In this paper a model is established for unstable seepage flow with polymer concentration and pressure diffusion coupling, considering the effects of polymer molecular diffusion, adsorption, and viscoelasticity of polymer solution in the formation. The factors are close to the actual seepage parameters of the injected reservoir. For the nonlinear adsorption, the combined variable and the analytical iterative method are used to obtain the approximate analytical solution of the model. According to the concentration model, the relationship between concentration and pressure distribution is obtained. Using the model theory curve to fit the well test data, the seepage parameters of the formation are obtained, and the reflection characteristics of the unstable wellbore pressure derivative curve are analyzed.
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Abbreviations
- D :
-
molecular diffusion coefficient, cm2/s;
- φ :
-
formation porosity, fraction;
- C p :
-
polymer solution concentration, g/cm3;
- C 0 :
-
initial concentration of polymer solution, g/cm3;
- V :
-
apparent flow rate, cm/s;
- q :
-
the adsorption rate, dimensionless
- ac, bc :
-
Langmuir isotherm adsorption coefficient, cm3/g;
- r :
-
radial distance, cm;
- r w :
-
wellbore radius, cm;
- ρ p :
-
polymer solution density, g/cm3;
- \( {\rho}_{\tilde{a}} \) :
-
rock density, g/cm3;
- Q :
-
injection amount of polymer solution, cm3/s;
- h :
-
effective thickness of the formation, cm;
- R k :
-
permeability reduction coefficient, dimensionless;
- R keq :
-
maximum permeability reduction coefficient, dimensionless;
- b k :
-
parameters in the permeability reduction coefficient formula, cm3/g;
- ì p :
-
apparent viscosity of the polymer solution, PaRs;
- μ 0 :
-
zero shear viscosity of the polymer solution, PaRs;
- μ w :
-
water viscosity, PaRs;
- μ aq :
-
viscosity of the polymer solution as it flows through the pores considering the effect of viscoelasticity, PaRs;
- p :
-
pressure, Pa;
- p 0 :
-
initial pressure, Pa;
- t :
-
injection time
- ν :
-
shear rate, s-1;
- ν 1/2 :
-
shear rate corresponding to the average of zero and infinite shear viscosity, s-1;
- P a :
-
Meter viscosity model index, dimensionless;
- μ elas :
-
viscoelastic viscosity of the polymer solution, PaRs;
- N deb :
-
Deborah number, dimensionless;
- C*:
-
coefficient in the viscoelastic expression, dimensionless;
- m :
-
elastic viscosity index, dimensionless;
- tfl, tpr :
-
respectively the relaxation time of the fluid and the characteristic time of the flow, s;
- K :
-
effective permeability of the formation before injection of polymer solution, cm2;
- η :
-
pressure transmission coefficient, cm2/s;
- C t :
-
formation comprehensive compression coefficient, Pa-1;
- D 1 :
-
coefficient of the relationship between the equivalent shear rate and the apparent velocity, dimensionless;
- A1, A2, and A3 :
-
influence coefficients of concentration on viscosity, cm3/g, cm6/g2, cm9/g3.
- D :
-
dimensionless;
- p :
-
polymer solution.
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Acknowledgments
This work is supported by National Natural Science Foundation (No. 51974247, No. 41502311, No. 51874241), Key Laboratory Research Project of Education Department of Shaanxi Province (No. 15JS088), and Shaanxi Basic Research Projects in Natural Sciences (No. 2018JM5054, No. 2019JQ-807).
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Translated from Khimiya i Tekhnologiya Topliv i Masel, No. 3, pp. 104 — 109, May — June, 2020.
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Xie, Q., Xu, J. & Chen, M. Unsteady Pressure Dynamics of Polymer Flooding Reservoirs Considering Concentration Changes. Chem Technol Fuels Oils 56, 481–491 (2020). https://doi.org/10.1007/s10553-020-01159-x
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DOI: https://doi.org/10.1007/s10553-020-01159-x