Dolomitisation of carbonate platform margins by fault‐controlled geothermal convection: Insights from coupling stratigraphic and reactive transport models

Reactive transport modelling is increasingly deployed to quantitatively evaluate conceptual models of diagenetic processes. However, construction of models of complex systems involves trade‐offs between accuracy and simplification. This tension is explored for models of fault‐associated dolomitisation by sea water convection in a syn‐rift carbonate platform, evaluating the contribution of incorporating stratigraphic growth and fault propagation. Simulations of the high heat flux southern margin of the Derbyshire Platform (Northern England), with heterogeneous matrix permeability that reflects the evolving stratal architecture and burial compaction focusses dolomitisation in more permeable units at all depths. A permeable platform margin fault zone enhances dolomitisation in a broad area on the upper slope and margin, and to a lesser but significant extent, across the interior as platform top waters are entrained and discharge via the fault. Stepwise simulation of flow and reactions during stratigraphic growth suggests that static models over‐predict dolomite abundance in younger sediments and show how regions optimally supplied with reactants and heat to drive dolomite formation migrate vertically and laterally during platform growth. Dolomitisation intensity increases with depth due to greater time for reactions and kinetically favourable temperatures. Adding the fault zone to this model focusses and accelerates flow, giving a more spatially restricted dolostone body and reducing dolomitisation temperature. Changes in fault connectivity with the surface of the evolving platform shift fluid flow pathways and change the rate and temperature of dolomite formation. Results concur with petrographic, isotopic and geochemical observations of the early dolomite on the Derbyshire Platform. This work demonstrates the importance of understanding diagenesis as the product of an evolving set of processes that respond to geological and palaeoenvironmental changes rather than as a sequence of individual diagenetic events. This is particularly critical for reactions, such as dolomitisation by geothermal convection of sea water, which occur over timescales synchronous with platform development.

the importance of understanding diagenesis as the product of an evolving set of processes that respond to geological and palaeoenvironmental changes rather than as a sequence of individual diagenetic events. This is particularly critical for reactions, such as dolomitisation by geothermal convection of sea water, which occur over timescales synchronous with platform development.

| INTRODUCTION
Reactive transport models (RTMs) that simulate coupled fluid flow, heat and solute transport and reactions offer the opportunity to rigorously evaluate conceptual models of diagenetic alteration. Given the inherent reactivity of carbonate sediments, water-rock reactions can substantially modify mineralogy, porosity and pore network structure starting at the time of deposition and continuing through burial and uplift. While most RTM simulations of carbonate diagenesis under-represent the complexities in geometry and rock properties of real platforms, they offer insights into the distribution of diagenetic products seen at outcrop as well as generating attractive predictive concepts for application to data-poor subsurface situations. As such, the design of models, specifically the degree to which they capture key controls on diagenetic processes, is of critical importance. In developing 'useful' models, the aim is to represent enough of the reality of the system to draw meaningful conclusions, and yet to avoid unnecessary complexity so that multiple model realisations can be deployed to understand uncertainties in the system. The key question remains, what complexity matters and what details have only secondary relevance to the question asked?
Given the challenging nature of developing simulations of coupled flow and reactions, early RTMs of carbonate diagenesis tended to use static platform geometries, constant boundary conditions and simple rock property distributions. There has been a sharp focus on application of RTMs to understand various aspects of the replacement of limestone by dolomite, despite the challenges inherent in the 'dolomite problem' (Machel, 2004;Whitaker et al., 2004;Xiao & Jones, 2018). However, the lack of integration with explicit simulation of sedimentological processes limits application of RTM to diagenetic reactions that occur soon after deposition and during early burial (Whitaker & Frazer, 2018). Attempts to replicate patterns of shallow reflux dolomitisation seen in outcrop demonstrate the importance of considering changes in boundary conditions and rock properties through time, even in systems where reaction rate is relatively rapid (Gabellone et al., 2016;Garcia-Fresca & Jones, 2011;Garcia-Fresca et al., 2012). Such coupling is, arguably, at least as important where reaction is slow relative to timescales of platform development. However, this approach has yet to be applied to dolomitisation by geothermal convection, which is a process that probably occurs in most carbonate platforms that are in hydraulic continuity with the ocean.
Heating and circulation of sea water by geothermal convection can facilitate the dolomitisation of carbonate platforms. The fundamental requirement for the formation of kilometre-scale dolostone bodies is the flow of sufficient volumes of Mg-rich fluids through a limestone succession (Machel, 2004;Whitaker et al., 2004). Additionally, increasing temperature reduces kinetic barriers that limit dolomitisation in many near-surface environments (Arvidson & Mackenzie, 1999). Geothermal convection is driven by density contrasts between warm water within the carbonate platform and cool water in the adjacent ocean and has the potential to operate continuously during the lifespan of a carbonate platform. The mechanism for flow was first recognised in Southern Florida (Griffin et al., 1977;Kohout, 1965) from groundwater temperature profiles that show an inverse geothermal temperature gradient resulting from the flow of cool sea water into the platform at depth. The potential of this flow system to drive dolomitisation is evidenced by magnesium depletion in groundwaters discharging from near-coastal springs (Fanning et al., 1981;Schijf & Byrne, 2007).
The numerical investigation of geothermal convection within a carbonate build-up by Sanford et al. (1998) replicated the inverse geothermal gradient seen in South Florida and explored patterns of geothermal convection and platform temperature in a generic platform with simplistic rock parameters. Sensitivity analysis showed that the size and shape of the platform and the elevation of sea level relative to the platform top exercise only a secondary control on the development of convection within a carbonate platform succession. Permeability reduction with depth, due to compaction, was seen to limit fluid supply below the upper 1000 m of a succession and permeability anisotropy was also seen to alter convective patterns. Simulation of flow within the Florida platform, with realistic horizontal and vertical variations in hydraulic properties, by Hughes et al. (2007) demonstrated the complex interplay between meteoric discharge and geothermal heat flow and the effect of complex 3D geometries and asymmetric emergence.
The RTM simulations of convection have shown that convection systems isolated from external fluid input have only limited dolomitisation potential (Jones & Xiao, 2006;Machel et al., 2008) and maintaining exchange with a reservoir of high Mg/Ca fluids ratio is key. Most subsurface brines are Ca-rich and Mg-poor (Robertson et al., 2022), but the ocean provides an effectively infinite source of reactants and sink for reaction products. Early models of geothermal convection of sea water suggested dolomitisation would occur over timescales of tens of millions of years (Whitaker & Xiao, 2010;Wilson et al., 2001). Simulations suggest that geothermal convection will dolomitise carbonate platform sediments irrespective of boundary conditions, although reactions are slower in smaller and/or isolated platforms where advective cooling is greater than in larger and/or attached platforms (Whitaker & Xiao, 2010). This study also illustrated the widely recognised importance of sediment permeability in controlling fluid flux and temperature distribution, and of effective reactive surface area of the sediment. Models with simple layering of finer-grained and coarser sediment show preferential dolomitisation of more reactive fine-grained beds at shallow depth where permeability is not limiting, switching to more permeable coarser beds at depth as compaction limits fluid flux. Simplistic representation of a bank-marginal fracture zone suggested that this limits dolomitisation of the platform interior, whether this zone is a conduit for flow, or fault gouge results in a local reduction in permeability (Whitaker & Xiao, 2010).
