Petroleum Geomechanics Design

Maurice Dusseault

Intro to Petroleum Geomechanics

Geomechanics…

 The petroleum geomechanics design approach  Uncertainty in geomechanics and petroleum engineering applications  Stress, pore pressure and effective stress  Rock strength and rock stiffness  Jointed and intact rock mass behavior  Geological history and rock properties  Coring, preparing, and testing rocks

Intro to Petroleum Geomechanics

Stress, Strength, Joints, etc…  Rock properties depend on geometry, materials, history, and so on  Rock masses have discontinuities…  Granular systems have contact forces  Frictional strength (μ) is a vital petroleum geomechanics concept  Also, pore pressures

Intro to Petroleum Geomechanics

F

W μ·F > W

F

Major Issues in Design

 We live with massive uncertainty  Rocks are deep, often inaccessible, no cores…  Properties may vary widely from bed to bed  Processes are very complex (  ′,  p,  T…)  Direct monitoring is usually impossible  This presents great challenges to the engineer who is doing design or predictive work  Petroleum geomechanics design is an iterative process based on monitoring and analysis

Intro to Petroleum Geomechanics

Reservoirs are heterogeneous & aniso tropic at all scales (microns to kilometers) …UNCERTAINTY… Intro to Petroleum Geomechanics

 70 m of Athabasca Oilsands, = 30%, S o = 0.8,  > 1,000,000 cP North of Fort McMurray, Alta

Geomechanics Design Elements

1.

2.

3.

4.

5.

Geometry, lithostratigraphy, classification of strata (shape, material types, extent, ...) History and present state (T, [  ], p, previous history of loading, ....) Appropriate behavioral law (   -T law; diffusion law for transport; Δp, ΔC effects…) Method of analysis (empirical, numerical, stochastic, analytic, similarity, ...) Verification (monitoring, autopsies…)

Intro to Petroleum Geomechanics

The Design Loop

Project Definition  Project goals  Technology drivers  Cost-benefit  … Design Verification  Monitoring strategy  Back-analysis  Modification of design  … Project Analysis  Empirical assessment  Numerical simulation  Model testing, pilots  Predictions

Intro to Petroleum Geomechanics

 … Preliminary Model  Geometry of wells…  Stratification  GMU choice  … Rock Behavior  - Y behavior  Correlations, logs  Literature  Lab tests  …

Preliminary Model

 Geometry of the proposed structure (eg: lay out of wells, structural units…)  Classification of the strata into geomechani cal units (behaviourally similar rock unit)  Location and geometry of the GMUs (eg: reservoir, overburden, ...) Geology!!

 Changes in geometry which are likely (new wells, further reservoir development) GMU = geomechanical unit (a behaviorally similar unit)

Intro to Petroleum Geomechanics

Geological Models: Logs vs. Rocks

REG. TIPO

ER-EO ER-EO ER-EO C-4 C-5 B-SUP B-SUP C-3 C-6 C-4 B-6/9 B-6/9 C-7 C-5 C-6 GUAS C-1 C-2 C-7 C-6 C-3 C-4 C-5 C-6 C-7 GUASARE C-7 GUASARE FALLA ICOTEA SVS-30 Intro to Petroleum Geomechanics GUASARE ER-EO B-SUP B-6/9 B-6/9 SMI

REG. TIPO

SVS-337

What is a GMU?



G

eo-

M

echanics

U

nit  Nature is too complex to “fully” model   Simplification needed A GMU is a “single unit” for design and modelling purposes  1 GMU = 1 set of mechanical properties  GMU selected from logs, cores, judgment

Intro to Petroleum Geomechanics

Log data Core data GMU 1 GMU 2 GMU 3 GMU 4 GMU 5 GMU 6 GMU 7 GMU 8

GMU’s and Rock Mechanics

  Rocks are heterogeneous, anisotropic, etc… For analysis, divide system into GMU’s…  Includes critical strata, overburden, underburden…  Too many subdivisions are pointless  Can’t afford to test all of them  Too few subdivisions is risky

TOO MANY?

