Geomechanics of Sand Production and Sand Control

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Geomechanics of Sand Production and Sand Control
Copyright Page
Contents
Acknowledgments
Introduction
One Fundamental rock mechanics theory of sand production from oil and gas reservoirs
1.1 Linear elasticity theory
1.1.1 Stress
1.1.2 Stress components
1.1.3 Strain components
1.1.4 Displacements
1.1.5 Symmetry of stress components
1.1.6 Number of unknowns
1.1.7 Displacement strain relation
1.1.8 Equation of equilibrium (Fig. 1.6)
1.1.9 Stress-strain relation for isotropic linear elasticity
1.1.10 Surface traction versus stress
1.1.11 Boundary conditions
1.1.12 Effective stress for deformation
1.1.13 Effective stress for failure
1.1.14 Tensor form of the fundamental elasticity equations
1.1.14.1 Tensor notation or index notation
1.1.15 Cylindrical coordinate
1.1.16 Spherical coordinate
1.1.17 Elasticity constants
1.1.18 2D problems
1.1.19 Eight elasticity equations for plane strain problems
1.1.20 Eight elasticity equations for plane stress problems
1.2 Finding analytical solutions useful for petroleum engineers
1.2.1 Compatibility condition
1.2.2 Stress method
1.2.3 Airy’s stress function
1.2.4 Airy’s stress function using analytic functions
1.2.5 Solution
1.2.6 Stress around a circular borehole
1.2.6.1 Stress around a circular borehole-continued
1.2.6.2 Stress around a circular borehole-continued
1.2.7 Solution at the borehole surface
1.2.8 Radially symmetric poro-elasticity problem
1.2.8.1 Stress induced by fluid flow
1.2.8.2 Inclined well
1.2.8.3 Finding a solution for τxy
1.2.9 Solving out-of-plane stress
1.2.9.1 Solution for inclined well with fluid flow
1.3 Application of the linear elasticity theory to thick wall cylinder test for predicting the onset of sand production
1.3.1 Tangential stress at a small cavity loaded with σx and σy from distance
1.3.2 Thick wall cylinder test
1.3.3 Mohr’s failure theory
1.3.4 Thick wall cylinder tests for nonlinear rock
1.3.5 Size effect
1.3.6 Field evaluation of thick wall cylinder tests
1.3.7 Triaxial perforation stability tests
1.3.8 Conversion: Uniaxial compressive strength (UCS) versus thick wall cylinder
1.3.9 Conversion: UCS versus thick wall cylinder (Indonesia offshore)
1.3.10 Conversion: UCS versus thick wall cylinder: Thailand, the North Sea offshore
1.4 Application of plasticity theory to medium-strength rock
1.4.1 Three types of nonlinearity
1.4.2 Initial nonlinearity
1.4.2.1 Plasticity theory
1.4.3 Shear plasticity versus pore collapse plasticity
1.4.3.1 Hardening or softening
1.4.4 Analytical solution related to perforation failure
1.4.4.1 Modification of effective stress due to capillary pressure
1.4.5 Plasto-elastic equations for spherical coordinate—Elastic region
1.4.6 Elastoplastic equations for the spherical coordinate—plastic region
1.4.7 Plasto-elastic equations for spherical coordinate—postfailure region
1.4.7.1 Yield envelop for consolidated and unconsolidated sandstone
1.4.7.2 Stress solution in the postfailure zone
1.4.7.3 Erosion failure
1.4.7.4 Failure condition inducing intact rock
1.4.7.5 Stress state in the plastic region
1.4.7.6 Sand production from the plastic region
1.4.7.7 Shear failure point at zero flow rate (Note: all net pressure and net stress)
1.4.7.8 Cavity stability envelope calculated by a numerical model
1.4.7.9 Perforation stability envelope in the coordinate of reservoir pressure versus bottom hole pressure
1.4.7.10 Perforation stability envelope in the coordinate of reservoir pressure versus bottom hole pressure
1.5 In situ stress
1.5.1 Vertical and horizontal in situ stress
1.5.2 Typical stress gradient for an offshore location
1.5.3 Typical minimum horizontal stress in the North Sea and the Gulf of Mexico
1.5.3.1 Faulting stress regimes
1.5.3.2 Normal fault
1.5.3.3 Strike-slip fault
1.5.3.4 Reverse fault
1.5.4 Stress polygon
1.5.5 In situ stress change during oil and gas production
1.5.6 Stress state and compaction within a depleted reservoir
1.5.7 Example calculations
1.5.8 Roof effect
1.5.9 Roof effect—continued
1.6 General rock properties
Two Natural completion
2.1 Field and laboratory observations of sand production from naturally completed wells
