Reactive Transport Modeling of Reflux Dolomitization of Carbonate Platforms: Enlightenment from Yingshan Formation in Shunnan Area, Tarim Basin

Abstract

Dolomite plays an important role in carbonate reservoirs. The topography in the study area creates conditions for reflux dolomitization. The northeastward paleogeomorphy during the deposition of the Yingshan Formation was favorable for reflux dolomitization. Furthermore, the petrological and geochemical evidence indicated that the formation of finely crystalline dolomites was penecontemporaneous to sedimentation. The content of powder crystal dolomites increases from grainstone, to packstone, to mudstone. Previous studies only analyzed the origin of dolomites based on traditional geological methods, but did not analyze the spatial influence of reflux dolomitization on the reservoir quality. In this study, the reflux dolomitization of platform carbonate sediments was evaluated using three-dimensional reactive transport models. The sensitivity of dolomitization to a range of intrinsic and extrinsic controls was also explored. The reflux dolomitization involves replacement dolomitization and over-dolomitization. The porosity change is the result of the abundance change of dolomite and anhydrite. The fluid flow pattern in the model is related to the injection rate and geothermal gradient. According to the spatial and temporal change of mineral, ionic concentration, and physical property, the reflux dolomitization could be divided into five stages. From the sensitivity analysis, high permeability promotes dolomitization only in the initial stage, while low permeability and high porosity means stronger dolomitization. Besides, the injection rate, reactive surface area (RSA), geothermal gradient, and brine salinity are all proportional to the dolomitization. Differently from porosity change, the permeability change is concentrated in the upper part of the numerical model. The location of “sweet spot” varies with the locations of change centers of porosity and permeability. In the stage-1 and 4 of dolomitzation, it overlaps with porosity and permeability growth centers. While in the stage-2, 3 and 5, it lies between the porosity and permeability growth/reduction centers.

1. Introduction

The oil–gas output of the carbonate rocks accounts for 60% of total reserves [1,2], and half of the output came from dolomite. Therefore, the production potentials of the dolomite reservoir or dolomitized reservoir are huge. In the Middle East, the Permian Khufu Formation of the North Dome of Qatar and Jurassic Arab-D Formation of the Ghawar field were partly dolomitized [3]. In addition to the Sichuan and Ordos Basin, high-quality dolomite reservoirs have also been found in the Yakela Oilfield and Lunnan Oilfield of the Tarim Basin in China [2,4]. Dolomite could not only behave as an effective reservoir, but also block the fluid movement, which depends on original depositional structure, dolomitization style, and the appearance of anhydrite cements [1]. Mineral resources are also found in dolomite, such as Mississippi-Valley-type (MVT) lead-zinc deposits and celestine deposits [5]. Thus, for the prediction of high-quality reservoirs, it is crucially important to figure out the region of dolomitization influence and its effect on the physical character of the reservoir.

The origin of dolomite has always been a geological enigma. Because strong kinetic barriers exist for the precipitation of dolomite under near-surface temperature and pressure, dolomite appears to be very limited in modern carbonate sediments [1,6]. In recent years, microbially mediated dolomite has been reported under specific circumstances, and may act as seeds for later pervasive dolomitization [1]. It is universally accepted that large-scale dolomite bodies are the result of replacement reactions between high Mg/Ca fluids with limestones (Whitaker & Jones, 2004). Under laboratory conditions, the rate of dolomitization is controlled by the Mg/Ca ratio in solution, reactive surface area (RSA), mineralogy of the reactant, reaction temperature, pH, and presence of sulfate [1,7].

The secondary dolomitization models mainly include microbial (biological), Sabkha, reflux seepage (reflux dolomitization), hydrothermal, and mixing zone dolomitization [5,8]. Many dolomite reservoirs with abundant hydrocarbon are closely associated with evaporitic tidal flat/lagoons or basinal evaporites and are explained by reflux dolomitization [9]. Reflux dolomitization was originally developed by Adams and Rhodes (1960) to explain the hyperhaline-related dolomitization of Permian carbonates in West Texas [10]. The reflux is mainly induced by the difference of fluid density caused by the difference of fluid salinity in space. At the top of an isolated or restricted platform, the evaporated seawater or brine could flow downward under the influence of gravity and dolomitize underlying permeable limestone [11]. The reflux is also believed to occur under mesosaline brine without the presence of evaporite [12]. At present, reflux dolomitization is widely used to explain the dolomitization of an entire carbonate platform or sedimentary basin. The Jurassic Feixianguan Formation dolomite in Northeast Sichuan Basin and Jurassic Arab-D Formation dolomite of Ghawar field are typical cases of reflux dolomitization [9,13,14,15,16].

There are more than 90% proved reserves in Ordovician carbonate rocks in Tarim Basin [17]. Natural gas is mainly stored in the dolomite reservoir of the lower section of Yingshan Formation, part of the Middle-Lower Ordovician [18]. The Shunnan area, located in the middle part of the Tarim Basin, has significant natural gas resources in the Lower Yingshan Formation dolomite [18]. Taking Well SN501 in Shunnan area as an example, the open flow rate of natural gas reaches up to 18.7 × 10⁴ m³ with cumulative gas production of 338.18 × 10⁴ m³ [17]. Various types of dolomite have been identified in the Lower Yingshan Formation, mainly including crystalline dolomite of micritic to coarse-sized crystals, and dolomite with residual structure (arenite fine crystalline dolomite, silty crystalline dolomite with a thin lamination of microbial origin) [19,20,21,22,23,24,25]. The thin section observation and geochemical data indicated that silty-fine dolomite was the product of penecontemporaneous dolomitization, while the Mg²⁺ was derived from evaporated sea water [19,22,25,26]. In addition, some scholars considered the coarse crystalline dolomite as the product of continuous dolomitization of silty-fine dolomite [21]. However, there was no study on the influence area of reflux dolomitization and its effect on the reservoir. The traditional method of dolomitization is mostly based on field observation and seismic data combined with sequence stratigraphy. However, there is considerable uncertainty of field scale prediction and spatial variation of associated diagenetic patterns [9,27]. The interface between dolomite and limestone is usually on the order of several meters to tens of meters, which can be difficult to identify underground without sufficient seismic or logging data. Reactive transport modelling (RTM), which combines basic hydrodynamic and geochemical processes, could be used to simulate temporal and spatial variation of diagenesis, especially under a large basin scale and time scale framework. For instance, Jones et al. (2002), Whitaker and Xiao (2010), and Al-Helal et al. (2012) simulated the process of dolomitization through RTM [1,28,29]. Through setting an appropriate numerical model and geochemical parameters, this paper discusses reservoir modification during reflux dolomitization and its controlling factors by means of RTM.

2. Geological Background

2.1. Tectonic Locations and Stratigraphic Characteristics

Tarim Basin is located in the southern part of the Xinjiang Uygur Autonomous Region in northwestern China (Figure 1A). The Shunnan area is located in the transitional region from the north of Katake Uplift to the Manjiaer Depression in Tarim Basin (Figure 1B), which created conditions for the migration of hydrocarbon [22]. It includes the northern slope of the Tazhong structure (Shunnan Block and Gulong Block) and the west area of Guchengxu Uplift (part of the Gucheng Block) (Figure 1B). The Ordovician of the study area is divided into Penglaiba Formation, Yingshan Formation, Yijianfang Formation, and Querqueke Formation from bottom to top (Figure 1D). From the Lower Ordovician to the Middle Ordovician, the sedimentary facies changed from restricted platform to open platform, and the dolomite content decreased gradually (Figure 1D).

The Yingshan Formation is 400–500 meters thick, gradually thinning to the northeast. The Upper part of the Yingshan Formation is mainly a transition of thin mudstone and dolomite. The Lower Yingshan Formation is mainly composed of thick dolomite in Gucheng Block, but is characterized by thickly bedded limestone interlayered with dolomite in Shunnan Block [33]. Due to episode I of the Mid-Caledonian, the Yijianfang Formation suffered severe erosion, while the Yingshan Formation also suffered varying degrees of erosion and had unconformable contact with the Querqueke Formation. The Late Caledonian–Early Hercynian movement only resulted in unconformable contact between the Carboniferous and the Ordovician, and conformable contact between Yijianfang Formation and Yingshan Formation.

2.2. Sedimentary Facies of Lower Yingshan Formation

From the Late Sinian to the Ordovician, in the Tarim Basin, the carbonate platform developed in the west, while the platform slope lied in the east [19]. The characteristics of sedimentary facies during the Lower Yingshan Formation deposition are shown below (Figure 1C): (1) the sedimentary facies document different environments—restricted platform, open platform, platform margin, platform slope, and continental shelf from west to east; (2) the platform shoals are evenly distributed in the whole platform facies region, but the scale of them is relatively small. In addition to the platform shoals, the lagoon subfacies, including dolomitic flat, limemud flat, and dolomitic limemud flat, are also found in the restricted platform [19,21,22,32,34,35].

According to the variation of sedimentary facies above, the southwest part of the study was at shallow depth, deepening to the northeast during the Lower Yingshan Formation deposition. This topography creates conditions for evaporated seawater to be formed in the lagoon and replace underlying limestone northeastward. Besides, based on the lithology data from cores and thin sections, dolomitic limestone, lime dolostone, and crystalline dolomite were dominant in the restricted platform [32].

2.3. Petrological and Geochemical Characteristics

Through the microscopic identification and analysis of the thin section, powder crystal dolomites were found within crystalline dolomites, packstones, and grainstones. In the powder crystalline dolomite, the weak laminated structure (Figure 2A), showing a light and dark alternating banded structure under plane-polarized light, is preserved, which indicates that the dolomites were formed in the penecontemporaneous stage [21,36]. The powder crystalline dolomites show subhedral-euhedral structure, which is generally considered to be caused by a large number of nucleating sites from mudstone formed in a tidal flat sedimentary environment [21]. As for the grainstone and packstone, the powder crystal dolomites show speckled or patchy distribution (Figure 2C,E). Under cathode luminescence, powder crystal dolomites of three types of rock all show bright orange-red (Figure 2B,D). For the dolomites under cathodoluminescence, Mn²⁺ is the activator, while Fe²⁺ is the quencher. Under the condition of oxidation, the iron and manganese exist in the state of Fe³⁺ and Mn⁴⁺, which can not enter the dolomite crystals. The diagenetic environment during penecontemporaneous period is highly oxidized. Therefore, the amount of iron and manganese in the dolomite is low, besides the ratio of Mn²⁺/Fe²⁺ approaches zero, which lead to the dark orange-red color of dolomites (Figure 2B,D). Under cross polarized light, the hemihedral and short columnar anhydrites show third-order purple to blue color under the Lower Yingshan Formation (Figure 2F). This anhydrite indicates an evaporitic environment.

