Description:

_Journal of Structural Geology 32 (2010) 1271–1278_ Contents lists available at ScienceDirect Journal of Structural Geology journal homepage: www.elsevier.com locate jsg Quantifying uncertainties in multi-scale studies of fractured reservoir analogues: Implemented statistical analysis of scan line data from carbonate rocks Vincenzo Guerriero a,*, Alessandro Iannace a, Stefano Mazzoli a, Mariano Parente a, Stefano Vitale a, Maurizio Giorgionib Dipartimento di Scienze della Terra, Università degli studi di Napoli ‘Federico II’, Largo San Marcellino 10, 80138 Napoli, Italy b Shell Italia E & P, Rome, Italy Article history: Received 13 March 2008 Received in revised form 10 April 2009 Accepted 27 April 2009 Available online 8 May 2009 Keywords: Structural analysis Fracture statistics Power-law distribution Confidence interval Abstract In this study we performed a fracture analysis on a Cretaceous bedded carbonate succession well exposed in the Sorrento Peninsula. The studied succession includes stratigraphic units that are very similar to the productive units of the buried Apulian Platform reservoir rocks in southern Italy. We analyzed eight carbonate beds, including both limestones and dolomites. The basic technique used in this study consisted of measuring fractures along bedding-parallel scan lines. For one limestone bed, a microscale scan line, about 15 cm long, was also analyzed using a digital microcamera. Provided the cumulative distribution of fracture apertures is well described by a power law, our analysis shows how the uncertainty in the estimate of fracture aperture cumulative frequencies grows for large aperture values. This feature results in a large uncertainty in the estimate of the slope of the least-squares line (in a bi-logarithmic diagram) approximating the data distribution, which is the exponent of the power law. As the latter represents a fundamental parameter characterizing a fracture set and fracture distribution over different scales, reducing the uncertainty in the estimate of the slope of the curve represents an important objective of quantitative fracture analysis. This is obtained in this study by the application of multi-scale analysis, and by integrating micro-scan line data with classic outcrop-based scan line analysis. The quantification of uncertainties in the cumulative distribution estimates of fracture apertures is performed by analyzing in detail the spacing distribution – and consequently fracture-density distribution – for each aperture value. Our results suggest that a meaningful statistical analysis of fracture attributes such as aperture (or opening displacement) may be effectively carried out by using properly determined confidence intervals and by the integration of outcrop-based and micro-scan line data sets. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction A fundamental issue in the characterization of fractured reservoirs is constituted by the limitations inherited in fracture sampling in the subsurface, as represented in well log data or cores. Fracture scaling relationships may be effectively used to overcome such limitations. Numerous studies have shown that, besides the largely studied scaling behaviour of faults, also opening-mode (i.e., Mode I) fracture size distributions are generally effectively described by a power law – i.e., parameters such as length or opening of fractures are self-similar over a range of scales (e.g., Das Gupta, 1978; Sinclair, 1980; Mandelbrot, 1983; Nelson, 1985; Gudmundsson, 1987; Heffer and Bevan, 1990; Barton and Zoback, 1992; Gillespie et al., 1993; Sanderson et al., 1994; Barton, 1995; Gross and Engelder, 1995; Johnston and McCaffrey, 1996; Marrett, 1997; Odling et al., 1999; Ortega and Marrett, 2000, 2006). On the other hand, fracture spacing appears to be controlled by a series of parameters including (Nelson, 1985): (i) rock composition; (ii) rock texture, grain size, porosity; (iii) structural position; and (iv) mechanical layer thickness. The latter parameter has been extensively analyzed, and the relationship of increasing fracture spacing for increasing bed thickness has been widely documented (Price, 1966; Huang and Angelier, 1989; Narr and Suppe, 1991; Gross, 1993; Mandal et al., 1994; Gross and Engelder, 1995; Wu and Pollard, 1995; Narr, 1996; Pascal et al., 1997; Bai and Pollard, 2000). Although most of the studies on fracture populations concerned fracture spacing or fracture length, fracture-opening distributions have also been effectively analyzed, confirming that the cumulative distribution of joint apertures is well described by a power law (Ortega et al., 1998, 2006; Ortega and Marrett, 2000). In order to further clarify the meaning and importance of power-law distributions, an example may be used, emphasizing some of the main quantities that can be obtained. Suppose that the cumulative distribution of joint apertures for a fracture set is described by the following power law: F(b) = c b^(-m); where b is the joint aperture, F is the cumulative frequency (i.e., the number of joints per meter having aperture greater than b), and c and m are experimental constants. Let us consider the mean aperture b* between two arbitrary limits b1 and b2: b* = ∫(b1 to b2) f(b) db, where f(b) is the aperture frequency distribution, given by the derivative of F(b). This non-dimensional quantity provides the contribution, given by those joints for which b1 < b < b2, to the longitudinal strain of the rock. Furthermore equation (2), providing the ‘void’ fraction estimate along the scan line for any values of b1 and b2, could furnish significant information about the porosity and permeability of the rock at different scales of observation. It should also be noted that the value m > 1 represents a ‘critical value’, because it is well known from mathematical theory that for |m| > 1, b2 → 1 and b1 → 0, equation (2) yields: b* ≈ N (in reality, a lower limit for the validity of power law