The Inﬂuence of Magmatic Intrusions on Diagenetic Processes and Stress Accumulation

: Diagenetic changes in sedimentary basins may alter hydrocarbon reservoir quality with respect to porosity and permeability. Basins with magmatic intrusions have speciﬁc thermal histories that at time of emplacement and in the aftermath have the ability to enhance diagenetic processes. Through diagenesis the thermal conductivity of rocks may change signiﬁcantly, and the transformations are able to create hydrocarbon traps. The present numerical study quantiﬁed the e ﬀ ect of magmatic intrusions on the transitions of opal A to opal CT to quartz, smectite to illite and quartz diagenesis. We also studied how these chemical alterations and the sills themselves have a ﬀ ected the way the subsurface responds to stresses. The modeling shows that the area in the vicinity of magmatic sills has enhanced porosity loss caused by diagenesis compared to remote areas not intruded. Particularly areas located between clusters of sills are prone to increased diagenetic changes. Furthermore, areas inﬂuenced by diagenesis have, due to altered physical properties, increased stress accumulations, which might lead to opening of fractures and activation / reactivation of faults, thus inﬂuencing the permeability and possible hydrocarbon migration in the subsurface. This study emphasizes the inﬂuence magmatic intrusions may have on the reservoir quality and illustrates how magmatic intrusions and diagenetic changes and their thermal and stress consequences can be included in basin models. Laboratory studies show that


Introduction
Magmatic intrusions are commonly emplaced with much higher temperatures compared to their host rocks. Therefore, when emplaced into sedimentary basins, they may influence all parts of the petroleum system [1]. Several studies have shown how such intrusions influence the temperatures and hydrocarbon maturation in sedimentary basins (e.g., [2][3][4][5][6][7][8][9][10][11]). Other studies focus on the stress induced by the sills on the host rocks as they intrude (e.g., [12,13]). However, only a few studies have reported on the effect magmatic sill intrusions have on the diagenetic processes in sedimentary basins. Haile et al. [14] concluded in their work at Edgeøya (Svalbard) that conductive heat from intrusions did not seem to have affected the diagenetic products in the area. However, at Wilhelmøya (Svalbard) there is evidence suggesting that hydrothermal fluid flow originating from sills has affected the chemical transformations [15]. In a study of sandstones at Traill Ø (East Greenland) it was concluded that a combination of conductive and convective heat from magmatism enhanced the diagenetic process [16].
In essence, porosity and permeability determine the quality of petroleum reservoirs [17,18]. At the time of sediment deposition, the process of sediment lithification starts [19], driven by mechanical

An Example of the Evolution of a Volcanic Basin-The Vøring Basin
The Vøring Basin is located offshore mid-Norway and is bounded by the Bivrost Lineament to the NE and the Vøring Transform Margin to the SW ( Figure 1). The area consists of grabens, basins, and structural highs developed over three main rifting episodes from Carboniferous to Eocene times (e.g., [49] and references therein); (1) Carboniferous-Permian; coincided with the onset of rifting in the North Atlantic [40,[50][51][52][53][54][55]; (2) Late-Mid Jurassic to Early Cretaceous; led to subsidence and development of accommodation space for the thick Cretaceous sedimentary sequence [56,57]; (3) Late Cretaceous to Early Eocene; coincided with the opening of the North Atlantic, development of the Vøring Marginal High, and intrusion of numerous sills in the Cretaceous basin fill [49,58]. Subsequent events were dominated by seafloor spreading and accretion of oceanic crust in the expanding Norwegian-Greenland/North Atlantic Sea [59,60]. In the post-rift phase, the Vøring area experienced localized tectonic uplift, erosion, sediment deposition, subsidence, flexure, and isostatic uplift partly due to numerous glaciations and deglaciations of the Fennoscandian landmasses [61,62]. The sedimentary deposits of the Vøring Basin mainly consist of marine to deep marine sediments (mainly shale) with intercalated shallow marine sediments (mainly sandstone) in the Upper Jurassic and Cretaceous [49]. The Paleocene consists of shale with minor sandstone and limestone deposits [63], and the Lower Eocene consists of shales. The magmatic intrusions were emplaced in lower Eocene time within the entire sedimentary sequence. Oligocene, Neogene, and Quaternary deposits are mainly shales with some ice rafted debris in the Plio-Pleistocene. The outer Vøring Basin was in the Miocene and early Pliocene dominated by deep-water deposits consisting of biosiliceous hemipelagic sediments [46,64].
The utilized 2D transect, VB-2-87-B (Figure 1), is about 100 km long and holds some 20 interpreted sills located at ~3-5 km depth with lateral extension of the sills varying from about 3 to 30 km ( Figure 2). A velocity model by Hjelstuen et al. [64] was used for depth conversion of the section. The time of intrusion activity is estimated at ~56 Ma, which is supported by ages derived from zircon dating of magmatic sills in the Vøring area (55.6 ± 0.3 Ma and 56.3 ± 0.4 Ma, 6607/5-2 and Utgard wells; [65]). The sedimentary deposits of the Vøring Basin mainly consist of marine to deep marine sediments (mainly shale) with intercalated shallow marine sediments (mainly sandstone) in the Upper Jurassic and Cretaceous [49]. The Paleocene consists of shale with minor sandstone and limestone deposits [63], and the Lower Eocene consists of shales. The magmatic intrusions were emplaced in lower Eocene time within the entire sedimentary sequence. Oligocene, Neogene, and Quaternary deposits are mainly shales with some ice rafted debris in the Plio-Pleistocene. The outer Vøring Basin was in the Miocene and early Pliocene dominated by deep-water deposits consisting of biosiliceous hemipelagic sediments [46,64].
The utilized 2D transect, VB-2-87-B (Figure 1), is about 100 km long and holds some 20 interpreted sills located at~3-5 km depth with lateral extension of the sills varying from about 3 to 30 km ( Figure 2). A velocity model by Hjelstuen et al. [64] was used for depth conversion of the section. The time of intrusion activity is estimated at~56 Ma, which is supported by ages derived from zircon dating of magmatic sills in the Vøring area (55.6 ± 0.3 Ma and 56.3 ± 0.4 Ma, 6607/5-2 and Utgard wells; [65]).
From Carboniferous and up to the beginning of Eocene, the Vøring Basin was part of an active rift phase [49]. As the active rifting ceased the Vøring area subsequently experienced thermal subsidence and ridge push due to continental break up and opening of the North Atlantic. Repeated glaciations, mainly since 2.6 Ma, have led to sediment depositions in the Vøring Basin. Currently the regional stress field of coastal and mainland Norway is somewhat affected by post-glacial uplift and erosional unloading/loading [62,[66][67][68][69][70] in addition to compressive ridge-push. To make our results generally applicable, the section from the Vøring Basin is solely used as a basis for the modeling, and site-specific parameters such as lithology and rock properties, are substituted by global values.  [40].
From Carboniferous and up to the beginning of Eocene, the Vøring Basin was part of an active rift phase [49]. As the active rifting ceased the Vøring area subsequently experienced thermal subsidence and ridge push due to continental break up and opening of the North Atlantic. Repeated glaciations, mainly since 2.6 Ma, have led to sediment depositions in the Vøring Basin. Currently the regional stress field of coastal and mainland Norway is somewhat affected by post-glacial uplift and erosional unloading/loading [62,[66][67][68][69][70] in addition to compressive ridge-push. To make our results generally applicable, the section from the Vøring Basin is solely used as a basis for the modeling, and site-specific parameters such as lithology and rock properties, are substituted by global values.