In order to study the response of different lithologies to dolomitization, the content of powder crystal dolomite in grainstones, packstones, and mudstones are calculated. The powder crystal dolomites under polarizing microscope (Figure 3A) are highlighted as purple (Figure 3B) with Photoshop v2018. The content of powder crystal dolomite (Powder crystal dolomite%) could be expressed as the percentage of purple area (S_Dolomite) in the view area (S_{Field of vision}). From the content distribution of powder crystal dolomite, the proportion of dolomite in mudstones is the highest (mainly ranging from 90% to 100%) (Figure 3E), while the proportions of that in grainstones and packstones are similar (mainly ranging from 65% to 75%) (Figure 3C,D). However, samples with 70–75% dolomite are more common in packstones than grainstones. Therefore, the degrees of dolomitization from weak to strong are grainstones, packstones, and mudstones.

With the help of bulk-rock and in situ carbon and oxygen analyses, the values of δ¹³C and δ¹⁸O values of micrite limestone and powder crystalline dolomites from the three types of rock above were obtained (Figure 4). Early findings [37] suggested that Early Ordovician marine carbonates’ values of δ¹⁸O_VPDB ranged from −8‰ to −6‰, while values of δ¹³C_VPDB ranged from −2‰ to −0‰. The values from the micritic limestones matches well with those from Early Ordovician marine carbonates. Some δ¹⁸O_VPDB values of micritic limestones are to the right of the δ¹⁸O_VPDB values range of Early Ordovician marine carbonates (Figure 4 blue rectangle), which shows slightly positive δ¹⁸O_VPDB anomaly. This may be due to the effect of evaporated seawater infiltration on the oxygen isotope values of micrite limestones. Thus, the isotopes of micritic limestone could reflect the nature of the seawater at that time. For the powder crystal dolomite, the values of δ¹⁸O_VPDB and δ¹³C_VPDB are near positive values, and values of δ¹³C_VPDB are higher than those from micritic limestone, which both suggest penecontemporaneous dolomitization [20,38,39]. However, due to the influence of fresh water, the oxygen isotopes of dolomite shifts toward negative values [20].

Combined with sedimentary facies, reflux dolomitization, as one type of penecontemporaneous dolomitization, has been established in the Shunnan area (Figure 5). The model shows that seawater from the storm supply is found in the Gulong Block and becomes the major source of brine for dolomitization. When the sea level rises, a small amount of seawater could be preserved in the platform edge shoals in Gucheng Block and evolve into brine due to evaporation. As the sea level changes, the location of brine ponds in Gulong and Gucheng Block changes horizontally. In the meantime, the brine (evaporated seawater) flows down by gravity and dolomitizes underlying limestone. Therefore, reflux dolomitization has a great influence on the physical properties of limestones in the Shunnan area, and the following numerical model was based on this.

3. Geochemical Modeling

There are four conditions to realize the dolomitization models [11,29,40]: (1) adequate supply of Mg²⁺; (2) a flow mechanism that allows required Mg²⁺ to circulate; (3) geochemical conditions conducive to the formation of dolomite; (4) adequate time for dolomite to form.

3.1. Model Tools

The model tool employed in this paper is TOUGHREACT (v1.2, University of California, Berkeley, USA), facilitated by an interactive graphical interface pre-processor and post-processor, Petrasim (v2017, Thunderhead Engineering, Manhattan, NY, USA). TOUGHREACT could be used to simulate the physical and chemical reaction progress in the one-, two-, and three-dimensional porosity/fracture media, including complex reaction in aqueous solution, gas dissolution and degassing equilibrium reaction, local equilibrium, and kinetic reactions such as dissolution and precipitation of minerals [2]. The integral finite difference (IFD) method is used for space discretization [41], while the solution method is implicit time weighting. The coupling method between water flow, solute migration, and chemical reaction module is the sequential iterative method [42]. The EOS7 module of TOUGHREACT is adopted for solving solute transport and chemical reaction problems in the mixing process of saline/hypersaline water and freshwater [43].

3.2. Kinetic Data of Dolomitization Reactions

Dolomitization is a kinetics-controlled reaction, thus the kinetic data of dolomite are essential. Over the past few decades, kinetic data of some mineral dissolution processes have been obtained by means of experiment; however, there is a shortage of kinetic data on precipitation rates. There is a general function for the mineral dissolution/precipitation [44]:

$$rn=f\left(c_1,c_2,\cdots ,c_{N\mathrm{C}}\right)=\pm knAn{\left|1-{\Omega }_n^{\theta }\right|}^{\eta }n=1,\cdots ,N_q$$

(1)

where positive values of r_n indicate dissolution, and negative values represent precipitation; k_n is the rate constant (moles per unit mineral surface area and unit time), which depends on temperature; A_n is specific surface area per kg H₂O; and n is the kinetic mineral saturation ratio. The kinetic expression for dolomite precipitation of Arvidson and Mackenzie (1999) is adopted in this paper [45], consistent with previous simulation of dolomitization [46]:

$$rdol=AsA{e}^{\frac{-Ea}{RT}}{\left(1-\frac{Q}{Keq}\right)}^{2.26}$$

(2)

where r_dol is the reaction rate of dolomite precipitation; A_s is the specific reactive surface area; and together, Q, the activity quotient, and K_eq, the equilibrium constant for ordered dolomite, define the saturation index. For the rate constant of dolomite, defined from laboratory experiments, A, the preexponential factor, is 11.22 mol/cm²; Ea, the activation energy, is 1.355 × 10⁵ J/mol; R is the universal gas constant; T is temperature (K); and 2.26 is the reaction order.

3.3. Thermodynamic Data of Calcite Dissolution and Anhydrite Precipitation

The precipitation of dolomite is accompanied by the dissolution of calcite and anhydrite precipitation. Since the rate of dolomite precipitation is much lower than that of the calcite dissolution and precipitation, both calcite and anhydrite are assumed to be thermodynamic minerals and controlled by mineral saturation ratio [1,29]. The mineral saturation ratio can be expressed as follows:

$${\Omega }_m=K_m^{-1}\prod _{j=1}^{N_C}{c}_j^{{\upsilon }_{mj}}{\gamma }_j^{{\upsilon }_{mj}}m=1,\dots ,Np$$

(3)

where m is the equilibrium mineral index, K_m is corresponding equilibrium constant, c is concentration, γ is the thermodynamic activity coefficient, and N_C is aqueous species. At equilibrium, Equation (3) can be expressed as follows:

$$S{I}_m={\log }_{10}{\Omega }_m=0$$

(4)

where SI_m is called the mineral saturation index.

3.4. Three-Dimensional Flow

We defined a typical three-dimensional (3D) model to analyze the influence of every single factor on mineral abundance change with the evolution of petrophysical properties. As Figure 6 shows, reflux dolomitization is simulated in a 3D 10,000 m × 5000 m × 500 m flow region. The node spacing is uniformly specified as 500 m in the x-axis direction, 500 m in the y-axis direction, and 50 m in the z-axis direction (Figure 6A). In the vertical direction, the model is composed of ten 50 m thick layers with different rock properties, representing the variation of porosity and permeability with depth. The boundary conditions are similar to the previous two-dimensional (2D) reflux dolomitization reactive transport model [2,3,5,9,47]. The front and back boundaries (i.e., surfaces dceh and abgf), and lower boundary (i.e., surface bcgh) with left boundary (i.e., surface abcd) are specified as no-flow boundaries (constant pressure boundary). The upper boundary (i.e., surface adef) is a fluid-pressure boundary, allowing the recharge and discharge of fluid, with a 500 m wide and 5000 m length zone with brine injection sites on the top of the model. Besides, the right boundary (i.e., surface fghe) is defined as outflow boundary. The outflow boundary belongs to the fixed gradient boundary, and is generally expressed as follows:

$${\frac{dC}{dx}|}_{\mathrm{x}=boundary}=f\left(t\right)$$

(5)

where C is the concentration and f(t) is a known function in the boundary area under investigation [48]. In this modelling, a no-gradient boundary condition, f(t) = 0, is utilized at the last column of vertical grid blocks to the outflow boundary. In order to satisfy this condition, the no-gradient boundary is set as fixed state by Petrasim v2017 to represent infinite volume [49]. Thus, the brine, injected from the injection sites (Figure 6A), is negligible compared to the formation water. The aqueous chemical composition and thermodynamic conditions (such as temperature, pressure, etc.) of the boundary grid blocks are kept unchanged as the primary formation water during simulation [50].

The temperature and pressure of the upper boundary (i.e., surface adef) of the model are set to 25 °C and 0.1 Mpa, respectively. The model is set to non-isothermal and non-isobaric. According to the geothermal gradients in the Shunnan area [51], the maximum, medium, and minimum geothermal gradients are 1.8 °C/100 m, 2.1 °C/100 m, and 2.68 °C/100 m. The geothermal gradient 2.1 °C/100 m is used for the baseline case. For the initial formation water and injection brines, we set their temperatures to 30 °C. To simplify the simulation, the formation pressure gradient is defined as 0.98 Mpa/100 m [52]. In other words, the temperature and pressure gradually increases as the vertical distance increases. Our simulated flow domain represents the profile of the carbonate platform where brine feeds from the top left and flows horizontally to the outflow boundary (Figure 6C). The zone of brine discharge, located basinward of the right boundary, is not simulated in this model. The reflux flow is driven by the density difference between brine and formation water. In order to analyze the effect of flow rate on dolomitization separately, we define the injection speed as 700 kg/s, 1200 kg/s, and 1800 kg/s. Among them, the injection speed 1200 kg/s is defined in the baseline case. Besides, the reflux dolomitization is simulated to 30 My in all cases.

