Matrix acidizing refers to one of two stimulation processes in which acid is injected into the well penetrating the rock pores at pressures below fracture pressure.

1. Behzad Hosseinzadeh 1

2.  Stimulation technique widely used for sandstones and
carbonates;
 In both, the same principle is applied (chemical dissolution) but
several
differences appear;
– Carbonates → Distinct dissolution patterns → Wormholes.
Face dissolution → Conical wormhole → Dominant wormhole → Ramified wormhole → Uniform
dissolution
2

3. ‫تزریق‬ ‫نرخ‬‫انتقال‬ ‫و‬ ‫مولکولی‬ ‫نفوذ‬ ‫نسبی‬ ‫تاثیر‬‫انحالل‬ ‫الگوی‬
‫کم‬ ‫بسیار‬‫نفوذ‬≪‫انتقال‬‫سطحی‬
‫کم‬‫نفوذ‬<‫انتقال‬‫مخروطی‬
‫متوسط‬(‫بهینه‬)‫نفوذ‬≈‫انتقال‬‫شکل‬ ‫کرمی‬
‫زیاد‬‫نفوذ‬>‫انتقال‬‫ای‬‫شاخه‬
‫زیاد‬ ‫بسیار‬‫نفوذ‬≫‫انتقال‬‫یکنواخت‬ 3

4. 4

5. Experimental Studies → Williams et al. (1979),
Daccord et al. (1987, 1993a, 1993b), Lund et al. (1973,
1975), Hoefner and Fogler (1989), Wang (1993), Prick
(1994), Bazin et al. (1995), Fredd and Fogler (1998),
Bazin (2001), Golfier et al. (2002), Ziauddin and Bize
(2007), Tardy et al.(2007), Omer Izgec (2009), Mehdi
Gommem (2015)
Mathematical Modeling Studies → Capillary Tube
Model, Fractal and Dimensionless Model, Network
Model, Continuum (Averaged) Model
5

6. Capillary Tube Model: Hung et al.
(1997), Buijse (1997), Huang et al.
(1999, 2000)
Fractal and Dimensionless Model:
Dacord (1993), Kurmayr (1992),
Pichler et al. (1992) Fred and
Fogler (1999)
Network Model: Hoefner and
Fogler (1988), Fred and Fogler
(1998)
Continuum (Averaged) Model:
Golfier et al. (2002), Panga (2005),
Kalia (2008), Cohen et al. (2008),
Maheshwari (2013)
6

7. a two-scale continuum model is used to describe the
reactive dissolution phenomenon and capture the
physics at both:
 Darcy Scale Model
 Pore Scale Model
7

8. Darcy Equation𝑈 = −
1
𝜇
𝐾 . 𝛻𝑝,
Continuity
𝜕𝜀
𝜕𝑡′
+ 𝛻. 𝑈 = 0,
Acid Transport
𝜕(𝜀𝐶𝑓)
𝜕𝑡′
+ 𝛻. 𝑈𝐶𝑓 = 𝛻. 𝜀𝐷𝑒. 𝛻𝐶𝑓 − 𝑘 𝑐 𝑎 𝑣(𝐶𝑓 − 𝐶𝑠),
Reaction Rate → first order
irreversible reaction
𝑘 𝑐 𝐶𝑓 − 𝐶𝑠 = 𝑅(𝐶𝑠), (R(Cs) = ks Cs )
Porosity Variation
𝜕𝜀
𝜕𝑡′
=
𝑅(𝐶𝑠)𝑎 𝑣 𝛼
𝜌𝑠
,
8
effect of local volume change
during dissolution on the flow
field
This equation balances the
amount of reactant
transferred from fluid phase to
the wall and the amount reacted
at the wall.
The fourth term describes the
transfer of acid species from the
fluid phase to the fluid-solid
interface

9. 9
 the quantities 𝑲, 𝑫 𝒆 , 𝒌 𝒄 , and 𝒂 𝒗 obtained from such a
calculation can be used as inputs from the pore scale model
to the Darcy scale model.
 Structure-Property Relations (𝑲, 𝒂 𝒗)
 Mass-Transfer Coefficient (𝒌 𝒄)
Fluid Phase Dispersion Coefficients (𝑫 𝒆)

10. 10
 The structure-property relations may
also not be accurately representative of
the different types of carbonates that
exist.
 Semi-Emphirical model
 β is used to account Carman-Kozney
relation for dissolution (obtain
experimentally).Permeability change
𝐾
𝐾0
=
𝜀
𝜀0
(
𝜀(1 − 𝜀0)
𝜀0(1 − 𝜀)
)2𝛽,
Pore radius change
𝑟𝑝
𝑟0
=
𝐾𝜀0
𝐾0 𝜀
,
Interfacial area change
𝑎 𝑣
𝑎0
=
𝜀𝑟0
𝜀0 𝑟𝑝
,
MurtazaZiauddin

11. 11
 Transport of the acid species from the fluid phase
to the fluid-solid interface inside the pores.
The value of 𝒌 𝒄 determines if the reaction is
mass-transfer or kinetically limited.
 Sherwood number is the dimensionless mass-
transfer coefficient:
𝑆ℎ =
2𝑘 𝑐 𝑟 𝑝
𝐷 𝑚
= 𝑆ℎ∞ + 0.35(
𝑑ℎ
𝑥
)0.5 𝑅𝑒 𝑝
1/2
𝑆𝑐1/3,
Sc=ν/Dm
Depend on the structure of the porous medium
(Diffusion)
depends on the local
velocity
(Convection)