2.1.1 Five conditions to induce sand problems
2.1.1.1 Rock failure
2.1.1.1.1 Cavity deformation experiments
2.1.1.1.2 Four modes of rock failure
2.1.1.1.3 Size effect of a small cavity
2.1.1.1.4 Three modes of sand production
2.1.1.1.5 Critical well pressure for perforation stability
2.1.1.1.6 Cavity stability envelope in the reservoir pressure drawdown coordinate
2.1.1.1.7 Sand rate from inclined wells
2.1.1.1.8 Transient sand rate
2.1.1.1.9 Effect of water cut
2.1.1.1.10 Oriented perforation in California
2.1.1.1.11 Stability of perforation oriented in maximum in situ stress
2.1.1.1.12 Model prediction
2.1.1.1.13 Sand problems for injection wells
2.2 Evaluation tool of onset of sand production
2.2.1 Procedure of core-based evaluation of onset of sand production
2.2.1.1 Standard sand production prediction procedure
2.2.1.1.1 Uniaxial compressive strength or thick wall cylinder distribution from top to bottom of a reservoir
2.2.1.1.2 Uniaxial compressive strength estimation using a portable hardness tester
2.1.1.2.1 Portable uniaxial compressive strength tester
2.2.1.1.3 Principle of the hardness meter and modification
2.2.1.1.4 Experiments to improve the accuracy of uniaxial compressive strength estimation
2.2.1.1.5 Conditions to improve the accuracy
2.2.1.1.6 To improve the uniaxial compressive strength estimation of cores
2.2.1.1.7 Example of uniaxial compressive strength estimation from Hardness tester
2.2.1.2 Neural network to estimate uniaxial compressive strength from logging parameters
2.2.1.3 Backward calculation using measured uniaxial compressive strength
2.2.1.4 Field example
2.2.1.5 Comparative studies of compact triaxial perforation stability tests and thick wall cylinder tests
2.2.1.5.1 Difference between thick wall cylinder and triaxial perforation stability tests
2.2.1.5.2 Four modes of breakouts
2.2.1.5.3 External size correction of loading factor
2.2.1.5.4 Equation to predict the onset of sand production from triaxial perforation stability test
2.2.1.6 Empirical results
2.2.1.6.1 Chiba-sandstone A
2.1.6.1.2 Sieve analysis of Chiba-sandstone A
2.2.1.6.2 Thick wall cylinder tests for Chiba-sandstone B
2.1.6.2.3 Sieve analysis of Chiba-sandstone B
2.2.1.6.3 Triaxial perforation stability tests for Chiba-sandstone B
2.2.1.7 Equations to predict the onset of sand production using triaxial perforation stability and thick wall cylinder testers
2.2.2 Prediction of onset of sand production using a finite element geomechanics code
2.2.2.1 The dual predictions of onset of sand production use TWC (or TPS) tests and the finite element code
2.2.2.1.1 Finite element algorithm
2.2.2.1.2 Loading sequence
2.2.2.1.3 Flow chart of the calculation sequence
2.2.2.2 Poro-elasticity with nonlinear stress-strain curves
2.2.2.3 Plastic hardening
2.2.2.4 Construction of constitutive relations from triaxial data
2.2.2.5 Adjustment of k-factor of Lade model
2.2.2.6 Failure judgment
2.2.3 Evaluation of onset of sand production from perforations using a finite element geomechanics code
2.2.3.1 Spiral perforations
2.2.3.2 Field data
2.2.3.3 Perforation instability caused by reservoir pressure depletion: highest density to induce instability
2.2.3.4 Perforation instability caused by reservoir pressure depletion: effect of perforation phasing
2.2.3.5 Perforation instability caused by reservoir pressure depletion: effect of perforation pattern and density
2.2.3.6 Perforation instability caused by drawdown: effect of the ratio σhe/σve
2.2.3.6.1 Effect of drawdown on the onset of sand production
2.2.3.7 Effect of staggered and nonstaggered perforation
2.2.3.8 Effect of non-Darcy factor for gas
2.2.3.9 Stability of perforations shot in inclined wells
2.2.3.10 Oriented perforation
2.2.3.11 X-shape staggered oriented perforation
2.3 Prediction of long-term sand production rate using an analytical model
2.3.1 Laboratory and field sand rate measurements
2.3.1.1 Laboratory sand rate tests
2.3.1.2 Field sand rate tests
2.3.2 Long-term and short-term sand rate models
2.3.2.1 Long-term or short-term sand rate prediction
2.3.3 Analytical sand rate models
2.3.3.1 Analytical sand rate model based on dimensional analysis using lab data
2.3.3.2 Sand rate model based on the dimensionless analysis using field data