Syndepositional fractures and faults are common in the margins of platform carbonates and serve as conduits for flow of shallow groundwaters and hydrocarbons and other fluids at depth. In addition to structural permeability (Sibson, 1996), they can contribute to diagenetic reservoir heterogeneity, for example by focussing meteoric dissolution (Kosa & Hunt, 2006;Whitaker & Smart, 1997) or dolomitisation (Frost et al., 2012;Melim & Scholle, 2002). On burial, reopening of these faults and fractures can create flow paths for deeper fluids to move vertically through the rocks and drive renewed diagenesis. For example, abundant syndepositional fracturing of Serpukovian microbial boundstones in the margins of the Tengiz Platform (Collins et al., 2006) is shown to affect geothermal convection after burial (Jones & Xiao, 2006), as well as facilitate migration of corrosive fluids and bitumen into the platform flanks (Collins et al., 2006).
Presented here are the results of coupling stratigraphic and RTMs in order to predict the distribution of dolomite formation over time. Modelling episodic diagenesis during platform growth allows simulation of the occurrence and distribution of dolostone as a function of changing circulation patterns. This leads to a new model for shallow burial dolomitisation on the Derbyshire Platform, Northern England, which has relevance to other steep-sided carbonate platforms, particularly in faulted, extensional basins with elevated heat fluxes. More generally, it also illustrates the impact of different elements of model complexity on predictions of the timing, rate and temperature of dolostone formation and the ultimate distribution of dolomite abundance.
Six tectonostratigraphic stages (EC1-EC6) are recognised within the syn-rift sediments that accumulated prior to thermal subsidence during the Late Mississippian and Pennsylvanian, and these are defined by alternating periods of rifting and tectonic quiescence (Ebdon et al., 1990;Fraser & Gawthorpe, 2003;Maynard & Leeder, 1992; Figure 2). The earliest stage of rifting within the Pennine Basin, designated EC1, is represented in the Widmerpool Gulf by conglomeratic alluvial fan sediments overlying the Precambrian basement. Later in EC1 sediments record the initial marine transgression into the Pennine Basin, which is recorded by deposition of evaporites within the deeper part of the Widmerpool Gulf (Maynard & Leeder, 1992). Marine transgression continued during EC2, flooding local platform highs across the Pennine Basin. During this period of relative tectonic quiescence carbonate sediment production was established upon the Derbyshire Platform, with both aggradation and progradation of the carbonate platform. Following the rejuvenation of the basin-bounding fault systems during EC3, relative sea-level change due to fault reactivation, footwall rotation and emergence led to platform erosion and deepening of the adjacent basins (Fraser & Gawthorpe, 2003). A period of platform progradation followed during EC4, which was tectonically quiescent, but active extension and fault rejuvenation was re-initiated during EC5, leading to footwall rotation and erosion as well as extrusive volcanic activity. The final stage in the development of the Derbyshire Platform (EC6), was one of relative tectonic quiescence, albeit with ongoing volcanism and localised fault movement, before thermal subsidence of the region and drowning of the platform during the latest Serpukhovian and Bashkirian. The platform was then buried beneath a thick overburden of deltaic sediments during the Moscovian (Fraser & Gawthorpe, 2003).
Synchronous with the intermittent rifting, volcanic vents developed both in the platform interior and at the northern and southern platform margins, leading to extrusion of lavas (Cheshire & Bell, 1976;Tomkeieff, 1928). Later, during the Pennsylvanian, hypabyssal intrusions were emplaced within the carbonate succession as the platform was buried (Kirton, 1984). On the southern margin of the Derbyshire Platform the Matlock volcanic centre within the Cinderhill Fault Zone ( Figure 1C), is thought to have been active from tectonostratigraphic stages EC3-EC6, with an extensive succession of volcanic deposits including multiple lava beds and several volcanic vents (Kirton, 1984;Macdonald & Walker, 1984).
The continuation of igneous activity into the Pennsylvanian is manifest by the presence of basaltic and doleritic sills (Mullineux et al., 2020;Stevenson et al., 1970). Most igneous products on the Derbyshire Platform are basaltic and were sourced from tholeiitic magmas held in the lower crust prior to ascent (Macdonald & Walker, 1984). Temperatures of basaltic lavas and magmas commonly exceed 1000°C (Parfitt & Wilson, 2009) and thus continued basaltic volcanism within the region is probably to have a marked effect on the local heat flow regime. The apparent absence of significant high-level magma chambers beneath the Derbyshire Platform (Macdonald & Walker, 1984), suggest that around the southern platform margin, the high heat flow anomalies would probably have been restricted to the volcanic centre near the Cinderhill Fault Zone.
The southern margin of the Derbyshire Platform is pervasively dolomitised, exhibiting a range of fabrics suggestive of multiple stages of dolomitisation (Ford, 2002;Hollis & Walkden, 2012). Five specific phases, D1-D5 (two principal and three subordinate dolomite phases) were described by Breislin (2018) and Breislin et al. (2020Breislin et al. ( , 2022; Figure 1). The largest mapped dolostone body in the Pennine Basin (>60 km 2 ) is on the southern margin of the platform, with a distinct spatial correlation to syn-rift and post-rift volcanic centres ( Figure 2). The large body on the southern platform margin mostly comprises D1 dolomite which is euhedral to subhedral with cloudy cores and clear rims and dull orange cathodoluminescence (Breislin et al., 2020). The earliest D1 phase, which is the focus of this study, forms up to 50% of the dolostone volume on the Derbyshire Platform and also occurs along E-W trending faults (Breislin et al., 2020(Breislin et al., , 2022. It is crosscut by stylolites and exhibits isotopic signatures and single-phase fluid inclusions consistent with formation from a relatively low temperature (<50°C), sea water-dominated fluid (Breislin et al., 2020).
