Improvements in the Unified Chalk Model and Evaluation of Coupled Geomechanics and Flow Models
JCR-VI/Project 6
Chalk Geomechanical Projects
Improvements in the Unified Chalk Model and Evaluation of Coupled Geomechanics and Flow Models
Project Leader: Tron Golder Kristiansen, BP,
I. Introduction
Geomechanics has played a central role in all the previous phases of Joint Chalk Research (JCR). Some 27% of the total 77 MMNOK spent to-date on JCR has been directed specifically for geomechanical aspects of chalk exploitation.
In Phase 1, AGIP and Fina were project leaders for two investigations into the mechanical properties of chalk. The first of the two projects looked at the stability of wells drilled in chalk, while the second investigated the actual mechanical behavior of chalk using various laboratory test procedures. During Phase 2, Fina again led a project on a further investigation of the mechanical properties of chalk and AGIP led another project on wellbore stability issues in chalk. In addition, Phillips led a project to investigate the possible changes in chalk mechanical behavior as a result of the long-term injection of seawater. Additional laboratory tests on the impact of seawater on the mechanical behavior of chalk were also conducted under a project led by Total concerning the potential for waterflooding of fractured chalk reservoirs.
In Phase 3 of JCR, various geomechanical efforts were included as part of the Fracture project, led by Hydro, the Productivity-Mechanical Properties project led by Total, and the Completion project led by Phillips. In particular, a failure criterion for chalk was developed, the effect of temperature on chalk mechanical behavior was investigated, and the stress field development around a producing well was simulated.
In Phase 4, Maersk led a project on a review of the existing chalk laboratory data and the development of a chalk constitutive model. Amoco led a project on further developments in the understanding of the constitutive properties of chalk, particularly the influence of seawater. Phillips also led a project on the compaction and surface subsidence associated with pressure depletion in chalk reservoirs as well as the long-term stability of deviated and horizontal wells in compacting chalk reservoirs.
The geomechanical objectives under the last phase of JCR, Phase 5, were:
· to progress the understanding of the basic rock mechanical processes for chalk in general and the effect of chalk-water interaction in special;
· to generate a complete and numerically stable constitutive model for chalk which incorporates all known rock mechanical parameters for chalk, their interdependence and their dependence of basic rock parameters like porosity, rock type, shaliness etc.; and
· to benchmark test the applicability of available coupled models (normal reservoir simulation models coupled with a stress/strain model) in the case of chalk reservoirs.
The primary product delivered from Phase 5 of JCR was a unified constitutive model for chalk, including the effects of water. In addition, a rudimentary methodology was developed for the inclusion of the fracture effects on the mechanical response of chalk. The developed chalk model was not coded numerically or extensively tested owing to budget and time constraints.
The review of coupled models was largely unsuccessful. Primarily, this was due to significant confusion over terminology (a “fully-coupled” vs. a “fully, fully-coupled model”) and model capabilities as well as the lack of a precise enough test case with which to differentiate between the various models studied.
II. JCR 6 Geomechanics Project Objectives
After the extensive testing of chalk performed under the previous five JCR phases, the host of tests performed by the individual sponsors as part of their participation in the various chalk fields, and some 30 years of production experience from chalk reservoirs in the North Sea, there are but a few remaining questions on the behavior of small chalk samples from a laboratory perspective. As a result, a prime focus of part 1 of the geomechanics project under JCR Phase 6 will be the implementation, validation, and refinement of a unified chalk constitutive model based upon the existing JCR lab tests.
While laboratory-scale behavior is largely known, there are a number of unanswered questions concerning the upscaling of these properties to field-scale applications. In part 2 of the geomechanics project, scaling and fracture issues will be investigated. In addition, tests and other evaluations will be undertaken in order to further clarify some outstanding issues related to water weakening, reservoir repressurization, temperature effects, and the impact of CO2 on chalk compaction.
Under part 3 of the project, coupled models will again be investigated. However, the intention under Phase 6 will be to arrange a industry workshop on coupled models in order to review the state-of-the-art.