3.5. Lithology

The initial mineralogy is 99% calcite and 1% ‘seed’ dolomite, which represents minor syndepositional dolomitization and provides nucleation sites, assuming prior stabilization of high-Mg calcite and aragonite [1,12]. As for the anhydrite, it is defined as a secondary mineral. The porosity is essential for the flux of fluid and closely associated with permeability. The porosity is calculated as a function of depth, from Jones and Xiao (2006) [52], which could be expressed as follows:

$$\Phi =P0e^{-bZ}+P1$$

(6)

where Φ is porosity, P₀ is the reducible porosity present at deposition, b is the compaction coefficient (km⁻¹), Z is depth (km), and P₁ is the irreducible porosity. As mentioned above, the powder crystal dolomites are mainly found in grainstones, packstones, and mudstones. The parameters used for Equation (6) of three rock types are documented in

Table 1. Constants specified to calculate porosity (modified from [57]).

Rock Type	P0	P1	b
Grainstone	0.4	0.01	0.55
Packstone	0.4	0.01	0.55
Mudstone	0.6	0.01	0.6

. The initial permeabilities are calculated from porosities according to rock-fabric petrophysical relationships from Lucia (1995) [53]. The porosity–permeability relationships for different types of rocks are shown in

Table 2. Porosity–permeability relations of different classes of carbonate rock fabric (modified from [1]).

Rock Class	Rock Fabric	Porosity-Permeability Relationship
Class 1	Limestone and dolomitized grainstones; large-crystalline-grain-dominated dolopackstones	k = (45.35 × 108) × Φ8.357
Class 2	Grain-dominated packstones; fine- to medium-grain-dominated dolopackstones; medium crystalline mud-dominated dolostones	k = (2.040 × 106) × Φ6.380
Class 3	Mud-dominated limestones; fine crystalline mud-dominated dolostones	k = (2.884 × 103) × Φ4.275

k is the maximum (horizontal) permeability in millidarcies (1 md = 10⁻¹⁵ m²); Φ is the fractional porosity.

. The Class 1 porosity–permeability relationship corresponding to grainstones is used for the baseline case. The sensitivity for the porosity–permeability relationship is analyzed using Class 2 for packstones and Class 3 for mudstones. As mentioned, the model is vertically divided into 10 layers (Figure 6B). The porosity and permeability of each layer are calculated using the middle depth of that layer. For instance, 25 m is used to calculate the porosity and permeability of Layer 10 (0 to 50 m). The physical properties of each layer of different rock types are shown in

Table 3. The porosity and permeability of different layers with different rock types.

Layer	Grainstone		Packstone		Mudstone
	Φ/%	kh/m2	Φ/%	kh/m2	Φ/%	kh/m2
Layer 1	0.318035349	2.56572 × 10−10	0.318035349	1.36591 × 10−12	0.461208553	1.05477 × 10−13
Layer 2	0.326623872	3.2211 × 10−10	0.326623872	1.61903 × 10−12	0.474949899	1.19582 × 10−13
Layer 3	0.335451857	4.04466 × 10−10	0.335451857	1.91934 × 10−12	0.489109731	1.35584 × 10−13
Layer 4	0.344525981	5.07974 × 10−10	0.344525981	2.27565 × 10−12	0.503700795	1.53739 × 10−13
Layer 5	0.353853105	6.38086 × 10−10	0.353853105	2.69849 × 10−12	0.518736222	1.74338 × 10−13
Layer 6	0.363440285	8.01668 × 10−10	0.363440285	3.20032 × 10−12	0.534229547	1.97712 × 10−13
Layer 7	0.373294771	1.00736 × 10−10	0.373294771	3.79596 × 10−12	0.550194714	2.24235 × 10−13
Layer 8	0.383424016	1.26604 × 10−10	0.383424016	4.50302 × 10−12	0.566646092	2.54334 × 10−13
Layer 9	0.393835681	1.59141 × 10−10	0.393835681	5.34245 × 10−12	0.583598489	2.88492 × 10−13
Layer 10	0.40453764	2.00072 × 10−10	0.40453764	6.33911 × 10−12	0.601067164	3.27259 × 10−13

Φ is the porosity, k_h is the horizontal permeability (x and y axes).

. The permeability anisotropy, which determines the range and flow rate of brines, is universal in carbonate platforms due to depositional and diagenetic factors [29,54]. For simplification, k_h (horizontal permeability)/k_v (vertical permeability) is specified as 100. In addition, the extent and nature of porosity and permeability modification by dolomitization are highly variable, ranging from fabric-retentive mimetic dolomitization to fabric-destructive recrystallization. The Carman–Kozeny relationship, which could approximate the porosity-permeability relationship for dolostones [55,56], is incorporated in TOUGHREACT.

The reactive surface area (RSA) is used to initialize nucleation of kinetic minerals. The 1% ‘seed’ dolomite produces a positive nucleation site, which creates equal conditions for dolomite growth at all sites [29]. The rate of reaction at the mineral surface is commonly approximated by RSA exposed to diagenetic fluids [58]. The RSA of rocks are assumed to be proportional to the average percentage of fines (times a factor of 100) [59]. Thus, the RSA increases from grainstones to packstones to mudstones. In order to figure out the effect of RSA on reflux dolomitization, the RSA is specified without considering the limestone types. Our baseline simulation assumes a specific RSA of 1000 cm² g⁻¹, which represents a sediment with an average diameter of 50 μm diameter idealized grains or larger, but morphologically more complex grains [60]. The sensitivity analysis tests RSA between a minimum of 100 cm² g⁻¹ and a maximum of 10,000 cm² g⁻¹, representing coarser (260 μm) and finer crystals (2.5 μm), respectively [12].

3.6. Geochemical Data

Nine primary aqueous species (Na⁺, Ca²⁺, Mg²⁺, K⁺, H⁺, Cl⁻, SO₄²⁻, HCO₃⁻, and H₂O) and their associated secondary aqueous species (

Table 4. Aqueous species included in reactive transport simulations of reflux dolomitization.

Primary Aqueous Species
Na+	Ca2+	Mg2+	K+	H+
Cl−	SO42−	HCO3−	H2O
Secondary Aqueous Species
CaCl+	CaCl2 (aq)	CaCO3 (aq)	CaHCO3+	CaOH+
CaSO4 (aq)	CO2 (aq)	CO32−	H2SO4 (aq)	HCl (aq)
HSO4−	KCl (aq)	KHSO4 (aq)	KOH (aq)	KSO4−
Mg4(OH)44+	MgCl+	MgCO3+ (aq)	MgHCO3+	MgOH+
MgSO4− (aq)	NaCl (aq)	NaCO3−	NaHCO3 (aq)	NaOH (aq)
NaSO4−	OH−

) are considered in TOUGHREACT. The Ordovician formation water in Tarim Basin belongs to high-salinity CaCl₂-type water. In this flow model, the chemical composition of formation water is generated from the balance between Ordovician formation water from Well YB1 and the initial minerals, which avoids the disruption caused by the reaction between initial formation water with minerals during the simulation [52]. The brines are assumed to be from the evaporation of seawater of that time. However, the specific aqueous species of Ordovician seawater are unclear from the fluids inclusions in halite [61]. Thus, the brines in this study are not obtained by evaporating seawater. Three known types of brines with different salinity and Mg²⁺/Ca²⁺ are selected in the simulation: Ibis Pond, Ralph Sink, and Phreatic Majanna [3]. The chemical composition of initial water and brines are shown in

Table 5. Chemical composition (mmol) of formation water and brine used in this study.

Concentration (mmol)	Initial Formation Water ▲	Ibis Pond *	Ralph Sink *	Phreatic Majanna *
Na+	485	1260	3180	4451
Cl−	566	1460	3693	5350
K+	10.6	25.56	65.6	103.8
Ca2+	53.95	24.44	22.2	12.22
Mg2+	4.855	137.2	339	597.8
HCO3−	0.3101	0.7	1.67	1.655
SO42−	23.47	77.8	137.2	211.1
pH	5.7	7.7	7.1	6.7
Log PCO2	−2.0	−3.2	−2.3	−2.1
Mg/Ca molar	0.09	5.6	15.3	48.9
Salinity(‰)	36	85	186	249

^▲: The Ordovician formation water from Well YB1 equilibrium with minerals (99% calcite and 1% dolomite) and atmospheric Log pCO₂ (−2.0) were calculated with TOUGHREACT v1.2. *: Chemical composition of brines from [3].

. The calculated saturation indices for the brines with respect to major carbonate and evaporite minerals are documented in

Table 6. Calculated saturation indices (Log Q/K) of major carbonate minerals for brines used in Table 4 (modified from [3]).

Mineral	Ibis Pond	Ralph Sink	Phreatic Majanna
Aragonite	0.14	−0.26	−0.31
Calcite	0.32	−0.07	−0.49
Dolomite	1.74	1.46	1.22
Magnesite	0.58	0.7	0.87
Gypsum	−0.19	−0.08	−0.03
Anhydrite	−0.37	−0.16	−0.03
Halite	−1.67	−0.7	−0.19

. For ionic activities calculation, the Debye–Hückel approach may underestimate the diagenetic potential of dolomitizing fluids [29]. The simulations of this study used the Pitzer ion-interaction equation to calculate ionic activities in accordance with the RTM study by Gabellone and Whitaker (2016) [12].

In addition to the baseline model, 10 different simulations, Cases 1–10, are set up to compare the effects of different factors on reflux dolomitization, including petrophysical property, RSA, geothermal gradient, injection rate, and brine salinity (

Table 7. Parameter settings for three-dimensional flow models.

Model No.	Rock Fabric	RSA (cm2/g)	G (°C/100 m)	Injection Rate (kg/s)	Brine Type
Baseline	Grainstone	1000	2.1	1200	Ralph Sink
Case 1	Packstone	-	-	-	-
Case 2	Mudstone	-	-	-	-
Case 3	-	100	-	-	-
Case 4	-	10,000	-	-	-
Case 5	-	-	1.8	-	-
Case 6	-	-	2.68	-	-
Case 7	-	-	-	700	-
Case 8	-	-	-	1800	-
Case 9	-	-	-	-	Ibis Pond
Case 10	-	-	-	-	Phreatic Majanna

Note: G is the geothermal gradient.

).

