The Academic Poster Showcase has become a staple at the annual Science in the Age of Experience conference and highlights the work of academics from all over the world. At the conclusion of this year’s conference we asked poster submitters to fill out a questionnaire detailing their efforts. Mahdi Haddad from the University of Texas at Austin is the first of these academic superstars to be featured here on the SIMULIA blog. 

Q. Please describe why you chose this topic for your project.  Why does this workflow need to be analyzed? 

A. Hydraulic fracturing has been developed for the economic development of ultra-low-permeability oil/gas shale formations which have spread all over the U.S. The design and inspection of hydraulic fractures requires more robust numerical tools in the lack of reliable diagnostic techniques. Abaqus has offered a great potential for providing high-fidelity, hydraulic fracture propagation solutions.

Primarily, I developed non-intersecting, multiple-stage hydraulic fracture simulations for the optimization of the fracture spacing and determination of the appropriate fracturing scenario. Subsequently, I developed hydraulic fracture propagation models in the presence of a natural fracture network. Notably, oil/gas reservoirs commonly contain natural fractures which significantly complicate the hydraulic fracture growth.

Q. Describe how you executed the simulations.

A. For the fracture intersection model in Abaqus I used pore-pressure cohesive elements (COH2D4P and COH3D8P), continuum solid 2D and 3D linear elements with pore pressure degree of freedom (CPE4P and C3D8P), fluid pipe elements (FP2D2), and fluid pipe connector elements (FPC2D2) for the fracture space, poro-elastic porous media, wellbore and the hydraulic fracture stage sequences, respectively.

The cohesive 2D pore-pressure element COH2D4P possesses four corner nodes with displacement and pore-pressure degrees of freedom, and two additional middle-edge nodes through the thickness with only pore-pressure degrees of freedom.

The coupling of pore-pressure degrees of freedom at the intersection can be accomplished by use of the command *EQUATION in Abaqus.

To impose the pore-pressure equilibrium in all four middle-edge nodes, the adjacent elements to the intersection must be initialized as fully damaged by use of the initial condition “Initial Gap” in Abaqus. Without this, the intersecting elements along the natural fracture do not accept any pore fluid after the pore-pressure increase. The mesh-based effect of this initial condition on the solution can be minimized by use of fine mesh at the intersection.

This intersection model in three dimensions requires defining four middle-edge node sets on the four surfaces of the hole at the intersection. Notably, these node sets must contain the node numbers in order such that the appropriate nodes are constrained together depending on their sequence in the node sets. To ensure the correct coupling, I developed an Abaqus plug-in that receives two node sets, pairs nodes depending on their distance, and couples the pore-pressure degree of freedom of the nodes in each pair by generating an include file (*.INC) containing the *EQUATION commands.

Q. Were there any key technical challenges you faced along the way? How did you solve them?

A. Local mesh refinement around the cohesive elements is essential for the solution convergence and accuracy. Abaqus is comparatively weak for the extremely local mesh refinement. Therefore, I partitioned the domain into many parts (e.g., narrow sub-regions on two sides of the cohesive layers) in order to refine the mesh only in the vicinity of these layers. This approach significantly reduced the computational expenses and the CPU time.

The substitution of C3D8P elements with reduced-integration poroelastic C3D8RP elements, C3D8RP (continuum solid 3D linear element with pore-pressure degree of freedom and reduced integration), has caused the hourglassing problem in some of our analyses, and even the hourglass-control option in Abaqus was not able to resolve these problems. In these cases, I decided to use the full integration element C3D8P, which resulted in higher computational expenses for the sake of higher solution-convergence rates and accuracy. Either of these finite elements should be selected after numerical experiments, starting with the reduced-integration elements and for the specific geomechanical-stress regime.

Natural-fracture characteristics, especially the proposed weakening factor and conductivity, critically affect fracture growth. The natural-fracture weakening factor should be acquired from laboratory experiments, and the conductivity should be carefully calibrated to obtain the closest match between the geomechanical model and the microseismic-event map. In my simulations, I attempted to optimize the natural-fracture parameters such that I obtain the fracture-propagation pattern almost similar to that from my observations in the microseismic survey (Haddad et al. 2016 at https://doi.org/10.2118/179164-MS).

Q. What were the advantages of using simulation in your project?  

A. My simulations can be extended to vast number of applications. Only a few of these applications are listed in the following:

• hydraulic fracture design and optimization
• wellbore integrity
• naturally-fractured reservoir behavior during fracturing
• geomechanical depletion of complicated and faulty formations
• fault activation
• hydraulically-driven fracture growth in civil structures

Q. Why did you choose Abaqus over other simulation products?

A. Abaqus includes strong direct solvers, nonlinear finite strains formulation, and pore-pressure cohesive elements, which are all essential and necessary for my specific large-deformation application of hydraulic fracturing. According to my experience, without any of these, my simulations could not be accomplished robustly and compliant with the engineering principles.

Q. Do you feel that learning simulation skills in University will provide you with an advantage in your career? Please explain.

A. Learning simulation skills at university definitely prepares me for my future career as the oil/gas industry challenges are too complicated to be resolved without simulation. Furthermore, the proliferating computational power of super clusters makes possible to simulate huge oil/gas problems cheaper, faster and more accurately.

Q. Is there anything else we should know about this project?

A. This project is accomplished through my PhD studies in petroleum engineering at The University of Texas at Austin. Further details about my work can be found in my LinkedIn and ResearchGate profiles.