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Unformatted text preview: PTE461
Formation Evaluation Fall Semester, 2007
Section 3 Petrophysics Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 1 Petrophysics Study of Physical Properties of Rocks & their Fluids Formation Evaluation Porosity Fluid Saturation Type of fluid(s) Permeability
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 2 Porosity Relative Amount of Void Space in a Rock is porosity (fractional or %) Vp is Pore volume Vb is Bulk Volume Vgr is Grain Volume = 100 = 100 = 100 Vp Vb Vb Vgr Vb Vp V p + Vgr , , Vb = V p + Vgr
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 3 Fluid Saturation Relative Amount of fluid in Pores (Fractional or %) Vw is water volume Vo is oil volume Vg is gas volume Vw Sw = 100 , Vp Vo So = 100 , Vp Vg Sg = 100 . Vp
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 4 V p = Vw + Vo + Vg
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Permeability Measure of ease in which a fluid can pass through a rock Q is fluid flow vector P) is pressure gradient vector is fluid viscosity k is rock permeability tensor Q= k P Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 5 Resistivity Difficulty of electrical current passing through a rock E is electric field vector J is current density vector R is rock resistivity tensor is rock conductivity tensor E = RJ or : J= E R=
PTE461: Fall 2007 Section 3: Petrophysics 1
Slide No.: 6 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Bulk Density The density of a rock (including fluids) RHOB = B is bulk density m is mass Vb is bulk volume is porosity ma is matrix (grain) density f is fluid density RHOB =
B B m = Vb = f + (1 ) ma Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 7 Hydrogen Index Measure of hydrogen ion density compared to that of water HIB is bulk hydrogen index H+ are hydrogen ions Vb is bulk volume w is water molecular density is porosity f is fluid hydrogen index HIma is matrix (grain) hydrogen index
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com HIB = 1 2 H+
Vb w Vb HIB = HI f + (1 ) HIma PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 8 Acoustic (Sonic) Velocity Speed at which sound waves will pass through a rock V is acoustic velocity t is acoustic interval transit time (inverse velocity) V & t can be anisotropic
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com 1 V= t
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 9 TriCone Bit Three sets of rollers, with cutting teeth Rotating bit  teeth bite into rock Jets allow drilling fluid to Cool the cutting teeth Lubricate the cutting teeth Remove cuttings and bring them to the surface Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 10 Side Wall Cores (SWC) Hollow bullets Shot into borehole from a W/L gun Return small samples Allow larger than cuttings samples from specific depths of interest
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 11 Core Barrels & Bits Core Barrel  Specialized Drill Collar Open Bit with Core Catcher at bottom Newer Core Barrels have Liners
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 12 Low Flow Core Bits Liner protects core from drilling fluid Mud jets positioned to reduce mud filtration invasion of the core Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 13 Friable & Unconsolidated Core Handling Careful wellsite core handling required Core & liner removed from Core barrel Core and liner cut into short sections for preservation, transportation & storage
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 14 Core Preservation & Slabbing Core segment drained, capped , and annulus filled with resin, for transport & storage Core kept in climatecontrolled storage at temperatures above freezing, until used Preserved core slabbed for visual examination, measurement sample plugging & photography
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 15 Core Handling Comparison Core on left was obtained, using normal protocols Core on right was obtained, using special friable coring,core handling, preservation, transport, and storage protocol Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 16 Routine Core Analysis Dean Stark Cleaning Porosity, Permeability & Saturation (PKS) Helium Porosity Air Permeability Residual Hydrocarbon Saturation Often include (as add on services): Grain Density Whole Core Gamma Ray Scan KH & KV Core Photography