Phase D1 is locally replaced by phase D2, a subhedral to anhedral dolomite with mottled, bright red cathodoluminescence found within the damage zone of NE-SW and NW-SE trending faults and fractures and comprises ca 40% of the dolostone volume. Isotopic and trace element signatures are consistent with dolomitisation from evolved, basinal brines at >80°C (Breislin et al., 2022). Phase D3 is much lower in volume (<10% dolostone volume) and forms replacive dolomite halos adjacent to N-S trending faults, while phases D4 and D5 each comprise <5% of the dolostone volume and occur as fracture filling dolomite cements, including saddle dolomite (Breislin, 2018;Breislin et al., 2022). These observations support suggestions from earlier modelling (Frazer et al., 2014) that tectonically induced release of over-pressured basinal fluids can drive Mississippi Valley Type mineralisation and contribute to associated dolomitisation, but the observed dolomite volumes require significant dolomitisation prior to basin dewatering.

| METHOD
One stratigraphic model was developed, and on this a series of four RTM simulations to investigate the potential for dolomitisation by geothermal convection of sea water during the growth of the Derbyshire Platform. These F I G U R E 2 Stratigraphic column of the Carboniferous with particular reference to the seismo-stratigraphic stages of the Pennine Basin defined by Fraser and Gawthorpe (2003). Periods EC2-EC6 are used as time stages for the reported simulations. address, in a stepwise manner, several important simplifications in previous models of geothermal convection (Whitaker & Xiao, 2010), specifically, the simplified distribution of porosity and permeability, and the failure either to model evolving patterns of fluid flow during sediment accumulation or to consider the progressive development of platform margin fracture systems.
The stratigraphic model (Model 0) is based upon that described by Frazer et al. (2014) developed using basin stratigraphy code Basin2 (Bethke, 1993), which assumes equilibrium compaction during progressive deposition and structural development. The 2D modelled domain spans the southern margin of the Derbyshire Platform (Red line, Figure 1C) from the Widmerpool Basin to the centre of the platform and reproduces part of an interpreted 2D seismic line from Fraser and Gawthorpe (2003). This model provides the position of key stratigraphic surfaces and rock-type distributions ( Figure 3) at the end of each of five periods of sediment accumulation (stages EC2 through EC6). This spatial distribution data, which is calculated in Basin2 on a curvilinear grid system, was mapped onto a common 2D rectilinear grid system ( Figure S1) which is used by the RTM. The rectilinear nature of the RTM grid ensures orthogonality of the cell interfaces to provide the greatest solution accuracy for the integrated finite difference method of TOUGHREACT (Narasimhan & Witherspoon, 1976;Xu et al., 2012). The width of cells within this grid ranges from 5 m at the faulted platform margin region to 1500 m towards the grid edges. Cell heights range from 20 m within the top 100 m of the grid, increasing linearly with depth to 50 m at ≥1000 m depth. A static platform model (Model 1) representing the platform-to-basin geometry at the end of deposition of the F I G U R E 3 Six stages of platform development simulated with Basin2. The resulting distribution of facies and porosity-permeability and evolving grid (Model 0) are used as a template for subsequent RTMs. Red lines show the position of the marginal fault zone and its progression upwards through the stratigraphy. Grey zones mark the regions around the fault in which local permeability anisotropy are decreased to represent disruption of layering close to the fault. Thin black lines mark timelines used to distribute rock-types.
Derbyshire Platform incorporates a matrix permeability and porosity distribution that reflects that of depositional rock-types within a broad sequence stratigraphic context, as well as rock-type specific compaction. Model 2 (the static faulted platform model) also uses a static grid but additionally considers the presence of a bank-marginal fault within this permeability architecture. In both Models 1 and 2, dolomitisation is simulated for a period of 19 Myr, representing the approximate total time for deposition of stages EC2-EC6. Model 3 (the evolving stratigraphy model) represents the accumulating stratigraphy and concurrent geothermally driven fluid circulation. Here, dolomitisation was modelled as the cumulative product of five sequential RTM simulations which capture progressive sediment accumulation and subsidence of the southern margin of the Derbyshire Platform during the Visean. Each simulation (of 3-5 Myr duration) represents each one of the regional tectonostratigraphic stages (EC2-EC6, Figure 2) defined by Fraser and Gawthorpe (2003) based on the chronostratigraphic scheme of Ebdon et al. (1990). Finally, in Model 4 (the faulted evolving stratigraphy model) the same approach is used, but additionally the progressive development of the fault zone is considered in relation to ongoing pulses of rifting within the accumulating sedimentary sequence. This final model captures many of the key aspects of platform development that may have impacted the patterns of geothermal convection, and thus early dolomitisation within the southern margin of the Derbyshire Platform and forms the basis for comparison with field data in the discussion section below.
Static RTM models (Models 1 and 2) use the entire stratigraphy generated from Model 0 at the end of deposition of EC6 and use the code TOUGHREACT (Xu et al., 2012). Simulation of geothermal convection and dolomitisation in the growing platform (Models 3 and 4) is achieved by a one-way coupling between the Basin2 model and TOUGHREACT, involving reconstruction at each stage of the RTM of the cell thickness, rock properties and boundary conditions based on the time equivalent step of the stratigraphic model. For each stage, the stratigraphic configuration, including distribution of rock-types and texturally controlled porosity and permeability, is calculated by Basin2, accounting for subsidence and compaction. The initial porosity distributions for each RTM stage are extracted from the basin stratigraphy model and permeability is calculated based upon rock-type specific porositypermeability relationships ( Figure S2). During the reactive simulation step, porosity increases as dolomitisation proceeds (reflecting the higher density of dolomite compared to calcite), and permeability is calculated from porosity (as described below).
Anisotropy in permeability for each rock-type is used to represent the effect of sediment layering and permeability heterogeneity that would have resulted from near-surface diagenetic processes prior to burial. It is specified by reducing vertical permeability relative to the horizontal value by a factor of 10 in grainstones, 50 in packstones, 100 in wackestones and 200 in mudstones, and is time invariant. To represent the fault and associated damage zone, the vertical permeability around and within the fault zone is increased by one order of magnitude within the outer fault zone and by three orders of magnitude in the fault plane. Anisotropy values are lower around the fault zone to reflect the disruption of sedimentary layering, by one order of magnitude within the outer fault zone and by three orders of magnitude along the fault plane. The pulsed nature of fault growth during rifting (Ebdon et al., 1990) is captured by the progressive upward penetration of the fault zone in EC3 and EC5. Within the simulations for these stages, the margin fault breaches the surface of the carbonate platform, while within EC2, EC4 and EC6 stage simulations, the fault is healed by younger sediments (Figure 3).
