Rock Compressibility. Reservoir Pressures. PET467E A Note on Rock Compressibility
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1 Rock Comessiility PET467E A Note on Rock Comessiility M. Onu Sing 007 A esevoi consists of an imevious cove o ca ock ovelying a oous and emeale ock. The density diffeences etween the oil, gas and wate hases can esult in ounday egions etween them known as fluid contacts (oil-wate and gas-oil contacts). Gas (Gas Ca) Oil Wate (Aquife) Ca Rock Gas Oil Contact Oil Wate Contact Oil and Gas Solution Gas Wate Coss-section of a comination dive tye anticline esevoi Resevoi Pessues In a liquid column eesenting vetical oe fluid continuity the essue at any oint is aoximated y the elationshi f,d =D.G l +C whee D is the deth and G l is the essue exeted y unit height of liquid (essue gadient). Fo fesh wate, G l is si/ft (9.79 ka/m, 0 m/atm). Hee, C is a constant. Note: si = ound e squae inch sia = asolute essue, sig = gauge essue
2 Rock Comessiility As sediment uilds u, oveuden essue inceases as ock is comacted. Fo a hydocaon esevoi, the esevoi ock gains ae sujected to extenal essue (stess) due to oveuden and to intenal essue eesented y the fluid essue. Resevoi Pessues Deth Pessue Fluid Oveuden Gain Thee is a alance in a esevoi system etween the essue gadients eesenting ock oveuden essue ( o ), oe fluids essue ( f ) and sediment gain essue ( g ): o = f + g f is also called esevoi essue and a tyical value of oveden essue ( o ) is si/ft Rock Comessiility As esevoi fluids ae oduced, the ock gains may exand causing a eduction in oosity which causes fluid to e exelled. (exansion of ock gains) At the same time, the oveuden may cause a decease in the ulk volume causing fluid to e exelled (ock comaction). In the exteme case, we get susidence. Rock Comessiility Of incial inteest to the esevoi enginee is the change in the oe volume of theockoalsoeffeedtoas effectiveock comessiility o fomation comessiility.
3 Rock Comessiility Effective ock comessiility is dv d( V c = = ) = V d V d d( V ) d( ) d( V d V ) ( ) ( + ) = + V d d V d d whee, is the oe essue, and assumes that oveuden essue () is held constant. Tyical values ae to 5 times 0 6 Effective Resevoi Rock Comessiilities (Hall) extenal essue intenal essue dv d( V ) c = = V d V d Fomation Comaction Comonent of Total Rock Comessiility (Hall) Rock Comessiility Thee kinds of comessiility can e distinguished in ocks: (a) ock matix comessiility (c s ), () ock ulk volume comessiility (c ), (c) oe comessiility (c ) c = ( ) c + c s extenal essue intenal essue dv d( V ) cc = = V d V d 3
4 Rock Comessiility Rock matix comessiility (c s ) is the factional change in volume of the solid ock mateial with a unit change in intenal essue Rock ulk comessiility (c ) is the factional change of ulk volume of the ock with a unit change in intenal essue. Poe comessiility (c ) is the factional change of oe volume of ock with a unit change in intenal essue. A Deivation Fo Rock/Poe/Bulk Comessiilities Fo a fixed extenal essue, and vaying intenal fluid essue (as is done in the exeiments conducted y Hall, we may deive the following exession: ( ) V V s V c = = V Vs V c = c ( ) c = c + c s ( ) c s A Deivation Fo Rock/Poe/Bulk Comessiilities Accoding to Geestma (957), we should teat vaiations of ulk volume and oe volue (o oosity) with esect to oth extenal essue, and intenal essue,. V V dv (, ) = d + d V V dv (, ) = d + d A Deivation Fo Rock/Poe/Bulk Comessiilities Geestma deives: V V = c V V V V c = m V V ( ) V cm = = V m 4
5 A Deivation Fo Rock/Poe/Bulk Comessiilities Geestma definitions: V V c = ; c = V V dvm dvm cm = = = c s V d V d m m ( ) cm c = = = c c = c c [ ] m Notes We can edict change of oosity with essue fom: ( ) = ( )[ + c ( )] o simly = [ + c ( )] As fluid essue deceases to a value fom an initial essue, oosity deceases slightly. Note on Resevoi Temeatues Resevoi temeatue may e exected to confim to the egional o local geothemal gadient. In many asins, this is aound K/m ( o F/00 ft). A figue of 4 o F/00 ft is a high gadient, wheeas 0.5 o F/00 ft is low. Note on Resevoi Temeatues A 5000-ft well in a egion with an aveage amient (suface) temeatue of 65 o F may e exected to have a ottom-hole temeatue of oughly x (/00) = 65 o F It is a easonale assumtion that esevoi condition ocesses tend to e isothemal (temeatue is constant thoughout the esevoi). 5
6 Coelations fo c It is usually the one of the difficult aametes to otain and effective ock comessiilities ae aely measued. Thee ae seveal coelations fo c deending on the ock tye (see Hone s ook Moden Well Test Analysis). c c 6 ( ) 0 6 ( ) 0 = ex x = ex x Consolidated limestones Consolidated sandstones 6
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