Hybrid procedure for evaluating stress magnitude and distribution on a liner

1. A method for evaluating an integrity of a liner disposed in a wellbore that contacts a formation through a cement layer between the liner and the formation, the method comprising:

obtaining geometric data and at least one property of the liner using at least one of a sonic measurement, a seismic measurement, a density log and a rock mechanics testing;

determining, by a computer processor, in-situ stress and pore pressure on the formation;

computing, by the computer processor, a stress on a boundary of the liner by an iteration procedure that implements an analytical solution of stresses on a liner-cement interface and a cement-formation interface using the geometric data, the at least one property, mean in-situ stress and the wellbore pressure;

constructing, by the computer processor, a computational numerical model for simulating interactions between the liner, the cement layer and the formation;

performing, by the computer processor, a plurality of numerical simulations using the computational numerical model to calculate a magnitude and distribution of stress acting on the liner-cement interface and the cement-formation interface, wherein the plurality of numerical simulations are repeatedly performed to obtain model-predicted stresses;

comparing, by the computer processor, the model-predicted stresses on the liner-cement and cement-formation interfaces with values provided by the analytical solution until the model-predicted stresses substantially match the analytical solution; and

performing, by the computer processor, the plurality of numerical simulations using actual in-situ stresses to replace the mean in-situ stress on an outer boundary of the formation layer to calculate the magnitude and distribution of stress acting on the liner-cement and cement-formation interfaces using a calibrated computational mesh where the analytical solution and numerical simulation results match;

applying, by the computer processor, the calculated stresses acting on the liner to a liner integrity evaluation model to determine the integrity of the liner at a plurality of stages of the wellbore;

determining, by the computer processor, a type of second liner based on the liner integrity evaluation model; and

performing a production operation using the wellbore and based on the type of second liner.

2. The method of claim 1 , further comprising: obtaining a thickness and mechanical properties of the cement layer; obtaining physical and mechanical properties of the formation from rock mechanics testing; and using the properties of the cement layer and the formation in the computational numerical model.

3. The method of claim 1 , further comprising: iteratively improving a computational mesh of the computational numerical model to obtain the calibrated computational mesh before repeating the numerical simulations and comparing the model-predicted stresses on the liner-cement and cement-formation interfaces with the values provided by the analytical solution.

4. The method of claim 1 , further comprising: adjusting variables and boundary conditions in the computational numerical model to reflect conditions of the liner, the cement layer, and the formation in the wellbore.

5. The method of claim 1 , wherein the computational numerical model is a two-dimensional liner-cement-formation computational mechanics model.

6. The method of claim 1 , wherein performing numerical simulation comprises: applying borehole pressure inside the wellbore and mean in-situ stress on an outer boundary of the formation; and running simulations of the interactions between the liner, the cement layer and the formation with the applied borehole pressure and the mean in-situ stress.

7. The method of claim 1 , wherein comparing the model-predicted stresses on the liner-cement and cement-formation interfaces with values provided by the analytical solution comprises: comparing the stress on an outer boundary of the liner in the computational numerical model with a corresponding analytical solution.

8. The method of claim 1 , wherein the analytical solution represents a three-layer, one-dimensional, axisymmetric model with a borehole pressure and a mean stress acting on different ends of the wellbore.

9. The method of claim 1 , further comprising: changing a stress condition on the outer boundary of the formation layer in the computational numerical model to calculate the stress on an outer boundary of the liner, in a case where vertical and horizontal in-situ stresses are unequal.

10. The method of claim 1 , wherein the liner integrity is evaluated on an unequal stress field.

11. The method of claim 1 , wherein geometric data of the liner comprises an inner diameter of the liner and an outer diameter of the liner, and wherein at least one property of the liner comprises at least one mechanical property of the liner.

12. A system for evaluating an integrity of a liner disposed in a wellbore that contacts a formation through a cement layer between the liner and the formation, the system comprising:

a measurement device configured to measure a property of the liner in the wellbore;

a computer processor comprising functionality for:

computing a stress on an outer boundary of the liner by an iteration procedure that implements an analytical solution of stresses on a liner-cement interface and a cement-formation interface using at least one mechanical property of the liner;

constructing a computational numerical model for simulating interactions between the liner, the cement layer and the formation;

performing a plurality of numerical simulations using the computational numerical model to calculate a magnitude and distribution of stress acting on the liner-cement interface and the cement-formation interface, wherein the numerical simulations are repeatedly performed to obtain model-predicted stresses;

comparing the model-predicted stresses on the liner-cement and cement-formation interfaces with values provided by the analytical solution until the model-predicted stresses substantially match the analytical solution;

performing the plurality of numerical simulations using actual in-situ stress to replace a mean in-situ stress on an outer boundary of the formation layer to calculate the magnitude and distribution of stress acting on the liner-cement and cement-formation interfaces using a calibrated computational mesh where the analytical solution and numerical simulation results match;

applying the calculated stresses acting on the liner to a liner integrity evaluation model to determine the integrity of the liner at a plurality of stages of the wellbore; and

determining, by the computer processor, a type of second liner based on the liner integrity evaluation model; and

performing a production operation using the wellbore and based on the type of second liner, and

wherein geometric data and at least one property of the liner are obtained using at least one of a sonic measurement, a seismic measurement, a density log and a rock mechanics testing.

13. The system of claim 12 , wherein the liner comprises an inner diameter and an outer diameter.

14. The system of claim 12 , wherein the computational numerical model is a two-dimensional liner-cement-formation computational mechanics model.

15. The system of claim 12 , wherein the integrity of the liner is determined by a magnitude and a distribution of a load on the outer boundary of the liner, wherein the magnitude and the distribution of the load is based on a plurality of parameters comprising a thickness of the cement layer, mechanical properties of the cement layer and the formation, in-situ stresses, and a pore pressure in the wellbore.

16. The system of claim 12 , wherein the analytical solution represents a three-layer, one-dimensional, axisymmetric model with a borehole pressure and a mean stress acting on different ends of the wellbore.

17. The system of claim 12 , wherein the integrity of the liner is evaluated in an unequal stress field.

18. The system of claim 12 , wherein the analytical solution and the computational numerical model are integrated by iteratively improving a computational mesh of the computational numerical model to obtain the calibrated computational mesh before repeating the numerical simulations and comparing the model-predicted stresses on the liner-cement and cement-formation interfaces with the values provided by the analytical solution.

19. The system of claim 12 , wherein variables and boundary conditions in the computational numerical model are adjusted to reflect changed conditions of the liner, the cement layer, and the formation in the wellbore before repeating the numerical simulations.