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 17 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Dean Stark Core Cleaning Plug sample placed above heated solvent Vaporized solvent, oil, and water from core passes into condenser Condensed oil & water collects in graduated tube
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 18 Dean Stark Summation of Fluids is Porosity VR is sample (rock) volume Vw is water volume Vo is oil volume Sor is Residual Oil Saturation Swf is Flushed zone Water Saturation
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Vw + Vo = , VR Vo Sor = , Vo + Vw Vw Swf = Vo + Vw
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 19 Grain Density
g = ma mg = Vg g = ma is grain (matrix) density Vg is (total) grain (matrix) volume, from Helium Porosimeter mg is (total) grain (matrix) mass (dry weight)
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 20 Helium Porosity vs. Air Permeability Used to select porosity cutoffs, for reservoir rocks Based on permeability values Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 21 KV vs. KH Used to evaluate reservoir anisotropy Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 22 Composite Core and wireline interpretation ads value to the result Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 23 Special Core Analysis Laboratory (SCAL) Measurements Restored net overburden Ka & He Liquid permeability, Kl Relative permeability, Kr Capillary pressure, Pc Formation factor, F Resistivity index, I
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 24 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Least Squares Regression
y = mx + b m=
2 x xy 2 x = 1 n j =1 n 2 (n 1)
1 (x j x ) )( = 1 n n 2 (n 1)
y = x2 j
j =1 j =1 n xj 1 n
n n xy = (n 1)
mx j =1 (x j x yj ) 1 (n 1) x jy j
j =1 xj
j =1 j =1 yj b= y x is the independent (known) variable y is the dependent (unknown) variable, subject to error
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 25 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Maximum Likelihood or Reduced Major Axis (RMA) Model
y = mx + b m=
2 x y x = 1 n j =1 2 (n 1)
mx (x j x ) = 1 n n 2 (n 1) x2 j
j =1 j =1 xj b= y Both y and x are subject to error RMA line is main axis of data ellipse
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 26 Restored Net Overburden Ka & HE Ambient condition measurements include expansion cracks  Optimistic Ka & He values RNO measurements close those cracks  More realistic values
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 27 Formation Factor Ro F= =a Rw m Rw is water resistivity Ro is resistivity of rock saturated with water
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 28 Archie Equation Models Completely empirical Archie: a = 1, m = 2 Winsauer: a = 0.62, m = 2.15 Humble: a = 0.81, m = 2.00 Phillips: a = 1.45, m = 1.54 Timur: a = 1.13, m = 1.73 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 29 ReservoirSpecific Formation Factor Models Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 30 Formation Factor Models Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 31 Resistivity Index Rt n I= = Sw Ro Archie value of n = 2 is widely accepted Values of 1.5 < n < 2.3 have been reported
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 32 Reservoir Specific Resistivity Index Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 33 Capillary Pressure 2 Cos Pc = r Pc is capillary pressure is interfacial tension between wetting and nonwetting phase is the contact angle at the matrix r is the pore throat radius
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 34 Leverett JFunction Pc J sw = Cos k 0.22Pc = Cos k Jsw is the Leverett JFunction Pc is capillary Pressure is interfacial tension is contact angle
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 35 Facies Variability & Heterogeneity Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 36 Confirmation of W/L Predicted High Recovery Factor Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 37 JFunction Sw overplotted on W/L Sw estimates increases confidence in both estimates Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 38 StressStrain Relationships1 Stress=Force/Unit Area Strain=Distortion/Original Dimension or Shape
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 39 StressStrain Relationships2
F = , A L , l = L d , t = d L = tan s = L ij = sijkl kl ,
ij , = c ijkl kl .
