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Unformatted text preview: PTE461
Formation Evaluation Fall Semester, 2007
Section 5 Resistivity Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 1 Why Run Well Logs For stratigraphic and structural correlation To be able to identify pay zones To quantify reserves estimates Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 2 Electrical Properties & Electric Field Vectors Force, F, Electric Field, E, Electric Displacement, D, & Polarization, P, are all vectors (first rank tensors) and are directional. Electric Charge, q is a scalar (zero rank tensor) and has no directional properties Electrical Permittivity, , and dielectric constant, e, are second rank tensors, and are directional Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 3 Magnetic Properties and Magnetic Field Vectors Force, F, Magnetic Field Intensity, H, Magnetic Induction, B, Magnetic (macroscopic) Polarization, M, and Magnetic dipole, m, are all vectors (first rank tensors) and are directional. Magnetic permeability, , and relative magnetic permeability, m, are second rank tensors and are directional.
PTE461: Fall 2007 Section 5: Resistivity Slide No.: 4 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Circuit Element Analogues Resistance: linear response current is in phase with voltage Capacitance: Current opposes voltage changes Current lags voltage Inductance: Voltage opposes current changes Current leads voltage
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 5 DiskShaped Measurement Sample Current density is distorted at sample edges Sample geometrical factor is given by: S' G= L
where: S' is the electrode area, corrected for E distortion, at the edges Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 6 Guarded (Disk) Sample Holder Center electrode and outer ring maintained at same potential, relative to full disk electrode Current density distorted at edge of outer electrode, only Geometrical factor is: So G= L
Note: There is no E distortion correction needed for So
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 7 Cylindrical Shell Sample Cylindrical sample Center bored out Inner & outer sample surfaces are concentric cylinders Electrodes placed on inner and outer wall Cylindrical analogue of disk sample Current density distorted at top and bottom edges of electrodes
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 8 Guarded Cylindrical Electrode Inner electrode replaced with three rings, held at same potential difference from outer electrode Cylindrical analogue of guarded disk electrode sample holder Current density distortion is only at top and bottom of electrode system No current density distortion from the center electrode
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 9 Point Electrode Relationships In Subsurface
V 4 R=G = I rB 4 rA V I At Surface
V 2 R=G = I rB
PTE461: Fall 2007 Section 5: Resistivity 2 rA V I Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Slide No.: 10 Surface Resistivity Array V R=G =2 I 1 rAM 1 rBM 1 rAN 1 rBN 1 V I Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 11 Schlumberger Array V R=G = I
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com rAM rBM rBM rAM
PTE461: Fall 2007 Section 5: Resistivity V I
Slide No.: 12 Equipotential Surfaces & Current Density Flow Sheets Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 13 Schlumberger Sounding Type Curves Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 14 Resistivity Profiling Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 15 Pechelbronn Well Electrode Array Surface Schlumberger Array,dropped down a borehole Technique was analogous to surface resistivity profiling Log Measure point at center of array Required L/2 "Rat Hole" below deepest formation of interest Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 16 How It all Began
After exhausting the Fr 500,000, from their father and both their wives Dowries, a precursor of Shell asked The Schlumberger brothers to drop their surface electrode array down a borehole at Pechelbronn Field, France Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 17 Where The Drill Goes, Schlumberger Will Follow Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 18 "Resistivity Log" Curves Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 19 Normal Array One Half of Schlumberger Array downhole Current return (B) electrode at surface Potential reference electrode (N) at surface Log Measure point is half way between A & M electrodes Only AM/2 "Rat Hole" needed
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 20 Lateral Array Attempt to overcome normal array resolution  investigation depth dilemma Three electrodes (A, M, & N)downhole MN spacing governs resolution AO spacing governs depth of investigation Log measure point is midway between M & N electrodes
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 21 Complex Lateral Array Responses Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 22 Normal/Lateral Log Response Comparison Normal array to bed boundaries is symmetrical Bed thickness and Ra is straightforward Lateral array response to bed boundaries is asymmetrical Bed thickness and Ra is not straightforward Thin bed analysis is problematic, for both arrays
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 23 API ELog Format: Short (16") Normal Long (64") Normal Note: Some slimhole ELogs use a 48" LN Both in Track 2 18' Lateral in Track 3 ELog Formats have evolved, early ELogs may not look exactly like this Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 24 Borehole model is essentially a cylindrical analogue to a four layered earth model Mud column Mudcake Flushed zone Invaded zone Uninvaded formation Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 25 Normal Array Departure Curves Analogous to 2Layer sounding type curves Vertical axis is ratio of apparent resistivity to mud resistivity Horizontal axis is ratio of AM spacing to well bore diameter Departure curves are for different Rt/Rm ratios Only valid for center of thick beds Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 26 Lateral Array Departure Curves Remarkably similar to those for Normal array O is measure point Horizontal axis is AO/d Only valid at center of very thick beds