2.3.3.3 Imaginary perforation cavity
2.3.3.4 Equation for qc
2.3.3.4.1 The flow rate required to remove sand particles from the cavity surface
2.3.3.5 Nomenclatures used in the equation for qc
2.3.3.6 Function for Sand rate versus Reynolds number and LF (perforated wells)
2.3.3.7 Function for Sand rate versus Reynolds number and LF (perforated wells) - Graph
2.3.3.8 Function for Sand rate versus Reynolds number and LF (openhole)
2.3.3.9 Function for Sand rate versus Reynolds number and loading factor (openhole) graph
2.3.3.10 Water cut correction
2.3.4 Example field applications
2.3.4.1 Sand rate calculation
2.3.4.2 Water effect
2.3.4.3 Sensitivity to drawdown
2.3.4.4 Flow rate effect
2.3.4.5 Selective perforation
2.3.4.6 Sand rate from openhole
2.3.4.7 Vertical openhole
2.3.5 Typical sand rate for a uniform reservoir with UCS=2056psi, porosity=0.26, and k=600 md
2.3.5.1 Reservoir conditions
2.3.5.2 Typical sand rate for the sandstone (UCS=2056psi, porosity=0.26, k=600 md)
2.3.5.3 The detailed sand rate between 350–450 days
2.4 Prediction of perforation cavity evolution during early sand production using Geo3D finite element code: sand release r...
2.4.1 Mechanical properties of the sandstones used for the triaxial sand rate measurement tests
2.4.1.1 Lade yield model
2.4.1.2 Constitutive relation for the Castlegate sandstone
2.4.1.3 Castlegate triaxial stress-strain data
2.4.1.4 Yield and failure envelopes
2.4.1.5 Calculated coefficients for constitutive relation and failure envelope
2.4.1.6 Sand production decline coefficient
2.4.1.7 Transient phenomena observed during step rate test
2.4.1.8 Step rate test for laboratory experiments
2.4.1.9 Cavity evolution models
2.4.1.10 Strategy of cavity evolution
2.4.1.11 Strategy of cavity evolution
2.4.1.12 Case-1 303 kr=(σrcon/σRcon)=1/3, kz=(σzcon/σRcon)=1
2.4.1.13 Loading sequence and measure variables for Case 1
2.4.1.14 Rock CT scan images and photos
2.4.1.15 Simulation for Case 1
2.4.1.16 Case-2 302b
2.4.1.17 Cavity evolution for Case 2
2.4.1.18 Extended simulation
2.4.1.19 Case-3 304
2.4.1.20 CT scans and photos for Case 3
2.4.1.21 Simulation for Case 3
2.4.1.22 Case-4 305
2.4.1.23 CT scan images and photos—Case 4
2.4.1.24 Case-5 306
2.4.1.25 CT scans and photos—Case 5
2.4.1.26 Case-6 308
2.4.1.27 CT scan images and photos for Case 6
2.4.1.28 Simulation for Case 6
2.4.1.29 Case-10 315
2.4.1.30 Slide 2.120 Case 10
2.4.1.31 Simulation for Case 10
2.4.1.31.1 Simulations using Saltwash South and Buff Berea sandstones
2.4.1.32 Extended simulation
2.4.1.33 Buff Berea
2.4.1.34 Reduced yield strength due to water
2.4.1.35 Simulation
2.4.1.36 Simulation
2.4.1.37 Extended sand production
2.4.1.38 Sand release rate coefficient
2.4.1.39 Matching A1 from sand rate experiment
2.4.2 Perforation cavity evolution during early sand production for typical North Sea field conditions
2.4.2.1 Simulation for perforation cavity evolution: eight shots per foot spiral pattern with 60 degrees phasing
2.4.2.2 Transient sand release rate A4=7.5 (quick decline)
2.4.2.3 Simulation with transient sand rate A4=3.75
2.4.2.4 Transient sand release rate A4=2.5 (slow decline)
2.4.2.5 Effect of depletion rate on sand rate
2.4.2.6 Depletion rate 1-kpsi/91.25 days
2.4.2.7 Effect of flow rate
2.4.2.8 Effect of well inclination, isotropic permeability (permeability kx=ky=kz=600mD)
2.4.2.9 Perforation stability of a vertical well
2.4.2.10 Perforation stability of a 30 degrees well with isotropic permeability
2.4.2.11 Perforation stability of 45 degrees well with isotropic permeability
2.4.2.12 Perforation stability for a 55 degrees well angle with isotropic permeability
2.4.2.13 Perforation stability for 70 degrees well angle with isotropic permeability
2.4.2.14 Perforation stability for 70 degrees well angle with isotropic permeability (perforation rotated 30 degrees)
2.4.2.15 Perforation stability for 90 degrees well angle with isotropic permeability (horizontal well)
2.4.2.16 Perforation stability for 90 degrees well angle with isotropic permeability (perforation rotated 30 degrees)
2.4.2.17 Well inclination effect for depletion rate=1-kpsi/365 day, anisotropic permeability (permeability kx=600mD, ky=600...