III. JCR 6 Geomechanics Project Budget Summary
The project consists of three parts. The proposed costs for these sub-projects and a total for the geomechanics project are shown below:
Part 1: Improvements in the Unified Chalk Model: 1.21 MMNOK
Part 2: Experiments on the Behavior of Chalk: 2.35 MMNOK
Part 3: Industry workshop on Coupled Geomechanics and Flow Models: 0.44 MMNOK
Anticipated Total Project Budget: 4.00 MMNOK
IV. JCR 6 Geomechanics Project Parts 1 & 2 Contractor Contacts
Prof. Marte Gutierrez
Virginia Tech
Civil and Environmental Engineering, 200 Patton Hall
Blacksburg, VA 24061 USA
Dr. Lee Chin
Phillips Petroleum Company
138 GB, Phillips Research Center
Bartlesville, OK 74004 USA
Professor Poul Lade
Department of Civil Engineering
The Catholic University of America
620 Michigan Avenue
Washington, D.C. 20064
USA
Mr. Bertold Plischke
ISAMGEO-Engineering GMBH
Bahnstrasse 12
D-65205 Wiesbaden, Germany
Ms. Helle Christensen
GEO-Danish Geotechnical Institute
Maglebjergvej 1
P.O. 119
DK-2800 Lyngby, Denmark
Dr. Fabrice Cuisiat
NGI
PO BOX 3930, Ulleval Hageby
0860 Oslo Norway
Prof. Rasmus Risnes
Stavanger University
PO BOX 2557, Ullandhaug
N-4091 Stavanger Norway
Prof. Christian Schroeder
University of Liege
Geologie de l'ingenieur, hydrogeologie et prospection geophysique
Bat. B19, Boulevard du Rectorat, 17
4000 Liege 1, Belgium
Geomechanics Project Part 1:
Validation, Improvement and Implementation
of the JCR V Unified Chalk Model
by
M. S. Gutierrez, Virginia Polytechnic Institute and State University
L. Y. Chin, Phillips Petroleum Company
Poul V. Lade, The Catholic University of America
Bertold Plischke, ISAMGEO GmbH
Background
In JCR Phase V, a unified chalk constitutive model was developed and tested against available laboratory data (Gutierrez, 2000). In general, the JCR V chalk model was able to match the laboratory data in good agreement and to simulate the complicated compaction behavior of chalk over a wide range of loading conditions. Also, the JCR V unified chalk model has the capability of quantifying the water effect and the time-dependent effect on chalk compaction. However, the JCR V unified chalk model was not critically evaluated and validated through an extensive testing program. Consequently, the sensitivity, stability, and robustness of the JCR V chalk model parameters are not known. In addition, the model was not numerically implemented into any general geomechanics code. As a result, the performance of the model on important field problems in chalk reservoirs cannot be evaluated. These important problems include subsidence prediction, wellbore stability analysis, and casing deformation study. Based on these needs, we propose a research project with objectives of validating, implementing, modifying, and testing the JCR unified chalk model in a numerical code.
Main Results from the JCR V Chalk Geomechanics Project
One of the main issues investigated in JCR V was the mechanism responsible for water-induced response of chalk. The main conclusion obtained in JCR V is that the response of chalk to waterflooding is most possibly due to material property changes, and only to a less extent due to the effective stress changes resulting from capillarity. It was concluded that chalk-water interaction can be viewed primarily as a modification of the time-dependent behavior of chalk. Due to the time-dependent nature of the waterflooding effects, the time-dependent behavior of chalks had to be included in the chalk constitutive model. Bjerrum's (1967) formulation, as implemented by Borja and Kavanzanjian (1985) within the framework of Cam clay plasticity, is adapted to model time-dependent chalk behavior. In addition, the model includes provisions for handling a variety of stress histories, including depletion-induced compaction as well as water-effect compaction. The advantages of the JCR V model over other models such as deWaal's (1986) model for rate-dependent rock behavior, and models based on visco-plasticity were shown. The validity of the model was verified against the experimental data provided by DGI (1996a, 1996b, 1998, 1999). The adequacy of the model, particularly the approach of changing the creep parameter y to simulate the response of chalk to water injection has been amply demonstrated in JCR V.
A principal deliverable from the JCR V Chalk Geomechanics Project was the creation of a unified chalk model. While the original intention was that the model would be delivered in the form of a numerical code, this was not completed, and instead only the equation form of the model was accomplished. There were several reasons for the inability to complete a fully coded version of the chalk model, chief among these was the time it took to achieve a consensus among the JCR participants, contractors and experts on the different elements of the chalk model.
During the past year following the completion of JCR V, the two PI’s (Gutierrez and Chin) have had ample time to re-evaluate the unified chalk model and has made further corrections and improvements to the model. However, these changes have not been communicated to the JCR community.
