Establishment of tensile failure induced sanding onset prediction models for cased perforated gas wells Accepted Manuscript Establishment of tensile failure induced sanding onset prediction models for[.]
Accepted Manuscript Establishment of tensile failure induced sanding onset prediction models for casedperforated gas wells Mohammad Tabaeh Hayavi, Mohammad Abdideh PII: S1674-7755(16)30262-1 DOI: 10.1016/j.jrmge.2016.07.009 Reference: JRMGE 302 To appear in: Journal of Rock Mechanics and Geotechnical Engineering Received Date: April 2016 Revised Date: 19 June 2016 Accepted Date: 13 July 2016 Please cite this article as: Hayavi MT, Abdideh M, Establishment of tensile failure induced sanding onset prediction models for cased-perforated gas wells, Journal of Rock Mechanics and Geotechnical Engineering (2017), doi: 10.1016/j.jrmge.2016.07.009 This is a PDF file of an unedited manuscript that has been accepted for publication As a service to our customers we are providing this early version of the manuscript The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain ACCEPTED MANUSCRIPT Establishment of tensile failure induced sanding onset prediction models for cased-perforated gas wells Mohammad Tabaeh Hayavi *, Mohammad Abdideh *Corresponding Author’s Email: m.hayavi2013@gmail.com SC Tel : +98 939 1835971 RI PT Department of Petroleum Engineering, Omidiyeh Branch, Islamic Azad University, Omidiyeh, Iran Abstract M AN U Sand production is an important challenge in upstream oil and gas industry, causing operational and safety problems Therefore before drilling the wells, it is essential to predict and evaluate sanding onset of the wells In this paper, at first the new poroelastoplastic stress solutions around the perforation tunnel and tip based on the Mohr–Coulomb criterion are presented Based on the stress models, the tensile failure induced sanding onset prediction models for cased-perforated gas wells are derived The analytical models are applied to field data in order to verify the applicability of the developed models The results from the perforation-tip tensile-failure induced sanding model are very close to field data Therefore, TE D this model is recommended for forecasting the critical conditions of sand production analysis Such predictions are necessary for providing technical support for sand control decision-making and predicting the production condition at which sanding onset occurs AC C EP Keywords: sand production, poroelastoplastic model, Mogi-Coulomb criterion, gas wells, tensile failure ACCEPTED MANUSCRIPT Introduction In the petroleum industry the sand production phenomenon refers to the production of solid particles together with the formation fluids This phenomenon is common mainly in unconsolidated sandstone reservoirs and it is a possible consequence of the degradation of the geomechanical properties of the rock surrounding wellbore due to the drilling, completion and production operations (Volonte et al., 2010) Sand production can cause serious damages on surface production equipment The damages are mainly erosion of both downhole and surface RI PT valves and pipelines and sand deposits in the separators In addition to the damages of sand production on production facilities another main problem is the instability of the production cavities and wellbore itself, which may in extreme cases result in a complete filling of the borehole In high pressure oil and gas wells, sand influx from formation erosion is considered negative, though this view is slowly changing (Dusseault et al., 2000; Fattahpuor et al., 2012) SC Two main mechanisms responsible for sand production are shear and tensile failures Shear failure refers to tangential stresses near the cavity wall exceeding the compressive strength of the formation Both stress concentration and fluid withdrawal can trigger this condition Tensile failure refers to tensile stress triggered M AN U exclusively around the perforation where drawdown pressure exceeding the tensile failure criterion (Ong et al., 2000) Based on modelling accounting for strain localization and grain rotations, tensile failure may only occur in small holes like perforations, not in open holes The reason for this is that shear failure will always precede tensile failure for a large cavity like an open hole Due to the size effect, a small cavity like a perforation has a much higher threshold for shear failure, hence tensile failure may occur first (Van