Saturation and Viscosity from Multidimensional Nuclear Magnetic Resonance Logging

Abstract

The last decade of nuclear magnetic resonance (NMR) logging has been dominated by T2 measurements and sparse sampling of polarization (differential spectrum) or diffusion (shifted spectrum) effects. Recent literature has expanded on the utility of NMR logging using T1 measurements to provide information on long time constants that are difficult or impossible to derive from T2 measurements using gradient tools. NMR logging modes have typically been designed to focus on a single specific NMR response, either very fast or very slow diffusion, or long T1 times, to identify either oil or gas. However, fluid properties can vary widely and often unpredictably downhole. A small number of NMR measurements that focus on just one NMR parameter may not provide sufficient information to identify and quantify fluid volumes, particularly when several different fluids are present. Achieving accurate fluid properties often requires data acquisition that simultaneously measures T1, T2, and diffusion contrasts. Inversion is most effective when all three NMR properties, T1, T2 and D, are obtained. We review the relative merits of T1, T2, and diffusion-based measurements in the light of petrophysics and instrumentation limitations. The relative merits of forward-model inversion and model-free analysis are discussed with reference to data sets recorded in a broad range of environments. Introduction A trend that has continued throughout the development of NMR fluid typing methods has been the increasing reliance on molecular diffusion (D) to identify and characterize different fluids.1–5 Recognizing the importance of diffusion, Hürlimann and coworkers6 developed diffusion editing (DE) acquisition and 2D NMR (2DNMR) methodology.7 The introduction of DE measurements represents an important advance in NMR logging because the method provides a substantial improvement in diffusion sensitivity relative to the conventional Carr-Purcell-Meiboom-Gill (CPMG) train.8 Also important has been the introduction of 2DNMR analysis. This analysis method invokes a model-independent inversion to generate 2D maps that display multimeasurement NMR data in an easily understandable format. Early examples of 2DNMR used DE data suites with different echo spacings to correlate diffusion rates and transverse relaxation times (T2).5,9 The resulting D- T2 maps provided clear separation of oil and water signals, allowing accurate determination of the fluid saturations and oil properties. Although DE acquisition and 2DNMR inversion processing were developed jointly, it was later demonstrated that the 2DNMR approach could also be extended to sequences comprised entirely of CPMG measurements10 if DE data were not available. As experience with 2DNMR methodology was gathered, it became clear that improvements in both acquisition efficiency and data analysis could be achieved by extending the technique to include longitudinal relaxation (T1). The resulting 3D approach (3DNMR) accounts for all relevant NMR properties, (i.e., T2, T1, and D) in a single comprehensive analysis of multimeasurement NMR data. The remainder of this paper provides a description of multimeasurement NMR analysis. The first section describes in more detail how the various maps (e.g., D-T2, D- T1) are generated and explains the relationships between them. It also discusses the effects of noise and regularization on the resolution and precision of 3DNMR inversion results. Sections two and three outline the application of 3DNMR to fluid typing in wells drilled with water-based mud (WBM) and oil-based mud (OBM) respectively. Field examples are used to illustrate points concerning the processing and interpretation. 3D NMR (3DNMR) Analysis There are several benefits offered by multidimensional NMR acquisition and analysis. First, the contour maps (e.g., D-T2, D-T1, T1- T2), provide a convenient and understandable means of visualizing complex NMR data, allowing identification of different fluids and calibrating their NMR response. From an operational perspective, the multimeasurement approach allows definition of a small set of acquisition sequences that are applicable in a wide range of environments. This approach simplifies NMR job planning, because there is no longer a need to define acquisition parameters for each job.

A novel method for NMR data compression

“…Equation 12 can be simplified as where e r×1 = (U m×r ) T b m×1 + (U m×r ) T ε m×1 is the compressed echo trains, its noise level is σ 2 , and C r×n = S r×r (V n×r ) T is the compressed kernel matrix.…”

“…Echo train data should be converted to a T 2 distribution through Laplace inversion in order to further obtain the formation porosity and permeability [4,17], distinguish the bound and free fluid [3,20], and identify the fluid properties of reservoir [12,13]. Meanwhile, the application of twodimensional (2D) and multi-dimensional (MD) NMR techniques for identify the reservoir fluid properties makes the acquired echo train data from NMR logging becoming more and more huge [2,5,11].…”

Computation of parameters in NMR using integral transforms: Tapered areas

“…An important aspect of this work is that it helps quantify parameters that can be reliably obtained from the data and their dependence on the signal to noise ratio (SNR) in the data. This integral transform method to estimate areas can be generalized to multiple dimensions such as other NMR modalities like diffusion-relaxation and T 1 − T 2 data [7]. Section 3 of this paper describes a few simple integral transforms such as the sinc, exponential Haar and exponential sine transforms to compute tapered areas as well as some ideas to deal with sharper transitions.…”

Evaluation of Residual Oil Saturation in the Secondary Gas Cap of a Mature Carbonate Reservoir from Multi-Dimensional Magnetic Resonance Logging

“…The result is a continuous log quantification of fluid saturations based on the resulting Diffusion-T 1 or Diffusion-T 2 correlation maps to subdivide the total NMR porosity into water, oil and gas volumes (Heaton, 2004). The obtained oil saturation is very shallow, affected by mud filtrate invasion, but since the oil saturation in the Mauddud gas cap is approaching residual condition, the results are useful.…”

“…There are references available detailing multi-dimensional NMR acquisition and interpretation techniques (Freedman 2001(Freedman , 2002(Freedman , 2004Hurlimann, 2002;Cao Minh, 2003;Heaton, 2004). To better understand certain conditions found in the Mauddud gas cap we will provide the basic ideas of this methodology and its interpretation.…”