In Tarek Ahmeds ‘Reservoir Engineering Handbook’ the fundamentals of rock properties are The petrophysicists’ primary role is the quantification of these properties, through the evaluation of laboratory and log evaluation.
Petrophysics Log analysis is part of the discipline of petrophysics ‘ A log analyst is a scientist, a magician and a diplomat…… He has extensive knowledge of geology, geophysics, sedimentology, petrophysics, mathematics, chemistry, electrical engineering and economics’ E. R Crain
NMR does not directly measure permeability, but does provide parameters useful for the calculation for of permeability from empirical equations
Mean pore size
Clay bound water
Porosity (after Hook). The ratio of void (or fluid space) to the bulk volume of rock containing that void space. Porosity can be expressed as a fraction or percentage of pore volume . 1) Primary porosity refers to the porosity remaining after the sediments have been compacted but without considering changes resulting from subsequent chemical action or flow of waters through the sediments. 2) Secondary porosity is the additional porosity created by chemical changes, dissolution, dolomitization, fissures and fractures. 3) Effective porosity is the interconnected pore volume available to free fluids, excluding isolated pores and pore volume occupied by adsorbed water (the engineers Porosity). 4) Total Porosity is all the void space in a rock and matrix, whether effective or non effective. Total porosity includes that porosity in isolated pores, adsorbed water on grain or particle surfaces and associated with clays.
Porosity Definitions TOTAL: Total void volume. Clay bound water is included in pore volume Not necessarily connected Core analysis disaggregated sample NMR core analysis Density, neutron log (if dry clay parameters used) NMR logs Effective (connected): Void volume contactable by fluids Includes clay bound water in pore volume? Possibly sonic log Effective connected Rock Bulk Volume Rock Matrix Clay Clay bound water Total Porosity Effective Porosity log analysis Capillary bound water Free water Hydrocarbons Minerals
Porosity logging tools if wet clay parameters used
Effective connected Rock Bulk Volume Rock Matrix Clay Clay bound water Total Porosity Effective Porosity Log Analysis Capillary bound water Free water Hydrocarbons Minerals
T2 Model 0.1 1.0 10.0 100.0 1000.0 10000.0 Rock Bulk Volume Rock Matrix Clay Clay bound water Total Porosity Effective Porosity Capillary bound water Free water Hydrocarbons Minerals T2 cutoff NMR is unique it measures total porosity and can be partitioned into pore-size and fluid component
T2 & Porosity - Echo Data Underlying CPMG decay CPMG echoes T 2 relaxation (msec) AMPLITUDE Calibrated To porosity At start of sequence Immediately after polarization All ‘fluid’ is polarised = Total Porosity Total porosity
Possible Error in Total Porosity Underlying CPMG decay CPMG echoes First echo (e.g TE = 200 usec) Noise Noise and timing of first echo effects the extrapolation to time = 0
Porosity From T2 Data 0.1 1.0 10.0 100.0 1000.0 10000.0 Inversion to T2 Distribution of Exponential Decays Porosity is calculated as sum of T2 bins in distribution
Exercise – Calculation of porosity The CMR tool is calibrated using a 100 p.u. signal using a water bottle. CMR porosity is calculated using the general equation: Actual equation for the CMR tool :
Calibration tank made of fibre glass, lined with thin metal coating
Tank acts as container for water sample and faraday cage to shield unwanted RF
Outer chamber, water is doped with cupric to reduce relaxation time of water and speed up relaxation
Inner chamber filled with brine to simulate bore hole conditions
Pore Size Distributions The NMR measurement measures the relaxation of proton spins. Relaxation occurs by three main processes Assuming the rocks are 100% water saturated relaxation due to surface relaxation is much faster then bulk relaxation (in the fast diffusion limit). In a homogenous field diffusion is negligible. Diffusion is an important process if field gradient of fluid has a high diffusion coefficient The fast diffusion limit is where all the pores are small enough and surface relaxation mechanisms slow enough that a typical molecule crosses the pore many time before relaxation.
Pore Size in 100% Water Saturated rocks Rock Grain Spin diffuses to pore wall where a proton spin has a probability for being relaxed In a porous system filled with a single phase Each pore-size has a characteristic T2 decay constant. The smaller the pores the faster the relaxation (short or fast T2)
Pore Size in 100% Water Saturated rocks 0.1 1.0 10.0 100.0 1000.0 10000.0 Rock Bulk Volume Rock Matrix Clay Clay bound water Total Porosity Effective Porosity Capillary bound water Free water Hydrocarbons Minerals T2 cutoff
Measurement of Relaxivity and Pore Size Pc/r & T2) Pc/r & (k*1/T2) Lab Calibration of Data Relaxivity ( ρ ) is expressed in units um/s
When comparing NMR and capillary pressure, NMR measures surface to volume ratio of the pore and capillary pressure equates to pore throat size.
The two are only exactly comparable if the pore systems approaches that of a bundle of tubes.
However comparison of NMR and capillary pressure does alllow NMR to be related to pore throat size.
