Specific Surface and Fluid Transport in Sandstones Through NMR Studies

Abstract

Summary Recent nuclear magnetic resonance (NMR) studies in water-saturated porousmedia showed that magnetic resonance relaxation of 1H nuclei is a powerful toolfor studying the interplay between geometry and fluid transport. Propercombinations of spin-lattice relaxation lifetime, T1, and porosity allowpermeability to be predicted. T1, as defined porosity allow permeability to bepredicted. T1, as defined here, provides a bridge between structural andtransport properties because it can be viewed as a dynamically weightedproperties because it can be viewed as a dynamically weighted (by diffusion)version of the specific surface. In this paper, we probe this role of T1 for asuite of clean sandstone samples in which, besides permeability and porosity, specific surface by mercury porosimetry and the formation resistivity factor(FRF) also have been measured. We studied the correlations among theseproperties and found that the ability of T1 to estimate permeability is aresult of its linear dependence on the PV-to-surface ratio, Vp/S. For cleansandstone rocks, one may view the reciprocal electrical resistivity formationfactor, 1/F, as representing the transport properties and the factor T21 asrepresenting the distance scale, giving k T 21/F. A suitable analysis of thespin-lattice relaxation curve can yield an estimate of an appropriate specificsurface pertinent to permeability because it indirectly accounts for theconnectivity of the pore space. This NMR approach constitutes a usefultechnique for a better reservoir characterization and for studying some elusiveproperties of natural porous media in a nondestructive manner. properties ofnatural porous media in a nondestructive manner. Theoretical andphenomenological correlations among permeability, porosity, FRF, and PV-to-surface ratio can be established. porosity, FRF, and PV-to-surface ratiocan be established. Introduction General Remarks. Specific surface is a very important characteristic ofreservoir rocks. We know that it affects permeability, and we know that, alone, specific surface is not sufficient to characterize the network of node andthroat interconnections or to establish how the pore-space architecture governsfluid flow. Specific surface can be determined only by indirect methods, andthe results obtained differ because each method measures a different surface. NMR is a powerful tool for studying the interplay between structural andtransport properties of porous media saturated by hydrogenous liquids. Inparticular, the improvement of previous findings, showed that magneticresonance relaxation of 1H nuclei of water filling the pore space can be usedto predict sandstone permeability through combinations of porosity and aproperly permeability through combinations of porosity and a properly definedspin-lattice relaxation lifetime, T1 (stretched exponential relaxation time;i.e., the time for decay by a factor of e). In this work, the origin of theobserved correlation of T1 with permeability is studied on a suite of 37 oil-and gasfield sandstone permeability is studied on a suite of 37 oil- andgasfield sandstone samples (30 of which were also studied in Ref. 22). Withthis aim, properties such as permeability, porosity, specific surface, FRF, properties such as permeability, porosity, specific surface, FRF, andrelaxation time were measured and their correlations studied. In this way, weprobed the dependence of permeability on structural properties. This studyyields an approach for better reservoir characterization and for studyingsandstone properties pertinent to hydrocarbon production. In addition, itfurnishes a pertinent to hydrocarbon production. In addition, it furnishes amethod to estimate a particular version of specific surface relevant toflow. Problem Outline. The strategy of the studies to predict sandstone Problem Outline. The strategy of the studies to predict sandstone permeability through T1 relaxation lifetime s is to look for values permeability through T1relaxation lifetime s is to look for values for exponents B and C in TC1 B termthat best predict measured k values. As Banavar and Schwartz noted, at firstglance, it would appear that NMR is not a likely candidate for providinginformation on permeability. In fact, two similar pore spaces with similar poregeometries and surface properties but with pore interconnections opened orblocked to flow, respectively, could have the same relaxation behavior butdifferent permeability properties. A good estimation of k, however, often canbe found by relaxation lifetimes, apparently because of the correlationexisting between pore-node and pore-throat sizes in sandstones. pore-node andpore-throat sizes in sandstones. After overcoming this conceptual difficulty, it appears that the origin of the statistical correlation between k and T1 hasa common dependence on the Vp/S ratio. Indeed, the relationship k L2 m'summarizes the findings of several authors. From time to time, the meaningattributed to L and m' variables has been specified. In all cases, m' is afunction of the cementation exponent, m, bound to the FRF by Archie's empiricallaw 1/F m, and L is a characteristic length of the porous medium. For modelsystems, such as the grain consolidation model, Banavar and Schwartz assumed that (1) where m = 1.8. Furthermore, it has been shown that T1 also depends on Vp/S. In the case of a single pore, T1 is directly related to Vp/S. In thefast-diffusion regime, when diffusion supplies the walls with enough protonsduring relaxation (which is the case for all samples reported here), 1/T1 =S/Vp. In the slow-diffusion regime, 1/T1 = GD(S/Vp). In these relationships, isa phenomenological factor with velocity dimensions that measures thephenomenological factor with velocity dimensions that measures the relaxationefficiency of the surface, whereas D is the self-diffusion coefficient of thebulk water and G is a geometrical factor. Thus, the exponent of Vp/S goes from1 to 2 as the diffusion regime goes from fast to slow. The T1 value of a samplereflects this dependence on Vp/S. In fact, in rocks, relaxation behaviordepends on the probability distribution of an average value of the Vp/S ratioover a region that can have a dimension of several pore spacings and for whichthe linear size is the diffusion length (the length that molecules diffuseduring the relaxation process). After these premises, the dependence of k on T1becomes conceptually acceptable. In recent papers, model systems that areappropriate to describe the diagenetic process by which granular systems evolvefrom high-porosity, poorly consolidated states to low-porosity, wellconsolidated materials have been used to investigate the origin of the T1 - krelation. The various quantities of interest (i.e., k, and T1) can becalculated and correlations can be studied.