Experimental and Numerical Evaluation of Acidizing Effect Duration for Diverting Acids in Reservoirs

Acidizing is one of the most economical and effective methods for ensuring the continuous and stable production of an oilfield and improving oil recovery. Diverting acids are more and more widely used in oilfields. However, it is difficult to accurately determine such parameters as acid discharge, concentration, and acid-rock reaction duration before construction, which may result in poor acidizing effect and low economic benefits. In this paper, the viscosity of diverting acid, reaction kinetics of acid rock, and residual acid limit are experimentally determined as well as numerically simulated using pressure, temperature, seepage, and geological models via the MATLAB software. The relationship between diverting time and peak viscosity time of diverting acid (DA) is studied and analyzed. For formation temperatures below the DA gel-breaking temperature, the DA with large displacement and low acid concentration should be selected. For formation temperatures close to the gel-breaking temperature, a medium acid concentration with large discharge rate should be selected. For a formation temperature exceeding the gel-breaking temperature, DA with high acid concentrations and small discharge rate should be selected. When the formation temperature is lower or close to the acid gel-breaking temperature, the acidizing effect of DA can be improved by adjusting the amount of injected acid. When the formation temperature is higher than the acid gel-breaking temperature, high-temperature corrosion inhibitors and adsorbent should be added in order to reduce the acid-rock reaction rate and improve the acidizing effect. The research results are of great significance in field acidizing construction.

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  1. 1.

    Y. Yan, Q. Xi, C. Una, et al., “A novel acidizing technology in carbonate reservoir: In-Situ formation of CO2 foamed acid and its self-diversion,” Colloids Surf. A: Physicochem. Eng. Aspects, 580: 123787 (2019).

    CAS  Article  Google Scholar 

  2. 2.

    Z. Luo, N. Zhang. L. Zhao, et al., “Numerical evaluation of shear and tensile stimulationvolumes based on natural fracture failure mechanism in tight and shale reservoirs,” Environ. Earth Sci., 78(175), 1-15 (2019).

    Google Scholar 

  3. 3.

    A. A. Bitanov, S.V. Nadezhdin, R.S. Adilgereev, et al., “Productivity impact from matrix stimulating thick intervals using a nondamaging self-diverting acidizing system:A Northwestern Kazakhstan case study,” SPE Middle East Oil and Gas Show and Conference, 12-15 March, Kingdom of Bahrain (2005).

  4. 4.

    D. Alleman, Q. Qi, and R. Keck, “The development and successful field use of viscoelastic surfactant-based diverting agents for acid stimulation,” SPE International Symposium on Oilfield Chemistry, Houston , TX, USA (2003).

  5. 5.

    B.R. Lungwitz, C.N. Fredd, M. E. Brady, et al., “Diversion and cleanup studies of viscoelastic surfactant-based self-divening acid,” SPE Prod. Oper., 22(01), 121-127 (2007).

    CAS  Google Scholar 

  6. 6.

    A. T. Jardim Neto, C. A. M. Silva, R.S. Torres, et al, “Self-diverting acid for effective carbonate stimulation offshore Brazil: A successful history,” SPE European Formation Damage Conference & Exhibition, 5-7 June, Noordwijk, the Netherlands (2013).

  7. 7.

    Sau R, Shuchart C, Clancey B, et al. Qualification and optimization of degradable fibers for re-stimulation of carbonate reservoirs,” International Petroleum Technology Conference, 6-9 December, Doha, Qatar (2015).

  8. 8.

    H. Xue, L.Q. Zhang, P.L. Liu, et a]., “Simulation and analysis of wormhole propagation in carbonates through the use of models with different dimensions,” Chem. Technol. Fuels Oils, 53(5), 727-738 (2017).

    CAS  Article  Google Scholar 

  9. 9.

    N. Li, J. Dai, P. Liu, et al., “Experimental study on influencing factors of acid-fracturing effect for carbonate reservoirs,” Petroleum, 1(2), 146-153 (2015).

    Article  Google Scholar 

  10. 10.

    H. Yoo, Y. Kim, W. Lee, et al., “An experimental study on acid-rock reaction kinetics using dolomite in carbonate acidizing,” J. Pet. Sci. Eng., 168,478-494 (2018).

    CAS  Article  Google Scholar 

  11. 11.

    S. Li, R. Huo, F. Yoshiaki, et al., “Effect of acid-temperature-pressure on the damage characteristics of sandstone,” Int. J. Rock Mech. Min. Sci., 122, 104079 (2019).

    Article  Google Scholar 

  12. 12.