12. 12
For homogeneous, isotropic porous media, the dispersion
tensor is characterized by two independent components,
namely, the longitudinal, 𝐷𝑒𝑋 and transverse, 𝐷𝑒𝑇, dispersion
coefficients
For a well-connected pore network, random walk models and
analogy with packed beds spheres may be used to show that
𝐷 𝑇 =
𝐷 𝑒𝑇
𝐷 𝑚
= 𝛼 𝑜𝑠 + 𝜆 𝑇 𝑃𝑒 𝑝, 𝑃𝑒 𝑝 =
𝑈 𝑑ℎ
𝜀𝐷 𝑚
,
𝐷 𝑥 =
𝐷 𝑒𝑋
𝐷 𝑚
= 𝛼 𝑜𝑠 + 𝜆 𝑋 𝑃𝑒 𝑝, 𝑃𝑒 𝑝=
𝑈 𝑑ℎ
𝜀𝐷 𝑚
,
Depends on the structure of the
porous medium (for example,
tortuosity or connectivity between
The parameter 𝛼 𝑜𝑠
may increase as the
tortuosity decreases.

13. 13
𝑢, 𝜈 = (−𝜅
𝜕𝑝
𝜕𝑥
, −𝜅
𝜕𝑝
𝜕𝑦
),
𝜕𝜀
𝜕𝑡
+
𝜕𝑢
𝜕𝑥
+
𝜕𝜈
𝜕𝑦
= 0,
𝜕(𝜀𝑐𝑓)
𝜕𝑡
+
𝜕(𝑢𝑐𝑓)
𝜕𝑥
+
𝜕(𝜈𝑐𝑓)
𝜕𝑦
= −
𝐷𝑎𝐴 𝑣 𝑐𝑓
1 +
𝜙2 𝑟
𝑆ℎ
+
𝜕
𝜕𝑥
𝛼 𝑜𝑠 𝜀𝐷𝑎
Φ2
+ 𝜆 𝑥 𝑢 𝑟𝜂
𝜕𝑐𝑓
𝜕𝑥
+
𝜕
𝜕𝑦
𝛼 𝑜𝑠 𝜀𝐷𝑎
Φ2
+ 𝜆 𝑇 𝑢 𝑟𝜂
𝜕𝑐𝑓
𝜕𝑦
,
𝜕𝜀
𝜕𝑡
=
𝐷𝑎𝑁𝑎𝑐 𝐴 𝑣 𝑐𝑓
(1 +
𝜙2 𝑟
𝑆ℎ
)
,
−𝜅
𝜕𝑝
𝜕𝑥
= 1 @ 𝑥 = 0,
𝑝 = 0 @ 𝑥 = 1,
−𝜅
𝜕𝑝
𝜕𝑦
= 0 @ 𝑦 = 0 & 𝑦 = 𝛼0,
𝑐𝑓 = 1 @ 𝑥 = 0,
𝜕𝑐𝑓
𝜕𝑥
= 0 @ 𝑥 = 1,
𝜕𝑐𝑓
𝜕𝑦
= 0 @ 𝑦 = 0 & 𝑦 = 𝛼0,
𝑐𝑓 = 0 @ 𝑡 = 0,
𝜀 𝑥, 𝑦, 𝑎, 𝑙 = 𝜀0 + 𝑓̂̂(𝑎, 𝑙) @ 𝑡 = 0,

14. 14

15. 15
0
5
10
15
20
25
30
35
40
45
0.0001 0.001 0.01 0.1 1
PVBT
1/Da
Kalia
Behzad

16. 16
0
5
10
15
20
25
30
35
40
0.0001 0.001 0.01 0.1 1
PVBT
1/Da
Effect of Rock Heterogeneity
Kalia
Behzad

17. 17

18. 18

19. 19
 Simulate reactive dissolution of
carbonate rocks in radial flow.
 With this assumption we can
investigate the wormhole density.

20. 20

21. 21
 Study the density of wormholes.
 Compare 2D and 3D simulations, in
both linear and radial geometry.

22. 22
First, the use of alternate boundary
conditions for concentration and flow.
It is found that heterogeneity in a rock
affects not only the structure of the
patterns formed during reactive
dissolution but also the amount of acid
required to achieve a given increase in
permeability.
 The amount of acid required to
breakthrough is found to depend on the
initial rock porosity and dimensions of the
rock being acidized.
 Using a heterogeneity parameter, ϖ as a
product of the heterogeneity magnitude
and length scale

23. 23
 Develop an empirical rheological
model to describe the variation of the
viscosity of in-situ cross-linked acids
with temperature, shear rate and pH.
 Analyze wormhole formation in single
and dual core set-ups.
 2D and 3D
Newtonian acidsin-situ cross-linked acids (ICA)

24. 24
 Present 3-D simulations of wormhole
formation in carbonate rocks.
 Define new two-parameter structure-
property relation (pore-connectivity
and pore-broadening).
 Work on vuggy and unvuggy
carbonate (Omer Izgec is also worked
on this type of rock)
 Study of flow dynamics inside a
wormhole.
 Study the reactive dissolution of
carbonate rocks with nongelled, gelled,
and emulsified acids in three
dimensions

25. 25
 Effect of variation of the viscosity of in-situ cross-linked acids
with temperature, shear rate and pH.
 2D -> 3D
 Comparison with core flooding experiments