den Hoek et al., 1996; Fjaer et al., 2008) TE D A moderate reservoir depletion may often increase the critical drawdown for tensile failure, but excessive reservoir depletion unstabilizes perforation tunnels The low well pressure tends to induce sand production because of shear failure, and the high normalized pressure gradient tends to induce sand production because of tensile failure However, such tensile failure can be also minimized by decreasing the pressure gradient at the cavity surface by use of high density shots or enlarged cavities Thus, to minimize sand problems, perforation EP tunnels should be structurally stable with a suitable perforation pattern and density but still should be designed to minimize the pressure gradient to prevent tensile failure (Morita et al., 1989) The estimation of critical drawdown and depletion for the initiation of sand production in boreholes and AC C perforations in sandstone reservoirs is important for the estimation of the sand production risk of a field during its lifetime of production (Papamichos and Furui, 2013) Sanding onset prediction involves stress calculation at cavity (including wellbore or perforation) surface Even though a numerical model, such as Finite Element model, is more general, analytical or semi-analytical models may be more convenient and easier to use under special conditions Besides, an analytical model is always useful to verify numerical models (Yi, 2003) Bratli and Risnes (1979) presented an elastoplastic model to predict the critical condition for sand arch stability In this model, steady state fluid flow was applied, and the effective radial stress in the plastic region of a sand arch was used to judge sand initiation If the effective radial stress became tensile, the sand arch was deemed to fail and sand grains would flow into the well Weigarten and Perkins (1992) derived an equation describing tensile failure induced sanding condition in terms of pressure drawdown, wellbore pressure, formation rock cohesion and frictional angle based on the Mohr- ACCEPTED MANUSCRIPT Coulomb criterion and assuming spherical geometry for perforation cavity In their work, dimensionless curves are provided for determination of the pressure drawdown at a specified wellbore pressure Yi et al (2004) derived the analytical poroelastoplastic models based on the thick-walled hollow cylinder and sphere geometries Based on these models the sand production prediction models assuming shear failure induced sanding and tensile stress induced sanding after shear failure are developed These models may be used to study sand production from open-hole well or perforation tunnel and tip for a cased well RI PT Ong et al (2000) developed an analytical model for the prediction of the onset of sand production or critical drawdown pressure in high rate gas wells This model describes the perforation and openhole cavity stability incorporating both rock and fluid mechanics fundamentals In this model the pore pressure gradient is calculated using the non-Darcy gas flow equation and coupled with the stress state for a perfectly Mohr-Coulomb material Furthermore, sand production is assumed to initiate when the drawdown pressure condition induces tensile SC stresses across the cavity face In this paper, analytical sanding onset prediction models are derived based on theory of poroelastoplasticity and assuming tensile failure induced sanding from the plastic region created around the perforations of a perforated M AN U gas well To verify the models, real field cases from two published literature gas fields have been simulated The model generated results that compare with the actual field observations Building the new Poroelastoplastic Model at Production Condition A sand formation at depth exists at an equilibrium state of in-situ stress, pore pressure and temperature Creation of a cavity and depletion of the reservoir cause redistribution of the stresses and pore pressure around the cavity When the drilling and production-induced redistribution of the stress and pore pressure exceeds the strength of TE D the sand around the cavity, the rock surrounding the cavity may become highly plastic and loss of mechanical integrity may take place (Bratli and Risnes, 1982; Wu and Tan., 2002) If the reservoir sand behaves plastically after elastic limit is reached, a yielded zone will be formed around the borehole Sand production will be occurred when a certain amount of plastic