PORTALE DELLA DIDATTICA

### Structural mechanics/Reservoir geomechanics

01QYMNW

A.A. 2018/19

2018/19

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

The course is subdivided into two main parts. The first part (SM) is related to the continuum mechanics, the theory of elasticity and to the calculus of civil and oil structures made of different materials (i.e. concrete and metal). The subject is addressed according to the most modern formulations, suitable for numerical implementation. The second part (RG) deals with the mechanical behavior of rock structures related to the oil and gas engineering. In particular this part is focused on the basic aspects of the stress strain behavior of rock material and rock masses and their interaction with fluids. Topics are discussed with reference to the reservoir geomechanics.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

The course Structural Mechanics/Reservoir Geomechanics aims at providing the fundamental principles of Continuum Mechanics, necessary for understanding the mechanical response of a system subject to external actions. Structural Mechanics The course presents the fundamental theoretical principles that allow to analyse the mechanical behaviour of elastic solids and in particular of beam systems. Reservoir Geomechanics The course provides the fundamentals of rock behaviour in relation to field operations. The main objective of the course is to teach students: 1) how rocks respond to the modification of the underground state of stress in relation to oil and gas operations 2) the models and methods used to solve practical problems. To reach this objective the following subjects are explained during the course: fundamentals of continuum mechanics, the role of fluids in rock behaviour, drained and undrained conditions, interpretation of laboratory tests, elasto-plastic models for predicting rock behaviour and methods of stability analysis for evaluating rock failure in oil and gas reservoirs.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

The course Structural Mechanics/Reservoir Geomechanics aims at providing the fundamental principles of Continuum Mechanics, necessary for understanding the mechanical response of a system subject to external actions. Structural Mechanics The course presents the fundamental theoretical principles that allow to analyse the mechanical behaviour of elastic solids and in particular of beam systems. Reservoir Geomechanics The course provides the fundamentals of rock behaviour in relation to field operations. The main objective of the course is to teach students: 1) how rocks respond to the modification of the underground state of stress in relation to oil and gas operations 2) the models and methods used to solve practical problems. To reach this objective the following subjects are explained during the course: fundamentals of continuum mechanics, the role of fluids in rock behaviour, drained and undrained conditions, interpretation of laboratory tests, elasto-plastic models for predicting rock behaviour and methods of stability analysis for evaluating rock failure in oil and gas reservoir.

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Ability to evaluate qualitatively and quantitatively the mechanical behaviour of man made (engineering works) and natural (rock masses) structures with reference to Oil and Gas Engineering and to adopt the proper approaches to the solution of specific engineering problems.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Structural Mechanics The student must be able to determine the reactions forces, the diagrams of bending moment, axial force and shear force for statically determinate and indeterminate beam systems; to calculate the stresses in the beams based on the De Saint Venant principle; to apply the strength criteria and to verify the strength of a beam system. Reservoir Geomechanics Upon completion of the course, the student should be able to: 1) Identify the appropriate rock mechanical parameters and select the tests necessary to characterize the rock material with reference to a given field problem; 2) Predict the hydro-mechanical response of porous rocks in oil and gas field operations; 3) Solve practical problems: wellbore stability, hydraulic fracturing, reservoir compaction and subsidence, solids production.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural Mechanics The student must be able to determine the reactions forces, the diagrams of bending moment, axial force and shear force for statically determinate and indeterminate beam systems; to calculate the stresses in the beams based on the De Saint Venant principle; to apply the strength criteria and to verify the strength of a beam system. Reservoir Geomechanics Upon completion of the course, the student should be able to: • Identify the appropriate rock mechanical parameters and select the tests necessary to characterize the rock material with reference to a given field problem; • Predict the hydro-mechanical response of porous rocks in oil and gas field operations; • Solve practical problems: wellbore stability, hydraulic fracturing, reservoir compaction and subsidence, solids production.

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

The basic concepts of Mathematics, Linear Algebra, Physics and Fluid Mechanics are required.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Structural Mechanics The student must know the kinematics and statics of the material point, the operations on the vectors (sum, multiplication by a scalar, scalar product and cross product) and on the matrices, the basic topics of linear algebra and geometry. Furthermore, he must know the rules of derivation and integration for functions with one or more variables. Reservoir Geomechanics The student must know the fundamental principles of Linear Algebra, Physics I, Fluid Mechanics and Geology

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Prerequisites Structural Mechanics The student must know the kinematics and statics of the material point, the operations on the vectors (sum, multiplication by a scalar, scalar product and cross product) and on the matrices, the basic topics of linear algebra and geometry. Furthermore, he must know the rules of derivation and integration for functions with one or more variables. Reservoir Geomechanics The student must know the fundamental principles of Linear Algebra, Physics I, Fluid Mechanics and Geology

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

A. Calculus of one-dimensional structures I. Statically determinate structures II. Statically indeterminate structures B. Continuum mechanics I. Definition and analysis of strains and stresses II. Theory of elasticity III. Theory of elastic beams IV. Collapse of structures C. Sedimentary rocks and rock masses I. Failure mechanics II. Mechanical properties of rocks III. In situ state of stress IV. Stresses around boreholes V. Reservoir geomechanics