Methods and Results for Magmatic Intrusion's Influence on Diagenetic Processes
To perform the modeling of structural evolution, geohistory, thermal development, maturation, and diagenesis, BMT TM (Tectonor AS) was used. All models are in 2D, which infer the third dimension to be infinite. This is a good approximation when sills and faults are modeled, as the third dimension commonly is much larger than the two others (e.g., [12]).

Geohistory, Temperature, Maturation, and Diagenesis
BMT is a high-resolution 2D basin modeling software utilizing a backstripping process, starting with present day geometry, in order to reconstruct the geohistory of an interpreted seismic section ( Figure 2) [48,71,72]. One horizon at a time is stripped from the section and fault restoration and decompaction (based on the given porosity-depth trends assigned for the lithologies) of underlying sequences follow. This process is repeated all the way to the top basement, thus building the geohistory. The fault restoration in BMT is performed by vertical simple shear, a method that leaves no gaps in the geometry and allows for thermal and maturation calculations to be performed (cf. [48]).

Methods and Results for Magmatic Intrusion's Influence on Diagenetic Processes
To perform the modeling of structural evolution, geohistory, thermal development, maturation, and diagenesis, BMT TM (Tectonor AS) was used. All models are in 2D, which infer the third dimension to be infinite. This is a good approximation when sills and faults are modeled, as the third dimension commonly is much larger than the two others (e.g., [12]).

Geohistory, Temperature, Maturation, and Diagenesis
BMT is a high-resolution 2D basin modeling software utilizing a backstripping process, starting with present day geometry, in order to reconstruct the geohistory of an interpreted seismic section ( Figure 2) [48,71,72]. One horizon at a time is stripped from the section and fault restoration and decompaction (based on the given porosity-depth trends assigned for the lithologies) of underlying sequences follow. This process is repeated all the way to the top basement, thus building the geohistory. The fault restoration in BMT is performed by vertical simple shear, a method that leaves no gaps in the geometry and allows for thermal and maturation calculations to be performed (cf. [48]).
BMT bases the thermal calculations on the finite difference method by conduction. The resulting temperature history depends on the thermal conductivity and specific heat capacity of the sediments as well as the basal heat flow from the mantle [48,71]. The surface temperature is the upper boundary condition in the calculations and is kept at 7 • C, whereas the lower boundary condition is the basal heat flow which is set to 47 mW·m −2 over the profile and over time. With these settings, the BMT calculations generate the basis for the maturation and diagenetic modeling. Kerogen type II is assumed for the maturation modeling, and maturation is calculated using classical first-order kinetics [48].

Silica Diagenesis-Quartz Diagenesis
Quartz diagenesis occurs over three connected steps involving dissolution of quartz grains, transport of dissolved silica over short distances, and precipitation of quartz cement on clastic quartz grains [19,73]. BMT performs quantitative estimates of quartz cementation caused by dissolution of silica as described in Walderhaug [74,75] and Lander and Walderhaug [76]. The method is based on an empirically derived quantification of quartz precipitation as a function of temperature, and the precipitation is considered rate limiting for the whole cementation process (in [75] and references therein). This is a different approach than several other quantitative models where quartz dissolution is considered the limiting factor (e.g., [77][78][79][80][81]). As the diagenesis is thermally dependent (e.g., [74,75]), quartz cementation is an indicator of the maximum reached temperature and the burial depth.
Diagenesis is a complex process consisting of a number of transformations occurring simultaneously. According to Walderhaug [74,75], the rate limiting step is the precipitation, which is described by first-order kinetics and is proportional to the rate constant (k) given by the Arrhenius equation (Equation (1)).
where k is the rate constant of mineral precipitation per unit surface area (mol/cm 2 s), A 0 is a pre-exponential constant/frequency factor (mol/cm 2 s), E a is the activation energy (J/mol), R is the real gas constant (8.314 J mol −1 K −1 ), and T is the temperature. A 0 is the number that describes how often molecules collide within the system under consideration. E a is the energy needed for a specific chemical reaction to occur and both parameters are unique for any reaction [17]. The kinetic equation is integrated over temperature and time for a given timestep. By multiplying this with the available grain surface area obtained from the porosity history of the reconstructed geohistory, the mineral cement precipitated is calculated. However, increasing grain coating on quartz minerals reduces the possibility for precipitation of diagenetic minerals. The porosity loss calculations in this study assume zero grain coating, the porosity loss due to cementation might therefore be overestimated.

Silica Diagenesis-Opal A to Quartz Via Opal CT
Diatoms and radiolarian are two examples of siliceous plankton that after death enrich deep water sediments with dissolved non-crystalline silica known as opal A [82]. Such fragments are associated with low-energy deposition environments and amorphous silica is commonly found in deep water sediments amongst clay and silt deposits. Through burial and increased temperatures opal A converts to quartz via opal CT; this is observed in several basins worldwide, as documented in the introduction. The conversion of biogenetic/amorphous silica, opal A, to diagenetic/microcrystalline silica, opal CT, and subsequently to stable/crystalline silica, quartz, occurs through several dissolutions and precipitations as the burial depth increases (e.g., [39,83,84]). This reorganization from non-crystalline to crystalline silica causes changes in rock structures, mechanical properties, porosity, and permeability and may potentially generate traps for hydrocarbons (e.g., [23,38,39,84,85]).
One approach to determine the depth of these diagenetic processes is an empirical derived schematic presentation of the relation between temperature, rock composition, and silica-phase changes [86,87], which can be used in areas of known temperatures. Another approach is to determine experimentally the reaction kinetics under given chemical conditions which can be used for basins worldwide (e.g., [22,38,88]. A third approach was discovered by Neagu et al. [25] who found a connection between rotated fault planes and amount of porosity loss due to the conversion of opal A to opal CT.
Generally, each chemical reaction has its specific pre-exponential constant and activation energy which can be derived experimentally [17]. Additionally, all chemical reaction rates are temperature dependent [89]. Therefore, the method described above for quartz diagenesis was used to predict the precipitation rate for the transition of opal A to opal CT to quartz. Laboratory studies show that the activation energy for the opal A to opal CT transition is lower than for the transition of opal CT to quartz and this indicates that reorganization of amorphous silica to microcrystalline silica require lower temperature than the conversion of microcrystalline silica to crystalline silica [22]. This implies that the opal A/opal CT transition is expected to be located at shallower depths than the opal CT/ quartz boundary.
In this study the values reported by Dralus et al. [39] for the transition of opal A→ opal CT→ quartz was used (Table 1), as their study results in improved predictions of the opal A to opal CT boundary compared to other published kinetics [38]. They also found that high content of organic matter slows the transitioning of opal A to opal CT and that different kinetic parameters are required for rocks with high and low organic content.

