Abstract
To promote hydraulic refracturing, plugging hydraulic fractures through forming artificial barriers with temporary plugging agent (TP) as an effective method has been widely used. Innumerable researches have been carried out on the process, mechanism, and influence factors of hydraulic fractures plugging. Despite great achievements, the fluid infiltration velocity, as an essential parameter in the transient solution of plugging process, still needs to be obtained by experiments in view of the variation of fluid infiltration, which is unfavorable to efficiency and economy. To solve this problem, in this work, the plugging process of hydraulic fractures of tight sandstone reservoirs was comprehensively analyzed and divided into two parts: fluid infiltration and TP accretion. Specifically, for the fluid infiltration part, the variation of fluid pressure with porosity was realized by modified Richards equation; for the TP accretion part, the governing equation was derived based on convection–diffusion equation. These two parts were coupled by fluid infiltration velocity and artificial barrier porosity, and a new model for plugging hydraulic fractures of tight sandstone reservoirs was proposed. To verify the accuracy of the model, we poured artificial analogue rock samples (AARS) with hydraulic fractures according to physical and mechanical parameters of 1832.5-m-deep tight sandstone reservoir in Shengli Oilfield, China, and carried out plugging experiments. In particular, the new model that is based on numerical calculations provides a more efficient and cost-effective way of obtaining fluid infiltration velocity in comparison with the traditional plugging experiments. After validation, we investigated the effect of TP concentration, injection pressure, and fluid viscosity commonly used in oilfield plugging operation on the plugging effect including plugging efficiency and pressure bearing capacity for hydraulic fractures in the oilfield scale. The results show that TP accretion in hydraulic fractures determines the plugging effect which is closely related to fluid infiltration when TP density is close to the fluid density. Fluid viscosity influences both plugging efficiency and pressure bearing capacity, and they are affected by TP concentration and injection pressure, respectively. The findings contribute to a more comprehensive understanding of the plugging mechanism of hydraulic fractures of tight sandstone reservoirs and the optimization of plugging operation parameters in the oilfield.
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Abbreviations
- (a,b,c):
-
Mesh number
- BTS:
-
Brazilian tensile strength (MPa)
- C :
-
Fluid capacity (Pa−1)
- d, d 0, d M :
-
Propagation distance of injection pressure in AARS along the Fl and that at plugging beginning/M point (m)
- D, D ii, D ij :
-
Hydrodynamic dispersion tensor and its diagonal entries/cross-terms (m2/s)
- D m :
-
Diffusion coefficient (m2/s)
- d r, d rI, d r II :
-
Average variation rate of d and that of part I/part II (m/s)
- E :
-
Young’s modulus (GPa)
- F l, F w, F h :
-
Length/width/height of hydraulic fracture (m)
- g :
-
Acceleration of gravity (m/s2)
- G´x ( a , b , c ), G´y ( a , b , c ), G´z ( a , b , c ) :
-
Distance gradient variation
- Gx ( a , b , c ), Gy ( a , b , c ), Gz ( a , b , c ) :
-
Distance gradient between fine mesh and hydraulic fracture along x, y, z
- h :
-
Pressure head (m)
- k, k ar :
-
Permeability of reservoir/AARS and that of artificial barrier at plugging completion (m2)
- K :
-
Relative hydraulic conductivity
- L d :
-
Distance between the fine mesh and hydraulic fracture
- L e :
-
Edge length of AARS (m)
- n, n r, n ar :
-
Porosity of artificial barrier and that of reservoir/AARS (initial value) and that of artificial barrier at plugging completion (final value)
- n :
-
Unit normal vector
- p, p 1, p 2, p 3, p a, p p, p r :
-
Fluid pressure, starting pressure, pseudo-starting pressure, critical pressure, injection pressure, pore pressure, residual fluid pressure (Pa)
- PS:
-
Porosity size (μm)
- R L :
-
Diffusion of TP with size smaller than reservoir pores with fluid in reservoir pores per unit time (s−1)
- R P :
-
TP accretion on reservoir particles per unit time (s−1)
- S :
-
Fluid storage coefficient (Pa−1)
- S C :
-
TP embedded in reservoir matrix per unit time (s−1)
- S e :
-
Coefficient of pore variation
- t, t n, t M :
-
Plugging time, completion time, and M point time (s)
- UCS:
-
Uniaxial compressive strength (MPa)
- v, v ar, v r, v 0, v M :
-
Fluid infiltration velocity that in artificial barrier/reservoir and that at plugging beginning/M point (m/s)
- v r, v rI, v r II :
-
Average variation rate of v and that of part I/part II (m/s2)
- β, β 1, β 2 :
-
Dispersivity and longitudinal/transverse dispersivities (m)
- δ, ε, ζ :
-
Constants that specify the type of medium
- Δx, Δy, Δz :
-
Size of fine mesh
- Δx 0, Δy 0, Δz 0 :
-
Size of coarse mesh
- η :
-
Poisson’s ratio
- λ, λ TP, λ TP M, λ TP n :
-
TP concentration and TP concentration of artificial barrier and that at M point/plugging completion
- λ p :
-
Mass of accreted TP per unit weight of reservoir (mg/kg)
- λ TPr, λ TP rI, λ TP r II :
-
Average variation rate of λTP and that of part I/part II (s−1)
- μ :
-
Fluid viscosity (Pa·s)
- ρ, ρ TP, ρ b :
-
Density of fluid and TP, bulk density of reservoir/AARS (kg/m3)
- τ :
-
Tortuosity coefficient
- ψ :
-
Fluid content
- ω, ω max :
-
Division level of mesh size and its maximum
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The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China (52034010, 51979281) and the Fundamental Research Funds for the Central Universities (18CX02079A).
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Zhang, Y., Yu, R., Yang, W. et al. A new model for plugging hydraulic fractures of tight sandstone reservoirs. Arab J Geosci 15, 1347 (2022). https://doi.org/10.1007/s12517-022-10646-w
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DOI: https://doi.org/10.1007/s12517-022-10646-w