This report talks about Application of a Swelling/Shrinkage Model for Analysis of Reservoir Performance at a Field Sit

Siriwardane, H.

Smith, D. H.

UNT Digital Library

Descriptor - include initials, /org#/dateAPPLICATION of a  SWELLING/SHRINKAGE MODEL for ANALYSIS of RESERVOIR PERFORMANCE at a FIELD SITE a presentation byHema Siriwardane* and Duane H. Smithduane.smith@netl.doe.govNational Energy Technology Laboratory, U.S. DOEto theCoal-Seq V ForumHouston, TXNovember 8-9, 2006*Permanent Address: West Virginia UniversityDescriptor - include initials, /org#/dateCH4 desorption causes coal to shrink during coalbed methane production.Shrinkage− increases apertures − increases productivity− may cause small subsidence− under some conditions, decreased pore-pressure effects may exceed effects of swelling, decreasing aperture & productivity.Descriptor - include initials, /org#/dateCO2 sorption causes coal to swell during sequestration/ECBM production.Swelling− decreases apertures − decreases injectivity− may cause small uplift− under some conditions, increased pore-pressure may overcome decreases of aperture & injectivitycaused by swelling.Descriptor - include initials, /org#/dateReservoir engineering studies support practical importance of shrinkage & swelling.• Allison field project interpretationsReeves & Oudinot, ICBM 2005• Simulator comparison studyGunter, Law, Mavor, ICBM 2005• Economic sensitivity studiesGorucu, …, Smith, SPE 97963 355300-510151.5 0.50 00 ..35.412025Descriptor - include initials, /org#/dateChanges in stresses, pore pressure, temperature, or fluid sorption cause matrix strains. σij = stress tensorεij = strain tensorp  = pore pressureG  = shear modulusK  = bulk modulusT  = temperatureαT = coefficient of thermal expansionα = poroelastic constant ijSHijSWijijTijkkijijdpKpfCdpKpfCdpdTKdGKGddδδδαδαδεεσ)()(3)32(221′+′−+−−+=Descriptor - include initials, /org#/datewhere)21(3 ν−=EK• E = modulus of elasticity (Young’s modulus) • ν = Poisson’s ratio)1(2 ν+=EGDescriptor - include initials, /org#/dateDesorption-sorption  shrinkage/swelling hysteresis is allowed by use of a different proportionality constant for each.aswswv dVCd =εdshshv dVCd =εshvεVa =  absorbed volume=  volumetric swelling strainswvε=  volumetric shrinkage strainCsh =   shrinkage constant, for each gasCsw =   swelling constant, for each gas Vd =  desorbed volumeDescriptor - include initials, /org#/dateIn the S/S model, “any” absorption or desorption isotherm is allowed.)(1 pfVa =• f1 and f2 = functions of the gas pressure • f1 need not equal f2 • f1 and f2 need not have same mathematical form • PSU-COALCOMP allows Langmuir, Toth, or UNILAN• Langmuir used in this study)(2 pfVd =Descriptor - include initials, /org#/dateLinear strains are allowed to be anisotropic.zzyyxxV εεεε ++=• εV =   volumetric strain• εxx, εyy, εzz =   linear strains in x-, y-,  z-directions Descriptor - include initials, /org#/datePermeability is assumed to vary with porosity according to the cubic equation: 300 ⎟⎟⎠⎞⎜⎜⎝⎛= φφkk• k = permeability• φ = porosity• K0, φ0 = reference permeability, porosity− Original reservoir state  (CBM)− No sorbed gas  (ECBM)• Palmer & Mansoori, SPE 36737, 1996 Descriptor - include initials, /org#/dateS/S model was added to an existing reservoir simulator.• PSU-COALCOMP• Dual-porosity flow• “Validated” in comparison study• Three isotherm models− Langmuir− Toth− UNILAN• ideal adsorbate solution (IAS) theory • Peng-Robinson equation of state• Langmuir isotherm used in this study.Descriptor - include initials, /org#/dateAssumed Reservoir and Fluid Properties for  Allison Field1-10Skin0.46 ft – 0.58 ftWellbore Radius120oFReservoir Temperature10 days  Sorption time constant250 psiaCO2 Sorption Pressure constant584 SCF/tonCO2 Sorption Volume constant514 psiaCH4 Sorption Pressure constant 400 SCF/tonCH4 Sorption Volume constant1.46 g/cm3Rock Density1650 psiaInitial Reservoir Pressure3440 ftDepth0.2 % - 0.4%Coal-cleat Porosity44 ftReservoir ThicknessDescriptor - include initials, /org#/dateStrategy for Figures 1-5:• Used measured production data for each well.• Bottom-hole pressures calculated (flow rate specified).Descriptor - include initials, /org#/dateFigure 1: Model predictions  (with no SS) matched simulations in the literature.Bottomhole Pressure at Producer well # 130 with porosity 0.2%0200400600800100012001400160018000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Bottomhole Pressure (psi)No Swelling and shrinkageSS ModelARI_Model (Reeves et. al., 2003)ARI_Actual (Reeves et. al., 2003)            SW      SH    CH4   3e-05   3e-05 CO2   1e-04   1e-04Descriptor - include initials, /org#/dateFigure 2: Model (without SS) gave good fit to the measured pressures (producer well # 130).Bottomhole Pressure at Producer well # 130 for No Swelling and Shrinkage case 0200400600800100012001400160018000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Bottomhole Pressure (psi)Porosity 0.2%Porosity 0.3%Porosity 0.4%ARI_Model(Reeves et. al., 2003)ARI_Actual (Reeves et. al., 2003)Descriptor - include initials, /org#/dateFigure 3: 0.2% porosity (no