The models are built, executed and visualised using an integrated program that allows the efficient implementation of single-stage and multi-stage simulations using scripts written in Python. This is an extension of the PyTOUGH library, originally developed at the University of Auckland (Wellmann et al., 2012), and provides highlevel access to model input parameters such as boundary conditions, the presence of the fault zone, and the relative duration of stratigraphic stages. These higher-level functions rely heavily upon the lower-level functionality of the PyTOUGH library that is tailored towards the manipulation of non-reactive flow models, supplemented by additional low-level functionality for reactive transport simulations developed for this project. This code prepares input and processes output files from the reactive transport simulator, TOUGHREACT (Xu et al., 2012) that forms the primary engine for RTMs. This allows capture of the effect of coupled heat and fluid flow, solute transport, and the progressive modification of porosity and permeability by diagenetic reactions within the suite of simulations.
After distributing rock properties from the stratigraphic simulations into the RTM grid, unpopulated cells are deactivated to maximise computational efficiency. A 500 m thick, low porosity and permeability basement layer is specified beneath the platform and basin stratigraphy to buffer any potential boundary layer influences on the targeted domain. In all RTMs, and throughout each simulation, the upper boundary is open, and pressure and temperature are constant, and the side and basal boundaries are closed to flow. Temperatures on the upper boundary decrease from a sea surface temperature of 25°C at a rate of 18°C km −1 depth increase. A locally elevated basal heat flux is specified near the platform margin, representative of a continental rift system. Appropriate boundary heat flow values are key to the accurate simulation of geothermally driven sea water convection processes. Rift systems commonly show heat flow values ranging from global thermal equilibrium values of 40 mW m −2 to over 800 mW m −2 (Leroy et al., 2010;Stern, 1987;Watanabe et al., 1977). This wide variation can occur over a lateral distance of a few kilometres (Leroy et al., 2010), over a few tens of kilometres (Stern, 1987) or even over many hundreds of kilometres (Watanabe et al., 1977) and is commonly affected by local fluid flow (Morgan, 1983). In all cases, the highest heat flow values are related to local volcanism and hydrothermal circulation. The Matlock volcanic centre, which developed on the southern margin of the Derbyshire Platform during the Visean (Figure 1), is represented by a high heat flux of 800 mW m −2 at the centre of the platform margin fault zone ( Figure S1). Within 1 km of this position, heat flow decreases linearly to a background value of 100 mW m −2 .
The initial hydrostatic temperature and pressure distribution for each RTM stage is derived from a steady state calculation for fluid and heat flow using TOUGH2, reflecting the laterally variable basal heat flow and local fluid convection. A geothermal gradient of 35°C km −1 is representative of that calculated from conduction for the basin region that receives a 100 mW m −2 basal heat flux. A temperature gradient cannot be generalised for the narrow zone around the fault as the strong lateral heat flow gradient results in dynamic patterns of convection. In the narrow zone around the fault a locally very high heat flux is specified (a maximum in the fault zone of 800 mW m −2 ). Although, the strong lateral heat flow gradient (70 mW m −2 /100 m either side of the fault zone) makes the steady state temperature distributions calculated by initialisation simulations somewhat variable, the result is increased temperatures around the fault due to the increased heat flux.
The RTM considers nine primary and 27 secondary aqueous species, listed within Table S1, and three solid mineral species (calcite, dolomite and anhydrite). The sea water composition is specified based upon the estimates of Demicco et al. (2005) for Mississippian sea water, detailed in Table 1. The simulation assumes dolomitisation results from calcite dissolution and dolomite precipitation, rather than a single-step reaction (Machel, 2004). Because the dissolution of calcite is significantly faster than dolomite precipitation, dolomite precipitation is considered to be the rate-limiting step of the dolomitisation process. Thus, dolomite precipitation is specified as a kinetic process using the rate law of Arvidson and Mackenzie (1999), and all other reactions are considered to be thermodynamically controlled. The use of this rate law is consistent with previous RTM simulations of dolomitisation (Al-Helal et al., 2012;Benjakul et al., 2020;Gabellone et al., 2016;Jones & Xiao, 2006;Whitaker & Xiao, 2010;Wilson et al., 2001;Yapparova et al., 2017).
As a kinetic reaction, dolomite growth rate is partly controlled by the reactive surface area of the mineral. This leads to a reaction rate that increases with dolomitisation, but also requires an initial dolomite content (specified at 1%) to provide a homogeneous potential for dolomitisation in all carbonate sediments. A dolomite reactive surface area of 10 3 cm g −1 is specified, representative of a modal dolomite crystal size of ca 50 μm (Lichtner, 1996). It is assumed that diagenetic modification of porosity is reflected in changing permeability using the Carman-Kozeny relationship (Xu et al., 2012). While there is considerable variety in dolomite textures which will influence the porosity and permeability of dolomite (see Gregg, 2004, and references therein) this relationship is considered appropriate for many dolostones formed by relatively low-temperature geothermal convection (Ehrenberg, 2004;Ehrenberg et al., 2006;Whitaker & Xiao, 2010).
At the start of the RTM simulation, a uniform initial mineralogy of 99% calcite and 1% dolomite is assumed. In Models 3 and 4, reactive mineral distributions for stages EC3-EC6 are populated based upon the results calculated within the previous stage of the RTM. The platform sediments are assumed to be 100% reactive. However, only dolomite formation within the platform sediments is investigated, and thus the reactive sediment proportion within basinal mudstones is specified as 15%. This is the proportion of calcite that is estimated within these sediments . Basinal sandstones and mudstones are specified as unreactive. The impact of different reactive surface areas within the carbonate sediments was not considered due to lack of constraints. The mass of dolomite formed is reported as kilograms (and also in mol) of dolomite for the entire 2D model assuming a 1 m width
for the 2D slice over a given time duration as simulations are 2D.

| SIMULATION RESULTS
TOUGHREACT calculates circulation of Mississippian sea water within accumulated sediments, driven by elevated heat flow associated with volcanic activity in the region of the Cinderhill Fault Zone ( Figure 1C). This gives rates for replacement of calcite by dolomite that vary both spatially and temporally, reflecting differences in flux and composition of fluids, temperature and carbonate mineralogy. The differences in the predicted patterns of dolomitisation reflect the presence/absence of the fault and the static/evolving stratigraphy, and comparisons between these simulations help to identify some of the aspects of complexity that matter to fluid flow, heat transport and diagenesis.