4. Results

4.1. Temporal and Spatial Evolution of the 3D Model

4.1.1. Influence of Dolomitization on Different Cells

(1) The Common Law of the Three Cells

Three cells (Figure 7) are selected from the flow model to analyze the differences in the influence of dolomitization in horizontal and vertical directions. Among them, Cell 1601 is directly above the Cell 1, while Cell 19 is on the right side of Cell 1. Firstly, the three cells are treated as a whole to analyze the changes in mineral abundance through time. The change of dolomite abundance curves (Figure 8A) shows that the precipitation rate of dolomite was fast in the first 6.8 My, and then the dolomite volume increased slowly in the left 23.2 My. In other words, the precipitation rate of dolomite is characterized by two stages which are separated by an inflection point (6.8 My), which is consistent with the RTM results of compaction dolomitization [47]. Meanwhile, the change of calcite abundance also shows two stages corresponding to those of the dolomite abundance change (Figure 8B). The change of anhydrite abundance has experienced rapid rise and decline, and eventually dropped to zero (Figure 8C). Therefore, the change of anhydrite abundance includes three stages divided by inflection point-1 (6.8 My) and inflection point-2 (15 My and 20 My). It should be noted that inflection point-1 of anhydrite is the same as the inflection point of dolomite and calcite.

As shown in Figure 8D–F, the porosity change consists of two ascending stages and two descending stages separated by three inflection points. The increase of porosity during dolomitization has been widely recognized [1,3,47]. The first ascending stage (Figure 8D) occurred when the abundance of both dolomite (Figure 8A) and anhydrite were low (Figure 8C). The second ascending stage (Figure 8D) occurred when the dolomite abundance was high (Figure 8A), while the anhydrite abundance vanished (Figure 8C). The descending stages of porosity have also been found in previous RTM studies of dolomitization [1,12,29,47]. The two descending stages in this paper correspond to the fast precipitation of anhydrite (Figure 8C) and the slow precipitation of dolomite (Figure 8A), respectively. Besides, the inflection point-2 of porosity corresponds to the inflection point of dolomite and calcite, while the inflection point-3 of porosity corresponds to the inflection point-2 of anhydrite.

(2) The Comparison of the Three Cells

There exists significant difference between Cell 1 and Cell 1601. Compared with Cell 1 and 19, Cell 1601 has the lowest changes of dolomite and anhydrite (Figure 8A,C), while Cell 1601 has the highest change of calcite abundance (Figure 8B). For the anhydrite abundance change, the inflection point-2 of Cell 1601 occurred earlier than that of Cell 1 and 19. The porosity change of Cell 1601 was larger than that of Cell 1 and Cell 19 before 18 My, and lower than that of Cell 1 and Cell 19 after that. Besides, for the porosity change, the inflection point-1 of Cell 1601 occurred later than that of Cell 1 and Cell 19, while the inflection point-3 of Cell 1601 was earlier than that of Cell 1 and Cell 19 (Figure 8D). The relationship between Cell 1 and Cell 19 is more complicated. For the dolomite, it was precipitated faster in Cell 1 than in Cell 19 (Figure 8A) before the inflection point, but slower after that. Before the calcite was completely dissolved (inflection point), the amount of dissolved calcite of Cell 1 was greater than that of Cell 19 (Figure 8B). For the anhydrite, it was precipitated faster in Cell 1 than in Cell 19 before inflection point-1, but slower between inflection point-1 and inflection point-2 (Figure 8C).

4.1.2. Temporal and Spatial Evolution of Minerals

Reactive transport simulation results indicate that dolomitization is by replacement of calcite, with no significant primary dolomite precipitation, which is consistent with previous RTM studies under gypsum-saturated brines over long time periods [1,3,9,29]. Based on the dolomite and anhydrite front shape after 100 y, all cases could be divided into two dolomitization patterns (Figure 9 and Figure 10). Except for Cases 6 and 7, the other cases belong to the dolomitization pattern-1. Among them, the baseline case and Case 7 (700 kg/s) are selected to represent these two dolomitization patterns (Figure 9 and Figure 10).

(1) Dolomite

According to the location of the dolomite body over time, both dolomitization patterns involve two stages (Figure 9). In stage-A (1 to 100 y), dolomite formed firstly beneath the injection sites (brine pool) (Figure 9(A1,A2)), and grew laterally and downward, replacing calcite (Figure 9(B1–C2)). The dolomite front was broad, with an exponential decline in dolomite abundance with the increase of lateral and vertical distance. There is a gradational contact between limestone and dolomite. In 100 y, the tabular asymmetric dolomite body extended 8 km from the brine source and penetrated to a maximum 480 m. In 100 y, the tabular asymmetric dolomite body extended laterally for 8 km and vertically for 480 m. Besides, the dolomite front advanced basinward from the brine source at an average speed of 80 m/y. In addition, the thickness of the dolomite body increased at a rate of 2.5 m/y to 4.5 m/y. From the maximum change of dolomite in stage-A, the dolomite abundance increases nonlinearly (Figure 9). This is consistent with high-temperature experimental results and RTM of early burial dolomitization by geothermal convection [1]. It is also worth noting that the center of dolomitization, shown in a red color in Figure 9, moved downward as time passed. In stage-B (20 ky to 8 My), the center of dolomitization had moved to the left of the lower boundary (Figure 9(D1,D2)). The dolomite body extended slowly laterally, and upward to the upper boundary at 3.759 10⁻⁴ m/y. After 8 My, the dolomite had little variation in extent and abundance, which is not shown here. The difference between the two dolomitization patterns are reflected in the falling wedge-shaped dolomite body in pattern-1 and rising wedge-shaped dolomite body in pattern-2. The temporal and spatial evolution of the change of calcite abundance is not shown here because the distribution of change of calcite abundance mirrors that of dolomite.

(2) Anhydrite

Previous RTM studies showed that precipitation of anhydrite occurred downstream or ahead of the advancing dolomite front during stage-A of dolomitization [3,29]. However, the anhydrite in this study lacks the stage of downward and lateral expansion, corresponding to stage-A of dolomite. The precipitation of anhydrite appeared initially on the lower boundary (Figure 10(A1,A2)) and then extended to the right and upper boundaries (Figure 10(B1,B2)), corresponding to stage-2 of the evolution of dolomite. From 20 ky to 6.8 My, the abundance and the distribution range of anhydrite (Figure 10(A1–B2)) were increasing. After 6.8 My, the anhydrite began to dissolve, reflected in the decrease of distribution range and abundance. In previous RTM studies, the anhydrite was dissolved as the dolomite front extended into the zone of anhydrite and then reprecipitated ahead of the advancing dolomite front [3,29]. However, when the anhydrite was increasing, the zone of anhydrite overlapped that of dolomite (Figure 9 and Figure 10) in this study. Similar to the dolomite body, the anhydrite body shows a falling wedge-shape in dolomitization pattern-1. while rising wedge-shaped anhydrite occurs in dolomitization pattern-2.

4.1.3. Temporal and Spatial Evolution of Porosity and Permeability

The changes in porosity and permeability are the result of dolomitization and anhydrite abundance change. The baseline case is used to analyze the evolution of porosity and permeability (Figure 11). The change of permeability depends on the porosity and permeability feedbacks approximated using a simplified Carmen–Kozeny equation [1]. Similar to the dolomite and anhydrite fronts, the difference between the two dolomitization patterns is also reflected in the change of porosity front, which is not shown here.

From 10 y to 100 y, the growth in porosity and permeability initially occurred beneath the injection sites, and then extended to the right and bottom boundaries (Figure 11(A1–B2)), corresponding to stage-A of dolomite (Figure 9(A1–C2)). The permeability variation extended further, both vertically and laterally, than the porosity variation (Figure 11(A1–B2)). From 100 y to 20 ky, both the porosity and permeability increased. The center of porosity change gradually moved down over time, similar to that of dolomite change (Figure 11(B1,C1)). In contrast, the center of permeability change did not move down with time (Figure 11(B2,C2)). This results in the falling wedge-shaped porosity change and rising wedge-shaped permeability change. From 20 ky to 6.8 My, both porosity and permeability were significantly lower than the initial values (Figure 11(D1,D2)). The centers of the porosity and permeability change remained unchanged, thus the decrease in permeability was spatially mirrored by the decrease in porosity (Figure 11(D1,D2)). From 6.8 My to 17 My, the porosity and permeability increased again (Figure 11(E1,E2)). Besides, the center of porosity growth rose vertically (Figure 11(E1)) compared to the porosity change center in 20 ky (Figure 11(C1)). From 17 My to 25 My, the porosity and permeability were further increased (Figure 11(F1,F2)), and the center of porosity change moved to the lower left of the model. However, according to the porosity change of the three cells, the porosity began to decrease in a slow rate after inflection point-3 (15 My and 20 My). Therefore, the porosity and permeability firstly increased and then decreased little, which is not shown in Figure 11.

4.1.4. Temporal and Spatial Evolution of Fluid Compositions

The process of dolomitization is also reflected in the change of Ca²⁺ and Mg²⁺ through time (Figure 12). From 10 y to 100 y, the low Ca²⁺ zone, shown in deep blue (Figure 12(A2,B2)), and a high Mg²⁺ zone, appearing in red (Figure 12(A1,B1)), match the geometry of the growing dolomite body (Figure 9). The brine reflux drove the replacement of calcite by dolomite, with a rapid decline in Mg²⁺ behind the high Mg²⁺ zone, mirrored by an increase in Ca²⁺ (Figure 12(A1–B2)), which agrees with previous results [1,3,9,29]. Besides, the low Mg²⁺/Ca²⁺ of fluids reaching the model interior (behind the high Mg²⁺ zone) limited dolomitization. From 20 ky to 6.8 My, Mg²⁺ was decreasing gradually (Figure 12(C1,D1)), but rose again in 6.8 My (Figure 12(E1)). The Ca²⁺ kept increasing during this stage (Figure 12(C2,D2,E2)). The high Mg²⁺ zone kept rising in wedge-shape until 200 ky (Figure 12(C1,D1)), and then transformed to the shape of a falling wedge-shape in 6.8 My (Figure 12(E1)). The high Ca²⁺ zone initially remained at the bottom of the model (Figure 12(C2,D2)) and then rose to the top of the model (Figure 12(E2)). From 6.8 My to 25 My, Mg²⁺ was increasing, with Ca²⁺ decreasing (Figure 12(F1–H2)). The high Mg²⁺ maintained a falling wedge-shape at the bottom (Figure 12(F1,G1,H1)). The Ca²⁺ zone was limited to the right boundary and showed a trend of increasing from left to right (Figure 12(F2,H2)). It should be noted that there was a temporary increase in the Ca²⁺ content in 17 My (Figure 12(G2)). From 25 My to 30 My, distribution patterns of the Ca²⁺ and Mg²⁺ were the same as those in 25 My.

