢɣ ɩɨɬɨɤɨɜ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ ɜ ɨɤɨɥɨɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ ɩɥɚɫɬɚ ɢ ɧɚ ɫɬɟɧɤɟ ɫɤɜɚɠɢɧɵ, ɜɟɪɧɟɟ, ɧɚ ɝɪɚɧɢɰɟ ɫɤɜɚɠɢɧɚ - ɩɥɚɫɬ. ɋɝɭɳɟɧɢɟ ɩɨɬɨɤɨɜ, ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ, ɨɛɭɫɥɨɜɥɟɧɨ ɬɟɦ, ɱɬɨ ɭɦɟɧɶɲɢɥɚɫɶ ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɫɤɜɚɠɢɧɵ, ɝɪɚɧɢɱɚɳɚɹ ɫ ɩɥɚɫɬɨɦ, ɩɨ ɫɪɚɜɧɟɧɢɸ ɫɨ ɫɥɭɱɚɟɦ ɨɬɤɪɵɬɨɝɨ ɡɚɛɨɹ ɫɤɜɚɠɢɧɵ, ɤɨɬɨɪɵɣ ɜɫɤɪɵɥ ɛɵ ɩɪɨɞɭɤɬɢɜɧɵɣ ɝɨɪɢɡɨɧɬ ɧɚ ɜɫɸ ɟɝɨ ɦɨɳɧɨɫɬɶ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɧɟɫɨɜɟɪɲɟɧɫɬɜɨ ɩɨ ɫɬɟɩɟɧɢ ɢ ɯɚɪɚɤɬɟɪɭ ɜɫɤɪɵɬɢɹ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɝɨɪɢɡɨɧɬɚ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɤɨɷɮɮɢɰɢɟɧɬɨɦ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɟɫɨɜɟɪɲɟɧɫɬɜɚ:
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R ɤ |
ɋ |
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rɫ |
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ɝɞɟ |
ɋ1, ɋ2 – ɛɟɡɪɚɡɦɟɪɧɵɟ |
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ɤɨɷɮɮɢɰɢɟɧɬɵ, |
ɭɱɢɬɵɜɚɸɳɢɟ |
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ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɢɡ-ɡɚ ɧɟɫɨɜɟɪɲɟɧɫɬɜɚ |
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ɫɤɜɚɠɢɧɵ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨ ɫɬɟɩɟɧɢ ɢ ɩɨ ɯɚɪɚɤɬɟɪɭ |
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ɜɫɤɪɵɬɢɹ ɩɥɚɫɬɚ. |
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0,9 |
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ɫɨɜɟɪɲɟɧɫɬɜɚ |
0,8 |
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0,6 |
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ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ |
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Ʉɨɷɮ. |
0,3 |
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0,2 |
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Ƚɥɭɛɢɧɚ ɤɨɥɶɦɚɬɚɰɢɢ, ɦ |
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Ɋɢɫɭɧɨɤ 2.5 |
– ȼɥɢɹɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɡɨɧɵ ɤɨɥɶɦɚɬɚɰɢɢ ɧɚ ɤɨɷɮɮɢ- |
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ɰɢɟɧɬ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ ɩɪɢ ȕ2 = 1. |
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ȕ1 - ɫɬɟɩɟɧɶ ɫɧɢɠɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɢ (2, 5, 10, 20, 50, 100, 200). |
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0,8 |
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ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ |
0,5 |
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Ʉɨɷɮ. |
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Ɋɢɫɭɧɨɤ 2.6 – ȼɥɢɹɧɢɟ ɩɚɪɚɦɟɬɪɨɜ ɡɨɧɵ ɩɪɨɧɢɤɧɨɜɟɧɢɹ ɮɢɥɶɬɪɚɬɚ ɧɚ ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ ɩɪɢ ȕ1 = 1. ȕ2 – ɫɬɟɩɟɧɶ ɫɧɢɠɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɢ (2, 5, 10, 20, 50, 100, 200).
