Propagation Resistivity
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Propagation Resistivity Resistivity and the Logging Environment
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Transcript of Propagation Resistivity
Propagation Resistivity
Resistivity and the Logging Environment
Propagation Resistivity
Why are we interested in log interpretation andformation evaluation ?
l Petrophysical log interpretation is one of the mostuseful and important tools available to a PetroleumGeologist
Propagation Resistivity
What do we get from logs and log interpretation ?
l correlation of zones and structural mapping.
l lithology, porosity and permeability.
l depth and thickness of productive zones.
l gas, oil and water within the reservoir.l estimation of hydrocarbon reserves.
Propagation Resistivity
Rock properties which affect logging measurementsare -
l Porosity
l Permeability
l Water Saturation
Porosity
l defined as the volume of void space betweenmineral grains of a rock.
l given the designation φ φ .l thus φ φ (%) = (pore vol./bulk vol.) x 100
Porosity (cont.)
l Total Porosity is the % of Total Pore Volumecompared to Total Bulk Volume
l Effective Porosity is the % of inter-connected PoreVolume compared to Total Bulk Volume
Porosity (cont.)
l determined from Sonic, Neutron or Density logs.
l combined Neutron / Density log is best if available.
Permeability
l is a measure of the ease with which a fluid willpass through a sediment and is therefore afunction of the inter-connectedness of pores.
l denoted as k.l expressed in units of millidarcy (md).
Permeability (cont.)
l can be estimated from logs.
l cores required for quantitative analysis.
Permeability (cont.)
Defined as :
ka x A x ∆∆ P
q = --------------------- µµ x L
Water Saturation
l is the percentage of pore volume in a rock which isoccupied by formation water.
l designated as Sw.l measured in percent.
l important because it can used to determine thehydrocarbon saturation of a rock.
l requires knowledge of the formation and fluidresistivities in order to be calculated
Water Saturation (cont.)
l Porosity = 20%
l Water Saturation = 100%Rock
Water
Water Saturation (cont.)
l Porosity = 20%
l Water Saturation = 75%
l H-C Saturation = 25%
Rock
Water
H-C
Basic Electricity
l electrical current is directly related to the flow ofelectrons
l size of the nucleus is a major factor in determiningelectron mobility
l larger the nucleus the less force likely to hold theelectrons
l metals have high number of free electrons thus aregood conductors
l hydrocarbon have electrons firmly bound withinatoms thus are electrical insulators
l it is this property of hydrocarbons which can beused in their identification
Basic Electricity
l Charge and Current– 6 x 1018 electrons = 1 Coulomb
– Current (I) measured in amperes (A), is the ammountof charge flow per unit of time i.e.
– I = C / t ( 1 ampere = 1 Coulomb per second )
l Voltage– the E.M.F. of a battery is defined as 1 volt if it gives
of 1 Joule of electrical energy to each Coulombpassing through it i.e.
– 1 Volt = 1 Joule / Coulomb
Basic Electricity
l Resistance ( r )– is the property of a substance that offers opposition
to the flow of electrical current.
– Ohms Law describes the behaviour of electricalcurrent flow through a material.
I = E / r
where: r = resistance, ohms
E = electromotive force, volts
I = current, amps
Basic Electricity
l Resistivity ( R )– is a measure of the resistance of a given volume of
material.
R = r A / L– In practice, the volume of formation measured is
constant dependent on the configuration of themeasuring instrument.
– Thus the measurement is expressed in terms ofresistivity.
Resistivity
l is the property of a rock on which the wholescience of logging was first developed.
l is a measure of a rocks ability to resist the flow ofelectrical current.
l measured in ohm.meters
l is the inverse of conductivity (R = 1000 / C)
l a basic assumption in all log analysis is thatsaltwater alone is the conductive medium in rocks
Resistivity (cont.)
l Resistivity will vary with temperature, so Formation /Bottom Hole Circulating temperature is important
l Transmitted from tool as TCDXl Once the appropriate temperature is determined, the
resistivity of a fluid can be determined from -– Rt2 = Rt1 x (T1 + 6.77) / (T2 + 6.77) deg F
– Rt2 = Rt1 x (T1 + 21.5) / (T2 + 21.5) deg C
Resistivity (cont.)
l Rw - is the resistivity of the formation water.
l Ro - is the resistivity of a formation 100% saturatedwith water of resistivity Rw.
l Rt - is the resistivity of the undisturbed / uninvadedformation.
