Summary
Accurate estimates of porosity, fluid saturations, and in-situ gas properties are critical for the evaluation of a gas reservoir. By combining data from a dual wait-time (DTW) nuclear magnetic resonance (NMR) log and a density log, these properties can be determined more reliably than by either of the data alone.
The density and NMR dual wait-time (DDTW) technique, introduced in this paper, is applicable to reservoirs where the pore-filling fluid consists of a liquid phase and a gas phase. The low proton density of the gas phase causes a reduction in the NMR signal strength resulting in underestimation of the apparent porosity. The polarization for different wait-times depends on the spin-lattice relaxation time of each fluid and may cause additional NMR porosity underestimation. The density log, on the other hand, delivers a porosity that is overestimated because of the presence of a gas phase. These data, together with known correlations for gas properties, yield a robust approach for the gas-zone porosity, f, and the flushed zone gas saturation, Sg, xo. DDTW also derives gas properties including the in-situ gas density, ?g, as well as the two NMR-related properties, hydrogen index, IH, g, and spin-lattice relaxation time, T1g. Two field examples illustrate the method, and an error propagation study shows the reliability of the technique.
Introduction
NMR well logging yields information about fluid and rock properties. Depending on the goal of the investigation, various NMR measurement procedures are employed. Differences in the acquisition pulse sequence - including the wait-time (tw) between the echo-train measurements - characterize these procedures. Common evaluation techniques estimate different petrophysical properties, such as incremental and total porosities or movable (fm, NMR) and irreducible (fir, NMR) fluid fractions. More sophisticated methods separate the response of multiple fluids for hydrocarbon typing and saturation estimation.
DTW NMR Log.
Water as the wetting phase is dominated by surface relaxation and usually has a shorter T1 than hydrocarbons. DTW NMR uses the T1 contrast between aqueous fluid and hydrocarbon phases to achieve partial or full polarization for different fluid phases. The DTW log acquires two echo trains with a long (tw, L) and a short (tw, S) wait-time in a single pass; tw, L is chosen to fully polarize both water and hydrocarbon, and tw, S is sufficiently long to fully polarize the water fraction, while the hydrocarbon fraction is only partially polarized, causing porosity underestimation.
An interpretation technique for DTW NMR data - used mainly qualitatively - is the differential spectrum method (DSM).1 A successful quantitative evaluation technique is the time domain analysis (TDA).2 Both techniques require the calculation of either differential echo signals or differential T2 spectra, where the spectra are derived from echo-train data by inversion. The differential signals are significantly weaker than the original signal, and the noise level increases because the incoherent noise of the echo trains is added. Differential data, therefore, are unfavorable in terms of their signal-to-noise ratio (SNR). SNR often limits the applicability of evaluation techniques that are based solely on NMR data. Particularly when coupled with low hydrocarbon saturation and the low proton density of a gas phase, poor SNR is the limiting factor in estimating accurate reservoir properties.
Density Log.
The density log provides a bulk density, ?b, of the investigated formation. Additional information about the density of the rock matrix and formation fluids determines the density porosity fr.
An established method to evaluate gas-bearing formations combines the apparent porosities provided by the density and the neutron logging tools. For many data sets, however, this method yields only semiquantitative results because of the strong influence of rock mineralogy on the neutron measurement.
Theory
The porosity of clean formations bearing only liquid-phase components can be accurately quantified by either the NMR or the density logging tool. However, the tool's responses are significantly altered by the presence of a gas phase, causing the estimated porosities to deviate from the formation porosity. Three main effects cause the deviation.Low IH, g decreases the NMR porosity.Partial polarization Pg<1 decreases the NMR-derived porosity, if the wait-time between the NMR measurements is insufficiently long.Low ?g increases the density porosity.
The characterization of a hydrocarbon gas by three key properties, ?g, IH, g, and T1g, effectively quantifies these effects.
DTW NMR Log.
In a two-phase system with one gas and one liquid phase, the total NMR porosity ft, NMR is expressed byEquation 1
where the first term on the right side describes the contribution of the gas phase and the second term describes the contribution of the liquid phase. The polarization P (with P?[0,1]) quantifies the reduction of the NMR signal caused by underpolarization. The termsEquation 2Equation 3
describe the polarization of the liquid and gas phases, respectively.
Some approximations can be made for common reservoir conditions.IH, l is close to 1 for an aqueous-phase liquid and most oleic-phase liquids. In the presence of a light liquid hydrocarbon, its value can be slightly smaller (IH, l =0.8-1).If tw 3T1, the polarization is nearly unity. Typical tw values range from 1 to several seconds, whereas typical T1 values for formation water range from a few milliseconds to a few seconds. However, in a porous medium saturated with two fluid phases, the wetting phase (i.e., water) saturates smaller pores, and the maximum T1 of the aqueous-phase liquid usually reduces to values less than several hundreds of milliseconds.3 Thus, Pl is unity for aqueous-phase liquids in a two-phase system, when data are acquired with typical wait-time parameters in an MRIL®* DTW acquisition (i.e., tw, S,˜1–2 seconds and tw, L,˜6–10 seconds).
Modification of the Redlich-Kwong-Aungier Equation of State to Determine the Degree of Dryness in the CO2 Two-phase Region