Part 1 Objectives
This project seeks to achieve the following objectives:
1.1 Evaluation of the existing JCR V unified chalk model.
1.2 If the JCR V chalk model is judged to be insufficient, develop an improved chalk model.
1.3 Implement the unified chalk model (including any improvements) into a robust and portable FORTRAN code with accurate algorithms for plasticity and creep calculations.
1.4 Evaluate and validate the model against the existing JCR geomechanical database, especially reproducing the stress path tests from JCR IV.
1.5 Modify the code, where needed, in order to address deficiencies and errors.
1.6 Coordinate with JCR VI Geomechanics Project 2 in order to perform limited and specific laboratory tests, as needed, in order to address deficiencies in the model.
1.7 Evaluate the performance of the numerical, unified chalk model on several test cases (a full-field subsidence prediction, a wellbore stability analysis, or casing deformation effects).
1.8 Optimize the computational efficiency of the model, when used for full-field simulations.
1.9 From Objective 2.1 of JCR VI Geomechanics Project 2, implement the chalk fracture model with water weakening in the unified chalk.
1.10 From Objective 2.4 of JCR VI Geomechanics Project 2, implement refinements in the unified chalk model based upon improvements in the understanding of water weakening below Swmax.
Part 1 Tasks
The four principal investigators (Gutierrez, Chin, Lade and Plischke) will achieve the JCR VI Geomechanics Project 1 objectives by dividing and accomplishing the following tasks:
TASK 1.1: Critical Evaluation of the JCR V Unified Chalk Model (Lade)
Starting point of the model evaluation is a review of chalk behaviour observed in the laboratory and in the field, including aspects referring to the geological time scale. Special attention will be given to :
· rate dependency/creep
· porosity dependency
· water sensitivity
· hardening and softening behavior (in the shear failure regime)
· impact of stress path
· the ratio between hydrostatic and uniaxial pore collapse strength
· the transition from pore collapse behaviour to shear failure
· dilatancy during plastic shear
· impact of the intermediate principle stress
· effect of elastic unloading
· effect of Biot coefficient
The next step will be a review of selected existing models, including recent research projects sponsored by other sources (e.g. the Joule program of the European Community). Especially with respect to the creep behaviour, it will be tried to find a link between different models (e.g. de Waal, Bjerrum and the unified chalk model), which should facilitate the evaluation of the role of the parameter Psi in the unified chalk model. For the unified chalk model, the equations delivered in JCR Phase V will be evaluated (some minor errors have already been identified). The interdependency of individual parameters will be checked. Aspects of the numerical implementation of the model will already be considered in this early state of the project. Most of the work will be done by Prof. Lade, but the entire project team will bring in their experience.
TASK 1.2: Develop an Improved Version of the Unified Chalk Model (Gutierrez)
Based on the review of in Task 1.1, the unified chalk model will be improved to include the recommendations made in Task 1.1. This will include model inconsistencies and the uniqueness of the material properties. Depending on the results of the review, a complete re-formulation of the model can be achieved. For example, the model can be re-formulated within the framework of elasto-viscoplasticity. Another possible formulation that has been suggested as an alternative to the unified chalk model is deWaal’s (1986) rate-dependent model. However, a great deal of effort has already been devoted in JCR V in comparing the unified chalk model against these two alternatives. Despite major similarities, the advantages of the unified chalk model over these two approaches have been amply shown in JCR V.
TASK 1.3: Implement the JCR V Unified Chalk Model (including any improvements) into a Robust and Portable FORTRAN Code (Chin)
As delivered from JCR V, the unified chalk model currently exists only in equation form. Once the governing equations from the unified chalk model have been finalized and reviewed by the external expert, the coding of the model will be initiated. Particular attention will be paid to making the numerical code robust and portable, given the widely different FE geomechanics codes currently used by sponsor companies (as well as the coupled models potentially used in the future). This should limit the model to being coded in standard FORTRAN as a set of subroutines with attention paid to means to ease the linking of the subroutines to common geomechanics.
A more robust implementation of the model will be written using an Ortiz and Simo (1986) type numerical integration procedure. In addition to a full implementation in the common geomechanics finite element code to be selected during the project, FORTRAN subroutines that can be used in implementing the model in other finite element codes will be provided. A FORTRAN stand-alone code for a single-element constitutive driver will also be provided, which could be used to run the subroutines. The stand-alone single-element code can be used to run the model in stress- or strain-control, or under mixed stress- and strain-control to test the performance of the chalk model.