Clay Diagenesis-Smectite to Illite
During burial diagenesis, illitization of smectite is a commonly occurring mineralogical reaction of clay rich sediments and shales. The conversion is a gradual process leading to mixed layers with different illite/smectite ratios [90] and is accompanied by volume loss and reduction in permeability [91]. With increasing burial depth and temperatures, the percentage of illitic beds in the illite/smectite mixed layers increases (e.g., [24,92]). The temperature is an important factor in the smectite to illite diagenetic process (e.g., [91]), but the presence of pore water and potassium (K + ) are also essential for this transition to take place [42,[93][94][95]. Smectite reacts with potassium, possibly sourced by K-feldspar, and the outcome is illite, silica, and water (e.g., [42]) from a complex dissolution/precipitation process where the precipitation is rate limiting (e.g., [96][97][98][99]). A common approach for modeling the conversion of smectite to illite is by using the Arrhenius equation and regarding the transformation as either a one step reaction with one reaction rate (e.g., [94,100]) or as several parallel reactions with rates spread over a defined range (e.g., [101]). The method described above for quartz diagenesis is also applied for the estimation of smectite to illite diagenesis. However, it is important to note that this method does not take into account the presence of chemical components that can act as catalysts or quenchers. As for quartz diagenesis, precipitation is considered rate limiting for the smectite to illite transition and it is assumed that critical chemical components, e.g., potassium, are present for the reaction to occur. Kinetic data from three different studies were tested: (1) Roaldset et al. [95], (2) Huang et al. [94], and (3) Hillier et al. [102]. Their preferred parameters are given in Table 1.

Opal A to Opal CT-Testing of the Method
To test the quantification methods described above for the diagenetic processes, 1D modeling was performed on a well in the North Sea. Roaldset and Wei [23] observed the opal A to opal CT transition to be at 1740 m depth in well 30/9-B-50H ( Figure 3) in the Oseberg area (North Sea). This area has experienced several millions of years of Cenozoic tectonic quiescence [104][105][106][107] and is presently close to maximum burial depth [95], which makes this particular well excellent for testing of the To test the quantification methods described above for the diagenetic processes, 1D modeling was performed on a well in the North Sea. Roaldset and Wei [23] observed the opal A to opal CT transition to be at 1740 m depth in well 30/9-B-50H ( Figure 3) in the Oseberg area (North Sea). This area has experienced several millions of years of Cenozoic tectonic quiescence [104][105][106][107] and is presently close to maximum burial depth [95], which makes this particular well excellent for testing of the method. The stratigraphy was obtained from a well close by (well 30/6-2; Figure 3) consisting mainly of sandstones and claystones (see Table 2 for parameters). Roaldset and Wei [23] showed that the opal A to opal CT transition zone coincided with a porosity reduction of around 20%. Results from the 1D model of well 30/9-B-50H shows that 20% porosity loss starts around 1740 m below seafloor ( Figure 4). This coincides with the observations by Roaldset and Wei [23], which gives a strong indication that the method gives realistic results.

Example from the Vø ring Basin, Section VB-2-87-B
To study the effect emplaced sills have on the diagenesis in basins, the methods described in   Roaldset and Wei [23] showed that the opal A to opal CT transition zone coincided with a porosity reduction of around 20%. Results from the 1D model of well 30/9-B-50H shows that 20% porosity loss starts around 1740 m below seafloor ( Figure 4). This coincides with the observations by Roaldset and Wei [23], which gives a strong indication that the method gives realistic results. Roaldset and Wei [23] showed that the opal A to opal CT transition zone coincided with a porosity reduction of around 20%. Results from the 1D model of well 30/9-B-50H shows that 20% porosity loss starts around 1740 m below seafloor ( Figure 4). This coincides with the observations by Roaldset and Wei [23], which gives a strong indication that the method gives realistic results.

Example from the Vø ring Basin, Section VB-2-87-B
To study the effect emplaced sills have on the diagenesis in basins, the methods described in

Example from the Vøring Basin, Section VB-2-87-B
To study the effect emplaced sills have on the diagenesis in basins, the methods described in Section 3.1 were used on the seismic line VB-2-87-B ( Figure 2) in the Vøring Basin ( Figure 1). This transect contains approximately 20 interpreted magmatic sills, as well as a horizon denoted opal CT ( Figure 2). The sills were modeled to intrude in one pulse at 56 Ma, with a magma temperature of 1000 • C which is within normal magma temperature range [12]. Table 2 summarizes the parameters used in the modeling. The thermal effect of sills and the effect on the diagenetic processes are largest the first million years after intrusion [5,10]. The figures below show results for 1 Myr after the intrusion of the sills.

Quartz Cement
The resulting diagenetic effects ( Figure 5) show large differences between models where sills are accounted for and when they are disregarded. It is well known that sill thickness plays a role in the size of the thermal aureole, as well as the amount of matured organic matter in the vicinity of sills (e.g., [5,10]). This is also clearly illustrated in Figure 5 where results for alternatives with no sills, 50 m and 100 m thick sills are shown. The entire basin is assumed to have sandstone lithology (see Table 2 for properties). Some areas show up to 40% difference in porosity loss between the models ( Figure 5). The areas where the largest differences are found are located close to the sills and in the areas between clusters of sills. With increasing sill thickness a larger area between the sill clusters have increased porosity loss ( Figure 5). This is in accordance with Sydnes et al. [10] who found that the vitrinite reflectance in a well in the Barents Sea is a function of the spacing and the possible heat exchange between neighboring sills. For single, relatively shallow lying sills, the sill thickness does not impact the size of the area of porosity loss to a significant degree. However, for deeper lying single sills, the sill thickness will impact the size of the diagenetically altered area ( Figure 5). Geosciences 2019, 9, x FOR PEER REVIEW 9 of 28

Opal A to Opal CT to Quartz
The transition from opal A to opal CT is considered to occur over some tens of meters and up to 200 m [41]. Roaldset and Wei [23] found the transition zone of opal A to opal CT to start where the porosity reduction is around 20%. Therefore, we assume that the transition zone starts where the modeling result show 20% porosity loss and ends around 200 m deeper down. The basin is now set as all shale and assumes presence of amorphous silica. Figure 6 shows the modeled opal CT transition zone for the studied transect in the Vøring Basin with and without sills included in the calculations. The largest contrast between the two models are found in the shallower areas and for sills situated at depths <1500 m below seafloor ( Figure 6). For the scenario where sills are not included, the transition zone results in a more or less horizontal zone around 1200 m depth. When the thermal contribution of sills is included in the calculations, the opal A/CT boundary is found as shallow as approximately 700 m depth. This implies that the additional heat from the sills moved the transition zone up to 500 m shallower depths. The influence of sills on the further transition of opal CT to quartz is more or less the same as for opal A to opal CT and therefore not shown here. Quartz diagenesis due to sill emplacement will have implications for the reservoir quality in the vicinity of sills, in particular for reservoirs lying between clusters of sills. For our basin with this particular geohistory and thermal development, sills intruding at any depth in the sedimentary rocks will enhance the porosity loss due to quartz diagenesis. The generated diagenetic changes as a result of intruding sills (as shown in Figure 5) should still be visible today, as the surrounding host rocks at the same depth have not yet reached the same amount of quartz diagenesis.

