Log Analysis

AN NMR HIGH-RESOLUTION PERMEABILITY INDICATOR
A. Sezginer, C. Cao Minh, N. Heaton, M. Herron, R. Freedman Schlumberger G. Van Dort Amerada Hess UK ABSTRACT NMR permeability schemes in use today are derived indirectly from the T2 distribution, i.e. through the estimation of the log-mean T2 or the bound fluid volume. However, obtaining the T2 distribution requires stacking the data to improve thesignal-to-noise ratio (SNR) before inversion. The drawback of stacking is either a slow logging speed or a reduced vertical resolution. A new NMR high-resolution permeability indicator is derived from the sum of echoes in a single phase-alternated pair (PAP) consisting of two Carr-PurcellMeiboom-Gill (CPMG) sequences. The sum of all echo amplitudes in the echo train is proportional to the productof porosity and the average T2. This, in turn, correlates to permeability. Because the sum of echoes has a high signal-to-noise ratio, it can be interpreted without stacking and, hence, with high vertical resolution. The vertical resolution achievable with the technique is equal to the antenna aperture plus the distance traveled during one CPMG sequence plus one polarization time, the sum of whichis a few inches. The technique is verified in a test well where the formation consists of well-characterized blocks of different lithologies, porosities, permeabilities and thicknesses. The CMR* Combinable Magnetic Resonance Tool, which has an antenna aperture of 6-in., was used in the tests. In a Gulf of Mexico turbidite example, the new NMR high-resolution permeability indicator is able toidentify several thin sand-shale laminations that are overlooked by conventional techniques. Other examples of the high-resolution indicator include a net-to-gross computation in laminated formations and a calibrated quantitative permeability computation. The new measurement is compared with standard NMR permeability estimators such as Timur-Coates permeability and also with core measurements.INTRODUCTION The proton magnetic resonance relaxation time of a water-filled pore is proportional to the volume-to-surface ratio of the pore. High surface-to-volume ratio indicates the presence of clay minerals in the pore space or microporosity, both of which impede fluid flow. Therefore, a correlation exists between the magnetic resonance relaxation time and permeability. One such correlation is theequation kSDR = af4T 22lm that estimates permeability of water-saturated rocks.1 The Timur-Coates equation, kTIM = bf4FF2/BFV 2, is another permeability equation.2,3 In the above equations, k is permeability, f is porosity, a and b are constants, T2lm is the log-mean T2, BFV is the bound fluid volume and FF is the free fluid volume. Magnetic resonance logs are generally processed to obtain porosity and theT2 distribution from which permeability is calculated. Either the precision or the resolution of the T2 distribution is limited by the SNR. Often, magnetic resonance logs are depth-stacked before signal processing to improve the SNR at the expense of vertical resolution. In thinly laminated sand-shale sequences, depth stacking averages the signals from the sand and shale layers and gives apessimistic picture of highly producible sands. PERMEABILITY INDICATOR The sum of echoes, p, is an increasing function of both porosity and transverse relaxation time T2 as shown below: p= =

n =1 N

å echo(n) å [noise(n) + ò0 A(T2 )e - nTE / T2 dT2 ]
¥

N

(1)

n =1

*Mark of Schlumberger

where A(T2) dT2 is the hydrogen index times the volume fraction of the fluid whose relaxation timeis between T2 – dT2 /2 and T2 + dT2 /2. The index n, which labels the echoes, runs from 1 to N, the number of echoes in the CPMG sequence. TE is the echo spacing in seconds. In Eq. 1, echo(n) is the n-th echo amplitude and noise(n) is

1

the zero-mean random additive noise in the measurement. We shall call the random part of p, x: x=

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