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 27 Early (ES) Resistivity Log Limitations Really Designed for use as a Correlation tool Normal Array Bed Resolution/Depth of Investigation Dilemma Lateral Array Asymmetrical Bed Boundary Response Linear Scales Have Poor Resolution for Low Resistivity Beds Pay Zones & Reserves Estimates based on ES data May be suspect
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 28 Focused (Current) Logs Focused Logs use a variety of potential electrodes and bucking currents to force the current streamlines deep into the formation
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 29 Guard Log (LL3) Henry Doll's attempt to overcome the Normal Log depth/resolution dilemma Analogous to the guarded cylindrical shell sample holder Large guard electrodes on either side of the current electrode force current streamlines deeply into formation
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 30 Guard Log Geometrical Factor
L 2 l d L L ln + d d
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com 2 1 2 1 L d
2 1 2 G 1 PTE461: Fall 2007 Section 5: Resistivity Slide No.: 31 LL3 (Guard Log) Departure Curves Works well, only when Ra > Rm
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 32 Dual Laterolog (DLL) Uses a combination of: Current electrodes Monitoring electrodes Focusing electrodes Bucking electrodes Servo logic control Results in better current focusing than LL3, for most situations Still is better suited for Ra > Rm
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 33 DLL Geometric Factor G 4 1 I' + Lo Io 1 1 + L1 L2 LLD operates at 35 Hz LLS operates at 280 Hz GLL is dynamic as I' is continuously modified so that V=0 at both M1M2, and M'1M'2
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 34 DLL Departure Curves Horizontal axis is ratio of apparent (log) to mud resistivity Vertical axis is ratio of corrected to apparent resistivity Curves are for different borehole diameters
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 35 DLL Shoulder Bed Corrections Correct log values for effects of beds which are too thin for the measured value to reach its full value Horizontal axis is bed thickness Vertical axis is ratio of corrected to apparent resistivity Curves are ratios of bed to shoulder bed resistivities Strictly valid for cylindrical symmetry and infinitely thick shoulder beds
PTE461: Fall 2007 Section 5: Resistivity Slide No.: 36 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Spherically Focused Log (SFL) A shallow Laterolog type measurement Used primarily with Induction logs Provides better thin bed resolution than induction logs Larger borehole and mud cake effects than deeper sensing tools
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 37 SFL Borehole Corrections Horizontal axis is ratio of SFL measured (apparent) resistivity to mud resistivity Vertical axis is ratio of boreholecorrected to measured resistivity Blue curves are for centered tool Red curves are for eccentered tool with 1.5" standoff
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 38 Schlumberger Focused Log Current Streamlines Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 39 Schlumberger Focused Log Geometric Factors Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 40 HighResolution Laterolog Array Tool Does Not Use Bridle Electrode Uses DownHole Microprocessors Uses Multiple Electrode Arrays Uses Multiple Signal Frequencies Records Both Amplitude and Phase Can Invert Measured Data to Provide Model Ring Resistivities
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 41 HRLA Geometric Factors Shallowest (0) Mode is closest to Rm Deepest (5) Mode is Close to Rt Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 42 MicroLaterolog (MLL) A pad (pressed against the borehole wall) tool Used for flushed zone saturation (Sxo) estimates Essentially measures resistivity of flushed zone (and mudcake) Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 43 MicroSpherically Focused Log (MSFL) An alternative Sxo tool, to the MLL
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 44 MSFL Mudcake Corrections Essentially Sxo tool Departure curves Horizontal axis is apparent to mudcake resistivity ratio Vertical axis is corrected to uncorrected resistivity ratio
PTE461: Fall 2007 Section 5: Resistivity Slide No.: 45 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com DLL Tornado Chart Allows estimation of true resistivity (Rt), from flushed zone (Rxo), intermediate, and deep resistivities Horizontal axis is deep (RLLD) to shallow (RLLS) resistivity ratio Vertical axis is deep (RLLD) to flushed zone (Rxo) resistivity ratio Solid curves are formation (Rt) to flushed zone (Rxo) resistivity ratio curves Dashed curves are depth of invasion (di) curves Red curves are formation (Rt) to deep (RLLD) resistivity ratio curves
PTE461: Fall 2007 Section 5: Resistivity Slide No.: 46 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com Maxwell's Equations Development to this point has used only Gauss's Law Induction logs are based on AC version of Ampere's Law Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 47 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 48 Both k and denote (transmission) attenuation The propagation factor, k, is more useful, when working with EM wave equations. The skin depth, , is more useful, when evaluating EM signal strength vs. transmission distance Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 49 Skin Depth Relationships Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 50 Conduction vs. Displacement Currents Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 51 Brine (0.001 M KCl) saturated Berea Sandstone electrical spectra: Over 103  104 Hz range: ~ 5  10 mrad phase shift () & 1  2% resistivity (R) decline per decade Above 105 Hz, increases sharply & R drops precipitously, due to increased displacement current. Relaxation peak, or Resonance at ~0.008 Hz probably due to Induced Polarization (IP).