2.4.2.18 Well inclination 30 degrees
2.4.2.19 Well inclination 45 degrees
2.4.2.20 Well inclination 70 degrees
2.4.2.21 Well inclination 90 degrees (horizontal well)
2.4.2.22 X-shape oriented perforation
2.5 Discussion and conclusions
2.6 Pressure profile around perforations
2.6.1 Pressure profile around a single perforation
2.6.1.1 Analytical solution
2.6.1.2 Numerical solution for pressure distribution around a single perforation
2.6.1.3 Computation of pressure gradient along various lines
2.6.1.4 Pressure around a perforation in the formation without permeability damage
2.6.1.5 Pressure profile around a perforation in the formation with permeability damage with drilling fluid and perforation...
2.6.1.6 Parameters for perforation flow model: permeability is damaged
2.6.1.7 Pressure around a perforation in the formation with permeability damage
2.6.1.8 Gas flow
2.6.1.9 Parameters for perforation flow model: permeability is uniform over the entire domain
2.6.2 Quantitative analysis of the effect of perforation interaction on flow efficiency
2.6.2.1 Evaluation of flow performance
2.6.2.2 Effect of perforation pattern and shot density and permeability anisotropy
2.6.2.2.1 Permeability anisotropy impact on perforations
2.6.2.3 Effect of perforation length and perforation diameter
2.6.2.4 Effect of perforation diameter
2.6.2.5 Effect of mud damage and perforation damage
Three Completion methods for weak formation
3.1 Gravel pack
3.1.1 Factors to control flow efficiency
3.1.2 A gravel pack is the best sand control method if the formation permeability is less than 100 md
3.1.3 Gravel pack in high permeable formation
3.1.4 Skin factor of gravel-packed wells after two years
3.1.5 Large skin for gravel-packed wells in the high permeable formation
3.1.6 Pressure distribution around a perforation for gravel-packed well
3.1.7 Field measurement of skin factor with time
3.1.8 A simulation model to find the cause of gravel pack damage
3.1.9 Pressure drop for ideal gravel pack with a high permeable formation
3.1.10 Pressure drop for non-ideal gravel pack with a high permeable formation
3.1.11 Ideal gravel pack and collapsed cavity gravel pack in a low permeable formation
3.1.12 Gravel pack with fines migration into the perforation tunnel in a formation with a low permeability
3.1.13 Improvement of gravel pack operation
3.1.14 Gravel size
3.1.15 Gravel size selection
3.1.16 Proper gravel size
3.1.17 Recommended screen diameter
3.1.18 What are Poly Glycolic Acid and Polylactic Acid?
3.1.19 Applications to oil fields with complex downhole tools
3.1.20 Example application: fluid-loss control material
3.1.21 Hydrolysis tests
3.1.22 Openhole gravel packing
3.1.23 Shunt tube and external protective shroud
3.1.24 High flow performance of a long openhole gravel pack
3.2 Frac packs
3.2.1 Frac pack with gravel
Flow performance
3.2.2 Fracture from strong interval
3.2.3 Fracturing from strong nonpermeable section
Field example of gravel pack and frac pack
3.2.4 Frac pack to reduce the sand rate
3.3 Selective perforation
3.3.1 Interval to perforate to require equivalent flow efficiency
3.4 Cased hole completion with a compartmentalized screen
3.4.1 Stand-alone screen
3.4.2 Skin factor for perforation willed with formation sand
3.5 Openhole completion
3.5.1 Merits of inclined/horizontal wells
3.5.2 Reduction of cost of horizontal wells with experience
3.5.3 Perforated liners, prepack screens, and slotted liners
3.5.4 Design of solid exclusion device
3.5.5 The ideal sand control device
3.5.6 Design basics of stand-alone screen
3.5.7 Screen base pipe strength
3.5.7.1 Base pipe for the standard screen
3.5.7.2 Strength of expandable screen
3.5.8 Openhole stability during drilling and installing a screen
3.5.8.1 Stability of vertical wells for depleted reservoir
3.5.8.2 Timing of drilling inclined wells