Inversion & Porosity and Pore Size Distribution T 2 x T 2 y T 2 z Exponential decay characterises Pore size Total amplitude characterises pore volume
Inversion T 2 x T 2 y T 2 z T 2 x T 2 y T 2 z T2x, y and z are T2 bins, or if scaled to pore size, pore size bins. Height of column is pore volume
T2 Distribution Reflects Porosity ‘Bins’ Porosity is sum of porosity bins (x+y+z) T 2 x T 2 y T 2 z
Inversion quality Control Underlying CPMG trend Fit 1 (good) Fit 2 (poor) T2 (ms) Echo Amplitude RMS Error of Fit Well fitted data with evenly distributed error of fit Poorly fitted data with systematic variation in error of fit
Hydrocarbon effect on T2 distribution Hydrocarbon effect on T2 distribution 100% Brine Saturated Water wet with oil Producible water (free fluid) Bound fluid (irreducible water) Producible hydrocarbon (free fluid) Bound fluid (irreducible water) T2 increases since hydrocarbon Is not limited by pore-size T2 is limited by pore size in 100% Sw rocks
Fluid Properties Calculator /*convert temp to kelvin temp_k = (0.555556)*(temp_F+459.67) /*calculate Bulk T1 T2 oil, water and gas /*convert to ms since equation for seconds /* MU in cp, density in g/cc, temp in Deg K T12B_OIL = (3*(temp_k/(298*MU_OIL))) * 1000 T12B_WATER = (3*(temp_k/(298*MU_WATER))) * 1000 T12B_GAS =(25000*(RHO_GAS/(temp_k**1.17))) * 1000
Logging Gas Reservoirs & Density NMR Porosity (DMRP) In the presence of gas: Density log overestimates porosity (Fluid density deficit) NMR log underestimates porosity (HI index deficit) Providing that the polarization effect is understood, the deficit between the porosity estimates of the two logs is proportional to the gas saturation. This effect can be approximated using the equation: PHIT_DMR = 0.6*PHIA_DEN + 0.4 * PHIT_NMR where: PHIT_DMR = combined density NMR porosity PHIA_DEN = apparent porosity derived from the density log PHIT_NMR = porosity derived from the NMR log Freedman, R., Chanh Cao Minh. Gubelin, G. Freeman, J. J. McGuiness, T. Terry, B. and Rawlence, D. 1998. Combining NMR and Density Logs for Petrophysical Analysis in Gas Bearing Formations . Transactions of the SPWLA 39th Annual Logging Symposium, May 26-29, Keystone Colorado. 1998. Paper II.
The connate water saturation is defined by capillary bound water, and defined by a finite minimum irreducible water saturation on a capillary pressure curve.
Connate Water Saturation Pc (or h) Water Saturation 0% 100% Pd Swc Pd = Displacement pressure. (minimum capillary pressure required to displace the Wetting phase from the largest capillary pore Swc = Connate irreducible water saturation
Variation In T2 Cutoffs FWL Borehole HAFWL Sw A B A B 100 0 Pc (psia) 480
T2 Cutoff From Capillary Pressure (Mercury) Pc Sh Sandstone ρ e = 23 um/s σ for oil water 22 dynes/cm θ for oil water = 35 degs σ for air mercury water 480 dynes/cm θ for air mercury = 140 degs pw=1.0 g/cc phc=0.85 g/cc Lab Data
The phase angle is used to extract the signal amplitude and signal noise from the x and ycomponents to generate the echo-train data used for inversion to T2 distributions.
In porous intervals, the signal phase should remain relatively stable (±100). In low porosity
In shaly zones, signal noise is difficult to estimate due to low signal to noise. Consequently, the
Signal phase should only be examined with respect to log quality in clean porous intervals.
Signal Phase Calculation Explained in CMR processing
CMR Quality Control (Polarisation Correction)
Older tools only where Tw < 3*T1 of formation & fluids.
As the tool is pulled past the formation, the formation experiences a time dependent magnetic field (wait time) and thus time dependent polarization.
For the CMR 200, at speeds higher than 5 cm/s there is a significant loss in polarization for fluids with a T1 greater than 1s.
Consequently, at logging speeds greater than 5 cm/s there is a significant loss of polarization
For fluids and large pores with long T1's. Since porosity is calculated as the sum of the amplitudes of the T2 distribution multiplied by the CMR calibration value, the porosity estimated from CMR data is affected by the polarization correction.
CMR Quality Control (Polarisation Correction) Analogue Model Inversion Fluid Sub Tw = 1 sec Lost porosity With Tw = 1 sec
CMR Quality Control (Polarisation Correction)
The polarization correction is
CMR Quality Control (Polarisation Correction)
As part of the quality control checks, three different porosity estimates are calculated usingthree different T1:T2 ratios (R). The default values taken for R are 1, 1.5 and 3.