SS) gave good fit to the measured pressures (producer #113).Bottomhole Pressure at Producer well # 113 with no swelling and shrinkage0200400600800100012001400160018000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Bottomhole Pressure (psi)Porosity 0.2%Porosity 0.4%ARI_Model (Reeves et. al, 2003)ARI_Actual (Reeves et. al, 2003)Descriptor - include initials, /org#/dateFigure 4. Fit appeared better without Swelling/Shrinkage (0.2% porosity, Well #113).Bottomhole Pressure at Producer well # 113 with porosity of 0.2% 0200400600800100012001400160018000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Bottomhole Pressure (psi)SS3SS1SS2ARI_Model (Reeves et. al., 2003)ARI_Actual (Reeves et. al., 2003)SS1 SW       SHCH4  8E-05    8E-05CO2  4E-04    4E-04SS2SW       SHCH4  3E-05    3E-05CO2  1E-04    1E-04SS3            SW        SHCH4      0           0CO2       0           0Descriptor - include initials, /org#/dateFigure 5. However, for 0.4% porosity fit was better with Swelling and Shrinkage (Well #113).Bottomhole Pressure at Producer well # 113 with porosity 0.4%0200400600800100012001400160018000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Bottomhole Pressure (psi)No Swelling and ShrinkageSwelling/Shrinkage_SS ModelARI_Model (Reeves et. al., 2003)ARI_Actual (Reeves et. al.,2003)Swelling and Shrinkage               SW          SHCH4    3E-05      3E-05CO2    1E-04      1E-04Descriptor - include initials, /org#/dateStrategy for Figures 6-11:• For each well, bottom-hole pressures before ~3500 days were calculated to fit production data.• After 3500 days, measured bottom-hole pressures were used (with slight adjustments to fit measured production data).• Same Shrinkage (CSH) and Swelling (CSW) Constants (ton/scf) used in all fits: SW SH CH4 3 x 10 -5 3x 10 -5 CO2 1.2 x 10 -4 1.2 x 10 -4  Descriptor - include initials, /org#/dateFigure 6: Fit to Total Gas Production Rate was good with No Shrinkage or Swelling.01000020000300004000050000600000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Gas Production Rate (MCF/day)MeasuredComputedDescriptor - include initials, /org#/dateFigure 7: Fit to Total Gas Production Rate was somewhat better with Shrinkage and Swelling.01000020000300004000050000600000 360 720 1080 1440 1800 2160 2520 2880 3240 3600 3960 4320Time (days)Gas Production Rate (MCF/day)MeasuredComputedDescriptor - include initials, /org#/dateFigure 8: SS model with reported Elastic Modulus gave excellent fit to Total Production. 010000200003000040000500006000070000800000 500 1000 1500 2000 2500 3000 3500 4000 4500Time (days)Total Gas Production Rate (MCF/day)Measured493 ksi521 ksi725 ksiDescriptor - include initials, /org#/dateFigure 9: Did CO2 injection reduce the elastic modulus? (Well # 113)0.E+001.E+062.E+063.E+064.E+065.E+066.E+067.E+068.E+069.E+060 500 1000 1500 2000 2500 3000 3500 4000 4500Time (days)Gas Production Rate (SCF/day)493 ksi521 ksi725 ksiMeasuredDescriptor - include initials, /org#/dateFigure 10: Porosity 0.2% gave best fit to production data (Well # 113).0.E+001.E+062.E+063.E+064.E+065.E+066.E+067.E+060 500 1000 1500 2000 2500 3000 3500 4000 4500Time (days)Gas Production Rate (SCF/day)MeasuredPorosity - 0.2Porosity - 0.25Porosity - 0.3Descriptor - include initials, /org#/dateFigure 11: Porosity 0.2% also gave best fit to Total production data. 01000020000300004000050000600000 500 1000 1500 2000 2500 3000 3500 4000 4500Time (days)Total Gas Production Rate (MCF/day)MeasuredPorosity - 0.2Porosity - 0.25Porosity - 0.3Descriptor - include initials, /org#/dateS/S model introduces additional generality into swelling/shrinkage chemistry & geomechanics.• CH4 desorption shrinks coal, increases apertures & productivity, may cause ground movements.• CO2 sorption swells coal, decreases apertures & injectivity, may cause ground movements.• SS model allows different isotherms for sorption & desorption, strain hysteresis, strain anisotropy, different amounts of sorption-induced strain for different fluids.Descriptor - include initials, /org#/dateThe SS model was used to investigate the influence of coal swelling/shrinkage on sequestration.• Porosity, Swelling and Shrinkage Constants all had a significant influence on the computed bottom hole pressures at Allison field.• An increase in porosity lowered the bottom hole pressure.• An increase in shrinkage constant increased the bottom hole pressure.• An increase in swelling constant decreased the bottom hole pressure.Descriptor - include initials, /org#/dateWhich of phenomena in the S/S model are not needed?  What effects should be added?Delete?Sorption/desorption isotherm hysteresis.Different strain proportionality constants for shrinkage and swelling.Strain anisotropy (x, y, z).Add?Sorption-dependent elastic constants.Explicit effective cleat-apertures.etc.

Application of a Swelling/Shrinkage Model for Analysis of Reservoir Performance at a Field Site

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Application of a Swelling/Shrinkage Model for Analysis of Reservoir Performance at a Field Site

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