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_Journal of Structural Geology 32 (2010) 1201–1211_ _Modeling Fracture Porosity Evolution in Dolostone_ _Julia F.W. Gale, Robert H. Lander, Robert M. Reed, Stephen E. Laubach_ _Bureau of Economic Geology, Jackson School of Geosciences, The University of Texas at Austin, USA; Geocosm LLC, Austin, USA_ _Article history: Received 27 February 2008; Received in revised form 16 October 2008; Accepted 9 April 2009; Available online 13 May 2009_ _Keywords: Cement growth Diagenesis Dolomite Opening-mode fracture_ _Abstract_ _Opening-mode fractures in dolostones buried to depths of ~5 km contain synkinematic dolomite cement, the amount and internal structure of which has a systematic relationship to fracture size. Narrow fractures (<0.01 mm) typically seal completely with either massive cement or cement with a crack-seal texture that indicates multiple incremental openings. Wider fractures can preserve considerable effective porosity, but anomalously thick dolomite cement bridges are commonly present in fractures that are otherwise lined with a thin veneer of cement. Dolomite bridges resemble quartz bridges that are common in fractured sandstones._ _We developed a geometric crystal growth model for synkinematic dolomite fracture fill in fractured dolostones, where periodic incremental fracture-opening events are introduced with concurrent cement growth. We assumed constant temperature and supersaturation with respect to dolomite. A key assumption in the model is that rapid dolomite accumulation within bridges is governed by high cement-growth rates on repeatedly broken grain surfaces during the process of crack seal. Slower cement-growth rates occur on euhedral crystals. This assumption is made on the basis of a comparison with quartz cement growth in fractured sandstones. Simulations with different fracture-opening rates mimic bridge and lining cement morphologies, including characteristic rhombic shapes of dolomite bridges._ _? 2009 Elsevier Ltd. All rights reserved._ _1. Introduction_ _Opening-mode fractures have an important influence over fluid flow in many dolostones (e.g., Montané, 1997; Antonellini and Mollema, 2000; Gale et al., 2004; Philip et al., 2005; Kosa and Hunt, 2006). The essential attribute for fluid flow is that fractures are open in the subsurface. Contrary to expectations of some fracture mechanical modeling, which predicts that subsurface loading conditions should close most large fractures (Zoback, 2007), core studies show that in dolostones, open fractures exist at depths up to 5 km (Gale et al., 2008) (Fig. 1). The stability and persistence of open fractures may reflect the stiffening effect of cements in host-rock pore space and isolated cement deposits within fractures (Laubach et al., 2004a). Here we investigate how such isolated cement deposits may form in dolostones._ _Much published work on fractured carbonates has focused on conditions leading to fracturing and fracture reactivation, including the roles of effective stress, fluid pressure and confining pressures (e.g. Mollema and Antonellini, 1999; Hilgers et al., 2006). There has been also much work on carbonate mechanical stratigraphy (Corbett et al., 1987; Ferrill and Morris, 2008), and on the properties of carbonate fault rocks (Agosta et al., 2007). Core-based studies have highlighted the important role of cement in closing fractures and reducing dolostone fracture permeability (Gale et al., 2004), effects that have been quantified in elastic fracture mechanical and flow modeling of fracture patterns with cement modification (Philip et al., 2005; Olson et al., 2007)._ _Cementation in a fracture can be separated into synkinematic and postkinematic deposits, depending on whether the cement precipitated while fractures were opening or after the opening process had ceased (Laubach, 1988). The purpose of this paper is to provide insight into synkinematic cement deposition mechanisms in dolostone fractures through microstructural analysis and modeling. We use examples from the Lower Ordovician Knox Group in Mississippi, the Lower Ordovician Ellenburger Formation in West Texas, and the Pennsylvanian Canyon Group in New Mexico. Our geometric crystal growth model for synkinematic dolomite fracture fill in fractured dolostones is a modification of a model (Prism2D) that simulates quartz cementation in sandstones (Lander et al., 2008). The key process modeled is the differential cement-growth rate on euhedral versus broken nucleation surfaces, as repeated episodes of crystal breakage occur during fracture growth (in multiple opening increments) must be comparable to the rate of cement precipitation. We simulated several different relative opening-rate to cementation-rate ratios, to represent a range of situations, from those where cementation proceeds more quickly than fracture opening, to those where fracture opening is dominant._ _Fractures accommodating opening displacement propagate along a plane of zero shear stress in isotropic rock, oriented perpendicular to the least compressive principal stress (Lawn and Wilshaw, 1975). This configuration makes fractures indicators of past stress orientations, but provides little information on the conditions that drive fracture growth. Fractures widen through some combination of diminished minimum stress and elevated pore fluid pressure. In our examples, synkinematic cement only spanned fractures in limited areas. Cement deposits must therefore be reacting to fracture opening rather than causing opening, for example by force of crystallization. Information on fracture rates would provide an essential constraint on conditions of fracture growth. Our model does not specify the loading conditions that drive fracture growth. Opening is represented as a uniform but incremental widening. We did not model the crack tip or reactivation in shear, which is a more complex situation, because