    P. Liu, X. Yan, J. Yao, et al., “Modeling and analysis of the acidizing process in carbonate rocks using a two-phase thermal-hydrologic-chemical coupled model,” Chem. Eng. Sci., 207, 215-234 (2019).

    CAS  Article  Google Scholar 

  13. 13.

    W. Zhang, J. Mao, X. Yang, et al., “Development of a stimuli-responsive Gemini zwitterionic viscoelastic surfactant for self-diverting acid,” J. Surfact. Deterg., 22(3), 535-547 (2019).

    CAS  Article  Google Scholar 

  14. 14.

    M.I. Miah, M.A. Elhaj, S. Ahmed, et al., “Modeling of temperature distribution and oil displacement during thermal recovery in porous media: A critical review,” Fuel, 226, 423-440 (2018).

    CAS  Article  Google Scholar 

  15. 15.

    N. Kalia and G. Glasbergen, “Wormhole formation in carbonates under varying temperature conditions,” SPE: 8th European Formation Damage Conference, 27-29 May, Scheveningen, T he Netherlands (2009).

  16. 16.

    W.J. Al-Mudhafar, “Bayesian kriging for reproducing reservoir heterogeneity in a tidal depositional environment of a sandstone formation,” J. Appl Geophys., 160, 84-102 (2019).

    Article  Google Scholar 

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This study was financially supported by the 13th Five-Tear National Project of China (Grant No.2017ZX05030005), and the National Natural Science Foundation of China No. (51974264).


vx Rate of fluid passing through yz interface (m/s)

vy Rate of fluid passing through xz interface (m/s)

vz Rate of fluid passing through xy interface (m/s)

‖∗‖ Norms of vectors or matrices

μeff Effective viscosity of DA related to pH, Ca2+ concentration, temperature, and flow rate (mPa∙s)

Y Rheological index (dimensionless)

K Reaction rate constant ([mol/L]-m∙ mol/s/cm2)

Ea Activation energy of reaction (J/mol)

J Reaction rate (mol/s cm2)

W1, W2 Experimental fit coefficient (dimensionless)

C Acid concentration (mol/L)

k0 Frequency factor ([mol/L]-m∙mol/s cm2)

γ Shear rate (s-1)

M Reaction order (diramsionless)

Cf Reactive liquid mass concentration in pore (mol/L)

R(Cs) Surface reaction rate (kmol/s∙m2)

av Pore specific surface area (m2/m3)

Tf Acid temperature (K)

Ts Rock temperature (K)

CPf Specific heat capacity of acid (J/kg∙K)

CPs Specific heat capacity of rock (J/kg∙K)

kef Acid thermal conductivity (W/m∙K)

kesRock thermal conductivity (W/m∙K)

hc Convective heat transfer coefficient between acid and rock (W/m2∙K)

Hr Reaction enthalpy (J/mol)

dfs Settlement rate of solid diverting agent film cake (g/cm2∙s)

kfs Settlement coefficient of solid diverting agent filter cake (dimensionless)

Cf Mass concentration of solid diverting agent in temporary plugging fluid (g/cm3)

vfd Destruction and shedding rate of solid diverting agent filter cake (g/cm2∙s)

kfd Shedding rate coefficient of solid diverting agent filter cake (g/N∙s)

s Porosity of solid diverting agent filter cake (dimensionless)

τs Shear stress of temporary plugging fluid on filter cake surface of solid diverting agent (Pa)

τf Minimum stress required for shedding of solid diverting agent (Pa)

k' Consistency coefficient of temporary plugging fluid (Pa∙sn)

n' Flow index of temporary plugging fluid (dimensionless)

0 Initial porosity (dimensionless)

Porosity at a time (dimensionless)

X,Y,Z Total grid length in three directions (m)

K0 Initial permeability (mD)

K Permeability at a time (mD)

β Experimental parameter (dimensionless)

G Arrays conforming to random normal distribution, ranging from-1 to 1 (dimensionless)

σ Standard deviation coefficient: value range 0-1 (dimensionless)

λ Undetermined weight coefficient

n Total sample size

N(j-x) Total number of sample points when separation distance is jx

\( \overline{Z}\left({x}_i\right) \) Sample average

\( \overline{Z}\left({x}_j\right) \) Sample average

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Correspondence to Runyu Wang.

Additional information

Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 2, pp. 83 -92, March-April, 2020.

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Zhao, L., Wang, R., Liu, P. et al. Experimental and Numerical Evaluation of Acidizing Effect Duration for Diverting Acids in Reservoirs. Chem Technol Fuels Oils (2020). https://doi.org/10.1007/s10553-020-01136-4

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  • diverting acid
  • peak viscosity
  • gel-breaking
  • acidizing