USC_Sec_3_Petrophysics_ppt

USC_Sec_3_Petrophysics_ppt - PTE-461 Formation Evaluation...

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Unformatted text preview: PTE-461 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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= PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 9 Tri-Cone 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 climate-controlled 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 29 Reservoir-Specific Formation Factor Models Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 34 Leverett J-Function Pc J sw = Cos k 0.22Pc = Cos k Jsw is the Leverett J-Function 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 PTE-461: 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 37 J-Function 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 38 Stress-Strain Relationships-1 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 39 Stress-Strain Relationships-2 F = , A L , l = L d , t = d L = tan s = L ij = sijkl kl , ij , = c ijkl kl . PTE-461: 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 + PTE-461: 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 PTE-461: 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 PTE-461: 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 semi-linear 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 PTE-461: Fall 2007 Section 3: Petrophysics Raymer, Hunt, Gardner Acoustic Porosity Transform RHG = RHG 1 t t ma Based on (well log) observed sandstone t - cross-plots 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 45 Schlumberger Sonic Porosity Nomogram S ( ss) 1.0218 + 0.02544 t 0.00013355 t 2 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 51 Simandoux Shale Volume Shaly-Sand 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 52 Waxman and Smitts Electro-Chemical Shaly-Sand Model Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 53 Waxman & Smitts Formation Factor-1 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 54 Waxman & Smitts Formation Factor-2 Assumption 3: For Clean Sands: Ce 0, and : F* F= Ro Cw = . Rw Co Using Electro-Chemical Notation: Co = 1 (BQv + Cw ), F* where : CEC Vp PTE-461: 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 Factor-3 And: B= [1 1000 e Na e Na e Na ae (C w / ) , a =1 ( )' , e Na where : e Na =( )' PTE-461: 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 Factor-4 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 58 Shaly-Sand Summary The Simandoux Shaly-Sand model is an example of a Shale Volume, Vsh, Shaly-Sand model: It is probably one of the simplest and easiest to understand of all shaly-sand models. The Waxman & Smitts Shaly-Sand model is the prime electro-chemical, 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 PTE-461: 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 PTE-461: Fall 2007 Section 3: Petrophysics Slide No.: 60 ...
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