comminution would need to be considered in addition to cement growth._ _Fig. 1. Opening-mode fractures in Pennsylvanian dolostone core from 2370 m depth. Most fractures in this sample are partly open. Variability in the degree of openness is linked to total fracture width (kinematic aperture), with wider fractures being more open. Fracture porosity is partly occluded by dolomite cement bridges and linings._ _Incremental fracture opening (Lander et al., 2008). Growth rates on broken surfaces tend to be higher than predicted by the growth kinetics as noted in laboratory experiments with the analogue material alum (Nollet et al., 2006)._ _Following work in sandstones by Walderhaug (1994, 1996, 2000) and Lander and Walderhaug (1999), we infer that cement precipitation in dolostones, rather than material transport, governs dolomite accumulation rates. With this assumption, and the insight that cement accumulation rates differ on fractured and euhedral mineral surfaces (Lander et al., 2008), we predict cement deposit geometries that can be compared to natural examples._ _2. Rates of Fracture Opening and Cement Precipitation_ _2.1. Rates of Fracture Opening_ _Seeing the sealing of opening-mode fractures during a phase of fracture growth as a competition between the rates of fracture opening and synkinematic cement precipitation, cements may fill the fracture completely, be present only as thin linings coating the fracture walls, or bridge across the fracture from one wall to the other. Cement bridges potentially contain much information on rates. In quartz systems, for example, fluid inclusion data from distinct crack-seal events in cement bridges provide information on the temperature during precipitation. As growth rate is dependent upon temperature, it is possible to calculate the growth rates on successive fracture surfaces. The growth rates, together with the kinematic aperture of each filled microfracture in the cement bridge, can then be used to calculate fracture-opening rates (Becker et al., 2008). Parris et al. (2003) used fluid inclusions from ankerite cements to constrain timing of fracturing events but did not investigate rates. The relative and absolute rates of fracturing and cement growth in the dolomite system remain poorly constrained or unknown. However, for bridges to form, the overall rate of_ _2.2. Precipitation Rate Laws_ _In an experimental study, Arvidson and Mackenzie (1999) determined that the precipitation rate of dolomite can be modeled with a rate law that is a function of saturation index:_ _r ? k?U ? 1?n_ _(1)_ _where r is the rate of precipitation per unit area, U is a unitless supersaturation term for ideal dolomite, and n is the order of the overall reaction. The rate term, k, takes an Arrhenius form:_ _k ? A e??Ea_RT?_ _(2)_ _where A is a constant, Ea is the activation energy for dolomite precipitation, R is the real gas constant, and T is temperature._ _Walderhaug (2000) recognized that temperature is the primary control for quartz precipitation; he used Eq. (2) to model quartz cementation and porosity loss in sandstones. Lander et al. (2008) noted that the supersaturation term is implicit in A because the fluid in sandstone reservoirs is at or above saturation with respect to quartz. We follow a similar line of argument for dolomite. We model the precipitation of dolomite in a fractured dolostone from a fluid supersaturated with respect to dolomite. Although stylolites are present in some samples (e.g., Fig. 1), we found no evidence of dissolution of fracture-filling cements in our examples._ Ключевые слова: model, opening-rate, rhomb, event, cementation, synkinematic, precipitation, olson, completely sealed, gomez, seal, spe, science, ebsd map, surface, fracture opening, bridge, permian basin, broken surface, crystal growth, carbonate, bulletin, dolomite precipitation, opening rate, ha, porosity loss, rst-order control, result, fracture trace, reservoir, open, crystallographic, journal structural, sem-cl, rst-formed cement, laubach, rhomb-shaped bridge, step, arvidson, fracture increment, sealed, journal, modeled, sandstone, natural, fracture sealing, growth, quartz, synkinematic cement, gale journal, open fracture, orientation, model scenario, wall, precipitation rate, fracture lling, aapg bulletin, process, provide insight, grain, continuous, wider fracture, rhomb face, tectonophysics, small, fast, opening-mode fracture, cement, west texas, crack, report, kosa hunt, fracture wall, brantley, geo?uids, zoback, fracturing, sandstone lander, rate, lake hilgers, hilgers, chemical, parris, modeled fracture, vein, fractured, euhedral, journal sedimentary, development, dolomite crystal, reed, polycrystal growth, fracture size, walderhaug, ?ow, structural, cement bridge, dolostone reservoir, time faster, model result, complete sealing, sem-cl image, geology, euhedral face, cement precipitation, sei image, quartz lander, modeling, aapg, increment, cement growth, texture, elsevier, hilgers urai, broken, structural geology, crystal, agosta, dolomite cement, dolomite, calcite, partly occluded, dolostones, wa, fracturing event, face, fracture-opening rate, growth rate, ?uid, size, sample, knox, fracture-opening, form, pore, dolomite bridge, crystallographic continuity, fracture event, crystallographic orientation, fractured dolostone, fracture pattern, urai, grow, experimental study, multiple, natural fracture, bons, sedimentary, opening, aperture, simulation, group, quartz bridge, texas, euhedral crystal, model template, multiple crystal, template, fastest rate, mollema, porosity, marrett, image, crack-seal, opening-mode, gale, fracture, lander, crack-seal texture, journal structural geology, completely, euhedral surface, fracture porosity, rst cement, host grain, corbett, fracture growth, rock, dolostone, uid, crack seal, unitaxial growth, crystal morphology, oil, sedimentary basin, postkinematic, sealing