| Dolomitisation in static model geometries (Models 1 and 2)
In static model geometries, dolomitisation is simulated for the entire sequence of sediments over 19 Myr. In Model 1, cool sea water is drawn into the platform through the slope sediments, with discharge of heated water at the platform top ( Figure 4A through D). Upward flow near the zone of high heat flow gives geothermal temperature gradients up to 50°C km −1 . This is almost twice that in the platform interior, which acts solely as a zone of discharge. Flow rates are slow and conduction dominates heat flow. The facies-controlled distribution of permeability localises fluid flux to within grainstones both at the upper margin of the succession and in the deeper part of the platform, where free convection occurs within the older marginal grainstone body (deposited in EC2-EC3). The presence of a progradational marginal grainstone unit (EC4) focusses flow from the deeper slope sediments into the base of the platform succession via mudstones at the margin of the basin. Throughout the system, flow lines are deflected at facies boundaries in response to permeability contrasts. Transport and heating of sea water within the platform succession produces a limited mass of dolomite-1.84 × 10 9 kg m −1 (1.0 × 10 10 mol m −1 )-over the 19 Myr of this simulation. Most of this dolomite occurs within the platform slope and margin zone, where approximately 10%-13% of the limestone is dolomitised. This is associated with sea water influx within marginal grainstones at the top of the platform succession and ascending warm fluids above the zone of high heat flux. Dolomitisation is minor (<5%) within the platform interior where fluxes are lower, and fluids are Mg-depleted after dolomitisation of the platform margin.
With the introduction in Model 2 of the transmissive fault, extending vertically through units EC2-EC5 and connecting with the EC6 marginal grainstones, predicted dolomite abundance is substantially increased both in the slope/margin zone and the top of the platform interior ( Figure 4E through H). Five times more dolomite (9.38 × 10 9 kg m −1 , or 5.0 × 10 10 mol m −1 ) is produced compared with the un-faulted static model (Model 1), yet most of the platform, aside from the fault zone itself, comprises <50% dolomite, even after 19 Myr. The EC4 deposits provide a high permeability pathway, focussing >1.05 × 10 −6 kg s −1 m −2 of heated water out of the deeper parts of the platform succession and into the base of the platform succession. This increases the influx of sea water, not only from the platform slopes but also from the platform interior, reversing the flow direction seen in the un-faulted static model. Both the platform interior and margin region are thus cooled by the influx of sea water, reducing the extent of warming above the zone of high heat flow but allowing waters of approximately 50°C to circulate to within 200 m of the platform top.
The increased fluid flow resulting from the inclusion of this high permeability pathway within the static model leads to both greater dolomitisation throughout the marginal and interior successions and much more pervasive dolomitisation around and above the fault zone ( Figure S3). Within the platform interior, up to 45% of the solid mineral fraction of the rock is converted to dolomite, while beneath the margin, dolomite values reach as high as ca 70%, although much of this dolomite forms at temperatures <50°C. Complete replacement of calcite by dolomite occurs within and above the fault zone, with the majority forming at only 50-60°C, reflecting rapid rates of advection, yet fault zone porosity and permeability remain high. Steep lateral gradients in dolomitisation develop as, for example, ascending fluids bypass a narrow region inboard of the fault.

| Dolomitisation in evolving stratigraphy (Model 3)
Stepwise dolomitisation by geothermal convection of sea water during five stages of platform evolution (EC2-EC6) over a total of 19 Myr is summarised in Figure 5. At the end of this multi-stage simulation, 1.22 × 10 9 kg m −1 (6.6 × 10 9 mol m −1 ) of dolomite is calculated to form, approximately one third less than formed within the model of fluid flow based on the static geometry of the fully formed platform (Model 1, Figure S4). Changes in dolomite distribution through time demonstrate how these differences arise from the cooler temperatures of older sediments in early model stages and the shorter period of time for dolomitisation of the younger sediments, as well as shifts in the pattern of fluid flux.
EC2 (0-5 Myr): During initial nucleation and growth of the platform, geothermal convection draws sea water into the upper slope ( Figure 5). The juxtaposition of a high local heat flux on a permeable platform margin focusses rapid discharge of buoyant fluids. A high fluid flux maintains near ambient temperatures (18-25°C), precluding significant formation of dolomite. Trace (2%-3%) dolomite forms within an approximately 200 m thick zone extending some 1250 m within the deeper platform slope, reflecting kinetically more favourable temperatures (40-45°C).
EC3 (5-9 Myr): Rapid convection through the platform margin is channelled within grainstone units that formed during progradation followed by backstepping, and this maintains low temperatures (<30°C) in the vicinity of the platform margin. Fluids discharge across the inner platform, ensuring continued flux of Mg and allowing rapid dolomitisation, focussed near the base of the platform in the zone of high heat flux. These factors combine to produce up to 40% dolomite at temperatures of ca 55°C, but this is localised to an area some 500 m wide and extending 100-200 m above the top of the basement.
EC4 (9-12 Myr): Substantial basinward progradation (by up to 8 km) separates the marginal convection system from convection-driven exchange with platform top waters above the high heat flux area. The relatively low vertical permeability of the packstones on the platform top means that most flow occurs within the upper EC4 grainstones with very minor dolomitisation. Most dolomite formation continues to be focussed at depth, in the zone of high heat flux, fed by lateral flow of sea water along buried EC2 and EC3 grainstones.
EC5 (12-15 Myr): Despite backstepping of the margin over the zone of high heat flux and increasing temperatures here beneath the thickening platform sediments, the lower dolomite body continues to form only slowly, limited by increasing hydrological isolation from the sea floor. EC6 (15)(16)(17)(18)(19): During the final 4 Myr of the evolving stratigraphy model, upward flow in the high heat flux zone is sufficient to draw sea water in from both the slope and the platform interior. However, most flow remains in relatively shallow grainstone units where low temperatures limit dolomitisation rate. Interestingly, with continued burial the zone of maximum dolomitisation becomes increasingly isolated from influx of sea water limiting further dolomite formation despite an expanding area of elevated temperature.

| Dolomitisation in evolving stratigraphy with platform margin fault (Model 4)
Results from the simulation of platform growth, incorporating stratigraphic evolution in matrix permeability due to stepwise burial compaction and faulting (Figure 6), show that geothermal convection produces a total of 3.63 × 10 9 kg m −1 (1.9 × 10 10 mol m −1 ) dolomite throughout the platform succession. This is three times greater than in the equivalent un-faulted model (Model 3, Figure S5C), with increases of <35% in the platform interior, <45% in the grainstone units of EC2-EC3, and <95% within and above the fault zone, particularly at the EC6 flowconvergence zone.
EC2 (0-5 Myr): Prior to fault development in EC3, the system is identical to that described in Model 3, with cooling, convective inflow through the slope. Most discharge occurring close to the margin and minimal dolomitisation.