4.2. Sensitivity Analysis

To evaluate the accuracy of the simulation with different extrinsic and intrinsic parameters, sensitivity analysis was done by comparing Case-1 to 10 with the baseline case. The variation of each parameter is listed in the Table 7. The simulation results are compared in the cross-section parallel to the front boundary in 5 My, during the period of rapid growth of dolomite and anhydrite abundance (Figure 8). As Figure 8A shows, the dolomite from the fast precipitation stage before the inflection point occupies the main position in the total dolomite. Therefore, the dolomite abundance in 5 My is reasonable to represent the strength of dolomitization during the whole process.

4.2.1. Intrinsic Controls

For the petrophysical property, permeability is considered to be the most important factor which determines the magnitude of fluid flux and the scope of influence of dolomitization [1,3,29,40,57,62]. The pores in rocks provide the main space for fluid flow. However, the effect of porosity on dolomitization has often been overlooked in previous studies. Three porosity–permeability relationships are included to study the comprehensive effect of porosity and permeability on dolomitization. Different rock types have different RSAs. The influence of RSA is explored by setting three different values.

(1) Initial Porosity and Permeability

The three different porosity–permeability relationships correspond to three different rock fabrics. As shown in Table 7, the baseline, Case 1, and Case 2 represent “grainstone”, “packstone”, and “mudstone”, respectively. According to Equation (6) and Table 2, the “grainstone” has the highest permeability, and the same porosity as the “packstone”; “mudstone” has the highest porosity and lowest permeability (Table 3). The overall changes of dolomite abundance from high to low are “mudstone”, “packstone”, and “grainstone” (Figure 13(A1–A3)), which differs from previous studies that show high permeability leads to high dolomite content [1]. The overall changes of anhydrite abundance from high to low are “packstone”, “grainstone”, and “mudstone” (Figure 13(B1–B3)). For the “grainstone” and “packstone”, the low porosity change zone (blue color) shows a falling wedge-shaped distribution (Figure 13(C1,C2)). For the “mudstone”, the low porosity change zone (blue color) shows a falling wedge-shape near the lower boundary, while the high porosity change zone (red color) shows a rising wedge-shape near the upper boundary (Figure 13(C3)). As for the grainstone and packstone, the porosity decreases throughout the model. The porosity of “grainstone” is reduced more than that of “packstone” (Figure 13(C1,C2)). For the “mudstone”, there is a transition from decrease to increase in porosity change from the bottom to the top of the model (Figure 13(C3)). Since previous studies have discussed permeability anisotropy in detail [29,40,57,62], permeability anisotropy of 100 is set in all simulations to simplify the calculation.

(2) RSA

The baseline simulation is conducted with an RSA of 10³ cm² g⁻¹, representative of dolomite rhombs with 50 μm diameters. We tests the sensitivity of reflux dolomitization to two additional RSAs of 10² and 10⁴ cm²/g, which represent coarse carbonate grains or large (500 μm) dolomite crystals and fine-grained muddy sediments or small (5 μm) dolomite crystals, respectively. The dolomite and anhydrite abundance change increases with the increasing of RSA, reflected in the expanding high dolomite and anhydrite change zones (Figure 14(A1–B3)). As for the porosity change, there is no increase with the RSA of 10³ or 10⁴ cm²/g (Figure 14(C2,C3)). From the bottom to the top of the model, there is a transition from a decrease to an increase in porosity change with the RSA of 10² cm²/g (Figure 14(C1)).

4.2.2. Sensitivity Analysis: Extrinsic Controls

The extrinsic controls of reflux dolomitization mostly concern climate and heat flux of the platform. Climate controls the evaporation of platform top seawater, which determines the salinity of the brine. The salinity of the brine induces density difference between brine and formation, which controls the flow rate. The heat flux can be equivalent to the geothermal gradient, while the climate controls the temperature at the top of the platform. In this paper, we examine the sensitivity to geothermal gradient, injection rate, and brine concentration or salinity.

(1) Geothermal Gradient

The sensitivity of the system to temperature is investigated by comparing simulations using different geothermal gradients while maintaining the platform top at 25 °C. The geothermal gradient of 2.1 °C/100 m is used in the baseline simulation. Besides, geothermal gradients of 1.8 °C/100 m and 2.68 °C/100 m represent minimum and maximum geothermal gradients in the Shunnan area. Similar to the effect of RSA on dolomitization, both dolomite and anhydrite abundance changes increase with the increasing of geothermal gradient (Figure 15(A1–B3)). The initial porosity also decreases with the increase of geothermal gradient (Figure 15(C1–C3)). It is important to note that the low porosity change zone (blue color) shows a falling wedge-shape with geothermal gradient of 1.8 °C/100 m and 2.1 °C/100 m, but appears as a rising wedge-shape with geothermal gradient of 2.68 °C/100 m (Figure 15).

(2) Injection Rate

The flow rate in the carbonate platform varies in a complex manner, with the gradient in effective head as well as permeability of the sediments, which will evolve during diagenesis [12]. The hydraulic head, relative to the formation water in the shallow subsurface, is maintained by the concentration of platform-top brines [63,64]. Previous studies have also suggested that reflux flow rate increases with brine salinity [65]. To isolate the control of flow flux, two additional injection rates are specified while maintaining salinity. Besides, the injection rate has no feedback from the changing petrophysical property during simulation. Previous studies indicated that the high flow rates corresponded to high dolomitization rates [3,12]. However, for the dolomite abundance change, the increase of abundance change with an injection rate of 700 kg/s is similar to that with an injection rate of 1800 kg/s (Figure 16(A1,A3)). The injection rate of 1200 kg/s has the smallest increase in dolomite abundance (Figure 16(A2)). The effect of injection rate on anhydrite is the same as that of dolomite (Figure 16(B1–B3)). As for the porosity, the porosity decreases under all injection rates. The porosity reductions with the injection rate of 700 kg/s and 1800 kg/s are about the same (Figure 16(C1,C3)), but the reduction in porosity with the injection rate of 1200 kg/s is the smallest (Figure 16(C2)). Only the low porosity change zone with the injection rate of 700 kg/s has the rising wedge-shape.

(3) Brine Salinity

The brine close to gypsum (Ralph Sink) is used in the baseline, and the brine close to halite saturation (Phreatic Majanna) and mesohaline brine (Ibis Pond) are added to analyze the effect of brine salinity on dolomitization (Table 5 and Table 6). On the one hand, the different salinities correspond to different ratios of Mg/Ca and other aqueous species (Table 5), which control mineral saturation state (Table 6). On the other hand, the rate of reflux is proportional to the fluid density caused by salinity. The brine concentrated beyond gypsum saturation might induce precipitation of the low-permeability evaporites, leading to a rate of reflux reduction [64]. Therefore, the injection rate remains the same for the different brine salinities in the simulation. As for the dolomite and anhydite, the abundance of them increases with increasing salinity (Figure 17(A1–B3)). The overall porosity reduction increases from Ralph Sink brine (186‰) to Phreatic Majanna brine (249‰). However, the high porosity change zone, representing porosity increase, occurs in the upper part of the model with the Ibis Pond (85‰).

5. Discussion

5.1. General law of Mineral Dissolution/Precipitation and Porosity Change

Different chemical reactions of dolomite are mainly controlled by the system closure and the supply of foreign Mg²⁺ and Ca²⁺, which has different effects on reservoir porosity. The dolomitization could be expressed in three different equations [66].

$$2{\mathrm{CaCO}}_3\left(calcite\right)+{\mathrm{Mg}}^{2+}\to {\mathrm{CaMg}({\mathrm{CO}}_3)}_2\left(dolomite\right)+{\mathrm{Ca}}^{2+}$$

(7)

$${\mathrm{CaCO}}_3\left(calcite\right)+{\mathrm{Mg}}^{2+}+{{\mathrm{CO}}_3}^{2-}\to {\mathrm{CaMg}({\mathrm{CO}}_3)}_2(dolomite)$$

(8)

Equation (7) is known as the mole-to-mole dolomitization. Since the volume of two moles of calcite (36.934 cm³/mol) is greater than the volume of one mole of dolomite (64.365 cm³/mol), the porosity theoretically increases by 13% [67,68]. If the system is in a completely open environment, the subsequent dolomitizing fluid induces high concentration of Mg²⁺ and CO₃²⁻, leading to Equation (8) [68,69,70]. Equation (8) will result in a decrease on porosity [69,71]. The actual reflux dolomitization simulation process is the mixture of Equations (7) and (8). If the influence of Equation (7) is equal to that of Equation (8), volume to volume dolomitization will occur, resulting in no change of porosity [72,73]. Which of these equations is predominant depends on the chemistry of the brine. The concentration of Mg²⁺ in brine is significantly higher than that of CO₃²⁻, thus Equation (7) is predominant in this study. When all the calcite in the system is converted to dolomite, the subsequent dolomite is precipitated as cement in the pores due to the continuous supply of dolomitization fluid, which refers to over-dolomitization and can be expressed as Equation (9).

$${\mathrm{Ca}}^{2+}+{\mathrm{Mg}}^{2+}+2{{\mathrm{CO}}_3}^{2-}\to {\mathrm{CaMg}({\mathrm{CO}}_3)}_2(dolomite)$$

(9)

In our study, the high concentration of SO₄²⁻ in the brine (Table 5) will react with the displaced Ca²⁺ from Equation (7) to form gypsum or anhydrite cement, leading to porosity reduction, as follows:

$${\mathrm{Ca}}^{2+}+{{\mathrm{SO}}_4}^{2-}\to {\mathrm{CaSO}}_4(anhydrite)\mathrm{or}{\mathrm{CaSO}}_4·2{\mathrm{H}}_2\mathrm{O}(gypsum)$$

(10)

The heterogeneity of the model is mainly reflected in two aspects. For petrophysical properties, different depths of the model correspond to different porosities and permeabilities (Equation (6), Table 2 and Table 3). For the brine reflux, due to the difference in the distance from the injection sites, it is different at different locations per unit time. However, the variation trends of mineral abundance and porosity change from the three cells are consistent, as discussed above. The fast precipitation of dolomite (Figure 8A before the inflection point) and anhydrite (Figure 8C before inflection point-1) corresponds to the fast dissolution of calcite (Figure 8B before the inflection point). This process refers to replacement dolomitization, corresponding to Equations (7) and (10). Besides, from the maximum of the dolomite abundance change (Figure 9), the fast precipitation of dolomite increases nonlinearly. Gabellone and Whitaker (2016) considered that the dolomite abundance during the replacement stage could be expressed as below [12]:

$$Dolt=Dol0e^{(xt)}$$

(11)

where Dol_t is the dolomite volume fraction at time t, Dol₀ is the initial (‘seed’) dolomite volume fraction, and time t is in ky. For the given brine, the value of the exponent x is determined directly by the degree of evaporative concentration (represented by the salinity). Therefore, locations where dolomitization occurs at a higher initial rate would be expected to continue to dolomitize with an increasing rate. This reflects the increasing total RSA of dolomite (Equation (2)). When the calcite was totally dissolved (Figure 8B after the inflection point), the slow precipitation of dolomite cement (Figure 8A after the inflection point) with fast dissolution of anhydite (Figure 8C after inflection point-1) occurred. This process refers to over-dolomitization, corresponding to Equation (9).