Opal A to Opal CT to Quartz
The transition from opal A to opal CT is considered to occur over some tens of meters and up to 200 m [41]. Roaldset and Wei [23] found the transition zone of opal A to opal CT to start where the porosity reduction is around 20%. Therefore, we assume that the transition zone starts where the modeling result show 20% porosity loss and ends around 200 m deeper down. The basin is now set as all shale and assumes presence of amorphous silica. Figure 6 shows the modeled opal CT transition zone for the studied transect in the Vøring Basin with and without sills included in the calculations. The largest contrast between the two models are found in the shallower areas and for sills situated at depths <1500 m below seafloor ( Figure 6). For the scenario where sills are not included, the transition zone results in a more or less horizontal zone around 1200 m depth. When the thermal contribution of sills is included in the calculations, the opal A/CT boundary is found as shallow as approximately 700 m depth. This implies that the additional heat from the sills moved the transition zone up to 500 m shallower depths. The influence of sills on the further transition of opal CT to quartz is more or less the same as for opal A to opal CT and therefore not shown here.
Geosciences 2019, 9, x FOR PEER REVIEW 10 of 28 Figure 6. The results for the opal A/CT transition zone when sills are disregarded (upper) and when they are included (lower). The transition zone is assumed to start where the porosity loss exceeds 20%.

Smectite to Illite
Transformation of smectite to illite may occur in sediments and rocks containing clay minerals, and the basin is therefore assumed to have only shale lithology. The results for all the tested kinetic values show that magmatic intrusions and their heat contribution influence the diagenesis and result in transition of smectite to illite at shallower depths than without sills ( Figure 7). However, the published and used A0 and Ea values give significantly different results (Figure 7). The values proposed by Roaldset et al. [95] with high frequency factor (Table 1; Figure 7) give results similar to the result for the transition of opal A to opal CT ( Figure 6). Without sills the transition from smectite to illite occurs around 1200 m depth and with sills this boundary lies about 500 m shallower. Results for the parameter values proposed by Hillier et al. (Table 1; [102]) show a porosity loss of 10% and increasing with depth, starting at >2000 m depths when sills are disregarded (Figure 7 pink, stippled lines lower left). For models where sills are included a porosity loss up to 40% is obtained in areas close to the sills (Figure 7). The results are quite similar to results displayed for quartz diagenesis ( Figure 5). For the Vøring Basin, a transition in seismic velocity, porosity, and density, believed to resemble the smectite to illite transition, has been observed at depths corresponding to 80-90 °C [24]. The modeled isotherms of 80 and 90 °C for the model without sills are shown in Figure 7 (left). According to Peltonen et al. [24], the kinetic parameter values preferred by Roaldset et al [95] result in a transition of smectite to illite at a shallower depth than 80-90 °C. The kinetic values of Hillier et al. [102] result in a transition zone that lies deeper than the 80-90 °C isotherm. The results for the opal A/CT transition zone when sills are disregarded (upper) and when they are included (lower). The transition zone is assumed to start where the porosity loss exceeds 20%.

Smectite to Illite
Transformation of smectite to illite may occur in sediments and rocks containing clay minerals, and the basin is therefore assumed to have only shale lithology. The results for all the tested kinetic values show that magmatic intrusions and their heat contribution influence the diagenesis and result in transition of smectite to illite at shallower depths than without sills ( Figure 7). However, the published and used A 0 and E a values give significantly different results (Figure 7). The values proposed by Roaldset et al. [95] with high frequency factor (Table 1; Figure 7) give results similar to the result for the transition of opal A to opal CT ( Figure 6). Without sills the transition from smectite to illite occurs around 1200 m depth and with sills this boundary lies about 500 m shallower. Results for the parameter values proposed by Hillier et al. (Table 1; [102]) show a porosity loss of 10% and increasing with depth, starting at >2000 m depths when sills are disregarded (Figure 7 pink, stippled lines lower left). For models where sills are included a porosity loss up to 40% is obtained in areas close to the sills (Figure 7). The results are quite similar to results displayed for quartz diagenesis ( Figure 5). For the Vøring Basin, a transition in seismic velocity, porosity, and density, believed to resemble the smectite to illite transition, has been observed at depths corresponding to 80-90 • C [24]. The modeled isotherms of 80 and 90 • C for the model without sills are shown in Figure 7 (left). According to Peltonen et al. [24], the kinetic parameter values preferred by Roaldset et al [95] result in a transition of smectite to illite at a shallower depth than 80-90 • C. The kinetic values of Hillier et al. [102] result in a transition zone that lies deeper than the 80-90 • C isotherm. From field observations it has been reported concurrent onset of oil generation and the conversion of smectite to illite (e.g., [110]). When comparing the resulting maturation assuming kerogen type II in the section from the Vøring Basin (   [102] are used (cf. Table 1). The modeled isotherm of 80-90 • C is marked for scenario without sills (left). Lower left, pink, stippled lines indicate location of 10% and 15% porosity loss.
From field observations it has been reported concurrent onset of oil generation and the conversion of smectite to illite (e.g., [110]). When comparing the resulting maturation assuming kerogen type II in the section from the Vøring Basin ( Figure 8) with and without sills, there is a good correlation for both scenarios when compared to the smectite to illite conversion, when kinetic values by Hillier et al. [102] were used. Without sills the maturation starts at depths >2900 m at lateral location 50 km on the transect (Figure 8

Methods and Results for Stress Accumulation Influenced by Diagenetic Processes and Sills Themselves
As stated in the introduction, the physical properties of rocks subject to diagenesis will be altered (e.g., [22,23,95]. The increase in rock stiffness, as a consequence of diagenesis is of particular interest when studying how diagenesis may change the way the rocks respond to stresses. Additionally, the sills themselves are much stiffer than the host rocks in sedimentary basins and will accumulate stresses when subject to compressional or extensional loading [12,111].

Stress Modeling
To investigate how diagenesis and sills might affect stress accumulations in the subsurface, we used Comsol Multiphysics 5.2.a (www.comsol.com), a commercial finite element method (FEM) software that solves problems based on partial differential equations. The stress effects were studied on two synthetic cases and on the section from the Vøring Basin ( Figure 2). All the models are in 2D and have fault zones divided into two separate units, consisting of a fault core which is surrounded by a damage zone with stiffnesses of 0.1 and 1 GPa, respectively (Figure 9). A typical Poisson's ratio of 0.25 [112] was used in all the models and they were all subject to either horizontal compressional or extensional stress of 5 MPa to resemble horizontal regional or local stresses. All sills were assumed to be solidified and have Young's modulus values resembling such a situation. Properties are as summarized in Table 3. The lower boundary was fastened in all models to avoid translation and rotation of the rock body.

Methods and Results for Stress Accumulation Influenced by Diagenetic Processes and Sills Themselves
As stated in the introduction, the physical properties of rocks subject to diagenesis will be altered (e.g., [22,23,95]. The increase in rock stiffness, as a consequence of diagenesis is of particular interest when studying how diagenesis may change the way the rocks respond to stresses. Additionally, the sills themselves are much stiffer than the host rocks in sedimentary basins and will accumulate stresses when subject to compressional or extensional loading [12,111].