EC3 (5-9 Myr): Breaching of the sea floor strata by a fault in the zone of high heat flux separates flow in the slope margin from the platform interior. Enhanced geothermal convection cools the margin to <30°C and there is only limited heating close to the fault zone. Cool water return flow within the fault zone feeds discharge across the platform interior, but very slow flow rates allow for a steep geothermal gradient inboard of the fault. Downward flow and elevated temperatures near the fault zone generate no more than 8% dolomite after 9 Myr.  Figure 1C). cooling effect of return flow within the fault zone, along with greater burial depths, allows higher temperatures to be maintained around the fault zone (up to 60°C). Free convection within the fault zone entrains fluids outboard of the fault and discharges fluids towards the platform interior. Local to the fault zone, dolomitisation accelerates, due to higher temperatures and the abundance of precursor dolomite, producing up to 25% dolomite, but large areas remain where dolomite is <5%.
EC5 (12-15 Myr): The platform margin backsteps to the position of the reactivated fault zone, which extends to the platform top. This focusses strong downward flow as fluids from the fault discharge into the surrounding sediments, and results in local cooling. Introduction of Mg-rich fluids directly to the base of the platform succession significantly increases the extent of dolomitisation. Alteration is greatest within basal EC2 grainstones, forming a laterally extensive body of 30%-40% dolomite.
EC6 (15)(16)(17)(18)(19): The platform margin progrades and the fault zone is healed. Upward flow within the fault zone locally heats the upper platform succession to ca 50°C. Efficient sea water supply to the fault zone and deeper platform succession is achieved through recharge from both the platform interior and margin. The combination of heating and focussed fluid flux promotes intense dolomitisation (up to 90 vol.% dolomite) on both sides of the fault. Downward flux of sea water across the platform interior, generates a broad zone of partial (<35%) dolomitisation in the lower part of the succession where temperatures are sufficient to overcome the kinetic barrier to dolomite formation.

| DISCUSSION
The results of the reported models provide insight not only into the potential for dolomitisation by geothermal convection on a steep-sided, faulted carbonate platform, but also into the nature of this dolomitisation mechanism, and how models of such systems should be constructed. Specifically, these models highlight the importance of considering realistic facies distributions, and the interaction  Figure 1C). between fault growth and platform evolution within simulations of such long-lived syndepositional diagenetic processes. Here, learnings from a stepwise increase in RTM model complexity are evaluated, as are the implications this has for understanding geothermal convection and dolomitisation. The degree to which this more complex model conforms with observational data is examined and thus can inform our understanding of the evolution of diagenesis within the Derbyshire Platform.

| Improving simulations of dolomitisation driven by geothermal convection
The models reported here were implemented using a methodology that has allowed construction of complex RTMs. In particular they expand the capabilities of the reactive transport code to more realistically represent reactions, such as dolomitisation, that occur over extended time scales. Progressively increasing model complexity (Models 1-4) provides insight into the role of individual elements of this complexity, from simple concept-driven models (previously described by Whitaker & Xiao, 2010) to models that incorporate complex rock-type distributions and fault growth within a platform that builds through time and accounts for reduction of porosity and permeability due to burial compaction.
Geothermal circulation of sea water driven by the Earth's heat engine will take place in most accumulating marine carbonate sequences , but is probably to be particularly active in areas of high heat flux such as rift basins, where tectonic and early diagenetic controls contribute to the development of rimmed platforms with steep margins. Previous models of geothermal convection in carbonate platforms Sandford et al., 1998;Whitaker & Xiao, 2010;Wilson et al., 2001) use simplistic distributions of permeability to show inflow of cool sea water through the platform slope, and upward flow as this water is heated and driven by buoyancy to discharge across the platform top. Incorporation of more realistic distributions of permeability show flow focussing within high permeability areas (e.g. marginal grainstone units) and at shallower depth, with the development of diverging and converging flow paths that also affect heat transfer. This observation is thought to be independent of the platform size, platform slope angle and basal heat input, and so not specific to the Derbyshire Platform modelled here.
Focussed flow that results from the more complex permeability architecture of the Derbyshire Platform model generates complexities in the predicted dolomite distribution, but the results also illustrate some important generalities. All models used suggest that despite grainstones close to the platform margin consistently experiencing higher than average fluid fluxes, they dolomitise at the same rate or more slowly than the lower permeability wackestones that comprise slope deposits. This occurs in all models used and arises because the high fluid fluxes in the grainstones which provide abundant reactants for dolomitisation also cool these sediments to the point that dolomitisation becomes kinetically inhibited. However, facies-dependent differences in rates of burial compaction mean that the hydraulic continuity of more permeable facies, which tend to develop at the platform margin, is key to the delivery of dolomitising fluids at depth where favourable temperatures allow dolomite to form with no significant kinetic hindrance.
This suggests that the response of platform architecture to changes in relative sea level and carbonate productivity may inform predictions of geothermal dolomitisation. Platforms that dominantly aggrade or show steady progradation will tend to maintain hydraulic continuity between marginal units, whereas backstepping can leave marginal grainstones less probably to be dolomitised, due to lower fluid flux, and prior consumption of Mg by dolomitisation of slope facies. This is illustrated by the more limited dolomitisation of grainstones formed during progradation in EC3 despite more favourable temperatures at depth as a result of backstepping during EC4. Additionally, dolomite is more abundant in the upper and basinward parts of this grainstone unit due to focussed inflow of Mg-rich fluid, but formation of this dolomite limits the potential for alteration of the grainstones further downflow. This supports findings from studies of reflux dolomitisation by Garcia-Fresca et al. (2012) and Gabellone et al. (2016) that show the temporal evolution of flow paths and resulting reactions in response to differences in location, extent and persistence of brine pools and sediment properties in evolving stratigraphic sequences formed due to changes in relative sea level.
Accurately capturing a realistic permeability architecture within numerical models also means the fault and fracture development of a carbonate platform need to be considered. The reported results contain multiple examples of how permeable fault zones may allow focussed upward or downward flow, resulting in more intense dolomitisation. Of note, when the fault is open to the platform top it acts as a conduit for downward flow of cooler water, producing little dolomite, whereas the healed fault is a conduit for upward flow and enhanced dolomitisation. In both cases the presence of a cross-cutting, high permeability element increases the vertical connectivity and the average permeability along the flow path. This facilitates flow through the deeper, hotter parts of the succession where dolomitisation rates are highest. Flow in the platform interior is reversed, with recharge of relatively warm (25°C) waters from the platform top that acts solely as a zone of discharge within the un-faulted static model (Model 1). This might suggest that in other scenarios (not simulated here), with restricted circulation of sea water in the platform interior, a geothermal drive could enhance density-driven reflux of elevated salinity and high Mg/Ca values leading to more intense dolomitisation in the platform interior.
