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~~J._.LL~L..
<br />J
<br />ruck
<br />~!~.
<br />~~i!
<br />m-
<br />
<br />,~ ?a
<br />ulomb
<br />.r mod-
<br />erative
<br />calcu-
<br />values
<br />n, bulk
<br />7 r-Cou-
<br />~r each
<br />eI time
<br />iity) of
<br />:oustic
<br />he rock
<br />iuation
<br />e sam-
<br />I with
<br />nbined
<br />the ter-
<br />n 3).a
<br />nbined
<br />dynamic modulus at o=0
<br />psi and any assumed rea-
<br />sonable value for ~ (Equa-
<br />tion 4).
<br />• Estimate the bulk modu-
<br />lus, K, from Ro from Table 2.
<br />The correlation can be found
<br />in the literature.°$
<br />• Calculate the "a" value
<br />for a plot of shear modulus
<br />vs. stress. Compare this val-
<br />ue with the "a" value calcu-
<br />lated from the Ivtohr-Cou-
<br />lomb strength plot (Equa-
<br />tions 5 and 6).
<br />The elastic identity R =
<br />(4/3)G + K is used, assum-
<br />ing the rock is homogeneous
<br />and isotropic. The rock ma-
<br />trix is assumed to be rigid,
<br />and the bulk modulus is as-
<br />sumed to remain constant
<br />with changing stress. Only
<br />R or G values may Change
<br />with stress (as in the proce-
<br />dure for partial differential
<br />equations).
<br />If the two values for "a"
<br />from Equations 5 and 6 are
<br />different, a new value for y
<br />is assumed in the third step.
<br />This iterative procedure
<br />sTiould be continued until
<br />the two "a" values match.
<br />• Calculate Go = (3/4)(R,
<br />- K). The angle of the G vs.
<br />o plot is (3/4)tan y.
<br />Table 3 lists the calculated
<br />values of G, and the shear
<br />modulus values for fire
<br />limestone samples reported
<br />by Wuerker.7
<br />The original lvork did net
<br />note the stress conditions
<br />when the dynamic modulus
<br />values were measured. It is
<br />likely that some stress lyai
<br />applied because these values
<br />were greater than the calcu-
<br />lated Go values by an aver-
<br />age algebraic difference of
<br />71 ;'a.
<br />Fig. 5 is a plot of dynamic
<br />modulus values calculated
<br />with the iterative procedure
<br />for limestone samples. usin~;
<br />a format convenient for wn-
<br />verting modulus data in'o
<br />equivalent 1`•tohr-Coulomb
<br />equations.
<br />The s-axis is the tangent of
<br />the shear modulus vs. stress
<br />plot. The }'-axis is the Mohr-
<br />Coulomb strength plot at a
<br />vertical stress eq~to 0 psi
<br />als. Geotechnical, and Grouna
<br />Nave AppLca dons. Las Vegas,
<br />Oct. 2-B, 1959.
<br />S. Dobrin, \LB, tntrnduction to
<br />Geophysical Prospecting.
<br />\ICGraw-Hill Book Co . New
<br />York. 195?.
<br />~. Stein, N., '?Ixch~rnic.+l Properties
<br />of Friable Sands from Conven-
<br />tional Log Data," Journal of Pe-
<br />troleum Technology. July 1976.
<br />S. Stein, N.. "Estimate Formation
<br />Strength C"sing Log Data,"
<br />lyorld Otl. November 1957.
<br />fi. Stein, N.. "How 7o Calculate
<br />Fracture Pressures From Wtll
<br />Logs," Petwieum Engineer, Au-
<br />gust 19tH.
<br />;, lyuerker. R.G., "Annotated Ta-
<br />bles of $trxngth and Elastic Prop-
<br />erties of Rucks." Petroleum
<br />TranssNoni Reprint Series, No.
<br />6. Drilling, 196.
<br />F. "Lug Interpretation Prinriples;'
<br />Bchlumbercer Ltd., Vcl. 1, 197?.
<br />9. Srxin, N., "Fxsisticib' and density
<br />logs kxy to Bind pressure esti-
<br />mates." OG7..4pr. 6, 195?.
<br />New systems
<br />used to speed and
<br />protect packaging
<br />U.$. CuIE Coast polyethyl-
<br />ene now heads overseas
<br />from a new state-of-the-art
<br />polyolefins packaging/distri-
<br />bution center in operation at
<br />La Porte, Ter. The~~facilit}~,
<br />built and operated by Ryan-
<br />4Valsh, amember of the Vec-
<br />hlm Group lnc.,~is~nest to
<br />the Port of Houston's con-
<br />In log measurements at
<br />stress levels less than termi-
<br />nal stress, Fig. 5 may be
<br />used to determine the pfohr-
<br />Coulomb strength plots
<br />In log measurements at
<br />depths with stresses greater
<br />than the terminal stress, the
<br />actual stress level is not
<br />needed.
<br />The well log data at the
<br />rock depth may be consid-
<br />ered to 6e at terminal prop-
<br />erty conditions. A value for
<br />tan p wilt be assumed to
<br />obtain the terminal stress
<br />from Fig. 4. The calculation
<br />procedure described in this
<br />article may then be applied.
<br />References
<br />1. K'~Ilie, b1.R.j., Gregoq', A.R,
<br />and G.vdna. G.H.F., "An E~-
<br />penmental Investigation of Fal-
<br />ters Affmting Elastic 4t'a ve l'x-
<br />bities in Porous Media," Gea
<br />ph+'sits. bbl. 13, Na3, 19 ~5.
<br />7. Stein, N., "Porosity of FriaFlx
<br />Sand Using Acoustic Pave \'e-
<br />Incit}'," Presxnted at thx Third
<br />International Symposium on
<br />borehole Geophysics for }hner-
<br />77re Nnaer Fonrr, Fitl 6 Sent packnging sys- Ryan-{1'nlsh uses ~a ~ Benuiner ~ Stretch-Hood
<br />tern yroduces nad fills thennoplnstie flnt or sys tern to rueather-proof and sentre~ loads,
<br />grtsseted bogs nt 1,000-1,200 rnrrts per hour. alto pn)lets.
<br />tainer terminal, the largest
<br />container port on the L'.S
<br />Gulf Coast. Tu-o key sys-
<br />tems are a Haver Form, Fill
<br />g Seal (FF&S) packaging
<br />unit and a Beauma slret:h-
<br />hood system.
<br />The FF&5 is a high-tapad-
<br />tv unit designed to package
<br />free tlolving, granular e.nd
<br />pellet pol}'ethylene or poly-
<br />propyleneinto flat or gusset-
<br />ed bags. The bags are pro-
<br />duced by the unit itself out
<br />of a roll of thermoplastic
<br />tube stock. The output ca-
<br />padty ranges from 1,000 to
<br />1,200 bags/ hr.
<br />The Beaumer Stretch-
<br />Hood system is a fully auto-
<br />maHc, computer-controlled
<br />machine. It puts a single ply
<br />pol}'eth}'lene hood, or cover,
<br />over the pallet, normally car-
<br />n-ing 40 bags of 25 kg each,
<br />or 1 metric ton, and provides
<br />stable~Peather protection for
<br />leaded pallets.
<br />This is the first use of the
<br />system in the U.S.
<br />2F. l99? F ~ Der 19. t99'_ • 0.1 d Gas Journal -~ - ~ - 99
<br />
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