Stress Modeling
To investigate how diagenesis and sills might affect stress accumulations in the subsurface, we used Comsol Multiphysics 5.2.a (www.comsol.com), a commercial finite element method (FEM) software that solves problems based on partial differential equations. The stress effects were studied on two synthetic cases and on the section from the Vøring Basin ( Figure 2). All the models are in 2D and have fault zones divided into two separate units, consisting of a fault core which is surrounded by a damage zone with stiffnesses of 0.1 and 1 GPa, respectively (Figure 9). A typical Poisson's ratio of 0.25 [112] was used in all the models and they were all subject to either horizontal compressional or extensional stress of 5 MPa to resemble horizontal regional or local stresses. All sills were assumed to be solidified and have Young's modulus values resembling such a situation. Properties are as summarized in Table 3. The lower boundary was fastened in all models to avoid translation and rotation of the rock body. Geosciences 2019, 9, x FOR PEER REVIEW 13 of 28

Stress Effects of Sills and Diagenesis
In general, stress accumulations indicate areas prone to either opening of fractures or activation/reactivation of faults. Areas where tensile stresses accumulate may lead to opening of fractures or keep existing fractures open, whereas activation/reactivation of faults may occur in areas where shear stresses accumulate. Active faults and open fractures increase the permeability in the area where they are located. Typical global properties of rocks were used in the models (Table 3) and the results show the location of stress concentrations, and how sills and diagenesis affect stress accumulations. The models were based on the assumption that rocks behave as linear elastic up to 1%-3% strain at low temperature and pressure [113,114] depending on the rock strength. Strain exceeding 1%-3% commonly results in failure. Normally the shear strength of rocks lies between 1 and 12 MPa and the tensile strength is half of the shear strength, normally between 0.5 and 6 MPa [115][116][117]. Stresses exceeding these limits will commonly initiate fault movement and open fractures, respectively.
When comparing models where sills and sill-initiated diagenesis are accounted for versus when it is disregarded, it is possible to determine if and how these units may have influenced fracture and fault related permeability. Laboratory studies show that the physical strength of rocks increases by more than 100% on the transition of opal A to opal CT [23]. Therefore, the stiffness of the diagenetically altered area is doubled compared to the Young's modulus value of the rocks not altered by diagenesis.

Synthetic Case
A synthetic case of arbitrary dimensions shows that in a homogeneous basin, stresses build up at and around the fault tips when subject to compression and extension ( Figure 10). Red and yellow colors in the models represent areas where stresses concentrate, while blue colors are areas of small

Stress Effects of Sills and Diagenesis
In general, stress accumulations indicate areas prone to either opening of fractures or activation/reactivation of faults. Areas where tensile stresses accumulate may lead to opening of fractures or keep existing fractures open, whereas activation/reactivation of faults may occur in areas where shear stresses accumulate. Active faults and open fractures increase the permeability in the area where they are located. Typical global properties of rocks were used in the models (Table 3) and the results show the location of stress concentrations, and how sills and diagenesis affect stress accumulations. The models were based on the assumption that rocks behave as linear elastic up to 1%-3% strain at low temperature and pressure [113,114] depending on the rock strength. Strain exceeding 1%-3% commonly results in failure. Normally the shear strength of rocks lies between 1 and 12 MPa and the tensile strength is half of the shear strength, normally between 0.5 and 6 MPa [115][116][117]. Stresses exceeding these limits will commonly initiate fault movement and open fractures, respectively.
When comparing models where sills and sill-initiated diagenesis are accounted for versus when it is disregarded, it is possible to determine if and how these units may have influenced fracture and fault related permeability. Laboratory studies show that the physical strength of rocks increases by more than 100% on the transition of opal A to opal CT [23]. Therefore, the stiffness of the diagenetically altered area is doubled compared to the Young's modulus value of the rocks not altered by diagenesis.

Synthetic Case
A synthetic case of arbitrary dimensions shows that in a homogeneous basin, stresses build up at and around the fault tips when subject to compression and extension ( Figure 10). Red and yellow colors in the models represent areas where stresses concentrate, while blue colors are areas of small to no stress accumulations. Fractures may open and increase the permeability close to the sides of the fault tips where the tensile stresses concentrate (Figure 10). The direction of the fractures will follow the direction of σ 1 (maximum principal compressive stress) and open in the direction of σ 3 (minimum principal compressive stress or maximum principal tensile stress) [111]. Initiation of fault movement may occur at the fault tips where shear stresses accumulate, and as the shear stresses are larger at the upper tip, this is the area most likely for fault slip initiation ( Figure 10).  (Figure 10). The direction of the fractures will follow the direction of σ1 (maximum principal compressive stress) and open in the direction of σ3 (minimum principal compressive stress or maximum principal tensile stress) [111]. Initiation of fault movement may occur at the fault tips where shear stresses accumulate, and as the shear stresses are larger at the upper tip, this is the area most likely for fault slip initiation ( Figure 10). As shown in Sections 3.3.1-3.3.3, magmatic sills will influence the diagenetic processes in their proximity (see Figures 5-7). In order to include this impact in the synthetic model, a second model featuring the same fault, but with one sill surrounded by a diagenetically altered area was added. The results ( Figure 11) show that in addition to accumulating shear and tensile stresses at the fault tips, due to compression, stresses mainly build up in the sill and in the area modified by diagenesis surrounding the sill. This occurs as stresses tend to build up in layers/zones of stiffer rocks in contrast to softer rocks in heterogeneous basins (e.g., [111,118,119]). These shear stress accumulations are also present in the fault zone, particularly where the sill crosses the fault, and consequently, potential fault reactivation may start in this area. The accumulated shear stresses in the sill and diagenetically modified area may result in linking of present weaknesses and potentially initiate growth of new faults within this area, if the shear strength of the rock is exceeded [111]. Tensile stresses concentrating in the area modified by diagenesis along the fault zone and within the diagenetically altered damage zone may, if the tensile strength of the rock is exceeded, open fractures [111]. Similar results are obtained for the same model subject to extension, however, the resulting tensile stresses will be much larger compared to when subject to compression (not shown here) and accordingly the chance of opening fractures will increase. As shown in Sections 3.3.1-3.3.3, magmatic sills will influence the diagenetic processes in their proximity (see Figures 5-7). In order to include this impact in the synthetic model, a second model featuring the same fault, but with one sill surrounded by a diagenetically altered area was added. The results ( Figure 11) show that in addition to accumulating shear and tensile stresses at the fault tips, due to compression, stresses mainly build up in the sill and in the area modified by diagenesis surrounding the sill. This occurs as stresses tend to build up in layers/zones of stiffer rocks in contrast to softer rocks in heterogeneous basins (e.g., [111,118,119]). These shear stress accumulations are also present in the fault zone, particularly where the sill crosses the fault, and consequently, potential fault reactivation may start in this area. The accumulated shear stresses in the sill and diagenetically modified area may result in linking of present weaknesses and potentially initiate growth of new faults within this area, if the shear strength of the rock is exceeded [111]. Tensile stresses concentrating in the area modified by diagenesis along the fault zone and within the diagenetically altered damage zone may, if the tensile strength of the rock is exceeded, open fractures [111]. Similar results are obtained for the same model subject to extension, however, the resulting tensile stresses will be much larger compared to when subject to compression (not shown here) and accordingly the chance of opening fractures will increase.