46
Ʉɨɷɮɮɢɰɢɟɧɬ ɋ1 ɨɩɪɟɞɟɥɹɟɬɫɹ ɫɬɟɩɟɧɶɸ ɜɫɤɪɵɬɢɹ ɩɪɨɞɭɤɬɢɜɧɨɝɨ ɩɥɚɫɬɚ, ɚ ɤɨɷɮɮɢɰɢɟɧɬ ɋ2 ɡɚɜɢɫɢɬ ɨɬ ɞɥɢɧɵ lɤ ɢ ɞɢɚɦɟɬɪɚ dɤ ɩɟɪɮɨɪɚɰɢɨɧɧɵɯ ɤɚɧɚɥɨɜ ɢ ɩɥɨɬɧɨɫɬɢ ɩɟɪɮɨɪɚɰɢɢ. ɗɬɢ ɤɨɷɮɮɢɰɢɟɧɬɵ ɧɚɯɨɞɹɬɫɹ ɩɨ ɢɡɜɟɫɬɧɵɦ ɝɪɚɮɢɤɚɦ ȼ.ɂ. ɓɭɪɨɜɚ, ɩɨɫɬɪɨɟɧɧɵɦ ɩɨ ɪɟɡɭɥɶɬɚɬɚɦ ɷɤɫɩɟɪɢɦɟɧɬɨɜ. ɉɪɢ ɷɬɨɦ ɩɪɢɧɢɦɚɟɬɫɹ, ɱɬɨ ɩɟɪɮɨɪɚɰɢɨɧɧɵɟ ɤɚɧɚɥɵ ɢɞɟɚɥɶɧɵ ɜ ɝɟɨɦɟɬɪɢɱɟɫɤɨɦ ɢ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɦ ɨɬɧɨɲɟɧɢɢ, ɬ.ɟ. ɢɦɟɸɬ ɩɪɚɜɢɥɶɧɭɸ ɰɢɥɢɧɞɪɢɱɟɫɤɭɸ ɮɨɪɦɭ, ɹɜɥɹɸɬɫɹ ɱɢɫɬɵɦɢ ɩɨ ɜɫɟɣ ɞɥɢɧɟ ɢ ɜɨɤɪɭɝ ɧɢɯ ɧɟɬ ɡɨɧɵ ɫ ɩɨɧɢɠɟɧɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ. Ⱦɥɹ ɬɚɤɨɣ ɢɞɟɚɥɢɡɢɪɨɜɚɧɧɨɣ ɤɚɪɬɢɧɵ ɝɪɚɮɢɤɢ ȼ.ɂ. ɓɭɪɨɜɚ, ɤɚɤ ɩɨɤɚɡɚɥɢ ɫɪɚɜɧɟɧɢɹ ɫ ɦɚɬɟɦɚɬɢɱɟɫɤɢɦ ɪɟɲɟɧɢɟɦ ɱɢɫɥɨɜɵɦ ɦɟɬɨɞɨɦ Ɇ. ɏɚɪɪɢɫɚ ɡɚɞɚɱɢ ɨ ɩɪɢɬɨɤɟ ɠɢɞɤɨɫɬɢ ɤ ɝɟɨɦɟɬɪɢɱɟɫɤɢ ɧɟɫɨɜɟɪɲɟɧɧɨɣ ɫɤɜɚɠɢɧɟ, ɞɚɸɬ ɞɨɜɨɥɶɧɨ ɬɨɱɧɵɣ ɪɟɡɭɥɶɬɚɬ ɜ ɩɪɟɞɟɥɚɯ ɢɫɫɥɟɞɨɜɚɧɧɵɯ ɡɧɚɱɟɧɢɣ ɩɚɪɚɦɟɬɪɨɜ ɩɟɪɮɨɪɚɰɢɢ.
