This paper presents a model to estimate permeability from well logs in carbonate reservoirs. The model relates permeability to interparticle porosity, makes special accommodation for separate vug porosity, and includes a rock-fabric classification scheme with an important dual petrophysical-geological significance. The dual significance of the rock-fabric classification provides an important link to geological models for use in distributing permeabilities between wells. Porosity and permeability are highly variable and are difficult to predict spatially in most carbonate reservoirs, but rock-fabric changes tend to be organized systematically within a sequence stratigraphic framework.
Reservoir characterization and modeling are primarily a problem of understanding the 3D spatial arrangement of petrophysical properties. Petrophysical measurements must be linked to spatial information when building a reservoir model, and geologic models contain vital spatial information to be applied in interwell areas in which direct petrophysical measurements are difficult. The link is best accomplished through the integration of geologic rock-fabric descriptions and petrophysical measurements.
A method for linking basic rock-fabric descriptions and petrophysical properties has been proposed by Lucia.1,2 Carbonate pore space is divided into interparticle (which includes both intergrain and intercrystal) and vuggy pore space (Fig. 1). Vuggy pore space is subdivided into separate and touching vugs on the basis of vug interconnection. Separate vugs are connected through the interparticle pore space (e.g., grain molds), and touching vugs form an interconnected pore system independent of the interparticle pore space (e.g., caverns and fracture pore space). Interparticle pore space is subdivided into rock-fabric classes on the basis of geologic descriptions of particle size and sorting.
In this paper, we present an approach to permeability modeling in carbonates on the basis of this rock-fabric classification. The paper is organized into five main sections:
the carbonate rockfabric classification is summarized, and its relationship to porosity and permeability is presented;
exponential and power-law porosity/ permeability models are compared, and a generalized power-law model relating interparticle porosity, permeability, and rock fabric is presented;
the generalized permeability model is compared with three others from the literature;
rock-fabricbased methods for permeability prediction from well logs are summarized; and
an approach to 3D modeling of carbonate permeability, taking advantage of the geological link provided by the rock-fabric method, is described.
Permeability and capillary properties of interparticle pore space can be related to interparticle porosity and geologic descriptions of particle size and sorting called rock fabrics.1,2 These rock fabrics were initially grouped into three categories called rock-fabric petrophysical classes on the basis of their porosity/permeability relationships and capillary properties1 (Fig. 2):
Class 1 is composed of grainstones, dolograinstones, and large crystalline dolostones.
Class 2 is composed of grain-dominated packstones, fine and medium crystalline, grain-dominated dolopackstones, and medium crystalline, mud-dominated dolostones.
Class 3 includes mud-dominated limestones and fine crystalline, mud-dominated dolostones.
The permeability of limestone increases with increasing intergrain porosity and increasing grain size and sorting (Fig. 3). Mud dominated limestones (mud-dominated packstones, wackestones, and mudstones) have the least permeability and generally fall on a porosity/permeability crossplot within a field associated with petrophysical class 3. Grain-dominated packstones have higher permeability values and generally fall within the Class 2 field. Grainstones have the highest permeability and generally fall within the Class 1 field.
Permeability in dolostone also increases with increasing intergrain porosity and increasing grain size and sorting of the precursor limestone (Fig. 4). The permeability of mud-dominated dolostone increases with increasing dolomite crystal size and increasing intercrystal pore space.1 Fine crystalline, mud-dominated dolostones have permeability characteristics of Class 3 limestones. Medium crystalline, mud-dominated dolostones have characteristics of Class 2 limestones. Large crystalline, mud-dominated dolostones have characteristics of Class 1 limestones.
Separate vugs contribute porosity but significantly less permeability than would be expected if the pore space were located between particles.1 However, touching-vug pore systems can have very large permeabilities that are not adequately predicted by this rock-fabric petrophysical classification.1 Fortunately, the flow properties of many carbonate reservoirs are not dominated by touching vugs.
Porosity/permeability relationships traditionally have been modeled with exponential functions of the form
where k is permeability, f is porosity, and a and ß are constants. These models plot as straight lines on semilogarithmic coordinates (Fig. 5), and they offer the advantages of simplicity and convenience. However, they unrealistically predict nonzero permeabilities when the porosity is zero, and they most likely overpredict permeability when the porosity is small. These overestimates of permeability could lead to significant errors in reservoir modeling if, for example, there are thin intervals restricting vertical flow that are poorly sampled and that have permeabilities being predicted by an extrapolation of an exponential model.