It is important to note that in these simulations the fault zone is associated with a specified zone of high heat flux which increases the potential for dolomitisation via focussing and enhancing fluid flow and kinetically favouring dolomitisation. In some extensional basins there seems to be a strong relationship between the occurrence of crustal-scale faults, platform margins and dolomitisation, often localised in zones of structural complexity (Breislin et al., 2020;Hollis et al., 2017). It is also possible that platforms in tectonically active settings, such as modelled here, will have deep-seated faults that crosscut the platform away from the platform margins. These can play an important role in vertical transfer of heat and fluids over many hundreds of metres to kilometres, with influx of surface-derived diagenetic fluids (Benjakul et al., 2020;Hirani et al., 2018;Stacey et al., 2021) or discharge of fluids from depth (Bons et al., 2014;Frazer et al., 2014). In contrast, open-mode tensile bank-marginal fractures that are intrinsic in carbonate platforms with cemented margins (Frost & Kerans, 2010) tend to pinch out at depth (Nolting et al., 2018). This would reduce both advective heat transfer to shallower strata and the flux of Mg-rich fluids to depth.
Evaluating geothermal convection during the progressive accumulation of a carbonate platform, even with a relatively low-temporal resolution, shows dramatic differences in predicted quantity and distribution of dolomite (compare Figures 5 and 6). Platform growth affects the distribution of geothermal dolomite in two important ways. First, the fluid flow regime responsible for supplying reactants that drive dolomitisation and control the distribution of heat within the platform varies as the platform progrades, aggrades and backsteps. Regions that are optimally supplied with reactants and heat to drive dolomite formation thus migrate both vertically and laterally as the platform grows. As such, one may speculate that characteristic distributions of dolomite may develop in platforms that are predominantly aggradational, progradational or backstepping.
Second, the sediments higher in a succession exist for a shorter period of time than those at the base of the succession. There is thus an obvious disparity between the younger and older strata in terms of the available time for dolomitisation. Early simulations of geothermal convection over 30 Myr with a static platform geometry using over-simplified permeability distributions (Whitaker & Xiao, 2010) suggest a wedge-shaped body of dolomite will develop, initiating at the top of the platform margin where permeabilities are highest and extending over time towards the platform interior. Where the simulations consider platform growth concurrent with ongoing dolomitisation (Models 3 and 4), they suggest that such a dolomite body is unlikely to develop as the zone of dolomitisation will migrate in response to changes in platform geometry and the developing facies architecture. In addition, the upper platform, as the last part of the succession to be deposited in an aggrading platform succession, would be expected to show the least dolomitisation. Rather, the intensity of dolomitisation should increase with depth, both due to increased duration of circulation of dolomitising fluids and kinetically favourable higher temperatures with increasing burial. As such, models of geothermal convection-driven dolomitisation using static geometries are applicable only in rare cases where dolomitisation begins after platform development has ceased, and subsequent deposition is limited by either prolonged exposure or platform drowning.
Counteracting this trend of increased dolomitisation with time ( Figure 7) and thus burial depth, matrix permeabilities decrease due to burial compaction and thus reactions at depth may be limited by fluid flux. The models of the Derbyshire Platform show that after a period of very slow dolomitisation in the initial 5 Myr, from EC3 onward, the mass of dolomite increases linearly through time in the un-faulted evolving platform model (Model 3). For flow that is captured by the fault zone (Model 4), the presence of a permeable vertical conduit allows circulation of sea water in to the deeper, hotter parts of the succession, where dolomitisation rates are higher. This allows an exponential increase in dolomite mass through time due to greater mass flux along the fault zone.
Both dynamic models (3 and 4) show that, despite a locally extremely high heat flux, dolomites can form at relatively low temperatures (<80°C). In the un-faulted evolving platform model (Model 3) most dolomite forms above the 50°C 'critical roughening temperature' that Gregg and Sibley (1984) suggested would exhibit non-planar textures ( Figure 7B). Of note, the presence of a permeable fault zone leads to lower average temperature and large variations in the rate and temperature of dolomite formation as the fault switches between acting as a zone of hot-water upwelling and cool-water downflow (Figure 7). The lowest temperature recorded in dolomite formed at the base of the fault, during the EC5 stage, occurs when the permeable fault zone extended to the platform top, despite a burial depth of up to 900 m.

| Comparison with the distribution of early-formed (D1) dolomites of the Derbyshire Platform
Model results broadly concur with field and petrographic data from the study area, which indicates dolomitisation prior to stylolitisation along the platform margin and E-W trending faults that are interpreted to have formed during basin extension (Breislin et al., 2020(Breislin et al., , 2022. Phase D1 dolomite was described from EC5 and EC6 strata within boreholes, mines and outcrops, with an irregular and diffuse lower dolomite-limestone contact at ca 200 m beneath the surface (Ford, 2002) within EC5 strata. Dolomitisation of deeper strata (EC4) has been described in detail elsewhere in Derbyshire (Schofield & Adams, 1986) and in the Widmerpool Basin (EC3-EC6; Breislin, 2018). Overall, therefore, comparison with limited surface and subsurface (mine and cave) data suggests that the distributions of dolostone from the RTM are robust. However, the high volume of dolomite that forms in EC2 strata, particularly near the fault, cannot be verified as no deep borehole data are available.
The dolostone body that extends sub-parallel to the southern margin of the Derbyshire Platform ( Figure 1C) for some 18 km contains at least 4.0 × 10 12 kg of dolomite (Breislin, 2018;Ford, 2002), of which 50% demonstrably formed during burial from evolved, crustal fluids (D2-D5; Breislin et al., 2022). Applying the results of the 2D simulation along-strike over this distance, the model suggests geothermal convection of sea water could form some 6.5 × 10 13 kg of dolomite. Geothermal convection during platform growth, thus, appears capable of generating the volume of D1 dolostone observed on the southern margin of the Derbyshire Platform. This supports the hypothesis of Frazer et al. (2014), that dolomitisation by geothermal convection may provide an essential foundation for later dolomitisation by basin expulsion fluids.
Isotopic and trace element data are consistent with formation of D1 dolomite predominantly from sea water, modified in part by mixing with igneous derived CO 2 (Breislin et al., 2020). Phase D1 dolomite has planar crystal textures and single-phase primary fluid inclusions suggesting dolomitisation at less than 50°C (Gregg & Sibley, 1984). This is consistent with modelled temperatures of <50°C in EC5 and EC6 facies. The D1 dolomite is weakly fabric retentive, particularly in outcrop and core, and preserved textures are consistent with dolomitisation of higher permeability platform margin packstone and grainstone facies (Breislin et al., 2020).
