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Wormhole Propagation Behavior Under Reservoir Condition in Carbonate Acidizing

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Abstract

In carbonate reservoirs, acid is injected into the formation under breakdown pressure to react with the rock to remove the contaminations caused by drilling and production, which is called carbonate acidizing in reservoir development. In carbonate acidizing, acid flows selectively through large pores to create wormholes. Wormhole propagation under experimental condition has been studied by many experts. In this paper, a model which couples a two-scale continuum model simulating wormholing in the invaded zone and a reservoir flow model for the compressed zone was used to study the wormhole propagation behavior under reservoir condition. In this model, the porosity values which are uniformly distributed used in former literature follow the normal law. Based on the model, we first compared the results of the two porosity generation methods, and then studied the wormhole propagation behavior under reservoir condition, and finally simulated a two-layer formation to study the effects of distance and permeability ratio between the two layers. The results show that the normally distributed porosities simulate wormholing better. The effect of compressed zone on wormhole propagation increases with the decrease of compressibility factor and wormhole has a maximal value in length. The effect of distance between the two layers on wormhole lengths and acid distributions can be divided into three zones based on the wormhole length in the lower layer. A critical value of permeability ratio between the two layers exists, below and above which the wormhole length in the low permeability layer decreases sharply and almost keeps constant, respectively.

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Abbreviations

a 0 :

Initial average interfacial area per unit volume of the medium (m−1)

a v :

Interfacial area per unit volume of the medium (m−1)

A v :

Dimensionless interfacial area

C f :

Cup-mixing concentration of acid in the fluid phase (mol  L−1)

c f :

Dimensionless cup-mixing concentration of acid in the fluid phase

C l :

Formation fluid compressibility factor (MPa−1)

C 0 :

Initial concentration of acid (mol L−1)

C s :

Concentration of acid at the solid–fluid interface (mol L−1)

c s :

Dimensionless concentration of the acid at the fluid–solid interface

c v :

Coefficient of variation

Da :

Damköhler number, ratio of reaction rate to mass transfer rate

D m :

Molecular diffusivity (m2 s−1)

D eR :

Effective dispersion tensor in the radial direction (m2 s−1)

D eθ :

Effective dispersion tensor in the circumferential direction (m2 s−1)

D r :

Dimensionless effective dispersion coefficient in the radial direction

D θ :

Dimensionless effective dispersion coefficient in the circumferential direction

Ĝ:

Standard Gaussian/normal distribution function

K :

Permeability of the medium (μm2)

K 0 :

Initial average permeability of the medium (μm2)

k :

Dimensionless permeability of the medium

K 0h :

Initial average permeability in the high permeability layer (μm2)

K 0l :

Initial average permeability in the low permeability layer (μm2)

k c :

Mass transfer coefficient (m s−1)

k s :

Surface reaction rate constant (m s−1)

m :

Ratio of pore length to pore diameter

N ac :

Acid capacity number, the volume of solid dissolved per unit volume of the acid

p :

Dimensionless formation pressure

P :

Reservoir pressure (MPa)

P e :

Initial reservoir pressure (MPa)

Pe :

Peclet number, ratio of diffusion time to convection time

P r :

Reservoir pressure in the compressed zone (MPa)

P I :

Pressure at the interface between the invaded zone and the compressed zone (MPa)

P bh :

Inlet pressure (MPa)

Re p :

Pore Reynolds number, ratio of inertial force to viscous force in the pore

r w :

Wellbore radius (m)

r invade :

Radius of the invaded zone (m)

r e :

Radius of the compressed zone (m)

r p :

Pore radius (m)

r po :

Initial average pore radius (m)

R(C s):

Reaction kinetics (m mol L−1 s−1)

Sc :

Schmidt number, ratio of kinetic viscosity of the fluid to the molecular diffusivity

Sh :

Sherwood Number, ratio of convective to diffusive mass transport

Sh ∞ :

Asymptotic Sherwood number for the pore

t′:

Time (s)

t :

Dimensionless time

u :

Dimensionless velocity in the radial direction

|U|:

Magnitude of the Darcy velocity (m s−1)

u 0 :

injection velocity (m s−1)

u r :

Darcy velocity in the radial direction (m s−1)

u θ :

Darcy velocity in the circumferential direction (m s−1)

v :

Dimensionless velocity in the circumferential direction

v s :

Kinetic viscosity of the fluid (m2 s−1)

α :

Dissolving power of acid, defined as grams of solid dissolved per mole of acid reacted. (g/mol)

α w :

Dimensionless wellbore radius

α os, λr, λθ :

Numerical coefficients that depend on the structure of the medium

β :

Exponent determined from experiment

\({\varepsilon}\) :

Porosity of the medium

\({\varepsilon_{0}}\) :

Initial average porosity of the medium

ζ p :

Dimensionless pore radius

η :

Dimensionless initial pore diameter

μ :

Viscosity of the acid (mPa s)

μ f :

Viscosity of the reservoir fluid (mPa s)

ξ :

Dimensionless wormhole length in the radial direction

ρ s :

Density of the rock (g cm−3)

\({\phi^{2}}\) :

Pore scale Thiele modulus

Φ2 :

Core scale Thiele modulus

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Authors and Affiliations

  1. MOE Key Laboratory of Petroleum Engineering, China University of Petroleum, Beijing, 102249, China

    Ming Liu, Shicheng Zhang & Jianye Mou

  2. Research Institute of Petroleum Exploration & Development, PetroChina, Beijing, 100083, China

    Fujian Zhou

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  1. Ming Liu
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  2. Shicheng Zhang
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  3. Jianye Mou
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  4. Fujian Zhou
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Correspondence to Ming Liu.

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This paper is dedicated to my father Kaizhen Liu and my mother Xi Wang.

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Liu, M., Zhang, S., Mou, J. et al. Wormhole Propagation Behavior Under Reservoir Condition in Carbonate Acidizing. Transp Porous Med 96, 203–220 (2013). https://doi.org/10.1007/s11242-012-0084-z

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