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Unformatted text preview: PTE461
Formation Evaluation Fall Semester, 2007
Section 6 Spontaneous Polarization (SP) Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 1 What is SP? Electrical potential difference between a stationary surface electrode and a moving borehole electrode A passive measurement A gradient due to changing electrode separation with a superimposed signal due to lithologic variations intersected by the borehole, causing variations in electrochemical conditions
PTE461: Fall 2007 Section 6: SP Slide No.: 2 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Background Observed as early as 1830, over buried metallic sulfide ore deposits Observed by Conrad Schlumberger during surface equalpotential surveys Measurable voltage difference in absence of power Named it: Polarisation Spontan Observed by Conrad Schlumberger during station logging of boreholes, in the absence of (known) metallic sulfide ore deposits
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 3 Potential SP Mechanisms Oxidation of metallic Ore Bodies Movement of brines through the subsurface Heat flow coupling Junction potential at interface between brines of different concentrations Membrane potential due to brines of different concentrations separated by cation selective membranes
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 4 Archie's Equations Assumptions Ro F= =a Rw Rt n I= = Sw Ro m Hydrocarbons are excellent insulators Formation waters conduct electricity Earliest Schlumberger papers noted that sands with hydrocarbons had higher resistivities than same sands with only water or the shales on either side. Archie quantified that relationship Water resistivity is needed to use Archie Equations Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 5 Hydrated Ions In the absence of any electric or pressure fields (gradients) each hydrated ion is surrounded by water molecules In the presence of electrical fields or pressure gradients, water molecule cloud becomes tear shaped, with the blunt end in the direction of movement, and tailing off in the opposite direction
PTE461: Fall 2007 Section 6: SP Slide No.: 6 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Onsager's Conductivity Equations
= =
o 82.48 8.20 10 6 + 1/ 2 2/3 ( T) ( T) o c o ( o + ) c is electrical conductivity o is conductivity of distilled water is the dielectric constant of distilled water T is absolute temperature (K) is viscosity of water c is electrolyte concentration (eq/L) & are arbitrary constants This empirical relationship holds only for dilute solutions
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 7 MonoValent Electrolytes Onsager's model worked well, only for very dilute monovalent electrolytes It encountered difficulties, when concentrations became large enough that ions could no longer be considered in isolation
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 8 Arps Equations
R2 = R1 Rw(@ 758F ) T1( F ) + 6.77 T2( F ) + 6.77 = R1 T1( C ) + 21.5 T2( C ) + 21.5 10 3.562 = 0.0123 + 0.955 SalNaCl Approximations ONLY Break down at extremes of temperature and salinity
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 9 Arps Equation Nomograph Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 10 ResistivitySalinityTemperature Nomogram Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 11 NaCl Equivalent Salinities Note: Horizontal Axis is Total Dissolved Solids
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 12 Electrokinetic (Streaming) Potential Overbalanced muds force mud filtrate through mudcake into permeable formations Mudcake acts as a cation selective membrane, leaving excess anions in borehole
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 13 Streaming Potential Example Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 14 Junction Potential Solutions of different salinities, in contact with one another via a porous material will also develop potentials across that contact Both anions and cations will migrate across the salinity junction boundary Because of ion mobility differences, there will be a (at least temporary) charge imbalance across the junction, setting up a measurable potential difference
PTE461: Fall 2007 Section 6: SP Slide No.: 15 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Membrane Potential Mud filtrate invading permeable formations is different salinity than connate (formation) waters, forming concentration gradients Only cations can pass into low permeability shales, because they act as cation selective membranes, leaving an anion excess opposite the shales
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 16 Coupled Flows Onsager's Equations
n Ji =
j =1 Li, j j Ji are generalized flow,or flux, vectors Grad( j) are generalized potential gradient, or force, vectors Li,j are generalized conductivities, or coupling coefficients (second rank tensors)
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 17 Onsager's Equations in Matrix Notation
J1 J2 J3 J4 = L1,1 L1.2 L2,1 L2,2 L3,1 L3,2 L1,3 L2,3 L3,3 L1,4 L2,4 L3,4
1 2 3 4 L4,1 L4,2 L4,3 L4,4
PTE461: Fall 2007 Section 6: SP Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Slide No.: 18 Matrix Notation, Continued If the cross coupling terms are not significant, the main diagonal terms and the potential gradient terms give rise to familiar flux/gradient relationships: e.g., J1 could be the Darcy fluid flow vector, Q J2 could be the electrical current density vector, J J3 could be the heat flow vector, q J4 could be the ion migration density flow vector Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 19 Darcy's Law J1 = Q = L1,1 k = 1 P Q is fluid flow vector Grad P is pressure gradient vector K is intrinsic permeability tensor is fluid viscosity
PTE461: Fall 2007 Section 6: SP Slide No.: 20 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Ohm's Law J 2 = J = L2,2 = 2 J is electrical current density vector Grad( ) is Electrical potential gradient vector is the electrical conductivity tensor