Resistivity (cont.)
l The Archie equation is the fundamental premise ofall resistivity logging interpretations.
l It calculates the Formation water saturation. Sw.l It is a measure of the actual formation resistivity, in
comparison to the same formation, were it 100%filled with formation water of Rw.
l From Sw hydrocarbon saturation is derived.
Fundamental Interpretation Relations
l consider a 1cubic meter tank of 10% NaCl solution.
l Voltage (V) is applied across electrodes on eitherside of tank and current I1 measured.
l Ratio V / I1 is Rw.
Fundamental Interpretation Relations
l 1 cubic meter tank
l 10% Na Cl Solution
l Voltage V appliedl Current I1 measured
l Ratio V / I1 = Rw
Fundamental Interpretation Relations
l Consider same tank, now with sand poured in,expelling water, resulting in a “porous, waterbearing formation.”
l The same voltage (V) is applied and current I2 ismeasured.
l I2 < I1 (there is less water to conduct).
l V / I2 = Ro and Ro > Rw.
Fundamental Interpretation Relations
l 1 cubic meter tank
l 10% Na Cl Solution
l Voltage V appliedl Current I2 measured
l I2 < I1l Ratio V / I2 = Ro
l Ro > Rw
Fundamental Interpretation Relations
l Ro must be directly proportional to Rw.
l Proportionality constant is Formation Factor - F.
l Thus : Ro = F x Rw
Fundamental Interpretation Relations
l Ro is indirectly proportional to the amount of waterpresent.
l Ro is directly proportional to F , thus F is alsoindirectly proportional to the amount of waterpresent.
l Water content must be related to porosity so Fmust be related to Porosity.
Fundamental Interpretation Relations
l Assuming constant Rw, if Ro increases, F mustalso have increased.
l If F has increased, Porosity or water content musthave decreased.
l Thus : F = 1 / φφ
Fundamental Interpretation Relations
l Porosity is not made up of straight cylindricaltubes.
l a factor - “m”- cementation exponent must beintroduced to reflect the tortuosity of the currentflow.
l Thus : F = 1 / φφ m
Fundamental Interpretation Relations
l It was found that generally m = 2 , based onempirical work by G.E. Archie.
l This was found not to hold true for all rock typesand other forms of the equation were introduced.
Fundamental Interpretation Relations
l other forms of the equation are :– F = 1 / φ φ 2 (Archie) - carbonate
– F = 0.81 / φ φ 2 (Tixier) - sandstone
– F = 0.62 / φ φ 2.15 (Humble) - sandstone
Fundamental Interpretation Relations
l some of the water in the tank is now replaced by oilto represent a formation containing hydrocarbon.
l for the same voltage (V) applied, a current I3 ismeasured.
l I3 < I2 (again less water to conduct).
l V / I3 = Rt and Rt > Ro > Rw.
Fundamental Interpretation Relations
l 1 cubic meter tank
l 10% Na Cl Solution
l Voltage V appliedl Current I3 measured
l I3 < I2 < I1l Ratio V / I3 = Rt
l Rt > Ro > Rw
Water Saturation
l is the percentage of the pore space filled withformation water.
l designated - Swl Rt is dependent on F , Rw and Sw.
l if Sw = 100% , Rt = Ro.
l As Sw decreases , Rt must increase.
Water SaturationFundamental Relations
l Thus : Rt = Ro / Sw
l Again the actual relationship is not simply indirect,and a factor - “n” - the Saturation Exponent mustbe introduced.
l Thus : Rt = Ro / Sw n
l Generally n = 2.
Water SaturationFundamental Relations
l A more familiar form of this equation is : Sw = √√ Ro / Rt
l Replacing Ro Sw = √√ F.Rw / Rt
l Replacing F ...............