exists, and the condition b1 → 0 has only a theoretical meaning). On the other hand, for |m| < 1, b2 → ∞ and b1 → -∞, it results: b* → ∞. The geological meaning is that m > 1 characterizes more ‘pervasive’ fracture sets. For m > 1, the larger contribution to fracture porosity (in case of non-filled joints), as well as longitudinal strain, is provided by the smaller fractures. Consequently fracture porosity grows slowly as the scale of observation increases. Conversely, for m < 1, fracture porosity and longitudinal strain increase markedly with the scale of observation. In outcrop-based studies, the parameters (e.g., fracture spacing, fracture length, fracture aperture) for fracture analysis are generally acquired by a widely used methodology involving the statistical analysis of fracture sets detected along scan lines. Despite the large amount of work carried out using this methodology, very few studies deal with the reliability of scan line data interpretation, especially concerning the quantification of uncertainties. In order to normalize data acquisition by this methodology, hence allowing for comparison between data gathered at different locations, Ortega et al. (2006) proposed the use of a common fracture size threshold, requiring the determination of fracture size distribution. The latter authors proposed the analysis of the standard deviation of consecutive fracture frequency estimates as a means to evaluate the uncertainty of fracture-density determinations. The aim of the paper is to afford the problem of fracture estimate uncertainty by analyzing the power-law distribution of fracture attributes, such as fracture opening and fracture spacing. In order to have a reliable statistical distribution, we needed to integrate naked-eye data collection with micro-observation by means of a digital microcamera directly on the field. The study has been performed on Cretaceous bedded carbonate succession cropping out in southern Italy. 2. Geological setting and fracture data collection Significant oil discoveries in the southern Apennines fold and thrust belt are associated with hydrocarbon traps consisting of reverse-fault-related, open, long-wavelength folds involving a 6–8 km thick Mesozoic–Tertiary carbonate platform succession (Shiner et al., 2004). These carbonate platform reservoir rocks, deformed by thick-skinned reverse faults and inversion structures involving the underlying basement (Mazzoli et al., 2001, 2008), represent a tectonically buried portion of the Apulian Platform carbonates, continuous with those exposed in the Apulian promontory to the NE (Fig. 1a). The outcropping thrust belt forms a displaced allochthon that has been carried onto such a footwall of Apulian Platform foreland strata (Fig. 1c). The allochthonous units include carbonate platform and pelagic basin successions, locally covered by Neogene foredeep and or thrust-top basin sediments. The structure at shallow levels is dominated by low-angle tectonic contacts separating the platform slope carbonates of the Apennine Platform, in the hanging wall, from underlying pelagic basin successions (Lagonegro Units; Mazzoli et al., 2008). The carbonate succession of the Apennine Platform includes stratigraphic units that are very similar to the productive units of the buried Apulian Platform reservoir rocks in terms of age, lithology, facies, overall thickness, mechanical layer thickness of single beds, and rock texture. As such, outcrops of Apennine Platform carbonates are used for fracture analysis of reservoir analogues. This is capable of providing important information, although the different tectonic evolution and burial conditions experienced by the Apennine Platform with respect to the Apulian Platform characterize their distinct geological settings._ Ключевые слова: con?dence, southern, multi-scale analysis, coefcient, aperture cumulative, tectonophysics, narr, density, mm, simple, set, layer thickness, joint spacing, data, fracture density, bed, data distribution, fractal geometry, porosity, carbonate, parameter, fracture-density, based, data set, doi, distribution fracture, methodology, relationship, succession, loglog diagram, standard, fracture attribute, segment, eds, con?dence interval, dolomite, signi?cant, fracture analysis, geological, limit, microscale scan, deviation, scan, power-law distribution, large uncertainty, poisson, slope, longitudinal strain, measuring fracture, angelier, data gathered, platform, fracture, cumulative frequency, apulian platform, italy, study, size, aapg, marrett, porosity he-porosity, analyzed bed, guerriero, rock, fracture aperture, mandelbrot, mandal, guerriero journal, diagram, structural, micro-scan, probabilistic theory, nelson, joint aperture, bedding-parallel scan, equal, large, fracture-density estimate, le, geology, scaling relationship, ortega marrett, method, structural geology, cumulative, sinclair, outcrop, aperture, mazzoli, shell italia, limestone bed, press, joint, interval, larger, engelder, parameter exponent, probability, upper limit, apennine platform, price, application, thickness, uncertainty, result, ha, measured fracture, apulian, multi-scale, limestone, spacing, unit, layer, law, scale, shiner, paper, fracture number, barton, analyzed, determination, journal structural, power law, sampling estimate, involving, spacing distribution, opening displacement, fracture set, sanderson, rapid method, number, variable, fractured, reservoir, frequency, generally, analysis, order, point, peninsula, aleatoric, standard deviation, power, fracture spacing, studied, study consisted, large aperture, case, gudmundsson, gross, online, petroleum, exact method, condence interval, observation, cumulative distribution, digital microcamera, monte faito, scale observation, error, efcient estimator, journal structural geology, journal, erto, aleatoric variable, inferential statistic, productive unit, estimate, ortega, sorrento peninsula, scaling, fracture detected, distribution