The Chinese Journal of Process Engineering ›› 2026, Vol. 26 ›› Issue (9): 1007-1020.DOI: 10.12034/j.issn.1009-606X.225312
• Research Paper • Previous Articles Next Articles
Yihan LI1(
), Zhixiao LI2, Xiaodong GE3, Kexian HU3, Zhengping WAN3, Zheng FAN1(
)
Received:2025-12-16
Revised:2026-03-02
Online:2026-09-28
Published:2026-09-28
Contact:
Yihan LI 897871730@qq.com;fanzheng@xsyu.edu.cn
李艺涵1(
), 李志潇2, 革晓东3, 胡科先3, 万征平3, 范峥1(
)
通讯作者:
李艺涵 897871730@qq.com;fanzheng@xsyu.edu.cn
作者简介:李艺涵,硕士研究生,化学工程专业,E-mail: 897871730@qq.com;基金资助:CLC Number:
Yihan LI, Zhixiao LI, Xiaodong GE, Kexian HU, Zhengping WAN, Zheng FAN. Interaction effects analysis and process parameter optimization for gel breaking of waste drilling fluid[J]. The Chinese Journal of Process Engineering, 2026, 26(9): 1007-1020.
李艺涵, 李志潇, 革晓东, 胡科先, 万征平, 范峥. 废弃钻井液破胶过程的交互作用分析与工艺参数优化[J]. 过程工程学报, 2026, 26(9): 1007-1020.
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URL: https://jproeng.ipe.ac.cn/EN/10.12034/j.issn.1009-606X.225312
| Item | Density/(g/cm3) | Plastic viscosity/mPa·s | Funnel viscosity/s | API filtrate volume/mL | pH | Zeta potential/mV | Ca2+ concentration/(mg/L) | Mg2+ concentration/(mg/L) |
|---|---|---|---|---|---|---|---|---|
| Waste drilling fluid | 1.428 | 34.5 | 87.21 | 11 | 12.5 | -41.6 | 685.52 | 156.98 |
Table 1 Test results of waste drilling fluid
| Item | Density/(g/cm3) | Plastic viscosity/mPa·s | Funnel viscosity/s | API filtrate volume/mL | pH | Zeta potential/mV | Ca2+ concentration/(mg/L) | Mg2+ concentration/(mg/L) |
|---|---|---|---|---|---|---|---|---|
| Waste drilling fluid | 1.428 | 34.5 | 87.21 | 11 | 12.5 | -41.6 | 685.52 | 156.98 |
| Level | Breaker dosage/(g/L), A | Reaction temperature/℃, B | pH regulator dosage/(g/L), C | Inorganic salt proportion in breaker/(w/w), D |
|---|---|---|---|---|
| -1 | 2 | 40 | 3 | 0.75 |
| 0 | 3 | 50 | 3.4 | 0.80 |
| 1 | 4 | 60 | 3.8 | 0.85 |
Table 2 Levels of factors
| Level | Breaker dosage/(g/L), A | Reaction temperature/℃, B | pH regulator dosage/(g/L), C | Inorganic salt proportion in breaker/(w/w), D |
|---|---|---|---|---|
| -1 | 2 | 40 | 3 | 0.75 |
| 0 | 3 | 50 | 3.4 | 0.80 |
| 1 | 4 | 60 | 3.8 | 0.85 |
| Run | A/(g/L) | B/℃ | C/(g/L) | D, W/W | Y/mV |
|---|---|---|---|---|---|
| 1 | 3 | 60 | 3.4 | 0.85 | -12.0 |
| 2 | 3 | 50 | 3 | 0.75 | -16.1 |
| 3 | 3 | 50 | 3.8 | 0.75 | -13.1 |
| 4 | 3 | 50 | 3.4 | 0.8 | -11.6 |
| 5 | 3 | 50 | 3.4 | 0.8 | -12.3 |
| 6 | 4 | 50 | 3 | 0.8 | -12.9 |
| 7 | 3 | 50 | 3.8 | 0.85 | -13.6 |
| 8 | 3 | 60 | 3 | 0.8 | -13.5 |
