Storage Properties of Porous Media 1. Specific Storage and Storativity Recall Eq 4.8 = !1 Let = (Eq 4.10), where Ss is the specific storage [L ], defined as Ss = A related term, storativity or storage coefficient, is defined as S = So, S = Ss×m, where m is the thickness of aquifer 2. Ss for Confined Aquifer (A) Fluid expansion/contraction (Lecture 5 notes) Y Y (1) ‡ ˆ ˆ (2) Substituting Eq 2 into Eq 1 gives (4.20) Eq 4.20 states that fluid density decreases with decreasing pressure (H2O expands) and increases with increasing pressure (H2O contracts). 1 From Eq 4.10 Assuming incompressible matrix and substituting Eq 4.20 into the above equation gives (4.22) is the Ss value resulting exclusively from expansion or contraction of water when pressure head changes. = 4.8×10!10 m2 N!1 (B) Matrix expansion/compression Following the treatment of fluid, assume (4.25) - bulk compressibility [L2 F!1] - bulk modulus of compression [F L!2] - bulk volume [L3] - effective stress [F L!2] (see Lecture 4 notes) - pore volume [L3] - vertical compressibility [L2 F!1] - modulus of vertical compression [F L!2] Constraints: incompressible grains, 1-D vertical compression, mass conservation for fluids and solids (4.23) When pumping from a confined aquifer, does not change, so Y Replacing partial derivatives with ordinary derivatives in Eq 4.25 and rearranging leads to Substituting into Eq 4.25 yields (4.26) 2 ‡ ˆ Eq 4.26 becomes (4.28) Dividing both sides by and considering = 1 and = 1 yields (4.29) The quantity [L!1], represents the volume of water removed from or added to a unit volume of porous medium when the pressure head declines or increases one unit due exclusively to matrix compression or expansion. listed in Table 4.1. (C) Fluid and matrix effects (4.30) 3. Ss for Unconfined Aquifer – For unconfined aquifer, when h 9, fluid expansion and matrix compression occur but the result is negligible compared to pore drainage –Terms Sy - specific yield, ratio of volume of water that drains by gravity Vwd to total rock volume VT S = Sy = Vwd/VT Sr - specific retention, ratio of volume of water the rock retains against gravity Vwr to total rock volume VT Sr = Vwr/VT n - the total porosity is the sum of Sy, Sr, and ratio of volume of water trapped in dead pores to the total rock volume 3.