Example from the Vø ring Area
For the transect VB-2-87-B in the Vøring Basin, the influence of sills and diagenetically altered area (as given in Section 3.3.1-3.3.3) was included to investigate its effect on the stress accumulations. The mid-Norwegian margin is presently experiencing compression. However, this is not a specific study of the Vøring area, therefore, to study the response to compressive and tensile horizontal stresses the model was subjected to both. The area to the left (Figure 12a) with several faults and sills, is of particular interest as it displays the interaction between faults, sills, and areas modified by diagenesis. As the smectite to illite transition zones (Figure 7) show boundaries much like the one of opal A to opal CT ( Figure 6) and quartz diagenesis ( Figure 5), this transition was not included in the study, as the results are expected to be more or less the same as for the opal CT transition zone and quartz diagenesis.
The transformation zone of opal A to opal CT starts when the porosity reduction is around 20% (cf. Figure 6; [23]) and is modeled to end around 200 m deeper (cf. [41]). Five different scenarios were tested and subject to horizontal compressive and tensile stresses of 5 MPa: (1) the basin with both sills and diagenesis disregarded (Figure 12), (2) the basin with sills but diagenesis disregarded, (3) the basin without sills but with opal A to opal CT transition zone included, (4) the basin with sills and opal A to opal CT transition zone included (Figures 13 and 14) and, (5) the basin with sills and quartz diagenesis (Figures 13 and 14).
Common results for all the models, whether subject to compressive or tensile stress, is that stresses build up at the fault tips (like the synthetic models), and in particular at the lower tips ( Figure  12a-c). This is due to the larger contrast in rock stiffness between the fault zones and the basement compared to the contrast between the fault zones and the host rock (cf. Table 3). Shear stresses are more or less the same with regard to location and strength of accumulations, whether they are subject to compression or extension. However, the tensile stresses are much lower for the models subject to compression (Figure 12b) than those subject to extension (Figure 12c).

Example from the Vøring Area
For the transect VB-2-87-B in the Vøring Basin, the influence of sills and diagenetically altered area (as given in Sections 3.3.1-3.3.3) was included to investigate its effect on the stress accumulations. The mid-Norwegian margin is presently experiencing compression. However, this is not a specific study of the Vøring area, therefore, to study the response to compressive and tensile horizontal stresses the model was subjected to both. The area to the left (Figure 12a) with several faults and sills, is of particular interest as it displays the interaction between faults, sills, and areas modified by diagenesis. As the smectite to illite transition zones (Figure 7) show boundaries much like the one of opal A to opal CT ( Figure 6) and quartz diagenesis ( Figure 5), this transition was not included in the study, as the results are expected to be more or less the same as for the opal CT transition zone and quartz diagenesis. When subject to both compression and extension, the synthetic models show that both shear and tensile stresses mainly concentrate in the sill and area modified by diagenesis, also where these features cross the fault zone ( Figure 11). Figure 13 shows the results for the Vøring basin subject to compression and when sills and the opal CT transition zone are included (Figure 13a,c), as well as when sills and the quartz diagenetically modified area are accounted for (Figure 13b,d). For all cases, areas of increased tensile stresses are few and small, but potential fractures may open along the fault open if stress concentrations grow high enough, thereby contributing to increased permeability in these areas. The shear stresses tend to build up in the areas modified by diagenesis and in the sills. Where the sills cross the faults, stress concentrations are, without exceptions, particularly high (Figure 13a,b) and may reactivate the fault if they exceed the rock's shear strength of 1-12 MPa. Elevated shear stresses in the opal CT transition zone and area modified by quartz diagenesis, may potentially initiate growth of new faults if the stresses become high enough, and thereby contribute to increased permeability.  When the basin is subject to extension the shear stresses concentrate in the same location with the same strength (Figure 14a,b), as when subject to compression (Figure 13a,b), for all scenarios. If the shear stresses exceed the shear strength of the rocks, fault slip will be initiated in some areas (colored red and yellow). However, the tensile stresses are much larger for the basin subject to extension (Figure 14c,d) as opposed to compression (Figure 13c,d). The entire sills tend to concentrate tensile stresses, not just when crossing fault zones (Figure 14c,d). Additionally, the diagenetically altered area of both opal CT and quartz accumulate higher tensile stresses compared to their surroundings. The high concentrations of tensile stresses show that the basin is prone to open fractures and increase the permeability in several areas. Due to the particularly high stress concentrations in the sills and the areas that have undergone diagenetic transitions, fractures are expected to first open in these places.

Discussion
Magmatic intrusions may influence the location and amount of porosity loss due to diagenesis, given that the necessary physical, biogenic, and/or chemical conditions are present. Two specific topics are addressed in this study: (1) quantification of the effect of magmatic intrusions on several diagenetic processes (opal A to opal CT to quartz, smectite to illite, and quartz diagenesis) and (2) the effect of sills and diagenetically altered areas on the fracture and fault permeability in basins with emphasis on the effect of these factors on petroleum systems.

Effects of Diagenesis on Petroleum Systems
Diagenesis contributes to loss of porosity and permeability in petroleum reservoirs and thus essentially harm the reservoir quality [90]. However, the same processes may also enhance the porosity and permeability through development of secondary porosity by dissolution, grain coating, and fracturing of layers that have become brittle [90]. All diagenetic products can aid in calibrating the thermal history of basins, as the transformation of each diagenetic product commonly occurs over The transformation zone of opal A to opal CT starts when the porosity reduction is around 20% (cf. Figure 6; [23]) and is modeled to end around 200 m deeper (cf. [41]). Five different scenarios were tested and subject to horizontal compressive and tensile stresses of 5 MPa: (1) the basin with both sills and diagenesis disregarded (Figure 12), (2) the basin with sills but diagenesis disregarded, (3) the basin without sills but with opal A to opal CT transition zone included, (4) the basin with sills and opal A to opal CT transition zone included (Figures 13 and 14) and, (5) the basin with sills and quartz diagenesis (Figures 13 and 14).
Common results for all the models, whether subject to compressive or tensile stress, is that stresses build up at the fault tips (like the synthetic models), and in particular at the lower tips (Figure 12a-c). This is due to the larger contrast in rock stiffness between the fault zones and the basement compared to the contrast between the fault zones and the host rock (cf. Table 3). Shear stresses are more or less the same with regard to location and strength of accumulations, whether they are subject to compression or extension. However, the tensile stresses are much lower for the models subject to compression (Figure 12b) than those subject to extension (Figure 12c).
When subject to both compression and extension, the synthetic models show that both shear and tensile stresses mainly concentrate in the sill and area modified by diagenesis, also where these features cross the fault zone ( Figure 11). Figure 13 shows the results for the Vøring basin subject to compression and when sills and the opal CT transition zone are included (Figure 13a,c), as well as when sills and the quartz diagenetically modified area are accounted for (Figure 13b,d). For all cases, areas of increased tensile stresses are few and small, but potential fractures may open along the fault zone to the right and increase the permeability if the stresses become high enough (Figure 13c,d). In addition, areas indicated by white circles in Figure 13c When the basin is subject to extension the shear stresses concentrate in the same location with the same strength (Figure 14a,b), as when subject to compression (Figure 13a,b), for all scenarios. If the shear stresses exceed the shear strength of the rocks, fault slip will be initiated in some areas (colored red and yellow). However, the tensile stresses are much larger for the basin subject to extension (Figure 14c,d) as opposed to compression (Figure 13c,d). The entire sills tend to concentrate tensile stresses, not just when crossing fault zones (Figure 14c,d). Additionally, the diagenetically altered area of both opal CT and quartz accumulate higher tensile stresses compared to their surroundings. The high concentrations of tensile stresses show that the basin is prone to open fractures and increase the permeability in several areas. Due to the particularly high stress concentrations in the sills and the areas that have undergone diagenetic transitions, fractures are expected to first open in these places.