Water SaturationFundamental Relations
l Sw = √√ a . Rw / Rt . φ φ m
l This is the fundamental equation of loginterpretation and is termed the ARCHIE EQUATION
Hydrocarbon Saturation
l Assumed that any fluid that is not water ishydrocarbon.
l Sh = 1 - Sw
Factors Affecting “m” and “n”
l m - tortuosity increases m (rocks with increasedtortuosity have m upto 2.2; fractured rocks have mas low as 1.5)
l n - affected by presence of shale and oildistribution.
Borehole Environment
l whenever a hole is drilled into a formation, the rockand the fluids it contains, are altered in the vicinityof the borehole.
Borehole Environment (cont.)
Some of the more important aspects to consider are -
l Hole Diameter (caving / wash out or mudcake buildup).
l Drilling Mud (excess borehole pressure overformation pressure leads to fluid invasion).
Borehole Environment (cont.)
l Invaded Zone - the zone which is invaded by mudfiltrate.
l consists of a flushed zone (Rxo) and a transitionzone (Ri).
l the amount of invasion is dependent on thepermeability of the mudcake and the formationporosity.
l invasion is deeper in low porosity rocks.
Invasion
l Replaces virgin water (Rw) with mud filtrate (Rmf).
l Pushes back hydrocarbons leaving only residualoil and gas.
l Requires 3 resistivity curves to correct deepreading to true Rt (shallow, medium, deep).
l Difference between water saturations in theundisturbed zone (Sw) and the flushed zone (Sxo)represents Moveable Hydrocarbon.
Invasion
Depth of invasion
Invasion
Invasion
Invasion Profile
Mud
Rm
Rxo Rt
Rs
RmcRmf Rw
Sxo Sw
Invasion Diameter
Un
inva
ded
Zo
ne
Flu
shed
Zo
ne
Tra
nsi
tio
n Z
on
eAdjacent Bed
Invasion - Transition & Annulus Profiles
BoreholeWall
Res
isti
vity
dj
Distance
Rxo
Ro
BoreholeWall
Res
isti
vity
dj
Distance
Rxo
Ro
RiRi
Ran
Rt
Invasion - Step Profile
BoreholeWall
Res
isti
vity
dj
Distance
Rxo
Ro
Invaded Invaded
Flushed Flushed
HoleRm
HoleRm
Rxo Rxo
Ri Ri
Uninvaded Rt Sw >> 60%
Uninvaded Rt Sw >> 60%
Rxo >> RwFresh Mud
Rxo = RwSalt Mud
Rxo
Rxo = RoRo Ro
Invasion Profile - Water Zone
Res
isti
vity
Res
isti
vity
Rxo >> RwFresh Mud
Invasion Profile - Hydrocarbon ZoneAnnulus
Invaded Invaded
Flushed Flushed
HoleRm
HoleRm
Rxo Rxo
Ri Ri
Uninvaded Rt Sw >> 60%
Uninvaded Rt Sw >> 60%
Rxo = RwSalt Mud
Rxo
Rxo = RoRo Ro
Res
isti
vity
Res
isti
vity
Annulus
Rt Rt
Ran
Ran
InvasionProfile
Moveable Oil Saturation
l once located, is the hydrocarbon that is presentmoveable ?
Moveable Oil Saturation (cont.)
l if invasion is moderate or deep, the flushed zoneformation water (Rw) is completely replaced bymud filtrate (Rmf).
l if oil is present in the flushed zone, then themoveable oil saturation can be determined fromthe difference between Sxo (flushed zonesaturation) and Sw.
Moveable Oil Saturation (cont.)
For the invaded zone, Archies Equation becomes -
Sxo = √√ a . Rmf / Rxo . φ φ m
Moveable Oil Saturation (cont.)
l if hydrocarbons do not move during the drillingprocess Sxo = Sw.
l if hydrocarbons have been flushed by invasionfluids Sxo > Sw.
l therefore (1-Sxo) < (1-Sw).
l MOS = Sh - Sho.
Recoverable Hydrocarbons
l Oil :
l NR = 7758 . φφ (1 - Sw) . h . A . RF
Bl Gas :
l GR = 43560 . φφ (1 - Sw) . h . A . Pr . 520 . RF
14.7 (460+Tr).Z