TOO FEW?

Intro to Petroleum Geomechanics

History and Current State

 Geological and tectonic loading history  History of project to the time of analysis (injection/production history, seismicity, ...)  Current state of extrinsic parameters: Temperatures, Stresses, Pressures  Future history of what is proposed: changes in T,  , p, V, ....

The Geological and Stress History of rocks is vital geomechanics knowledge

Intro to Petroleum Geomechanics

Stress History and Rock Response

 ′ v diagenesis History is vital! In this example, deep burial and erosion have led to the following conditions: •

The rock is much stronger

•

The rock is much stiffer

•

Compaction is unlikely

• •

Sanding is less likely Now,



v is



3

•

Fracturing now “horizontal”

Current state

Intro to Petroleum Geomechanics

 ′ h Before any systematic reservoir geomechanics, the reservoir history should be studied by a structural geologist who understands stresses, diagenesis and rock properties

Sufficient Behavioral Law (I)

 For each GMU, we need a “sufficient” behavioral law to apply to the

entire

GMU   For p, T, and C diffusion (transport) processes: [k ij ], [  ij ], [D ij ], [  ij ] For   processes: strength model, stiffness, viscosity (creep), yield behavior, ...

 For seismic analysis: [v ij ] P , [v ij ] S , [Q ij ], ...

 Clearly, the number of parameters increases dramatically with anisotropy and complexity

Intro to Petroleum Geomechanics

Simplified Rock Strength “Law”

 “True” strength criteria can be complex; however, we often fit straight lines to the data to make analysis simpler.

  Y cohesion c ′ T o  3  1  n

Sufficient Behavioural Law (II)

 Choose a behavior model which adequately describes the behaviour (   example)  Linear-elastic model (A: no rupture; B: brittle rupture)  Non-linear elastic model E = f(σ 3 ′, ε v ...)  Elastic, perfectly plastic model  Elastic with strain-weakening, then plastic  Viscoelastic (shales, some rocks at high T)  Viscoplastic (salt and other halides)  Thermoelastic, thermoelastoplastic models, and so on…

The model must fit the problem: too much complexity confuses and discredits analysis

Intro to Petroleum Geomechanics

What Type of Stress-Strain Law?

C D A E B +ve E C, D B -ve

Strain (%) Intro to Petroleum Geomechanics

A Constitutive models: A: Linear elastic, no deviatoric dilation B: Perfect plasticity, no deviatoric dilation C: Instantaneously strain-weakening, post failure dilation angle D: Gradual weakening, post-failure dilation E: Damage mechanics emulation of a real geomaterial

Sufficient Behavioral Law (III)

 Data may be found in the literature, in data bases, from geological inference, ....

 Experienced persons can give estimates  A few simple tests may suffice, allowing comparisons to existing data bases  A laboratory test program may be used  Post-analysis may help refine the behavioral laws used, improving analysis

Don’t undertake complex testing pro grams unless potential benefits are large

Intro to Petroleum Geomechanics

Wilmington. California

 Bowl shaped  Casings sheared on the shoulders of the subsidence bowl  Few shears in middle, where  z greatest  Few on flanks  +earthquakes  Data analysis led to proposed solutions…

Intro to Petroleum Geomechanics

Methods of Analysis (I)

 Analysis must be founded on a “conceptual” model which is correct (get the physics right!!) 

Empirical models

are based on practice and “qualitative” assessments  Experience is a powerful tool, and requires a strong understanding of the physics 

Analytical

(closed-form) and

semi-analytical models

are sets of equations which can be solved directly (e.g. T(t) around a borehole)

Intro to Petroleum Geomechanics

Analytic Solution Example

The “simplest” borehole stress analysis model Hollow cylinder model Elastic stress solution (Lamé)

p b a p a q r b

r

q 

b

2 2 (

r r

2 (

b

2 

a

2 ) -

a

2 )

pb

-

a

2 2 (

r r

2 (

b

2 

b

2 )

pa

-

a

2 )  r 

b

2 2 (

r r

2 (

b

2 -

a

2 )

pb

-

a

2 ) -

a

2 2 (

r r

2 (

b

2 -

b

2 )

pa

-

a

2 ) (Usually, b >> a)