strain is reached (Tao et al., 2008) Assuming the linear shear criterion to hold in this region, the stress solutions can be calculated This requires, EP however, knowledge of which principal stress will be the smallest and which will be the greatest (Fig 1) AC C Fig Progressive growth of yielding from wellbore wall and redistribution of stresses (Bratli and Risnes, 1982) The sandstone rock around the perforations was assumed to be isotropic and homogeneous with the pores completely filled with gas and deform linear elastically prior to yielding and perfect plastically after yielding No strain hardening rule was assumed for the plastic model, i.e yield function was assumed to coincide with the failure points Furthermore, it was assumed that in plastic region both the Mohr-Coulomb failure criterion and the equilibrium equation are satisfied Fig illustrates the model used for the sanding analysis, which is a horizontal cylindrical perforation connecting to a vertical wellbore The tunnel and tip of perforations are approximated as thick-walled hollow cylinder and hemi-sphere, respectively The plain strain condition and axial symmetry about the tunnel axis are assumed Fig Idealized geometry of perforation tunnel and tip (Franquet et al., 2005) ACCEPTED MANUSCRIPT The Mohr–Coulomb criterion is the most commonly used strength criterion for geomaterials The Mohr– Coulomb criterion can be expressed in terms of shear stress ( ) and effective normal stress on the shear ′) as follows (Mohr 1900): plane ( + = (1) where So and are the cohesion and internal friction angle of rock, respectively The Mohr–Coulomb criterion can also be expressed in terms of the major and minor effective principal stresses, ′ and ′ : + = the uniaxial compressive strength of the rock and q is a parameter related to internal friction angle ( 1+ 1− = (3) 1− SC Where ): ′ (2) RI PT ′= (4) where M$ = = +! −2 1− N$ = (5) (6) −2 1− (7) TE D − For peak strength, where Mp, Np, M* = ( −2 ( 1− N* = + !( ( −2 1− ( ( ( (8) (9) (10) AC C where = where Mr, Nr, and So are peak strength parameters Similarly: EP − M AN U By rearranging Equation (2), yield: ( and Sor are residual strength parameters For a producing well, - and ( are the maximum and minimum effective principal stresses, respectively (Zoback, 2007) So Equation (8) becomes: ( − - = ( + !( ( (11) The axial dimension of a wellbore is characteristically several orders of magnitude larger than the in-plane dimensions Hence, it is appropriate to assume plane strain geometry for the wellbore model Gradients of gravitational forces are small compared to stress changes in the cross-sectional planes of interest, and therefore ignored These two assumptions lead to the popular plane strain deformation for oil and gas wells (Santarelli et al., 1986; Wang et al., 1991; Bradford and Cook, 1994; McLellan and Wang, 1994; Wu and Tan, 2002; Yi et al., 2004; Sherif, 2010) The equilibrium equation under plane strain condition and at production condition is (Fjær et al., 2008): ACCEPTED MANUSCRIPT (′ + / (′ − / -′ +0 = (12) / Where 0 is the Biot’s coefficient, Cp=1 for perforation tunnel and Cp=2 for perforation tip The flow rule associated with the above yield function (Equation (11)) is (Wang et al.,1991;Yi et al., 2004): 26 (7 = /, 9, :) (13) RI PT 234 = 25 Written in matrix form, the flow rule is: 23( 1+ ( ;23- = = 25 > ( − 1? (14) 23< SC where 25 is a plastic scalar multiplier 3( , 3- and 3< are the radial, tangential and axial plastic strains, respectively 2.1 Stress Solution in the Plastic Region around the Perforation Tunnel M AN U Introducing Equation (11) into Equation (12) and setting Cp=1, the stress solution in the plastic region around the perforation tunnel at production condition is as follows: @A ( / B 2/ + D E / @AB − (15) / ! ( (FG = −0/ @AB C ( ( @A ( / B 2/ + D E (1 − !( )/ @AB − (16) !( (FG / = −0(1 − !( )/ @AB C - ( TE D Where / H is the perforation tunnel radius, is the angular position around the perforation circumference and IJ is the poroelastic stress coefficient defined as and D E − 2K (17) 1−K = ( !( EP IJ = + (1 − 0)LM /H @AB (18) AC C ∆1 = L ( − L (19) Where PPQ is the bottomhole flowing pressure, P$* is the pore pressure at specific radius of formation, P$Q is the farfield pore pressure and K is the Poisson’s ratio ′< , the effective stress component along the axis of the cavity can be obtained by using the plane strain condition in that direction i.e., 3< = 3< + 3