The specification of a constant elevated heat flux to the fault zone means that the simulation probably overestimates total D1 dolomitisation. The intensity of volcanic activity probably varied, and Breislin et al. (2020) suggested there may have been a shift from extrusive to intrusive volcanism in the late Visean/early Serpukhovian that facilitated continued dolomitisation of the uppermost strata (EC5 and EC6) during platform drowning. Indeed, it is recognised that magma at shallow depth cools rapidly (Andersen & Weis, 2020;Samuel et al., 2016) and large volumes of upper crustal melt are likely to be ephemeral (Cashman et al., 2017). This would lead to periods when both reduced heating and fluid fluxes would have limited dolomitisation potential. Furthermore, much of the porosity (over 70%) within the interior of the Derbyshire Platform was occluded by sparry, dull luminescent calcite cement either synchronous with or immediately after dolomitisation (Breislin, 2018;Walkden & Williams, 1991). As with the D1 dolomitisation, this cementation pre-dates compaction and could have decreased flow and reaction rates in the platform interior. This effect may have been compounded by periodic exposure which would have focussed discharge of convecting fluids at the margin (Hughes et al., 2007;Sanford et al., 1998).
Deformation (including faulting and dilation), fluid flow and chemical processes are all dynamic within fault zones (Zhang et al., 2008), and modelling these processes is beyond the remit of this study. The simple fault representation in these models produces greater matrix dolomitisation than might be expected from a 3D fault representation (Benjakul et al., 2020), dependent on the permeability of the matrix relative to that of the fault zone. It is clear, however, that dolomitisation by geothermal convection occurs slowly, even in the presence of a local elevated heat flux, and that locally enhanced permeability and heat flux plays a critical role.
This study highlights the importance of integration of geological context within process-based models if they are to be applied to investigations of specific geological problems. The incorporation of multiple rock-types, accumulating stratigraphy, and an evolving fault system is a key step in this progression and suggests a mechanism for fault-related dolomitisation during early burial. The predicted dolomite distribution is distinctly different from that suggested for the same mechanism with a simple depth-dependent distribution of permeability (Whitaker & Xiao, 2010). While simple, static models can help understand the operation and controls of diagenetic processes, they can be misleading, and it is imperative that interactions between these controls are considered as part of a larger story of geological evolution. In particular when diagenesis occurs soon after deposition, explicit coupling of stratigraphic and diagenetic models at high temporal resolution is key to meaningful prediction of mineralogical changes and associated evolution of porosity and permeability.

| Implications for modelling evolving geological systems
Science is underpinned by models, and most of us use some type of model almost every day. Numerical simulations of depositional and diagenetic processes in sedimentary systems such as discussed here are perhaps an uncommon endmember of a spectrum of models that extends through geocellular representations of the distribution of rock properties, to box diagrams, and the geological cartoons that adorn many of our desks. Underpinning all these varied manifestations of a model is the natural tendency of the human brain to simplify and impose order on complex natural systems. Despite recognition that geological systems are inherently complex, we try to distil their essence to understand their underlying structure and function. This is key to palaeoenvironmental interpretation of the sedimentary record, and also provides a route to prediction of; (i) properties of a system that cannot be directly observed, for example due to limitations inherent in outcrop and particularly subsurface data; and (ii) behaviour of a system when it is perturbed by natural or anthropogenic changes, ranging from the increase in atmospheric CO 2 from burning fossil fuel to engineering applications such as injection of CO 2 for storage in reservoirs.
The process of model development usually starts with geological observations that identify a problem for which one or (ideally) more conceptual models are developed. These can sometimes be tested by direct observational data, or rigorous application of physical, chemical and/ or biological principles, but this is challenged by the slow rate of many sedimentary and diagenetic processes. The complexity of the system often requires these to be represented in computer simulation models. Three key principles underlie the systems approach on which such models are built (Churchman, 1968); the system must be defined such that its boundaries are set at the outer limit of the interactions of interest; the elements of the system must in some sense encompass order and regularity; and the processes of change within the system must imply some sort of equilibrium, albeit often dynamic. Few geological systems are truly closed, they are characteristically heterogeneous and are often far from equilibrium. Although this intrinsic complexity challenges models focussed on prediction of system properties and behaviour, models offer value as demonstrations of the underlying principles and their operational application should be based on their ability to quantify uncertainty.

| CONCLUSION
Using RTMs it has been possible to demonstrate the potential for geothermal convection of sea water driven by volcanic heating to form a spatially extensive (tens of kilometres) dolostone body on the southern margin of the Derbyshire Platform during accumulation of platform carbonates. The geochemistry and petrography of dolomites formed thus would reflect a dominantly sea water origin, but the high water-rock ratio means that the temperature of dolomitisation is not particularly high (<50°C), despite flow driven by locally high heat flux. This study suggests that geothermal convection would be expected to affect platform margins during early burial, especially those with high matrix permeability, syn-sedimentary faulting/ fracturing and elevated heat fluxes.
Simulations may overestimate the total volume of earlyformed dolomite due to several inherent simplifications, most importantly the failure to model the synchroneity of sediment accumulation, burial compaction and early diagenesis. However, models demonstrate the importance of inclusion of stratigraphic growth and an evolving fault system. Resulting dolostone distributions differ markedly from static-stratigraphy RTMs that have formed the basis for conceptual models of early burial geothermal convection dolomitisation. The high heat flow and high permeability fault zone plays a critical role in focussing fluid flux and reducing kinetic barriers to dolomitisation, resulting in a more extensively altered, and spatially restricted dolostone body than would have occurred by platform margin convection alone. Important uncertainties remain in such systems about the timescales of diagenesis, in view of both the ephemeral nature of magmatic heating in the upper crust and the development of meteoric groundwater discharge during periods of platform top exposure. However, another critical challenge for modelling diagenesis driven by geothermal convection in fractured systems is now to extend simulations into 3D.
Models can contribute to generating predictive concepts to better understand the distribution of geological heterogeneity and their impacts, for example on fluid flow. They provide a physically and chemically rigorous tool to explore the interactions between individual controls on depositional facies and diagenesis, and their expression in spatial variations in rock properties. The work presented here is a limited foray into the controls on one specific hydrological system and its implications for one diagenetic reaction. However, it serves to illustrate that models are as valuable in the questions they force us to address in their design and parameterisation as they are in demonstrating the principles of the system investigated.

ACKNO WLE DGE MENTS
We would like to thank Al Fraser for assistance obtaining seismic data and Alessandro Mangione and Wenwen Wei for stimulating discussions. This work was supported by a National Environment Research Council CASE studentship (grant number NE/I528142/1) in association with Chevron Energy Technology Company (ETC). The views expressed herein are those of the authors and not those of Chevron ETC. We thank Dr Bea Garcia-Fresca, an anonymous reviewer, and Editor Prof. Peter Swart for comments that helped hone the manuscript.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from Dr Miles Frazer upon reasonable request.