ɍɤɚɡɚɧɧɵɟ ɜɵɜɨɞɵ ɫɩɪɚɜɟɞɥɢɜɵ ɬɨɥɶɤɨ ɞɥɹ ɢɞɟɚɥɶɧɵɯ ɭɫɥɨɜɢɣ ɩɪɢɬɨɤɚ ɜ ɫɤɜɚɠɢɧɭ, ɤɨɝɞɚ ɩɨɪɨɜɚɹ ɫɪɟɞɚ ɜɨ ɜɫɟɯ ɬɨɱɤɚɯ ɩɥɚɫɬɚ ɢɦɟɟɬ ɨɞɢɧɚɤɨɜɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ, ɚ ɰɢɥɢɧɞɪɢɱɟɫɤɢɟ ɤɚɧɚɥɵ ɱɢɫɬɵ ɩɨ ɜɫɟɣ ɫɜɨɟɣ ɞɥɢɧɟ. Ɋɟɚɥɶɧɚɹ ɠɟ ɤɚɪɬɢɧɚ ɞɚɥɟɤɚ ɨɬ ɢɞɟɚɥɢɡɢɪɨɜɚɧɧɨɣ. ɋɯɟɦɚɬɢɱɧɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɵ ɩɟɪɮɨɪɢɪɨɜɚɧɧɨɝɨ ɩɥɚɫɬɚ ɩɨɤɚɡɚɧɨ ɧɚ Ɋɢɫɭɧɨɤ 2.7. ɂɡ ɧɟɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɮɨɪɦɭɥɭ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ ɧɟɨɛɯɨɞɢɦɨ ɜɜɟɫɬɢ ɟɳɟ ɢ ɤɨɷɮɮɢɰɢɟɧɬ Sɩ (ɫɤɢɧ-ɷɮɮɟɤɬ ɩɟɪɮɨɪɚɰɢɢ), ɭɱɢɬɵɜɚɸɳɢɣ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ ɜɨɤɪɭɝ ɩɟɪɮɨɪɚɰɢɨɧɧɵɯ ɤɚɧɚɥɨɜ.
ɇɚ ɨɫɧɨɜɚɧɢɢ ɭɤɚɡɚɧɧɨɝɨ ɜɵɲɟ ɮɨɪɦɭɥɚ ɞɥɹ ɪɚɫɱɟɬɚ ɞɟɛɢɬɚ ɪɟɚɥɶɧɨɣ ɫɤɜɚɠɢɧɵ, ɩɪɨɛɭɪɟɧɧɨɣ ɧɚ ɧɟɮɬɹɧɨɣ ɨɛɴɟɤɬ ɢ ɢɦɟɸɳɟɣ ɜɫɟ ɜɢɞɵ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɧɟɫɨɜɟɪɲɟɧɫɬɜɚ, ɩɪɢɧɢɦɚɟɬ ɜɢɞ:
47
Qɮ |
pɩɥ pɫ |
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2 S h k pɩɥ pɫ |
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(2.49) |
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C1 C2 Sɛ Sɩ ¸ |
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ɉɪɢ ɷɬɨɦ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ:
Zɞɨɩ |
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P |
C1 |
C2 |
Sɛ Sɩ . |
(2.50) |
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2 |
S h k |
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Ɋɢɫɭɧɨɤ 2.7 – ɋɯɟɦɚɬɢɱɟɫɤɨɟ ɢɡɨɛɪɚɠɟɧɢɟ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɵ ɩɥɚɫɬɚ ɢ ɩɟɪɮɨɪɢɪɨɜɚɧɧɨɣ ɫɤɜɚɠɢɧɵ.
į – ɬɨɥɳɢɧɚ ɡɨɧɵ ɭɯɭɞɲɟɧɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɜɨɤɪɭɝ ɩɟɪɮɨɪɚɰɢɨɧɧɨɝɨ ɤɚɧɚɥɚ, k3 – ɩɪɨɧɢɰɚɟɦɨɫɬɶ ɩɨɪɨɞɵ ɜ ɡɨɧɟ ɜɨɤɪɭɝ ɩɟɪɮɨɪɚɰɢɨɧɧɨɝɨ ɤɚɧɚɥɚ.