Discussion
Magmatic intrusions may influence the location and amount of porosity loss due to diagenesis, given that the necessary physical, biogenic, and/or chemical conditions are present. Two specific topics are addressed in this study: (1) quantification of the effect of magmatic intrusions on several diagenetic processes (opal A to opal CT to quartz, smectite to illite, and quartz diagenesis) and (2) the effect of sills and diagenetically altered areas on the fracture and fault permeability in basins with emphasis on the effect of these factors on petroleum systems.

Effects of Diagenesis on Petroleum Systems
Diagenesis contributes to loss of porosity and permeability in petroleum reservoirs and thus essentially harm the reservoir quality [90]. However, the same processes may also enhance the porosity and permeability through development of secondary porosity by dissolution, grain coating, and fracturing of layers that have become brittle [90]. All diagenetic products can aid in calibrating the thermal history of basins, as the transformation of each diagenetic product commonly occurs over a specific temperature range. Thereby, they are markers for maximum temperatures and burial depths and may uncover areas exposed to unusual environments, i.e., uncommon heat flow or uplift and erosion, and they can be used together with for instance vitrinite reflectance and fluid inclusion data to calibrate thermal predictions.
The thermal conductivity of sediments could rise 4-5 times when opal CT transitions to quartz [120], as a result of the porosity loss. In the Bjørnøya Basin (Barents Sea) this difference in thermal conductivity results in about 10 • C higher temperatures in the Paleocene/Eocene shales for opal CT rich shale compared to quartz rich shale [118]. This temperature difference is caused by the nature of clay minerals that have a flattened structure favoring horizontal over vertical heat transport [120]. This is an example of the importance of including diagenesis in basin modeling. Modeling of diagenesis will ensure good thermal models when assessing the petroleum potential of sedimentary basins [120].
When the effects of diagenetic processes on petroleum reservoirs are considered, it is important to realize that chemical compounds in subsurface fluids can be catalysts or quenchers for the processes. First of all, the transition of opal A to opal CT to quartz requires presence of amorphous silica in the sedimentary rocks. Kastner et al. [83] studied the chemical controls on the opal A to opal CT transition and found that the diagenetic process is increased in carbonate rocks and reduced in clay-rich rocks. The presence of magnesium and hydroxide ions was found to enhance the conversion of opal A to opal CT. Subsequent transformation of opal CT to quartz released magnesium and hydroxide ions [83] and fluids enriched in magnesium and hydroxide ions were expelled upwards along faults increasing the transformation of opal A to opal CT at shallower depths [121]. Conversion of smectite to illite requires the presence of clay minerals in the sedimentary rocks. Furthermore, the presence of potassium has proved to enhance this conversion process. The transformation rates of smectite to illite increases with high potassium concentrations and lower temperatures are needed to start the conversion [95]. The potassium is commonly sourced by k-feldspars, which requires such minerals to be present for diagenesis to occur [91]. On the other hand, laboratory studies indicate that the presence of magnesium ions retards the conversion process in the early phases of the smectite to illite conversion [94]. Therefore, although thermal requirements are met for diagenetic alterations to occur, it is ultimately the biogenic and/or chemical compounds in the rocks and pore fluids that determine the possible diagenetic processes.

Effect of Magmatic Sills on the Diagenetic Process in Reservoir Rocks
Earlier studies of magmatic intrusions and their effect on porosity evolution and diagenesis of reservoir rocks have come to contrasting conclusions (e.g., [14,15,[122][123][124]). The diagenetic processes of sandstone reservoirs are likely to be controlled by the initial composition of the sand, original pore water composition, content of neighboring lithologies, burial and thermal history, and timing of cementation relative to accumulation of petroleum [17,47,82]. These criteria can largely explain the contrasting conclusions that are put forward in the referenced literature.
Haile et al. [14] conclude in their study at Edgeøya (Svalbard) that quartz cementation is unaffected by the short-lived heating of magmatic sills in reservoir rocks. They suggest that slow quartz cementation rates are in contrast to the relatively short-lived magmatic heating and will therefore not leave fingerprints on the diagenetic process. This conclusion contrasts from the results in our study which clearly show that magmatic sill intrusions affect the diagenesis in their proximity (Figures 5-7). Nejbert et al. [125] state that most sills in the Svalbard area are about 10-30 m thick. The sills are relatively thin and the distances between the sills are unknown in the study by Haile et al. [14], which could explain the contrasting conclusions of their study and ours. The magmatic sill thickness, distance from sills, and clusters of sills are pointed out in several studies to have significant importance on the thermal effect of magmatic intrusions (e.g., [3,5,6,[9][10][11]). Our study shows that thermal effects will also affect diagenetic transformations (i.e., Figure 5). The location of sampling in the study by Haile et al. [14] might also be too far from sills to be thermally affected by them.
Another aspect is the temperature of the intruding magma. As the thermal effect of sills is a function of the temperature of the intruding magma, a lower magma temperature than 1000 • C (used in this study), would result in smaller thermal aureole surrounding the sills and consequently decrease the area affected by diagenesis. This could also to some degree explain the contrasting conclusions. The host rock pre-intrusion temperature is identified to be crucial for the thermal effect of magmatic intrusions (e.g., [5,8,11]), and ultimately the effect of magmatic intrusions on diagenetic processes. Factors such as fault displacement, time span of faulting and sediment deposition, fault angle, rock thermal conductivity and specific heat capacity, basal heat flow, and restoration method used to simulate the fault movement through time, are all factors that influence the host rock pre-intrusion temperatures. For a specific, detailed area study, all these factors are crucial and require thorough assessment [11].

