Train Load. Examples of Aquifer Elasticity. Outline. Oscar E. Meinzer 1928, Compressibility and elasticity of artesian aquifers 6/30/2006

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1 Poroelsticity of Frctured Rock Outline Herb Wng Geology nd Geophysics UW-Mdison Exmples of poroelstic behvior Constitutive Equtions of Single Porosity Medium Constitutive Equtions of Dul Porosity Medium Consolidtion of Dul Porosity Medium Applictions to Brometric Loding nd Reservoir Seismicity AIST, Tsukub, July 3, 2006 Dkot Sndstone Aquifer Drought nd into 90 s led to 10,000 wells in S. Dkot nd 8000 wells in N. Dkot by Powell 1891 testified before Congress s to whether or not rtesin wter of the Dkot sndstone ws dequte to develop the whole Americn west. N. H. Drton 1897 Preliminry Rept. On Artesin Wters of Portion of the Dkots Woonsocket rtesin well flowed 8000 gl/min (30.4 cubic meters/min) nd hd pressure of 153 psi (1 MP). Oscr E. Meinzer 1928, Compressibility nd elsticity of rtesin quifers Averge withdrwl of 3000 gl/min (11.4 cubic meters/min) for 38 yers between 1886 nd 1923 from 6 townships (36 sq. miles = 93 sq. km) Q = KIA = 500 gl/min (1.9 cubic meters/min) s rechrge from Blck Hills. Where is the other 2500 gl/min (10.5 cubic meters/min)? Exmples of Aquifer Elsticity Trin Lod Mechnicl lods (trins, brometric pressure, ocen tides, erthqukes) ffect wter levels Fluid pressure chnges induce seismicity in reservoir lkes Fluid extrction produces subsidence Reverse wter-level fluctutions 1

2 6/30/2006 Induced Seismicity: Monticello Reservoir, SC (Tlwni, 1997) Subsidence due to Fluid Extrction Coseismic Pore Fluid Pressure (Msterlrk) Distnce, km (North) 1992 Lnders nd Big Ber Erthqukes Distnce, km (Est) Poroelstic Coupling Reverse Wter-Levels 1992 Lnders 1992 Big Ber Erthqukes Slip Potentil, S S = σs + f (σn +P ) Distnce, km (North) S (MP) Distnce, km (Est) 50 Lngguth, H. R., nd C. Tresktis (1989) 2

3 Poroelsticity * : Geomechnics meets Hydrogeology Solid-to-fluid coupling occurs when chnge in pplied stress produces chnge in fluid pressure (trin, brometric pressure). Fluid-to-solid coupling occurs when chnge in fluid pressure produces chnge in the volume of the porous mteril (subsidence). *Anlogous to thermoelsticity but temperture coupling is importnt in only one wy: therml stresses brek rocks but pressing on rock does not increse its temperture very much. Increment of Fluid Content ζ Increment of fluid content is the volume of fluid dded t reference pressure to n REV divided by the volume of the REV. This volume of wter is not just the pore volume it occupies due to its compressibility. ζ is nlogous to quntity of het in thermoelsticity Biot s Constitutive Equtions for Isotropic Stress Blloon Lb/Demo 1. Add Vf to empty blloon to height h 1 nd volume V 1. "To interpret the constnts H nd R consider smple of soil enclosed in thin rubber bg so tht the stresses pplied to the soil be zero. Let us drin the wter from this soil through thin tube pssing through the wlls of the bg. If negtive pressure -p o is pplied to the tube certin mount of wter will be sucked out. This mount is given by ζ = -p o /R. Biot (1941) 2. V b = V f V 1 3. Add V f nd record h 2 nd V 2. V f = V b + (V2 V1) 4. ζ = [ V f (V 2 V 1)]/V b 5. S = ζ/(h 2 h 1) 1/R is nlogous to specific het t constnt pressure in thermoelsticity. Effect of Stress/Strin BC s on Stortivity Anlogous to difference between specific het t constnt volume vs. t constnt pressure If perfectly tight nd inelstic tnk were filled with wter under gret pressure nd were then tpped, only minute quntity of wter, equl to the expnsion of the wter itself, would hve to be dischrged in order to relieve ll the pressure. On the other hnd, if the tnk were mde of elstic mteril, such s rubber, the dischrge would continue t constntly diminishing rte, until the strin of the wlls of the tnk would be lmost completely relieved Meinzer (1928) 3

4 Elstic properties of rocks t core scle cn be pproximted to be double porosity. Stress Formultion for Double Porosity Medium Wet Dry Spirit River Sndstone Velocities (Murphy, 1982) Velocity vs. pressure curve is pproximtely biliner Low pressure slope is closure of crck (soft) porosity High pressure slope is closure of equnt (stiff) porosity Wter in pores stiffens rock both in P nd S House Creek sndstone, Powder R. Bsin Dul-Porosity Constitutive Equtions (Coefficients) Skempton s Coefficient B = p f /p c Single porosity: B = p f /p c 11 is drined compressibility 12, 13 re poroelstic expnsion coefficients 22, 33, 23 re poroelstic storge coefficients Berrymn nd Wng (1995) show how these six constnts cn be determined from the 3 constnts mesured on core, joint stiffness of single frcture, nd the ssumption the cross-storge coefficient 23 =0. Double porosity: Two Skempton s Coefficients: p / p < p / (1) f c (2) f p c Double porosity piston effect of Elsworth nd Bi (1992) due to ssm. A 23 = 0. 4

5 12 6/30/2006 Consolidtion of A Double-Porosity Column Pressure Profiles in Frctures versus Mtrix Higher loding efficiency in frcture phse initilly rises fluid pressures in mtrix bove its undrined response Assumption tht A 23 = 0 leds to the unphysicl result tht pore pressure buildup exceeds pplied stress. Effective Stress Lw (continued) β β p f = =

6 150-m deep, 6-cm dimeter borehole in frctured volcnics [Desbrts et l., WRR, 1999] Frcture density (no./ m) Decresing brometric efficiency cn be due to: Horizontl wter flow to well Upwrd wter flow in quifer to wter tble Downwrd ir flow in unsturted zone Or decresing brometric efficiency cn be due to unrelxed pore pressures with different time constnts Desbrts et l. (1999) ssumed δe (1) = 0 when δp c = δp f (1) -- OK for very low mtrix porosity Instntneous Undrined Undrined, Locl Equilibrium Frcture Dringe Stiffest Nerly s Stiff Less Stiff Desbrts et l. inversion of instntneous brometric efficiency gives effective stress coefficients β p = 0.10 nd β f = Induced Seismicity t Koyn, Indi Criticl filling rte > 40 ft/week triggers erthqukes of mgnitude > 5.0 in 1967, 1973 nd Eq s of mgnitude >5 generlly do not occur for filling rtes < 40 ft/week. Flse positives occurred in 1969 nd Could be explined by pressure bleed-off from frctures to mtrix. Gupt, BSSA, 1983 Conclusions Double-porosity constitutive equtions re rigorous extension of Biot s originl equtions for single porosity Skempton effect in double-porosity medium induces differentil pore pressures in frcture nd mtrix phses. Locl flow between frcture nd mtrix pressures introduces new time constnt dependent on size of mtrix blocks nd mtrix diffusivity. Time-dependent brometric efficiency, rock elsticity, nd rte-dependent induced seismicity re possible pplictions of double-porosity theory. 6