48
Ⱦɥɹ ɪɚɫɱɟɬɨɜ ɩɪɢɬɨɤɚ ɠɢɞɤɨɫɬɢ ɢɥɢ ɜɪɟɦɟɧɢ ɞɥɹ ɫɢɫɬɟɦɵ ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɳɢɯ ɧɟɫɨɜɟɪɲɟɧɧɵɯ ɫɤɜɚɠɢɧ ɛɨɥɶɲɨɟ ɡɧɚɱɟɧɢɟ ɢɦɟɟɬ ɩɨɧɹɬɢɟ ɩɪɢɜɟɞɟɧɧɨɝɨ ɪɚɞɢɭɫɚ rɩɪ. ɗɬɨ ɪɚɞɢɭɫ ɬɚɤɨɣ ɮɢɤɬɢɜɧɨɣ ɫɤɜɚɠɢɧɵ, ɞɟɛɢɬ ɤɨɬɨɪɨɣ ɩɪɢ ɨɫɬɚɥɶɧɵɯ ɪɚɜɧɵɯ ɭɫɥɨɜɢɹɯ ɪɚɜɟɧ ɞɟɛɢɬɭ ɪɟɚɥɶɧɨɣ
ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢ ɧɟɫɨɜɟɪɲɟɧɧɨɣ ɫɤɜɚɠɢɧɵ |
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ɂɫɯɨɞɹ ɢɡ ɷɬɨɝɨ, ɮɨɪɦɭɥɭ (2.49) ɦɨɠɧɨ ɡɚɩɢɫɚɬɶ ɜ ɫɥɟɞɭɸɳɟɦ ɜɢɞɟ: |
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Qɮ |
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2 S h k pɩɥ pɫ |
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2 S h k pɩɥ |
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R |
ɤ |
C C |
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· |
P ln |
R ɤ |
(2.51) |
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P ¨ln |
r |
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¸ |
rɩɪ |
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c |
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Ɉɬɫɸɞɚ ɜɵɪɚɠɟɧɢɟ ɞɥɹ ɨɰɟɧɤɢ ɩɪɢɜɟɞɟɧɧɨɝɨ ɪɚɞɢɭɫɚ ɫɤɜɚɠɢɧɵ ɩɪɢɦɟɬ
ɜɢɞ:
rɩɪ rc ɟ- C1 C2 Sɛ Sɩ . |
(2.52) |
Ʉɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧ ɡɚɜɢɫɢɦɨɫɬɶɸ:
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ln |
R ɤ |
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r |
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ɩɪ |
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ȼ ɬɨ ɠɟ ɜɪɟɦɹ ɢɡɦɟɧɟɧɢɟ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɪɨɞɵ ɜ ɩɪɢɫɤɜɚɠɢɧɧɨɣ ɡɨɧɟ ɩɥɚɫɬɚ ɢ ɝɟɨɦɟɬɪɢɹ ɡɚɛɨɹ ɫɤɜɚɠɢɧɵ ɫ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɢɦɟɸɬ ɨɱɟɧɶ ɫɥɨɠɧɭɸ ɤɚɪɬɢɧɭ ɢ ɧɟ ɩɨɞɞɚɸɬɫɹ ɬɨɱɧɨɦɭ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦɭ ɨɩɢɫɚɧɢɸ. Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ, ɜ ɪɟɚɥɶɧɨɣ ɫɤɜɚɠɢɧɟ ɜ ɩɪɨɦɵɫɥɨɜɵɯ ɭɫɥɨɜɢɹɯ ɬɟɯɧɨɥɨɝɢ ɧɟ ɡɧɚɸɬ, ɧɚɩɪɢɦɟɪ, ɪɚɡɦɟɪɵ ɢ ɮɨɪɦɭ ɩɨɥɭɱɟɧɧɵɯ ɩɟɪɮɨɪɚɰɢɨɧɧɵɯ ɤɚɧɚɥɨɜ, ɫɬɟɩɟɧɶ ɢɡɦɟɧɟɧɢɹ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɩɨɪɨɞ ɜɨɤɪɭɝ ɩɟɪɮɨɪɚɰɢɨɧɧɵɯ ɤɚɧɚɥɨɜ ɢ ɬ.ɞ. Ɍɟɯɧɨɥɨɝɢ ɬɚɤɠɟ ɧɟ ɢɦɟɸɬ ɞɨɫɤɨɧɚɥɶɧɨɣ ɢɧɮɨɪɦɚɰɢɢ ɢ ɨ ɞɪɭɝɢɯ ɩɚɪɚɦɟɬɪɚɯ, ɩɨ ɤɨɬɨɪɵɦ ɨɩɪɟɞɟɥɹɸɬɫɹ ɡɧɚɱɟɧɢɹ ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɮɢɥɶɬɪɚɰɢɨɧɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ. ɉɨɷɬɨɦɭ ɨɩɪɟɞɟɥɢɬɶ ɫɬɟɩɟɧɶ
49
ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ ɩɨ ɮɨɪɦɭɥɟ (2.53) ɨɛɵɱɧɨ ɧɟɜɨɡɦɨɠɧɨ, ɬɚɤ ɤɚɤ ɧɟɢɡɜɟɫɬɧɵ ɬɨɱɧɵɟ ɡɧɚɱɟɧɢɹ ɛɟɡɪɚɡɦɟɪɧɵɯ ɤɨɷɮɮɢɰɢɟɧɬɨɜ, ɭɱɢɬɵɜɚɸɳɢɯ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɮɢɥɶɬɪɚɰɢɨɧɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ.
ȼ ɬɨ ɠɟ ɜɪɟɦɹ, ɛɚɡɢɪɭɹɫɶ ɧɚ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɦɟɬɨɞɚɯ ɢɫɫɥɟɞɨɜɚɧɢɹ ɫɤɜɚɠɢɧ, ɦɨɠɧɨ ɩɨɥɭɱɢɬɶ ɮɨɪɦɭɥɭ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ, ɟɫɥɢ ɜ ɮɨɪɦɭɥɭ ɞɟɛɢɬɚ ɪɟɚɥɶɧɨɣ ɫɤɜɚɠɢɧɵ
ɜɜɟɫɬɢ ɤɨɷɮɮɢɰɢɟɧɬ ɝɢɞɪɨɩɪɨɜɨɞɧɨɫɬɢ |
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(2.55) |
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R ɤ |
C |
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ɉɪɟɨɛɪɚɡɨɜɚɜ ɷɬɭ ɮɨɪɦɭɥɭ ɨɬɧɨɫɢɬɟɥɶɧɨ ɡɧɚɦɟɧɚɬɟɥɹ ɜɢɞɢɦ, ɱɬɨ
ɫɭɦɦɚ
ln R ɤ C |
C |
2 |
S |
ɛ |
S |
ɩ |
2 |
S H pɩɥ pɫ |
(2.56) |
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ɞɨɩɨɥɧɢɬɟɥɶɧɵɯ ɮɢɥɶɬɪɚɰɢɨɧɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɦɨɠɟɬ ɛɵɬɶ ɜɵɪɚɠɟɧɚ ɱɟɪɟɡ ɢɡɜɟɫɬɧɵɟ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ – ɤɨɷɮɮɢɰɢɟɧɬɵ ɝɢɞɪɨɩɪɨɜɨɞɧɨɫɬɢ ɢ ɩɪɨɞɭɤɬɢɜɧɨɫɬɢ ɫɤɜɚɠɢɧɵ.
ɉɨɞɫɬɚɜɥɹɹ (2.56) ɜ (2.55), ɩɨɥɭɱɚɟɦ ɫɥɟɞɭɸɳɭɸ ɮɨɪɦɭɥɭ ɞɥɹ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɷɮɮɢɰɢɟɧɬɚ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɝɨ ɫɨɜɟɪɲɟɧɫɬɜɚ ɫɤɜɚɠɢɧɵ:
50