Modeling of Multiple Echo-Time NMR Measurements for Complex Pore Geometries and Multiphase Saturations
- E. Toumelin (The U. of Texas at Austin) | C. Torres-Verdin (The U. of Texas at Austin) | S. Chen (Baker Atlas)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- August 2003
- Document Type
- Journal Paper
- 234 - 243
- 2003. Society of Petroleum Engineers
- 4.3.4 Scale, 5.2 Reservoir Fluid Dynamics, 5.2.1 Phase Behavior and PVT Measurements, 5.1 Reservoir Characterisation, 5.6.1 Open hole/cased hole log analysis, 1.14 Casing and Cementing, 1.2.3 Rock properties, 5.3.1 Flow in Porous Media
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We develop a numerical algorithm to simulate nuclear magnetic resonance (NMR) measurements in the presence of constant magnetic field gradients. The algorithm is based on Monte Carlo conditional random walks in restricted and unrestricted space. Simulations can be performed of 3D porous media that include both arbitrary bimodal pore distributions and multiphase fluid saturations. The ability to account for the presence of a constant external magnetic field gradient allows us to replicate actual well-logging conditions that include the effect of Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences at a microscopic level. This is accomplished by simulating ideal pulse-acquisition techniques that include multiple interecho times (TE) similar to those currently used by the well-logging industry. Benchmark examples are presented to validate the accuracy and internal consistency of our algorithm against previously published results for the case of a null magnetic field gradient. Validation examples also are presented against actual NMR measurements performed on core samples of carbonate rock formations.
Interpretation work is focused on the petrophysical assessment of both partial oil/water saturations and pore structures exhibiting diffusive coupling. Simulation examples are designed to quantify whether the inclusion of diffusion under a magnetic field gradient can improve the interpretation of multiphase fluid saturations when diffusion coupling is significant. The simulation algorithm sheds light on new NMR data-acquisition strategies that could be used to improve the detection and quantification of fluid types, complex fluid saturations, and complex pore geometries.
The presence of diffusion pore coupling in carbonate rocks (mainly grainstones) challenges conventional NMR interpretation techniques. Although pore-coupling phenomena are commonplace in the majority of rock pore systems, they become relevant to assess NMR measurements when the following three conditions are met: (a) microporosity regions are present within the grains; (b) micropores are well-connected (not cemented) to outer macroporous regions exhibiting low surface-to-volume ratios, thereby allowing fluid diffusion between both pore scales; and (c) rock surface relaxivity is low enough to prevent the decay of proton magnetization within the macroporosity before protons can enter the microporous regions. In addition, fluid diffusivity must be sufficiently large for diffusion coupling to be significant within the time scale of NMR measurements. This is usually the case only for water and light hydrocarbons. As a result, fluid magnetization will be exchanged between micro- and macropore regions, and no obvious relationship will exist between NMR transverse relaxation (T2) distribution and pore-size distribution. Fig. 1 illustrates conditions (a) and (b), described previously, with an example of scanning electron microscope (SEM) images of a carbonate rock exhibiting diffusion coupling.
Varying TE is a common NMR data-acquisition technique used for in-situ reservoir fluid identification.1-3 However, in the case of NMR measurements performed in carbonate rocks, there are no published reports dealing with the impact of diffusion coupling on hydrocarbon typing and quantification using multiple-TE logging techniques. The objectives of this paper are twofold: (a) to develop a simulation algorithm capable of reproducing NMR measurements in complex pore geometries under a variety of experimental conditions and (in particular) under the influence of a constant magnetic field gradient, and (b) to provide simulation examples that will help assess the validity of fluid phase discrimination using multi-TE measurements in porous media exhibiting diffusion coupling.
In the past, numerical models of NMR decay were proposed based on periodic bimodal packs of spheres that accounted for surface relaxation effects. We have reproduced and extended Ramakrishnan et al.4's Monte Carlo algorithm to account for the effect of an external constant magnetic field gradient of the type enforced by modern NMR tools, and in the presence of a nonwetting phase. The first part of this paper introduces the Monte Carlo simulation algorithm applicable to a bimodal pack of spheres in the presence of a constant magnetic field gradient. A subsequent section describes examples of numerical simulation that illustrate the versatility of the algorithm. Finally, we derive and interpret simulation examples intended to address specific issues of fluid discrimination using multiple interecho times in the presence of diffusion coupling. We address four specific cases of NMR T2 distributions (two unimodal and two bimodal) by modeling several possible combinations of pore structure, diffusion coupling, and fluid distribution. These case studies were designed so that different pore configurations created identical NMR signals at low values of TE but exhibited differences at high values of TE.
Model for the Simulation of NMR Decay
The algorithm developed to numerically simulate NMR magnetization decay in carbonate rocks makes use of conditional Monte Carlo random walks. It is based on the algorithm described by Ramakrishnan et al.,4 further generalized to include microscopic diffusion effects in the presence of a constant magnetic field gradient. 5 The assumption of a constant gradient across the zone probed by NMR tools is generally an accurate approximation in the presence of small contrasts of magnetic susceptibility (i.e., in the absence of paramagnetic materials). Porous media can include micro- and macroporous regions (grainstone model) to form a bimodal pore distribution, or they can exhibit a single pore size with solid grains (wackestone model).
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