As for the porosity change, theoretical volumetric calculations of replacement dolomitization by Weyl (1960) [68] and dissolution of anhydrite are thought to increase porosity. Anhydrite cements were also verified to occlude porosity [3,29]. The first ascending stage (Figure 8D before inflection point-1) occurred when dolomite began to precipitate and anhydrite was low. In this stage, the porosity produced by calcite replacement was higher than the porosity reduction by anhydrite cementation. The second ascending stage (Figure 8D between inflection point-2 and 3) occurred when dolomite grew slowly and anhydrite dissolved rapidly. In this stage, the porosity increase by anhydrite dissolution was higher than the porosity reduction by dolomite cementation. The two descending stages of porosity occurred when the anhydrite precipitated quickly or the dolomite cement precipitation occurred. For the first descending stage (Figure 8D between inflection point-1 and 2), the decrease in porosity caused by anhydrite precipitation exceeded the increase in porosity caused by calcite replacement, leading to the overall porosity reduction. For the second descending stage (Figure 8D after inflection point-3), after the anhydrite had been completely dissolved, the slow precipitation of dolomite cement led to the overall porosity reduction. The permeability change is calculated from the porosity change by Carmen–Kozeny equation. Theoretically, permeability change is considered to be consistent with porosity change, which will be discussed in detail below.

5.2. Fluid Flow Pattern

The distribution range of mineral abundance change, physical properties, and ion concentration vary with time depending on the fluid flow pattern. With the help of Petrasim graphical interface, two different fluid flow patterns (Figure 18) are identified corresponding to two dolomitization patterns (Figure 9 and Figure 10). The fluid flow pattern remained stable after 1 y according to simulation results. The length and thickness of the arrow are proportional to the strength of the fluid flow. Besides, the color changes from red to blue to indicate the fluid flow from strong to weak (Figure 18). It is obvious that the fluid flux is most rapid at shallow depth (<100 m), due to the initial permeability depth relationship and specified anisotropy (k_h/k_v = 100). The fluid flow pattern-1, corresponding to dolomitization pattern-1, shows that the fluid seeps down from the injection sites and flows out horizontally from the right boundary (Figure 18(A1)). This pattern is consistent with those of previous reflux dolomitization simulations [3,9,29]. Compared with fluid flow pattern-1, fluid flow pattern-2, corresponding to dolomitization pattern-2, has a countercurrent feature in the lower right corner of the model (Figure 18(A2)). The countercurrent feature causes dolomite and anhydrite bodies to appear as a rising wedge-shape (Figure 9 and Figure 10). The flow trend of the fluid can also be reflected in the spatial variation of pressure change (Figure 18(A2,B2)). The direction perpendicular to the pressure change contour lines is the direction of fluid migration. It should be pointed out that the pressure change in the lower right corner of the model appears negative in flow pattern-2. The negative values lead to the fluid flowing back into the model. Compared with the baseline case, the lower injection rate (700 kg/s) and higher geothermal gradient (2.68 °C/100 m) cause fluid backflow. The effect of injection rate and geothermal gradient on flow pattern is different. For the injection rate of 700 kg/s, the fluid in the model cannot reach the lower right corner of the model. Under Bernoulli’s principle [74], formation water in the lower right corner is driven to the upper part with higher permeability. For the geothermal gradient of 2.68 °C/100 m, the formation water of the lower left corner has stronger upward migration due to thermal convection.

5.3. The Effect of Dolomitization on Different Locations over Time

According to the spatial and temporal evolution of dolomite, anhydrite (Figure 9 and Figure 10), ionic concentration (Figure 12), and porosity (Figure 11), reflux dolomitization can be divided into five stages (Figure 19). The variations of dolomite and anhydrite are the result of Mg²⁺, Ca²⁺, and CO₃²⁻ interaction (Equations (7)–(10)). The concentration of Ca²⁺ in brines is very low compared to the initial formation water. Thus, the Ca²⁺, used for the precipitation of dolomite and anhydrite, comes from the dissolution of calcite. For the Mg²⁺, it mainly comes from the brines. The diffusion direction of Mg²⁺ indirectly indicates the direction of brine migration. Lu & Cantrell (2016) suggested that the high Mg²⁺ zone and low Ca²⁺ zone were buffered by the dolomite; besides, the Mg²⁺ and Ca²⁺ outside these zones were controlled by the interplay of dispersion and chemical reactive progress between the brine and the primary formation water [9].

In stage-1 of dolomitization (<100 y), the growth center of dolomite abundance gradually moved down from the upper left corner (Figure 19(A1,B1)). During the replacement of calcite, the high Mg²⁺ zone (Figure 12(A1,B1)) resembled the shape of the dolomite body (Figure 9(A1–C2)). The increased Mg²⁺ concentration was due to the fact that dolomite formation consumed less Mg²⁺ than brine replenishment. Behind the dolomitization front, the high Ca²⁺ zone from the dissolution of calcite dissolution gradually shrunk (Figure 12(A2,B2)). This was because most of the Ca²⁺ was discharged from the right boundary under the high flow rate. Besides, the Ca²⁺ could not remain in place for a long time due to the high injection rate in stage-1, and thus there was no anhydrite precipitation. At the same time, porosity and permeability increased with the dolomitization (Figure 11(A1–B2)). The growth centers of porosity and permeability change also lay in the upper left corner (Figure 11(A1–B2) and Figure 19(A2,B2)). Given the distribution of porosity and permeability change, the dolomitization had a greater effect on permeability than porosity (Figure 11(B1,B2)), which was contrary to the study from Lu and Cantrell (2016), which found that reflux dolomitization had a greater impact on permeability [9]. As the center of growth continued to shift downward, Cell 1601 underwent dolomitization earlier than Cell 1 and Cell 19. In other words, the changes of mineral abundance and porosity (Figure 20A–C) of Cell 1601 were higher than those of Cell 1 and Cell 19. Laterally, the dolomitization occurred from left to right (Figure 19(A1,B1)). Therefore, the changes of mineral abundance and porosity (Figure 20A–C) of Cell 1 were higher than those of Cell 19.

In stage-2 of dolomitization (100 y to 20 ky), the dolomitization center was at the lower left of the model (Figure 19(C1–C3)). Different from stage-1, the anhydrite began to precipitate at the end of stage-2 in 20 ky (Figure 19(C2)). Due to the acceleration of the calcite replacement by dolomite, the content of the Mg²⁺ began to decline, while the content of Ca²⁺ began to rise (Figure 12(C1,C2)). Porosity and permeability continued to increase. The growth center of porosity also moved to the lower boundary (Figure 19(C3)), while the growth center of permeability remained unchanged (Figure 11(C2)). The variation of porosity was greater than that of permeability in space. The relationship between Cell 1, Cell 19, and Cell 1601 remained the same as before.

In stage-3 (20 ky to 6.8 My) of dolomitization, the location of the dolomitization center remained unchanged (Figure 19(D1–D3)). Due to the fast replacement dolomitization, the Mg²⁺ content gradually decreased (Figure 12(C1,D1)). However, in the 6.8 My, the Mg²⁺ rose again due to the absent calcite for replacement (Figure 12(E1)). The Ca²⁺ content kept increasing, because the calcite dissolution provided more Ca²⁺ than that of anhydrite consumption (Figure 12(C2,D2,E2)). In the 6.8 My, Ca²⁺ was concentrated in the top of the boundary, due to the complete dissolution of calcite (Figure 12(E2)). Both the dolomite and anhydrite abundances were in a period of rapid growth. According to the location of the dolomitization center, the dolomitization strength decreased from Cell 1 to Cell 19, and then to Cell 1601. The growth amount of dolomite and anhydrite and the reduction amount of calcite decreased from Cell 1 to Cell 19 to Cell 1601 (Figure 8A–C). From Figure 8D, the inflection point-1 of porosity change for Cell 1 and Cell 19 occurred earlier than for Cell 1601. This was due to the fact that the precipitation rate of Cell 1 and Cell 19 was faster than that of Cell 1601. Before inflection point-1 of porosity change, the dolomite created more pores than anhydrite blocks, leading to the porosity increase. The porosity change increased from Cell 1 to Cell 19 to Cell 1601, due to the difference in dolomite abundance. However, between inflection point-1 and point-2 (6.8 My), the pores created by dolomite were less than the pores occluded by anhydrite. Thus, both porosity and permeability decreased significantly (Figure 8D,E and Figure 11(D1,D2)). The porosity reduction center lied in the bottom left of the model (Figure 19(D3)), while the reduction center of permeability remained in the upper left (Figure 11(D2)). The lowest anhydrite precipitation rate in Cell 1601 led to the highest porosity change (Figure 8D). The highest dolomite precipitation rate in Cell 1 lead to the middle porosity change (Figure 8E). Besides, the middle precipitation rate of dolomite and anhydrite resulted in the lowest porosity change in Cell 19 (Figure 8E).