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 21 Heat Flow J 3 = q = L3,3 =K 3 q is heat flow vector K is the material thermal conductivity tensor Grad( ) is the temperature gradient vector
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 22 Fick's Law J 4 = L4,4 c J4 is ion flow vector L4,4 is the Fick's Law coefficient tensor Grad(c) is the ion concentration gradient vector
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 23 ElectroOsmosis J1 = Q eo = L1,2 2 = L1,2 Qeo is electroosmotic fluid flow vector L1,2 (L1,2 = L2,1, under Onsager's Principle) is the electroosmotic coupling tensor Grad( ) is the electrical potential gradient vector
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 24 Streaming Potential J 2 = J SP = L2,1 1 = L2,1 P JSP is Streaming Potential current vector L2,1 (L1,2 = L2,1, under Onsager's Principle) is the Streaming Potential coupling tensor Grad(P) is pressure gradient vector
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 25 (concentration induced ion flow) Junction Potential J 4 = J conc = L4,2 = L4,2 2 Jconc is ion concentration flux vector L4,2 (L4,2 = L2,4, Under Onsager's Principle) is the induced ion flow coupling tensor Grad( ) is electrical potential gradient vector
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 26 (cation selective) Membrane Potential J 2 = J mem = L2,4 4 = L2,4 c Jmem is membrane potential current vector L2,4 (L2,4 = L4,2, under Onsager's Principle) is the membrane potential coupling tensor Grad(c) is ionic concentration gradient vector
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 27 (free fluid) Ionic Dissociation and Hydration Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 28 Double Layer Formation No anions within Bound (Stern) Layer Only water and hydrated cations within the Outer (Gouy) Layer
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 29 Pore Throat Double Layer Effects Pore throat diameter, for free fluid movement, is reduced by thicknesses of double layer
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 30 Cation Selective Membrane Only hydrated cations can pass through a cation selective membrane Salinity gradient will set up an anion excess upstream and a cation excess downstream from a cation selective membrane
PTE461: Fall 2007 Section 6: SP Slide No.: 31 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Static & Pseudo Static SP Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 32 Schlumberger Analogue Circuit Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 33 SP Departure Curves Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 34 Nernst Equation and Rw from SP
E Nernst RT aw = ln F amf RT Rmfeq ln F Rweq E is the relative (I.e., from clay to sand) SP anomaly, in mv R is the universal gas constant F is the Faraday constant aw and amf, are the formation water and mud filtrate electrochemical activities, respectively Rweq and Rmfeq, are the formation water and mud filtrate effective resistivities, respectively
PTE461: Fall 2007 Section 6: SP Slide No.: 35 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] Nernst Equation Nomograph Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 36 Rw vs. Rweq Conversion Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 37 Estimating Rw, from the SP Select measured depth (MD) for Rw determination Using the BH temperature gradient, for the SP log, determine the borehole temperature TBH at that MD Convert [email protected] to [email protected], using Arps equation, or the RSalT Nomograph Convert [email protected] to [email protected], using the Rmf/Rmfeq Nomograph Determine Rmfeq at TBH, Using the Arps Equation or the RSalT Nomograph, Establish SP "sand" and "shale" lines
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 38 Estimating Rw, from the SP, 2 Determine the PseudoStatic SP (SPlog SPshale), from the SP log Determine Static SP (SSP) from PSSP, using the SP Departure Curves (only if needed) Determine formation temperature ([email protected]) at true vertical depth, sub sea (TVDSS), corresponding to the MD from the Formation Temperature  Depth model, for the well/field/region
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 39 Estimating Rw, from the SP, 3 Determine [email protected], using SSP, [email protected], [email protected], and the Nernst Equation Nomograph Determine [email protected], using [email protected], [email protected], & the Arps Equation or the RSalT Nomograph Determine [email protected], using the Rw/Rweq Nomograph Determine [email protected] & Salinity, using Arps Equations, or the RSalT Nomograph
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 40 BiModal ShalySand Model Grain supported framework of coarsegrained particles Finegrained particles (1:50100) fill in coarsegrained framework pore spaces
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 41 BiModal Sieve Analysis Grain size frequency plot shows two modes: at 0.002 mm and 0.2 mm (two orders of magnitude apart)
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 42 BiModal Model Total & Effective Porosity SP Sand line is near Xc 1.0 SP Shale line is near Xc for e
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] 0.00
Slide No.: 43 PTE461: Fall 2007 Section 6: SP Estimating Shale Volume, Vsh, from the SP Establish SP "Sand" and "Shale" lines Determine PSSP, for the sands, of interest Determine SSP, from PSSP, using SP Departure Curves Determine Vsh from: Vsh SP SPlog SPsd = SPsh SPsd
PTE461: Fall 2007 Section 6: SP Slide No.: 44 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] SP Log Limitations SP Response Related to Mud Filtrate/Formation Water Salinity Contrast Clay Minerals in Sands (i.e., Shaly Sands) Reduce the SP "Sand" Deflection Presence of Hydrocarbons Can Also Reduce SP "Sand" Deflections
Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 45 Donald G. Hill, Ph.D., R.Gp, R. G., R.P.G., L.P.Gp. [email protected] PTE461: Fall 2007 Section 6: SP Slide No.: 46 ...
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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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