| 9 | 4 | 50 | 3.4 | 0.85 | -12.6 |
| 10 | 3 | 50 | 3.4 | 0.8 | -11.5 |
| 11 | 2 | 50 | 3.8 | 0.8 | -13.3 |
| 12 | 2 | 40 | 3.4 | 0.8 | -15.4 |
| 13 | 3 | 40 | 3.4 | 0.75 | -14.2 |
| 14 | 3 | 50 | 3.4 | 0.8 | -11.2 |
| 15 | 3 | 60 | 3.8 | 0.8 | -11.7 |
| 16 | 2 | 50 | 3 | 0.8 | -16.2 |
| 17 | 3 | 60 | 3.4 | 0.75 | -14.2 |
| 18 | 3 | 40 | 3 | 0.8 | -15.1 |
| 19 | 3 | 40 | 3.8 | 0.8 | -13.2 |
| 20 | 2 | 50 | 3.4 | 0.85 | -14.3 |
| 21 | 4 | 40 | 3.4 | 0.8 | -11.8 |
| 22 | 4 | 60 | 3.4 | 0.8 | -11.9 |
| 23 | 3 | 50 | 3 | 0.85 | -13.7 |
| 24 | 3 | 50 | 3.4 | 0.8 | -12.1 |
| 25 | 4 | 50 | 3.8 | 0.8 | -12.7 |
| 26 | 2 | 50 | 3.4 | 0.75 | -16.8 |
| 27 | 2 | 60 | 3.4 | 0.8 | -14.1 |
| 28 | 4 | 50 | 3.4 | 0.75 | -12.8 |
| 29 | 3 | 40 | 3.4 | 0.85 | -13.4 |
Table 3 Box-Behnken design matrix and experimental results
| Run | A/(g/L) | B/℃ | C/(g/L) | D, W/W | Y/mV |
|---|---|---|---|---|---|
| 1 | 3 | 60 | 3.4 | 0.85 | -12.0 |
| 2 | 3 | 50 | 3 | 0.75 | -16.1 |
| 3 | 3 | 50 | 3.8 | 0.75 | -13.1 |
| 4 | 3 | 50 | 3.4 | 0.8 | -11.6 |
| 5 | 3 | 50 | 3.4 | 0.8 | -12.3 |
| 6 | 4 | 50 | 3 | 0.8 | -12.9 |
| 7 | 3 | 50 | 3.8 | 0.85 | -13.6 |
| 8 | 3 | 60 | 3 | 0.8 | -13.5 |
| 9 | 4 | 50 | 3.4 | 0.85 | -12.6 |
| 10 | 3 | 50 | 3.4 | 0.8 | -11.5 |
| 11 | 2 | 50 | 3.8 | 0.8 | -13.3 |
| 12 | 2 | 40 | 3.4 | 0.8 | -15.4 |
| 13 | 3 | 40 | 3.4 | 0.75 | -14.2 |
| 14 | 3 | 50 | 3.4 | 0.8 | -11.2 |
| 15 | 3 | 60 | 3.8 | 0.8 | -11.7 |
| 16 | 2 | 50 | 3 | 0.8 | -16.2 |
| 17 | 3 | 60 | 3.4 | 0.75 | -14.2 |
| 18 | 3 | 40 | 3 | 0.8 | -15.1 |
| 19 | 3 | 40 | 3.8 | 0.8 | -13.2 |
| 20 | 2 | 50 | 3.4 | 0.85 | -14.3 |
| 21 | 4 | 40 | 3.4 | 0.8 | -11.8 |
| 22 | 4 | 60 | 3.4 | 0.8 | -11.9 |
| 23 | 3 | 50 | 3 | 0.85 | -13.7 |
| 24 | 3 | 50 | 3.4 | 0.8 | -12.1 |
| 25 | 4 | 50 | 3.8 | 0.8 | -12.7 |
| 26 | 2 | 50 | 3.4 | 0.75 | -16.8 |
| 27 | 2 | 60 | 3.4 | 0.8 | -14.1 |
| 28 | 4 | 50 | 3.4 | 0.75 | -12.8 |
| 29 | 3 | 40 | 3.4 | 0.85 | -13.4 |
| Source | Sum of squares | df | Mean square | F value | P value | Significance |
|---|---|---|---|---|---|---|
| Model | 60.1400 | 14 | 4.3000 | 26.9500 | <0.0001 | Significant |
| A | 19.7600 | 1 | 19.7600 | 124.0100 | <0.0001 | Significant |
| B | 2.7100 | 1 | 2.7100 | 16.9900 | 0.0010 | Significant |
| C | 8.1700 | 1 | 8.1700 | 51.2500 | <0.0001 | Significant |
| D | 4.8100 | 1 | 4.8100 | 30.2000 | <0.0001 | Significant |
| AB | 0.4900 | 1 | 0.4900 | 3.0700 | 0.1014 | |
| AC | 1.8200 | 1 | 1.8200 | 11.4400 | 0.0045 | Significant |
| AD | 1.3200 | 1 | 1.3200 | 8.3000 | 0.0121 | Significant |
| BC | 0.0025 | 1 | 0.0025 | 0.0157 | 0.9021 | |