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 40 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Elastic Moduli
Young' s _ Modulus : ( 3 + 2 ) = 3K (1 2 ) = 2G(1 ) + l t Shear _ Modulus :
E=
l = t = G= s = E 2(1 + ) 3K (1 2 ) 2(1 + ) Poisson' _ Ratio 1 E = t = = 2 6K 2( l Bulk _ Modulus : K= G) 2G(1 + ) p E = = V V 3(1 2 ) 3(1 2 ) Lam' s _ Constant : = E 3K = (1 + )(1 2 ) 1 + PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 41 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Compressional (Dilatational) Waves 2 = 1
2 2 t 2 , = K + 4 3G
Slide No.: 42 = vp =
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com + 2G PTE461: Fall 2007 Section 3: Petrophysics Shear (Transverse) Waves 2 A= G 1
2 2 A t2 =
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 43 Wylie Time Average Equation
Wyl 1 = cp t tf t ma t ma There is no Macroscopic relationship between and V or t There is a semilinear relationship between and observed t, over short ranges cp is arbitrary (adjustable) coefficient, with: 1.0 < cp < 1.6
Slide No.: 44 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Raymer, Hunt, Gardner Acoustic Porosity Transform
RHG = RHG 1 t t ma Based on (well log) observed sandstone t  crossplots from several wells RHG is arbitrary constant, with 0.4 < RGH < 0.8 (RHG 0.625 seems to work quite well
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 45 Schlumberger Sonic Porosity Nomogram S ( ss) 1.0218 + 0.02544 t 0.00013355 t 2
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 46 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Schlumberger NaCl Equivalent Salinity Nomogram Note: Horizontal axis is in TDS.
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 47 Schlumberger Arps Equation Nomograph Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 48 NaCl Dissociation in Water Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 49 Formation of Double Layer Adjacent to Clay Minerals Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 50 Effects of Double Layer at Pore Throat Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 51 Simandoux Shale Volume ShalySand Model
Archie :
n 1 Sw m = Rt aRw Simandoux : m V ( 1 2 e = Sw( n 2) + sh Swn 2) Rt aRw (1 Vsh ) Rsh 0= m e aRw (1 Vsh ) Vsh Rsh
2 2 Sw( n 2) + Vsh ( n 2) Sw Rsh 1 Rt Vsh Rsh ( Swn 2) = 4 em 1 + aRw (1 Vsh ) Rt 2 em aRw (1 Vsh ) Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 52 Waxman and Smitts ElectroChemical ShalySand Model Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 53 Waxman & Smitts Formation Factor1 Assumption 1: Parallel current pathways in double layer and free pore fluid Ct = xCe + yCw Assumption 2: Geometric factors for both current pathways are the same 1 x=y= , F* or : 1 Co = (Ce + Cw ) F*
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 54 Waxman & Smitts Formation Factor2 Assumption 3: For Clean Sands:
Ce 0, and : F* F= Ro Cw = . Rw Co Using ElectroChemical Notation:
Co = 1 (BQv + Cw ), F* where : CEC Vp
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 55 Qv =
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Waxman & Smitts Formation Factor3 And:
B= [1 1000
e Na e Na e Na ae (C w / )
, a =1 ( )' ,
e Na where :
e Na =( )'
PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 56 when : Cw = 0.
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Waxman & Smitts Formation Factor4 For Very Fresh Waters:
Cw e
(C w / ) 0, 1,
e Na and : Ce ( )' Q .
1000
v For Very Saline Brines: Cw e >> 1, 0,
e Na (C w / ) and : Ce =
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com 1000 Qv .
Slide No.: 57 PTE461: Fall 2007 Section 3: Petrophysics W&S Summary W&S Formation Factor:
1 Co = (BQv + Cw ), F* B=
e Na [ 1000 1 ae (C w / )
. W&S Resistivity Index:
Rt Co G * = = = Swn* , Ro Ct F * Cw G* = . Ct I=
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 58 ShalySand Summary The Simandoux ShalySand model is an example of a Shale Volume, Vsh, ShalySand model: It is probably one of the simplest and easiest to understand of all shalysand models. The Waxman & Smitts ShalySand model is the prime electrochemical, EC, shaly sand model: It summarizes most of the prior EC data, and is the model against which all more recent models are tested. Neither the Simandoux or W&S models account for current leakage between the free fluid and double layer.
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 59 Capillary Pressure Laboratory Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 3: Petrophysics Slide No.: 60 ...
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