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 52 Induction Log Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 53 INDUCTION LOG
DOLL'S SHELLS OF EQUAL GEOMETRIC FACTOR Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 54 Induction Log Field Calibration Check Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 55 Induction Log PseudoGeometric Factor Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 56 Induction Log Borehole Corrections Induction log must be corrected for signal generated by loss currents induced within the borehole mud column Induction log resistivities also need shoulder bed corrections and Tornado chart corrections to estimate Rxo and Rt
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 57 Induction vs Laterolog Induction and Laterologs are complementary Laterologs work best with conductive muds Induction logs work best with fresh water muds, oil based muds, mist, or air
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 58 Induction Log Tool Span Assumed TwoCoil Induction log tool response, for a 1 m tool separation Peak response is in interval equal to coil separation Lesser response extends several feet beyond on either side
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 59 Six Coil (6FF40) Thin Bed Resolution Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 60 Dual Induction Log limitations While very successful for most resistive borehole fluid (air, OBM, fresh water mud)/conductive formation situations, there were problems: Low signal/Noise (S/N) for resistivities above 2,000 Ohmm, made the tool unreliable Poor thin bed resolution (8 ft. for ILD & 6 ft for ILM) Single signal frequency (20 kHZ) Poor response for conductive muds, even for low resistivity pays Automated shoulder bed correction algorithms were not very successful High cable noise, for analog signals, sent to the surface Only impedance magnitude (I.e., no Phase) measured
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 61 Phasor (DITE) Induction Improvements Fully digital downhole sonde Downhole A/D conversion, (some) downhole processing, & multiplexed digital data transmission to the surface Measured both inphase and quadrature signals Three possible frequencies: 10 kHz, 20 kHz (default), & 40 kHz Surface processing includes borehole and shoulder bed corrections via deconvolution Improved S/N & sonde stability
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 62 DITE Tool Response Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 63 DITE Low Conductivity Target Convolution & Deconvolution Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 64 DITE High Conductivity Target Convolution & Deconvolution Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 65 DITE Induction Limitations DITE went about as far as it could go, with only three sets of coil separations Remaining problems were Overcoming cave (washout) effects Better Rt estimates in presence of deep invasion and/or complex transition zones Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 66 AIT Schematic Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 67 AIT Signals to Curves
borehole & shoulder bed corrected Inverted to produce set of model resistivity curves with multiple depths of investigation and thin bed resolution Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 68 AIT Thin Bed Tuning Example of thinbed resolution via AIT process tuning Note increased thin bed resolution at 2195  2208 & 2275 2295 Left: 4ft AIT logs Center: 2ft AIT logs Right: 1ft AIT logs
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 69 Recent Induction Log Improvements Downhole A/D conversion, quadrature measurement, and multiplexed data transmission Improved focused coil design and surface deconvolution of borehole and shoulder bed signals Array induction design, which better define radial resistivity models
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 70 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. dgh@hillpetro.com PTE461: Fall 2007 Section 5: Resistivity Slide No.: 71 ...
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This note was uploaded on 02/27/2008 for the course PTE 461 taught by Professor Donhill during the Fall '07 term at USC.
 Fall '07
 DonHill

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