In stage-4 of dolomitization (6.8 My to 17 My), the location of the dolomitization center remained the same as before (Figure 19(E1,E2)). During this period, over-dolomitization (Figure 8A,B after inflection point) occurred with the dissolution of anhydrite (Figure 8C after inflection point-1, Figure 19(E2)), due to the brine being unsaturated with anhydrite. Since the calcite had been completely converted into dolomite, there was an excess of Mg²⁺ relative to over-dolomitization, and the Ca²⁺ from calcite dissolution was absent. Therefore, Mg²⁺ was increasing during this stage (Figure 12(F1,G1)). The 17 My is between the two inflection point-2s (Figure 8C), corresponding to the widespread disappearance of anhydrite. The widespread disappearance of anhydrite led to the temporary increase in Ca²⁺ in 17 My (Figure 12(F2,G2)). The growth center of anhydrite gradually shrunk due to the injection of brine (Figure 19(E2)). Therefore, increases in both dolomite and anhydrite of Cell 1601 were the lowest among the three cells (Figure 8A,C). Besides, due to the lack of Ca²⁺ produced by the calcite dissolution, the remaining Ca²⁺ was limited to the right boundary and increased gradually from left to right (Figure 12(F2)). Thus, Cell 19 had more dolomite cement and remaining anhydrite than Cell 1 (Figure 8A,C). The pores created by the anhydrite dissolution were much more than the dolomite cement blocked. Thus, the porosity was increasing in this stage. According to the anhydrite abundance in the three cells, the porosity increases from high to low were Cell 1601, Cell 1, and Cell 19 (Figure 8D). As for the permeability, the increase of it concentrated in the upper part of the model (Figure 11(E2)).

In stage-5 of dolomitization (17 My to 30 My), the dolomitization center remained unchanged (Figure 19(F1)). The Mg²⁺ continued to increase with the brine supply (Figure 12(H1)), and the Ca²⁺ was limited to the right boundary with no content change (Figure 12(H2)). The anhydrite was absent, while the dolomite cement precipitated slowly. The porosity kept increasing (Figure 8D before inflection point-3) until the anhydrite was completely dissolved (Figure 8C inflection point-2). The dolomite from calcite replacement was much greater than the dolomite cementation from over-dolomitization (Figure 8A). Therefore, after the anhydrite was completely dissolved, the porosity change depended on the content of dolomite from replacement. According to the dolomitization center, the dolomitization influence and the porosity change decreased from bottom to top (Figure 8D after inflection point-3, Figure 11(F1)) and from left to right (Figure 8F). The permeability varied little, and its growth center lay in the upper part of the model (Figure 11(F2)).

5.4. Intrinsic and Extrinsic Controls on Reflux Dolomitization

On the basis of analyzing the evolution of dolomitization in different positions of the model, the next target is to evaluate the various extrinsic and intrinsic parameters. The ranges of values of each parameter for the sensitivity analyses are shown in Figure 21. The sensitivity analysis is helpful to analyze the response of carbonate platform to reflux dolomitization in different geological settings. Through sensitivity analysis, some parameters have a strong control effect on dolomitization and should be given priority. Different simulations are compared in terms of average and maximum volume fraction of dolomite, with average percentage of calcite replaced in the 3D model in 5 My, which could be compared with the time to dolomitize all the calcite [12] or the dolomitization maximum rate [3].

5.4.1. Sediment Properties

Different depositional textures have different sediment properties, including porosity, permeability, and RSA. Previous studies have shown that diagenetic alteration of permeability had a decisive control on the flow pattern, distribution of the dolomite body, and reaction rates of dolomitization in natural systems [12,47]. However, the effect of porosity has often been ignored in previous studies. Besides, for a certain rock type, RSA is closely associated with permeability. For example, grainstone corresponds to low RSA with high permeability, while mudstone corresponds to high RSA with low permeability. In order to analyze the effect of each parameter on dolomitization, permeability and RSA are not combined with a certain rock type in this study. In other words, the rock fabrics of “grainstone”, “packstone”, and “mudstone” described above did not involve differences in RSA.

Initial Porosity and Permeability

Compared with packstone, grainstone has the same porosity but higher permeability. From Figure 13 and Figure 21, it can be seen that there is little difference in dolomitization degree between “grainstone” and “packstone”. Besides, the amount of dolomite growth and the amount of calcite replaced in “packstone” (Figure 21) are little higher than those in “grainstone”, which challenges the explanation cases where brine reflux is more likely to dolomitize the rocks with high permeability, such as grainstone [3,11,12,29,63]. Lu and Cantrell (2016) also found that a higher dolomite abundance occurred in packstone layers compared with grainstone layers [9]; however, this was the result of considering both permeability and RSA.

“Mudstone” has higher porosity and lower permeability than grainstone. The average and maximum dolomite abundance of “mudstone” is the lowest among the three rock types (Figure 21). This is because “mudstone” has the highest porosity, resulting in the lowest amount of calcite for replacement. However, the average percentage of calcite replaced with “mudstone” is much higher than the other two rock types (Figure 21), which is evidence of strong dolomitization. In terms of porosity change, the porosity of both “grainstone” and “packstone” decrease due to anhydrite cementation (Figure 13(C1,C2)), while the upper part of the “mudstone” model shows porosity growth (Figure 13(C3)), which is consistent with the increase in porosity caused by anhydrite dissolution (Figure 11(E1)). The dissolution of anhydrite leads to the lowest anhydrite abundance in “mudstone” (Figure 13(B3)). In other words, “mudstone” underwent much stronger dolomitization than “packstone”. The strengths of dolomitization alteration from strong to weak are “mudstone”, “packstone”, and “grainstone”. As previously analyzed, after 20 ky, dolomitization extends from the lower left corner of the model to the right and above (Figure 9, Stage-2). Lower permeability means longer fluid stagnation time, which will facilitate dolomitization. Besides, higher porosity means higher flow per unit time, which also contributes to the dolomitization, and its influence is much more than that of permeability.

High permeability is generally considered favorable for dolomitization. In order to verify this hypothesis, Cell 1 of the model is selected to study the increase of dolomite abundance in the early stage of dolomitization (Figure 22). As Figure 22 shows, the dolomite abundance of “grainstone” temporarily exceeded that of “packstone” before 0.3 My (Figure 22(A2)), which indicates that high permeability promotes the early stage of dolomitization. After 0.3 My, the low permeability of “packstone” induced long dolomitizing fluid retention time, which leads to higher dolomite than “grainstone” (Figure 22(A1,A2)). Compared with “grainstone”, “mudstone” has higher porosity and lower permeability, which complicates the relationship between them. At the beginning of dolomitization, the dolomite abundance curve of “grainstone” intersected that of “mudstone” (Figure 22(B2)). This is because the permeability of “mudstone” is low, but its high porosity is conducive to dolomitization. After the initial stage, the dolomite abundance of “mudstone” exceeded that of grainstone, due to high porosity and low permeability (Figure 22(B1)). However, after the completion of calcite replacement in “mudstone”, the dolomite abundance of “grainstone” gradually exceeded that of “mudstone” due to the higher calcite abundance in “grainstone”(Figure 22(B1)). Therefore, the effect of high permeability on reflux dolomitization is limited to the initial stage.

Reactive Surface Area

The influence of RSA on dolomitization is more prominent than that of rock type (Figure 21). From Equation (2), the RSA controls the dolomitization rate. The higher RSA results in greater lateral extension of the dolomite body (Figure 14(A1–A3)) and higher dolomite abundance (Figure 21). This is consistent with previous research works that have found that high RSA or fine-grained sediments are more reactive, leading to faster dolomitization rate according to the power law [12]. However, the high RSA leads to massive anhydrite deposits (Figure 14(B1–B3)), causing a rapid decline in porosity (Figure 14(C1–C3)). In natural systems, RSA will change during dolomitization with the progressive increase in rhomb size [12]. Thus, it may be a mistake to simply assume that RSA remains constant during simulation. Under geological conditions, RSA increases gradually from grainstone to packstone to mudstone. Therefore, if RSA is combined with the physical properties of rock, the difference in dolomitization influence caused by initial porosity and permeability will be greater.

5.4.2. Geothermal Gradient

The effect of geothermal gradient on dolomitization is also the effect of temperature. Temperature not only controls the dolomitization rate constant, but also the mineral saturation rate (Equation (2)). Besides, temperature has some influence on the fluid density and viscosity [75], but this is outside the scope of our study, given its minor effect when compared with the range of geothermal gradient. Previous research has also found that platform top-temperature and basal heat flux would influence the distribution area and precipitation rate of dolomite [29]. The heat flux could be equivalent to geothermal gradient. The platform-top temperature is controlled by solar insolation [29]. To simplify the simulation, the model top-temperature is fixed at 30 °C. The difference of dolomitization caused by the difference of geothermal gradients is not obvious in terms of dolomite- and calcite-replaced volume fraction (Figure 21). The high geothermal gradient does speed up the dolomitization process. With the increase of geothermal gradient, the abundance of dolomite (Figure 15(A1–A3) and Figure 21) and anhydrite increases (Figure 15(B1–B3)), leading to a further decrease of porosity (Figure 15(C1–C3)). Previous studies have shown that the saturation state (Q/K in Equation (2)) decreases with the increase of temperature [3], thus leading to more dolomite precipitation.

5.4.3. Flow Rate

The injection rate does not reflect the flow rate inside the model. Thus, for a more intuitive expression of flow rate, the flow rate of Cell 1 was selected to represent the flow rate of the whole model. The injection rates of 700 kg/s, 1200 kg/s, and 1800 kg/s correspond to 5 m/y, 8 m/y, and 12 m/y in Cell 1. Previous studies have suggested that very low flow fluxes (≤0.01 m/y) controlled the dolomitization rate [3,12]. However, conclusions from previous studies are only suitable for the initial stage of dolomitization, corresponding to stage-1 of dolomite evolution (Figure 9(A1–C2)). During stage-2 of dolomite evolution (Figure 9(D1–E2)), the flow flux on the order of meters per year plays a key role. The difference of dolomitization rate caused by the change of flow rate is also small in Figure 21. The flow rate of 12 m/y (injection rate of 1800 kg/s) has the highest dolomitization rate. The dolomitization rate of the flow rate of 12 m/y (injection rate of 1800 kg/s) is the highest in dolomite (Figure 16(A1–A3) and Figure 21) and anhydrite abundance (Figure 16(B1–B3)). The highest anhydrite abundance resulted in the highest porosity reduction (Figure 16(C1–C3)). Except for the maximum volume fraction of dolomite, the dolomitization rate of the flow rate of 8 m/y (injection rate of 1200 kg/s) is higher than that of flow rate of 5 m/y (injection rate of 700 kg/s), which is reflected in the average volume fraction of dolomite and average percentage of calcite replaced (Figure 21). In short, the faster the flow rate is, the stronger the dolomitization is.