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Structural Mechanics Classification of the structural elements based on the number of prevalent dimensions, introduction to the various structural typologies, illustration of the external loading that can act on the structures and the reactions forces that oppose them. Matrix formulation of the geometry of the areas and examples of calculation. Methods for determining the reaction forces. Characteristics of internal reactions of the beams. Main types of statically determinate beam systems in construction practice: Gerber beams, truss structures, three-hinged arches. Summary of analysis of strain and stress and of the Elasticity theory. De Saint Venant solid (cylindrical solid loaded on the bases) and elementary and compound loading cases: centered and eccentric axial force, shearing force, uni- and bi-axial flexure. The Principle of virtual work for deformable beams: calculation of elastic displacements and solution of statically indeterminate beam systems. Reservoir Geomechanics 1) Continuum mechanics. >The state of stress and strain >Constitutive laws: Theory of elasticity and plasticity; Creep 2) Failure mechanics: Mohr-Coulomb, Hoek & Brown, Griffith, Jaeger strength criteria 3) Mechanical properties of rocks from lab tests 4) Elements of Critical state Soil Mechanics. Modified Cam Clay Model 5) In situ state of stress: geostatic and in fault regime 6) Compaction and subsidence of reservoirs during depletion 7) Stresses around boreholes. Stability during drilling: geomechanical aspects 8) Principles of hydraulic fracturing 9) Solids production

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural Mechanics Classification of the structural elements based on the number of prevalent dimensions, introduction to the various structural typologies, illustration of the external loading that can act on the structures and the reactions forces that oppose them. Matrix formulation of the geometry of the areas and examples of calculation. Methods for determining the reaction forces. Characteristics of internal reactions of the beams. Main types of statically determinate beam systems in construction practice: Gerber beams, truss structures, three-hinged arches. Summary of analysis of strain and stress and of the Elasticity theory. De Saint Venant solid (cylindrical solid loaded on the bases) and elementary and compound loading cases: centered and eccentric axial force, shearing force, uni- and bi-axial flexure. The Principle of virtual work for deformable beams: calculation of elastic displacements and solution of statically indeterminate beam systems. Reservoir Geomechanics 1) Continuum mechanics. >The state of stress and strain >Constitutive laws: Theory of elasticity and plasticity; Creep 2) Failure mechanics: Mohr-Coulomb, Hoek & Brown, Griffith, Jaeger strength criteria 3) Mechanical properties of rocks from lab tests 4) Elements of Critical state Soil Mechanics. Modified Cam Clay Model 5) In situ state of stress: geostatic and in fault regime 6) Compaction and subsidence of reservoirs during depletion 7) Stresses around boreholes. Stability during drilling: geomechanical aspects 8) Principles of hydraulic fracturing 9) Solids production

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

(SM) Calculation of statically indeterminate structures Analysis of the collapse of structures (RG) Stresses in a continuum medium: principal stresses; Mohr circles; total and effective stresses; stress paths Interpretation of laboratory tests: strength and deformability of rocks Failure Mechanics: interpretation of the rock strength by different failure criteria

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

The course is organized in theoretical and practical lessons. During the practical lessons the students have to solve exercises by applying the theory explained in lectures. The interpretation of lab tests and the solution of practical problems are developed in the Informatic Lab About 6 hours are devoted to seminars with the additional presence of expert instructors from industry.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

One/two theoretical classes per week and two/one practical class per week (for the preparation of the written exam)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

(SM) Carpinteri A., Structural Mechanics: a unified approach, Taylor & Francis, 1997 Notes and materials distributed in the classroom (RG) Fjaer, Holt, Horsrud, Raaen & Risnes, Petroleum related Rock Mechanics, 2nd edition, Elsevier, Oxford, 2008. Brady & Brown Rock Mechanics, 3rd edition, Kluwer Academic Publisher, Dordrecht, 2004 Texts, equations, figures, showed during lectures will be available on the web site of the course.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Reference Books: Fjaer, Holt, Horsrud, Raaen & Risnes, Petroleum related Rock Mechanics, 2nd edition, Elsevier, Oxford, 2008. Brady & Brown Rock Mechanics, 3rd edition, Kluwer Academic Publisher, Dordrecht, 2004 Lancellotta, 2009. Geotechnical Engineering, 2nd edition, Taylor & Francis, New York The slides presented during lectures will be periodically uploaded on the web site of the course.

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Carpinteri A., Structural Mechanics Fundamentals 2013, CRC Press Notes and solutions of past written exams are available on the web site of the course.

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Modalità di esame: prova scritta;

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Modalità di esame: prova scritta;

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Written test (2 hours) consisting of two main parts: theoretical questions and exercises and for RG discussion of a technical/scientific paper

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

Exam: written test;

Structural mechanics/Reservoir geomechanics (Structural mechanics)

Exam: written test;

Structural mechanics/Reservoir geomechanics (Reservoir Geomechanics)

The exam is aimed at evaluating knowledge, competences and skills acquired during the course. The student should be able to interpret lab tests and determine the rock parameters; to discuss the theoretical models of rock behaviour; to examine a practical problem and to select models and methods to reach the solution. The exam consists of a written test, closed books. A sheet with formulas is provided. The use of mobile phones or PDAs is not allowed during the exam. A pocket calculator is required. The test is organized as follows: - Eight multiple-choice questions (8/30 points). These questions are aimed at evaluating the general knowledge of the student acquired during the course - Two open questions (8/30 points). These questions, to be contained in not more than 2 A4 pages, are aimed at evaluating the ability of the student to discuss topics explained in class - Three exercises (14/30 points). The exercises are aimed at evaluating the skills of the students in interpreting lab tests and in finding the solution to practical problems The duration of the exam is 1,5 hours

Structural mechanics/Reservoir geomechanics (Structural mechanics)

The duration of the written test examination of Structural Mechanics is three and half hours . There are three problems to solve: 1) reactions forces, the diagrams of bending moment , axial force and shear force for statically determinate beam systems and calculation of an elastic displacements (10/30 points) 2) reactions forces, the diagrams of bending moment , axial force and shear force for statically indeterminate beam systems (10/30 points) 3) calculation of the central axes of inertia and the stresses in the cross section of a De Saint Venant cylinder (10/30 points)

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