| BD | 0.4900 | 1 | 0.4900 | 3.0700 | 0.1014 | |
| CD | 2.1000 | 1 | 2.1000 | 13.1900 | 0.0027 | Significant |
| A2 | 6.9900 | 1 | 6.9900 | 43.8800 | <0.0001 | Significant |
| B2 | 1.6300 | 1 | 1.6300 | 10.2100 | 0.0065 | Significant |
| C2 | 7.5100 | 1 | 7.5100 | 47.1100 | <0.0001 | Significant |
| D2 | 10.7700 | 1 | 10.7700 | 67.5600 | <0.0001 | Significant |
| Residual | 2.2300 | 14 | 0.1594 | |||
| Lack of fit | 1.4200 | 10 | 0.1419 | 0.6991 | 0.7064 | |
| Pure error | 0.8120 | 4 | 0.2030 | |||
| Cor total | 62.3700 | 28 |
Table 4 ANOVA for the response surface model
| Source | Sum of squares | df | Mean square | F value | P value | Significance |
|---|---|---|---|---|---|---|
| Model | 60.1400 | 14 | 4.3000 | 26.9500 | <0.0001 | Significant |
| A | 19.7600 | 1 | 19.7600 | 124.0100 | <0.0001 | Significant |
| B | 2.7100 | 1 | 2.7100 | 16.9900 | 0.0010 | Significant |
| C | 8.1700 | 1 | 8.1700 | 51.2500 | <0.0001 | Significant |
| D | 4.8100 | 1 | 4.8100 | 30.2000 | <0.0001 | Significant |
| AB | 0.4900 | 1 | 0.4900 | 3.0700 | 0.1014 | |
| AC | 1.8200 | 1 | 1.8200 | 11.4400 | 0.0045 | Significant |
| AD | 1.3200 | 1 | 1.3200 | 8.3000 | 0.0121 | Significant |
| BC | 0.0025 | 1 | 0.0025 | 0.0157 | 0.9021 | |
| BD | 0.4900 | 1 | 0.4900 | 3.0700 | 0.1014 | |
| CD | 2.1000 | 1 | 2.1000 | 13.1900 | 0.0027 | Significant |
| A2 | 6.9900 | 1 | 6.9900 | 43.8800 | <0.0001 | Significant |
| B2 | 1.6300 | 1 | 1.6300 | 10.2100 | 0.0065 | Significant |
| C2 | 7.5100 | 1 | 7.5100 | 47.1100 | <0.0001 | Significant |
| D2 | 10.7700 | 1 | 10.7700 | 67.5600 | <0.0001 | Significant |
| Residual | 2.2300 | 14 | 0.1594 | |||
| Lack of fit | 1.4200 | 10 | 0.1419 | 0.6991 | 0.7064 | |
| Pure error | 0.8120 | 4 | 0.2030 | |||
| Cor total | 62.3700 | 28 |
| Fold | R2 | RMSE/mV | MAE/mV |
|---|---|---|---|
| 1 | 0.957 | 0.367 | 0.2218 |
| 2 | 0.8607 | 0.2665 | 0.2192 |
| 3 | 0.8033 | 0.2101 | 0.3953 |
| 4 | 0.7926 | 0.455 | 0.4371 |
| 5 | 0.6488 | 0.2973 | 0.2695 |
| Mean±SD | 0.8125±0.1123 | 0.3192±0.0947 | 0.2571±0.1112 |
Table 5 5-fold CV results of the BP-ANN model
| Fold | R2 | RMSE/mV | MAE/mV |
|---|---|---|---|
| 1 | 0.957 | 0.367 | 0.2218 |
| 2 | 0.8607 | 0.2665 | 0.2192 |
| 3 | 0.8033 | 0.2101 | 0.3953 |
| 4 | 0.7926 | 0.455 | 0.4371 |
| 5 | 0.6488 | 0.2973 | 0.2695 |
| Mean±SD | 0.8125±0.1123 | 0.3192±0.0947 | 0.2571±0.1112 |
| Fold | R2 | RMSE/mV | MAE/mV |
|---|---|---|---|
| 1 | 0.7981 | 0.6287 | 0.5489 |
| 2 | 0.7065 | 0.6093 | 0.5486 |
| 3 | 0.8598 | 0.7084 | 0.619 |
| 4 | 0.1986 | 0.7268 | 0.6678 |
