Modeling, simulation and comparison of models for wormhole formation during matrix stimulation of carbonates

• US 20060184346A1
• Filed: 12/22/2005
• Published: 08/17/2006
• Est. Priority Date: 02/07/2005
• Status: Active Grant

• Current Assignee: Schlumberger Technology Corporation (Schlumberger NV)
• Original Assignee: Schlumberger Technology Corporation (Schlumberger NV)
• Inventors: Panga, Mohan K.R., Ziauddin, Murtaza, Balakotaiah, Vemuri
• Granted Patent: US 7,561,998 B2
• Time in Patent Office: Days
• US Class Current: 703/9
• CPC Class Codes: E21B 43/16 Enhanced recovery methods for obtaining hydrocarbons
• CPC Class Codes: E21B 43/25 Methods for stimulating production by vibrating earth formations E21B43/003
• CPC Class Codes: E21B 43/27 by use of eroding chemicals, e.g. acids

Abstract

Disclosed are methods of modeling stimulation treatments, such as designing matrix treatments for subterranean formations penetrated by a wellbore, to enhance hydrocarbon recovery. The modeling methods describe the growth rate and the structure of the dissolution pattern formed due to the injection of a treatment fluid in a porous medium, based on calculating the length scales for dominant transport mechanism(s) and reaction mechanism(s) in the direction of flow l_X and the direction transverse to flow l_T. Methods of the invention may further include introducing a treatment fluid into the formation, and treating the formation.

Claims

1. A method of modeling a subterranean formation stimulation treatment involving a chemical reaction in a porous medium, the method comprising describing the growth rate and the structure of the dissolution pattern formed due to the injection of a treatment fluid in a porous medium, based on calculating the length scales for dominant transport mechanism(s) and reaction mechanism(s) in the direction of flow l_X and the direction transverse to flow l_T.

2. The method of claim 1, wherein the transport mechanism(s) is convection, dispersion or diffusion, of any of the components of the fluid or of the porous medium, or any combination thereof.

3. The method of claim 1, wherein the reaction mechanism(s) includes reactions between the components of the injected fluid and the porous medium.

4. The method of claim 1, wherein the porous medium comprises carbonate based minerals.

5. The method of claim 4, wherein the carbonate based minerals comprise calcite, dolomite, quartz, feldspars, clays, or any mixture thereof.

6. The method of claim 1, wherein the treatment fluid comprises mineral acids, organic acids, chelating agents, polymers, surfactants, or mixtures thereof.

7. The method of claim 1, wherein l_X is determined by balancing the convection and reaction mechanism(s)

$l_X\sim$

u tip k eff .

8. The method of claim 1, wherein l_T is determined by balancing the dispersion and reaction mechanism(s)

$l_T\sim$

D eT k eff .

9. The method of claim 1, wherein the growth rate and the structure of the dissolution pattern is described as function of l_X and l_T, as follows:

$\mathrm{\Lambda <br><br>}=\frac{l_T}{l_X}=\frac{\sqrt{k_{\mathrm{eff}}<br><br>D_{\mathrm{eT}}}}{u_{\mathrm{tip}}}$

whereby k_eff is the effective rate constant, (D_eT) is the effective transverse dispersion coefficient, and u_tip is the velocity of the fluid at the tip of the wormhole, and whereby optimum rate for the formation of wormholes is computed by setting Λ

in the range 0.1<

Λ

<

5;

flow rate for uniform dissolution is computed by setting Λ

<

0.001;

or, flow rate for face dissolution is computed by setting Λ

>

5.

10. The method of claim 1 wherein the model describes correlations for experimental data at one set of operating variables and subsequently applied to make predictions for a different set of operating variables, wherein the variable comprise temperature, concentration, pressure, flow rate, rock type, radial flow geometry, linear flow geometry, or any combination thereof.

11. The method of claim 1 wherein the model describes the impact of the magnitude and length scale of heterogeneity on the branching of wormholes, the pore volume of acid required to breakthrough the core (PVBT), or the scale-up of experimental data from one reservoir core to make predictions on reservoir cores with different type of heterogeneity.

12. The method of claim 1 wherein the model describes degree of wormhole branching as a function of magnitude of heterogeneity.

13. The method of claim 1 wherein the model describes optimum injection rate and the pore volume of acid required to breakthrough the core (PVBT) as a function of pore scale mass transfer and reaction wherein structure-property relations play a minor role in determining the optimum injection rate when the pore scale reaction is in the kinetic regime, f²<

<

1, or where both the optimum injection rate and PVBT are strongly dependent on the structure-property relations in the mass transfer controlled regime f²>

>

1.

14. The method of claim 1 wherein the model describes that in a wormholing regime, diameter of the wormhole scales inversely with the macroscopic Thiele modulus, equivalently, with the reciprocal of the effective dissolution rate constant.

15. The method of claim 1 wherein the model describes matrix acidizing or hydraulic fracture treatments.

16. The method of claim 1 further comprising introducing a treatment fluid into the formation, and treating the formation.

17. The method of claim 1 wherein the model describes a wormhole pattern.

18. The method of claim 1 wherein the model describes a face pattern.

19. The method of claim 1 wherein the model describes a conical pattern.

20. The method of claim 1 wherein the model describes a ramified pattern.

21. The method of claim 1 wherein the model describes a uniform pattern.

22. A method of modeling a subterranean formation stimulation treatment involving a chemical reaction in a porous carbonate medium, the method comprising describing the growth rate and the structure of a wormhole pattern formed due to the injection of a treatment fluid into the medium, based on calculating the length scales for convection and/or dispersion transport mechanism(s) and heterogeneous reaction mechanism in the direction of flow l_X and the direction transverse to flow l_T, wherein the growth rate and the structure of the dissolution pattern is described as function of l_X and l_T as follows:

$\mathrm{\Lambda <br><br>}=\frac{l_T}{l_X}=\frac{\sqrt{k_{\mathrm{eff}}<br><br>D_{\mathrm{eT}}}}{u_{\mathrm{tip}}}$

whereby k_eff is the effective rate constant, (D_eT) is the effective transverse dispersion coefficient, and u_tip is the velocity of the fluid at the tip of the wormhole.