5.4.4. Brine Salinity

The salinity of brines is influence by a combination of many factors including solar radiation, wind speed, and residence time of waters on the platform top. The salinity from evaporation controls the Mg²⁺/Ca²⁺ ratio, lowers ion activities due to ion pairing, and changes the saturation state with respect to carbonate minerals [29]. All three brines used in the simulation (Ibis Pond, Ralph Sink, and Phreatic Majanna) are supersaturated with respect to dolomite, but undersaturated with anhydrite (Table 6). Since the three brines are not derived from the same seawater, the saturation indices of carbonate do not increase with increasing salinity. However, the Mg²⁺/Ca²⁺ ratio and saturation indices of anhydrite increase significantly with the increase of brines. The simulation results show that the brine salinity has a great influence on the diagenetic potential of reflux dolomitization (Figure 17 and Figure 21). With the increase of salinity, the abundance of dolomite and anhydrite increases rapidly (Figure 17(A1–B3) and Figure 21), leading to a rapid decline in porosity (Figure 17(C1–C3)). These controlling effects of salinity on dolomitization can be comparable to previous simulations [3,12,29,47]. For the same seawater, the saturation indexes of carbonate minerals (calcite and dolomite) increases with increasing degree of evaporation or salinity [12]. Therefore, under geological conditions, the increasing Mg²⁺/Ca²⁺ ratio and mineral saturation indexes will enhance dolomitization.

5.4.5. Reflux Dolomitization Model Insights

These simulation results indicated that the critical parameters for reflux dolomitization are the rock physical property, brine salinity, and RSA (Figure 21). The permeability difference between “grainstone” and “packstone” has a slight effect on dolomitization, and lower permeability has longer fluid stagnation time, which promotes dolomitization. Compared with the other two lithologies, the high porosity of “mudstone” corresponds to the much stronger dolomitization due to the high fluid flux. As for the RSA, its influence on dolomitization is generally accepted: high RSA corresponds to strong dolomitization. Under geological conditions, from grainstone to packstone to mudstone, the RSA and porosity increase with the decrease of permeability, which results in an increasingly higher dolomitization rate. This is consistent with our finding that the degree of dolomitization from weak to strong is grainstone, packstone, and mudstone in Lower Yingshan Formation (Figure 3). The brine salinity controls the Mg/Ca and the saturation indices of minerals, which directly affects the dolomitization capacity. The injection rates difference results in an insignificant difference in flow rate in Cell 1 (5 m/y, 8 m/y, and 12 m/y), therefore the dolomitization difference induced by injection rate is not obvious. Because the injection rate is closely related to the brine salinity, it is incorporated into the effect of brine salinity. The high geothermal gradients do promote the dolomitization rate; however, its effect is not obvious in the simulation because of its small range of variation in the Shunnan area. As previously analyzed, low injection rate or low geothermal gradient only changes the morphology of the dolomite and anhydrite body, and its effect on dolomitization strength is weak and could be ignored.

Through the simulation of reflux dolomitization, not only the intensify of dolomitization at different locations at different times (Figure 19), but also the location of the “sweet spot” can be predicted with the analysis of porosity and permeability evolution. The “sweet spot” refers to the rock with relatively high porosity and high permeability. In stage-1 of dolomitization (<100 y), the growth centers of both porosity and permeability lie in the upper left corner of the model (Figure 11(A1–B2) and Figure 19(A2,B2)); thus, the “sweet spot” also lies there. In stage-2 of dolomitization (100 y to 20 ky), the growth center of porosity has moved to the lower left of the model (Figure 11(C1) and Figure 19(C3)), while that of permeability still remains in the upper left corner (Figure 11(C2)). Therefore, the “sweet spot” should be located near the middle of the left boundary. In stage-3 of dolomitization (20 ky to 6.8 My), both porosity and permeability decrease. The reduction center of porosity lies in the lower left of the model (Figure 11(D1) and Figure 19(D3)), while the reduction center of permeability lies in the upper left of the model (Figure 11(D2)). The “sweet spot ” at this time is still located near the middle of the left boundary. In stage-4 of dolomitization (6.8 My to 17 My), both the growth centers of porosity and permeability are located in the upper left of the model (Figure 11(E1,E2) and Figure 19(E3)); thus, the “sweet spot” also lies in the upper left of the model. In stage-5 of dolomitization (17 My to 30 My), the growth centers of porosity and permeability (Figure 11(F1,F2) and Figure 19(F2)) are consistent with those in the stage-2; thus, the “sweet spot” is also located near the middle of the left boundary.

The reactive transport modelling in this study needs to be improved, and some factors are not incorporated in the simulation. Firstly, the 3D platform model in this study is too simple and regular. For the influence of the platform itself on dolomitization, the “linear platform”, “radially symmetrical platform”, platform thickness and width, platform shape, platform exposure, and drowning [1], which have obvious influences on dolomitization, are not included in this study. Besides, the temperature at the platform top in this study is fixed at 25 °C. However, the reduction of the temperature at the platform top is verified to reduce the rates of dolomitization dramatically [29], so this will be added in a further study. Secondly, in the absence of brines, fluids will circulate by geothermal convection of the platform itself [29]. To simplify the effect of temperature on reflux dolomitization, geothermal convection is not included. Thirdly, the salinity of the brines controls the fluid-density contrast that drives reflux [9,11,29], so there is no need to specify the injection rate. In our study, the injection rates are specified for two reasons. The first reason is that the effect of salinity can be ruled out by setting the injection rates. The second reason is that in order to achieve the transition from dolomitization by calcite replacement to over-dolomitization in 30 My, the injections rates must be set at such a high rate. Compared with the flow rates on the order of meters per year, previous studies discussed flow rates on the order of centimeters per year [3,12]; thus, low flow rates models will be added in later studies. Fourth, the coupling between porosity and permeability in the rock will change with the progressive dolomitization. In addition, the porosity–permeability feedbacks in this study are simplified using the Carmen–Kozeny equation through the simulation. Besides, the permeability anisotropy is set to a single value, which cannot be applied to different types of platform. Other influencing factors include the pCO₂ on the pH and carbonate alkalinity of seawater, heterogeneity of lithology in the platform, sealed or open fracture, and sediment subsidence, which all indirectly affects the dolomitization rate.

6. Conclusions

The topography derived from sedimentary facies and petrological and geochemical evidence all suggest that the Shunnan area is favorable to the occurrence of reflux dolomitization. The main rock types of penecontemporaneous dolomitization in the Shunnan area include grainstone, packstone, and mudstone. Reflux dolomitization was conducted on a three-dimensional model using TOUGHREACT. Combined with the paleogeothermal gradients of the Shunnan area, we simulated the reflux dolomitization of these three types of rocks and conducted other sensitivity analysis, including injection rate, brine salinity, and RSA.

The simulation results include the spatial and temporal evolution of dolomitization of calcite, precipitation of anhydrite cements, and physical properties. The simulation results solve the problem in Lower Yingshan Formation of why the content of silty-crystal dolomite gradually increases from grainstone to packstone to mudstone. Besides, the effects of dolomitization at different locations within the model and other extrinsic and intrinsic controlling factors are studied in detail. The main results of our reflux dolomitization model are listed below.

(1)

The reflux dolomitization involves replacement dolomitization and over-dolomitization. The porosity consists of two ascending and two descending stages. The replacement dolomitization and anhydrite dissolution contribute to the porosity increase, while the over-dolomitization and anhydrite dissolution contribute to the porosity decrease.

(2)

According to the shape of dolomite or anhydrite front, two fluid flow patterns are discerned. The fluid flow pattern-1 shows that the fluid seeps down and flows out horizontally from the right boundary, which is consistent with previous reflux dolomitization. Different from fluid flow pattern-1, fluid flow pattern-2 has a countercurrent feature in the lower right corner of the model. Bernoulli’s effect by low injection rate and geothermal effect by high geothermal gradient are the key factors of the fluid backflow.

(3)

According to the spatial and temporal evolution of change of dolomite, anhydrite, ionic concentration, and porosity, reflux dolomitization can be divided into five stages. At different stages, there are differences in the location of mineral or porosity growth or reduction centers. In stage-1, the dolomitization strength gradually decreases from top to bottom and from left to right. From stage-2 to stage-5, the dolomitization strength gradually decreases from bottom to top and from left to right. After the calcite was completely dissolved, from left to right, the degree of over-dolomitization increases, while the dissolution anhydrite decreases due to the remaining Ca²⁺ content. Besides, unlike porosity change, the permeability change is concentrated in the upper part of the model.

(4)

Sensitivity analysis shows that the most sensitive parameters are the rock physical property, RSA, and brine salinity. As for the rock physical property, high permeability promotes the dolomitization only in the initial stage. Lower permeability means longer fluid retention time, while higher porosity means greater fluid flux, which all promotes dolomitization to varying degrees. Except for the rock property, the other parameters are all proportional to dolomitization. For the RSA and geothermal gradient, they control the kinetic rate of dolomitization. However, the variation range of geothermal gradient in the Shunnan area is small and has little effect on dolomitization. The brine salinity controls the mineral saturation rate and Mg/Ca of the fluid, which indirectly affects the dolomitization. Besides, the flow rate determines the fluid flux per unit time. However, the difference between flow rates is little, resulting in small difference in dolomitization.

(5)

The location of the “sweet spot” depends on where the growth/reduction centers of porosity and permeability are. In stage-1 and stage-4 of dolomitization, the “sweet spot” overlaps with porosity and permeability growth centers. While in stage-2, stage-3, and stage-5, the “sweet spot” lies between the porosity and permeability growth/reduction centers.