Intro to Petroleum Geomechanics

(Another equation is used to calculate radial displacements)

Methods of Analysis (II)



Numerical models

are for complex geometries, varying boundary conditions, non-linear cases, coupled processes (eg: flow +  T +   )  Finite difference (FD), Finite element (FEM)  Boundary discretization methods (BE, DD, BI)  Discrete element methods (DEM)  Hybrid approaches (DD + FEM, closed-form solutions + FD…)

Different approaches may be better for different problems (FD for



T &



p; FEM for



-



-

T

; FEM + DD for large problems…)

Intro to Petroleum Geomechanics

Numerical “Discretization”

 Reality is complex…     To solve problems, a rock mass is “divided” into many “elements” This is “

discretization

” {  }, {T}, {p}, {Q} {f} (inputs, outputs, loads, BC’s) are applied where and as required σ ij , ε ij , T, p… are computed as required

Intro to Petroleum Geomechanics

f 1 discrete element “grain” model f 1 f 2 f 2 network or FD model Q 1  Q 2 Q 3 finite element (FEM) model Q 2 

Methods of Analysis (III)



Probabilistic models

use “sampling” techniques for the variables to study outcome probabilities (e.g. “Monte-Carlo simulation”) 

Stochastic models

could mean that properties are varied according to pre-defined distributions  In Petroleum Geomechanics, statistical approaches have been sparingly used to date; “deterministic” models are widely preferred

Statistical approaches are necessary for quantitative risk and cost analysis

Intro to Petroleum Geomechanics

Monte Carlo Simulation

Many samplings and solutions are made to explore the overall probabilities. These are then related to cost and risk factors.

Parameter 1 Parameter 2 Random sampling + problem solving A, no B B, no A A+B Cases A, no B B, no A A+B Parameter 3

Intro to Petroleum Geomechanics

Parameter 4 Risk/cost factor

Monitoring (I)

 Used to verify the assumptions in the analysis and the behavioral laws  Used to clarify the physical processes and thus refine the conceptual model and analysis  Used as a means of controlling processes through “feed-back”  Used to assure that environmental or safety regulations are being met (e.g.: MS-monitoring)

Intro to Petroleum Geomechanics

Microseismic Array

1 local processors 2 fibre-optics or telemetry 3 4 workstation 5

Intro to Petroleum Geomechanics

monitoring or future production wells zone of interest sensors

Data from a mine monitoring case in South Africa

Intro to Petroleum Geomechanics

Monitoring (II)

 There are several different general approaches  PVT + chemical analyses of inputs/outputs  Wellbore methods, generally logs  Seismics, active and passive (microseismic)  Electrical methods  Magnetotelluric probing, electrical impedance tomography, special multiple electrode methods…  Deformation measurements and gravity  Miscellaneous methods (casing strain, ...)

Intro to Petroleum Geomechanics

Hydraulic Fracture Mapping

Characteristic deforma tion pattern makes it easy to distinguish frac ture dip, horizontal and vertical fractures



Gradual “bulging” of earth’s surface for horizontal fractures



Trough along fracture azimuth for vertical fractures



Dipping fracture yields very asymmetrical bulges

Dip =90° Maximum Δz: 0.00026 inches

Tiltmeters are used for fracture mapping

Intro to Petroleum Geomechanics

Dip = 0° Maximum Displacement: 0.0020 inches Dip = 80° Maximum Displacement: 0.00045 inches

Lessons Learned…   Uncertainty and complexity dominate petroleum geomechanics So, design is an ongoing process based on…  Use of existing knowledge  Lithostratigraphy, geophysical data, cores…  Stresses, pressures, temperatures and changes  Rock behavioral “laws”  Appropriate analysis and predictions  Measurements and refinement of predictions  Additions to the knowledge base

Intro to Petroleum Geomechanics