| 5 | 0.8845 | 0.4371 | 0.4118 |
| Mean±SD | 0.6895±0.253 | 0.6221±0.1028 | 0.5592±0.0864 |
Table 6 5-fold CV results of the GPR model
| Fold | R2 | RMSE/mV | MAE/mV |
|---|---|---|---|
| 1 | 0.7981 | 0.6287 | 0.5489 |
| 2 | 0.7065 | 0.6093 | 0.5486 |
| 3 | 0.8598 | 0.7084 | 0.619 |
| 4 | 0.1986 | 0.7268 | 0.6678 |
| 5 | 0.8845 | 0.4371 | 0.4118 |
| Mean±SD | 0.6895±0.253 | 0.6221±0.1028 | 0.5592±0.0864 |
| Fold | R2 | RMSE/mV | MAE/mV |
|---|---|---|---|
| 1 | 0.2353 | 0.9079 | 0.7848 |
| 2 | 0.5788 | 0.7525 | 0.8865 |
| 3 | 0.3483 | 0.6788 | 0.5819 |
| 4 | 0.3811 | 0.906 | 0.7459 |
| 5 | 0.478 | 0.5412 | 0.8778 |
| Mean±SD | 0.4043±0.1305 | 0.7573±0.1563 | 0.7754±0.1237 |
Table 7 5-fold CV results of the RF model
| Fold | R2 | RMSE/mV | MAE/mV |
|---|---|---|---|
| 1 | 0.2353 | 0.9079 | 0.7848 |
| 2 | 0.5788 | 0.7525 | 0.8865 |
| 3 | 0.3483 | 0.6788 | 0.5819 |
| 4 | 0.3811 | 0.906 | 0.7459 |
| 5 | 0.478 | 0.5412 | 0.8778 |
| Mean±SD | 0.4043±0.1305 | 0.7573±0.1563 | 0.7754±0.1237 |
| Method | A/(g/L) | B/℃ | C/(g/L) | D, w/w | Zeta potential/mV | Relative error | |
|---|---|---|---|---|---|---|---|
| Predicted | Measured | ||||||
| GA-BP | 3.3 | 57.7 | 3.45 | 0.8 | -10.735 | -10.85 | 1.06% |
Table 8 GA-BP optimization and validation results
| Method | A/(g/L) | B/℃ | C/(g/L) | D, w/w | Zeta potential/mV | Relative error | |
|---|---|---|---|---|---|---|---|
| Predicted | Measured | ||||||
| GA-BP | 3.3 | 57.7 | 3.45 | 0.8 | -10.735 | -10.85 | 1.06% |
| Treatment | Sample | Density/(g/cm3) | Plastic viscosity/mPa·s | Funnel viscosity/s | pH | Zeta potential/mV | Ca2++Mg2+ concentration/(mg/L) |
|---|---|---|---|---|---|---|---|
| With gel breaking | Filtrate | 1.0369 | 8.0 | 40.09 | 8.6 | -10.85 | 638.24 |
| Reconstituted drilling fluid | 1.0694 | 8.3 | 46.83 | 8.5 | -5.68 | 62.42 | |
| Without gel breaking | Reconstituted drilling fluid | 1.1256 | 12.4 | 56.87 | 9.2 | -28.74 | 84.74 |
Table 9 Comparison of properties of gel-broken filtrate and reconstituted drilling fluids with and without gel breaking
| Treatment | Sample | Density/(g/cm3) | Plastic viscosity/mPa·s | Funnel viscosity/s | pH | Zeta potential/mV | Ca2++Mg2+ concentration/(mg/L) |
|---|---|---|---|---|---|---|---|
| With gel breaking | Filtrate | 1.0369 | 8.0 | 40.09 | 8.6 | -10.85 | 638.24 |
| Reconstituted drilling fluid | 1.0694 | 8.3 | 46.83 | 8.5 | -5.68 | 62.42 | |
| Without gel breaking | Reconstituted drilling fluid | 1.1256 | 12.4 | 56.87 | 9.2 | -28.74 | 84.74 |
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