3.5.8.3 Example of overcoming the differential sticking problems
3.5.8.4 Well stability during production
3.5.8.5 Tensile failure is rarely induced for openhole
3.5.8.6 Installing enlarged prepack liners or metal-woven screens
3.6 No sand control
3.7 Oriented perforation
3.7.1 Oriented perforation—staggered x-shape oriented perforation
3.8 Casing patch
3.9 Resin treatment
3.10 Skin damage and risk of completion methods
Four Sand control for heavy oil reservoirs
4.1 Heavy oil resources
4.1.1 Heavy oil production
4.2 Cold heavy oil production with sand
4.2.1 Well design
4.2.2 Controlled sand rate
4.3 Field operation to identify the magnitude of matrix bypass event and the plugging capability
4.3.1 Causes of MBE
4.3.2 Wettability
4.4 Laboratory experiments observing long stable finger growth
4.4.1 Observation
4.5 Simulation of laboratory flow tests
4.6 Field simulation
4.6.1 Case 1
4.6.1.1 Case 1–1 Layer homogeneous model with uniform k and single wettability
4.6.1.2 Case 1–2 Random heterogeneous model with random k and single wettability
4.6.1.3 Case 1–3 Allocate heterogeneous layers at specific layers and locations
4.6.1.4 Case 1–4 Allocate heterogeneous layer at specific layers and locations with a local grid refinement
4.6.2 Case 2 Short water breakthrough with a large amount of sand production during PIP
4.6.3 Case 3 Small amount of sand production during a long period of PIP
4.7 Conclusion of simulation and laboratory test analyses
Five Guidelines to solving sand problems for water or gas injection wells
5.1 Completion methods for water or gas injection wells
5.2 A phenomenon observed for perforated injection wells—rock strength distribution
5.3 A phenomenon observed for perforated injection wells—injectivity
5.4 Sand settlement in the rat hole
5.4.1 Effect of formation sand in perforations
5.4.2 Failure initiates at the top and bottom of perforation cavities during injection
5.4.3 Rock strength required for perforation stability for injection wells
5.5 Cross flow
5.5.1 Cross flow in injection well with production well with single completion
5.5.2 Cross flow in injection well with production well with single completion- continued
5.6 Screenless frac pack
5.7 Guidelines for completing water and gas injection wells
six Erosion and sand production monitoring
6.1 Typical high flow gas/condensate production facilities
6.2 Hot spots
6.2.1 Example of flow velocities at hot spots with an extremely high rate gas well
6.3 Types of erosion
6.3.1 Shear stress erosion
6.3.2 Liquid impingement erosion
6.3.3 Erosion caused by solid particles
6.4 Equations of erosion
6.4.1 Example calculations for Choke erosion (conventional choke)
6.4.1.1 Choke life
6.4.2 High flow rate choke
6.5 Erosion analysis of wellhead and Xmas tree
6.5.1 Wellhead and Christmas tree erosion
6.5.1.1 Example calculations for Xmas tree erosion
6.5.2 Example erosion calculation of wellhead
6.5.2.1 Wall thickness erosion (D50=100-micron sand) is calculated in Table 6.5
6.5.3 Erosion analysis of surface piping
6.5.4 Example calculation: Erosion analysis of the 6″ flow line from the wellhead (OD=6.624,″ID=5.761″)
6.5.5 Example calculations for 24″ production manifold
6.6 Sand rate monitoring
Bibliography
Appendix 1 Proof of continuity and uniqueness of displacement with compatibility condition
A1.1 Gauss theory
A1.2 Stokes theory
Appendix 2 Strain nuclei method
Appendix 3 Erosion equations induced by sand particles
A3.1 Solid particle erosion rate
A3.2 Erosion equation for flowline and Xmas tree. (Empirical relation, University of Tulsa consortium)
A3.2.1 Methods proposed by the University of Tulsa
A3.2.1.1 Vm: fluid velocity m/sec
A3.2.1.2 Equivalent flow stream velocity
A3.2.2 Mamdouh’s method
A3.3 WCU separator system erosion
A3.4 Upper completion erosion
A3.5 Wellhead and Christmas tree erosion
Index
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