ERRMINUS and ERRPLUS are the differences between the default and limit values for R
The CMR log can be checked for incomplete polarization (insufficient wait time) by comparing the three different porosity estimates calculated using the three different values of R. Where theformation has been subject to a sufficient wait time, and complete polarization has occurred,there should be no difference in porosity calculated using different wait times. In cases wherethe wait time was insufficient for complete polarization, porosities will differ over the range ofT1:T2 ratios selected.
Insufficient wait time is normally flagged when the difference between porosity calculated using the minimum R and maximum R is greater than 2 p.u. (WAIT_FLAG)
CMR Porosity Calibration. Alternatively CMR porosity can be calibrated directly to another measurement (i.e. core data).
CPMG (Echo) Processing CPMG data is collected using a quadrate detection system in which the signal is recorded in two channels (R and X). The R and X data is used to estimate the phase of the signal and the two channels are combined to generate (1) a phase coherent channel that contains the signal, and (2) a noise channel. Echo R Echo X Phase Angle signal noise
CPMG (Echo) Processing The phase angle is calculated as: where φ = phase angle i = ith echo of the echo train k = number of echoes to be used in the phase angle calculation
CPMG (Echo) Processing R and X = inphase and quadrature detected component of the CPMG The CPMG signal and noise is calculated by rotating the channel data through the phase angle . signali = Ri *cos φ + Xi * sin φ noisei = Ri *sin φ - Xi *cos φ where: signali = signal of the ith echo noisei = noise of the ith echo Ri = inphase component of the ith echo Xi = quadrature component of the ith echo
S:N and Vertical Resolution (data stacking) 8 Level Stack Stack Base to Top
CPMG data is collected using a quadrate detection system in which the signal is recorded in two channels (R and X). The R and X data is used to estimate the phase of the signal and the two channels are combined to generate (1) a phase coherent channel that contains the signal, and (2) a noise channel. Echo R Echo X Phase Angle signal noise
The salinity correction is only applied if the Rmf < 10 ohm.m at 75° C. The correction compensates from the loss of hydrogen atoms replaced by salt ions.
Temperature affects the thermal relaxation of protons and reduces the amplitude of the returned signal. The temperature correction should always be applied.
Hydrogen Depletion Correction
Increased temperature of the formation reduces the density of the formation fluid and decreases the hydrogen index. Higher pressures increase the hydrogen index. This effect is compensated for by using a Hydrogen Depletion Multiplier, which is a function of porosity and temperature.
Environmental corrections are applied during phase rotation of the real and imaginary data.
is dependent upon the loading of the MRIL transmitter coil by borehole fluids and the formation, and is measured continuously throughout logging. Gain is also frequency dependent, and generally, the operating frequency is chosen to achieve the maximum gain.Gain should be constant; spiking usually indicates tool problems.
is an estimate of coil quality; certain MRIL activations are designed to run at agiven Q Level (high, medium or low). Q Level depends on the Gain.
The B1 Field is responsible for generating the pulse sequence that is used to acquire the CPMG sequence. With every pulse sequence, the B1 is measured using a test coil.
The B1 Field should remain relatively constant but should show some variation with changes inconductivity and gain. Consequently, the B1 Field should be checked for overall variation andvariation with conductivity and gain.
Use core calibration (i.e. porous plate de-saturation)
Remove free fluid from T2 distribution
Substitute in ‘hydrocarbon’ with bulk properties
Model raw data
Forward Modelling Spectral bound fluid = Swirr 2. Remove free-fluid (water) 3. Add in free fluid water so that T2LM of free fluid = T2 predicted for hydrocarbon 1.
Forward Modelling : Optimising Inversion of Log Data Inversion: SVD T1 min = 0.3 T2 max = 3000 No Bins = 30 T2 maximum is not long enough to capture Long T2 associated with carbonate Analogue Model Inversion
Forward Modelling : Optimising Inversion of Log Data Inversion: SVD T1 min = 5 T2 max = 5000 No Bins = 30 Analogue Model Inversion New bin range better captures the full T2 spectrum
Fluid substitution to construct psuedo 100% Sw T2 distribution
Method only exists for sandstones at present
Calculate Swirr (using SBFV method)
Predict theoretical T2LM in water wet sandstones
Remove free fluid part of spectrum using SBFV method
Add in water spectrum such that T2LM = theoretical T2LM
T2LM in Sandstones (from sandstone rock catalogue) Log10(1-Swirr/Swirr) T2LM Yakov Volokitin, Wim Looyestijn, Walter Slijkerman, Jan Hofman. 1999. Constructing capillary pressure curves from NMR log data in the presence of hydrocarbons . Transactions of the Fortieth Annual Logging Symposium, Oslo, Norway, 1999. Paper KKK 10**(0.772*(LOG10((-1-SWirr)/SWirr))+k K = 1.5
Pseudo 100% Sw T2 Spectral bound fluid = Swirr 1. 2. Remove free-fluid (hydrocarbon) T2LM =10**(0.772*(LOG10((-1-SWirr)/SWirr))+k K = 1.5 3. Predict T2LM Add in free fluid water so that T2LM = predicted T2LM 4.