Modeling acid distribution for acid stimulation of a formation

Patent metadata

Field	Value
Publication number	US-9534489-B2
Application number	US-201414169241-A
Country	US
Kind code	B2
Filing date	Jan 31, 2014
Priority date	Mar 6, 2013
Publication date	Jan 3, 2017
Grant date	Jan 3, 2017

Abstract

A method of evaluating a stimulation operation includes: receiving parameter information for the stimulation operation, the stimulation operation including injecting an acid stimulation fluid into an earth formation along a selected length of a borehole from a tubular disposed in the borehole; and generating, by a processor, a thermal model based on one or more energy balance equations that account for at least a first heat source and a second heat source, the first heat source expected to produce heat during the stimulation by a chemical reaction between an acid in the stimulation fluid and the formation, and the second heat source including expected geothermal heat from the formation.

First claim

The invention claimed is:

1. A method of evaluating a stimulation operation, comprising:
receiving parameter information for the stimulation operation, the stimulation operation including injecting an acid stimulation fluid into an earth formation along a selected length of a borehole from a tubular disposed in the borehole; and
generating, by a processor, a thermal model based on one or more energy balance equations that account for at least a first heat source and a second heat source, the first heat source expected to produce reaction heat during the stimulation by a chemical reaction between an acid in the stimulation fluid and the formation, and the second heat source including expected geothermal heat from the formation, the thermal model configured to predict an amount of the reaction heat per unit length of the borehole.

2. The method of claim 1 , further comprising receiving a plurality of temperature measurements taken along the selected length by a sensor assembly disposed in the borehole.

3. The method of claim 2 , further comprising calculating a predicted temperature profile along the selected length based on the model.

4. The method of claim 3 , further comprising comparing the predicted temperature profile to a measured temperature profile generated based on the plurality of temperature measurements.

5. The method of claim 2 , further comprising generating acid distribution data based on the model and the temperature measurements, the acid distribution data representing a distribution of an amount of acid injected in the formation along the selected length of the borehole.

6. The method of claim 5 , further comprising generating an acid distribution profile from the acid distribution data, and comparing the acid distribution profile to a predicted acid distribution to identify at least one of an over-acidized region and an under-acidized region.

7. The method of claim 1 , wherein the thermal model is configured to predict the amount of the reaction heat per unit length of the borehole based on an expected distribution of acid along a stimulation zone.

8. The method of claim 7 , wherein the one or more energy balance equations account for expected heat exchange between the tubular and the annulus during the stimulation operation.

9. The method of claim 8 , wherein the one or more energy balance equations include the following equation for a region in the annulus:
( W 1 −W 2 )[ dHa/dz−g sin(θ)/( J c g c )+ V a /( Jg c )*( dV a /dz )]+ W 2 Cp ( T exit −Ta )/ dz=Q 1 +Q 2 −Q 3,

wherein W 1 is the fluid mass rate of acid flowing axially in the annulus, W 2 is the fluid mass rate of acid flowing into the formation, Q1 is a heat flow rate from the first heat source, Q2 is a heat flow rate from the second heat source and Q3 is a heat flow rate from the heat exchange, Ha is the fluid enthalpy in the annulus, z is a variable well depth, g is the gravitational acceleration, θ is an inclination angle, J c and g c are conversion factors, “V a ” is acid velocity in the annulus, Cp is a heat capacity, T exit is a temperature of the acid in the annulus passing to the formation, and Ta is a temperature of fluid in the annulus.

10. The method of claim 9 , wherein the one or more energy balance equations include the following equation for a region in the tubular:
W t [dH t /dz+g sin(θ)/( J c g c )+ V t /( Jg c )*( dV t /dz )]= Q 3

wherein W T is a fluid mass rate of acid, Ht is the fluid enthalpy in the tubular, and V t is fluid velocity in the tubular.

11. An earth formation stimulation system comprising:
a stimulation assembly configured to be disposed in a borehole and perform a stimulation operation, the stimulation assembly including a tubular and at least one injection device configured to inject an acid stimulation fluid into an earth formation;
a sensor assembly configured to take a plurality of temperature measurements along a selected length of the borehole; and
a processor in operable communication with the sensor assembly, the processor configured to receive the plurality of temperature measurements and apply a thermal model to the plurality of temperature measurements, the model based on one or more energy balance equations that account for at least a first heat source and a second heat source, the first heat source expected to produce reaction heat during the stimulation operation by a chemical reaction between an acid in the stimulation fluid and the formation, and the second heat source including expected geothermal heat from the formation, the thermal model configured to predict an amount of the reaction heat per unit length of We borehole.

12. The system of claim 11 , wherein the injection device is configured to provide flow of the stimulation fluid between the tubular and an annulus formed between the tubular and a borehole wall.

13. The system of claim 12 , wherein the one or more energy balance equations account for expected heat exchange between the tubular and the annulus during the stimulation operation.

14. The system of claim 13 , wherein the model accounts for acid flowing through the tubular, acid flowing into the formation and acid in a fluid counterflow in the annulus.

15. The system of claim 14 , wherein the one or more energy balance equations includes the following equation for a region in the annulus:
( W 1 −W 2 )[ dHa/dz−g sin(θ)/( J c g c )+ V a /( Jg c )*( dV a /dz )]+ W 2 Cp ( T exit −Ta )/ dz=Q 1 +Q 2 −Q 3,

wherein W 1 is the fluid mass rate of acid flowing axially in the annulus, W 2 is the fluid mass rate of acid flowing into the formation, Q1 is a heat flow rate from the first heat source, Q2 is a heat flow rate from the second heat source and Q3 is a heat flow rate from the heat exchange, Ha is the fluid enthalpy in the annulus, z is a variable well depth, g is the gravitational acceleration, θ is an inclination angle, J c and g c are conversion factors, “V a ” is acid velocity in the annulus, Cp is a heat capacity, T exit is a temperature of the acid in the annulus passing to the formation, and Ta is a temperature of fluid in the annulus.

16. The system of claim 15 , wherein the one or more energy balance equations includes the following equation for a region in the tubular:
W t [dH t /dz+g sin(θ)/( J c g c )+ V t /( Jg c )*( dV t /dz )]= Q 3

wherein W T is a fluid mass rate of acid, Ht is the fluid enthalpy in the tubular, and V t is fluid velocity in the tubular.

17. The system of claim 11 , wherein the processor is configured to calculate a predicted temperature profile along the selected length based on the model.

18. The system of claim 17 , wherein the processor is configured to compare the predicted temperature profile to a measured temperature profile generated based on the temperature measurements.

19. The system of claim 11 , wherein the model accounts for the first heat source by predicting reaction heat per unit length of the borehole based on an overall reaction factor.

20. The system of claim 19 , wherein the overall reaction factor is calculated by an iterative process including:
selecting a reaction factor value and calculating a predicted temperature curve based on the reaction factor value and an assumed acid distribution for the stimulation operation;
comparing the predicted temperature curve to a measured temperature profile based on the plurality of temperature measurements, wherein comparing includes calculating a di

Assignees

• Wang Xiaowei
• Bussear Terry R
• Baker Hughes Inc

Inventors

• Wang Xiaowei
• Bussear Terry R

Classifications

• E21B43/28 Primary

  Dissolving minerals other than hydrocarbons, e.g. by an alkaline or acid leaching agent (E21B43/241 takes precedence) · CPC title

• E21B47/06

  Measuring temperature or pressure · CPC title

• E21B47/07 Primary

  Temperature · CPC title

• E21B47/135

  using light waves, e.g. infrared or ultraviolet waves · CPC title

• E21B47/065 Primary

  Fixed Constructions · mapped topic