Silica Diagenesis
Silica diagenesis embraces two distinct types of chemical compaction processes, both of which are thermally dependent. The first studied here is quartz diagenesis and is related to pressure dissolution of quartz minerals, diffusion of dissolved silica and precipitation of quartz cement. Quartz cementation is the number one porosity reduction process in sandstones below 2000 m depth (e.g., [17,126,127]). Rapidly increasing porosity loss due to quartz cementation occurs when temperatures exceed 100-110 • C [75] and hydrocarbons do not seem to influence the porosity reduction process [91]. Grain coatings of clays have been found to inhibit quartz cementation and contribute to porosity preservation (e.g., [128][129][130]). Furthermore, at depths for peak mineral dissolution, such as quartz dissolution, the porosity is found to increase through secondary porosity production before it decreases again at deeper burial depth [130]. For basins without magmatic intrusions the porosity loss in petroleum reservoirs due to quartz diagenesis are expected to be found at depths corresponding to the mentioned temperature range (100-110 • C). As the results in this study show, magmatic intrusions in sedimentary basins contribute to abrupt changes in the diagenetic processes ( Figure 5) and reservoirs with reduced porosity may thus be found at shallower depths than expected. Reservoirs located between sills in a cluster are particularly prone to porosity reduction due to quartz diagenesis.
The transition of siliceous sediments from opal A through opal CT to quartz, starts at lower temperatures than the silica transition discussed previously. Opal A dissolves and subsequently precipitates to opal CT at about 50-60 • C, and further transition into crystalline quartz starts around 80-90 • C [131]. These transformations are known to create hydrocarbon traps. In Onnagawa Formation, Yurihara oil and gas field (Japan) and Monterey Formation in California (USA), the opal CT/quartz boundary acts as a seal due to its low permeability, while the quartz rich layers underneath, with higher permeability, act as a reservoir [38,132]. For basins following the thermal development without particular interruptions, the transition zone of opal A to opal CT will normally be in the temperature range of 50-60 • C, and the opal CT to quartz transition at depths corresponding to 80-90 • C. Results from this study show that sills intruding at depths <1500 m moves the opal A/CT transition zone to significantly shallower depths. For basins with magmatic sill intrusions emplaced at shallow depths, such a hydrocarbon trap model would lie at shallower depths than basins without sills, and could possibly go undiscovered if sills are not included in the thermal and diagenetic calculations during basin modeling. The opal A/CT boundary has been mistaken for a flat spot as oil/water contact and drilled (e.g., [22]). When incorporating the diagenetic transition of opal A to opal CT in basin modeling, such errors may be avoided.

Opal CT Boundary in the Vøring Basin
The opal A to opal CT transition zone is found at surprisingly shallow depths in some areas of the Vøring Basin. Several reasons for this fossilized opal A/CT transition have been suggested. The transition zone is proposed to have developed during Miocene and died out in Early Pliocene (e.g., [44,49,133]). As the transition of amorphous silica to opal CT is a temperature dependent reaction (e.g., [22,24,[73][74][75]) the fossilized transition is a record of peak paleo temperatures which may reflect max burial depth of the basin, uplift and erosion of the area, higher thermal gradient in the past, or another unknown thermal event [22,44,49,131]. The Eocene magmatic sills are, however, not the cause of the observed shallow opal A/CT zone because the extra heat provided by the intrusions did not affect the diagenesis as shallow as the Miocene/E Pliocene formations.

Smectite to Illite
The conversion of smectite to illite is one of many different clay diagenetic processes occurring in the subsurface. Illite has a fibrous texture and small amounts of this clay may dominate the pore space and largely reduce permeability [91]. The smectite to illite transition is of particular interest for the oil and gas industry as it may coincide with the onset of oil generation [90]. For the Vøring Basin, Peltonen et al. [24] found that major smectite to illite conversion occurred at depths corresponding to a temperature interval of 80-90 • C. For shales in the Gulf Coast (USA), the major rate of smectite to illite conversion was found at temperatures of 90-120 • C [134]. Other studies conclude that the illitization process starts at 50 • C and ceases around 100 • C [135]. These diverse temperature ranges for the smectite to illite conversion is also reflected in the modeling results in this study, when different published kinetic parameters are used (Figure 7). This emphasizes the complexity of the smectite to illite conversion, and possibly clay diagenesis in general. An area influenced by magmatic activity in western Pannonian Basin (Hungary), show a divergent effect of magmatic heating on clay minerals and the smectite to illite transformation [103]. Such results emphasize that, although thermal requirements are met for diagenetic processes to take place, other factors must also be fulfilled for chemical reactions to occur (cf., [136]). For the smectite to illite diagenetic functionality described here, caution must be exercised in the interpretation of the results. This means that the described method can be used to locate areas that fulfill the required kinetics for alterations to occur. This is a good first approximation in pin pointing areas prone to have undergone diagenetic changes in the basin. However, subsurface chemical knowledge is needed in order to examine if other necessary criteria are met for diagenetic alterations.

Influence of Sills and Diagenesis on Stress Accumulations
When sills have solidified and are subject to compressive and tensile stresses, this study shows that the sills and the diagenetically altered areas accumulate stress (Figures 10-14). When stresses exceed the shear and/or tensile strengths of the rock, the rocks will fail and fault movement will be initiated or fractures will develop, respectively. This occurs because stresses tend to build up in the stiffer layers as opposed to softer rocks (e.g., [111,116,117]), which will be decisive for where fractures develop and faults could be reactivated. From the models (Figures 10-14) it can be deduced that the higher the contrast in rock stiffness, the higher the stress concentration in the stiff layers. For diagenetically modified areas, with higher increase in rock stiffness than studied here (doubled the stiffness of the host rock), the potential stress accumulation in the area modified by diagenesis will be higher, and the likelihood of fault initiation and fracture opening is increased. On the other hand, in an opposite situation, the potential stress concentration will be lower and so will the likelihood of fault movement and fracture opening.
It has been proposed that diagenetic processes may affect the fluid flow properties in the subsurface (e.g., [14,47]), a statement which is confirmed by the results in this study. This is the case, not just due to how diagenesis modifies rocks porosity and permeability, but also to how these diagenetic alterations change the rock's physical properties. An active fault may increase the temporary permeability many times, and faults and fractures may dominate the fluid transport in the rock masses if they are interconnected [111]. The results in this study show that sills or diagenetically altered areas (Figures 11-14) could ultimately lead to opening of fractures or initiate fault movements if the tensile or shear stresses of the rocks are exceeded. For a petroleum system, such an outcome can be crucial, as opening of fractures and fault movement increase the permeability and supports fluid flow, possibly to new locations. Thus, we conclude that sills and their related diagenetically modified areas may influence the subsurface fluid migration pathways through time and space and increase the permeability, as opening of fractures and reactivation of faults may act as fluid conduits.

Limitations of the Calculations
All basins have their particular thermal and structural histories concerning e.g., sediment source, lithology, fluid circulation, pore fluid chemistry, and structural development. These variations all play a part in possible chemical alterations in the subsurface and lead to unique diagenetic development. Therefore, information regarding these elements must be included for more detailed local studies.
In numerical modeling there is a direct link between the quality of the input data and the quality of the output from the models. When studying a particular area, caution must be taken regarding various parameters. For instance, we only studied conductive heat transfer in the subsurface and heat convection by fluids is not accounted for. Convection by fluids could influence the resulting thermal and diagenetic calculations to various degrees (cf., [137][138][139][140][141]). The Vøring area shows proof of fluid convection (e.g., [142]), our results therefore show maximum porosity loss, at least for some areas. However, for basins that show little to no signs of convecting fluids, the presented estimations are adequate. We argue that the method presented here is a good approach to reveal areas needing further investigation of possible diagenetic alterations and thus possible alterations of reservoir properties.

Concluding Remarks
This study quantified the porosity loss due to the transition of opal A to opal CT to quartz, smectite to illite and quartz diagenesis and how magmatic intrusions may affect the diagenetic process. As the diagenetic alterations change the physical properties of the rock, it was shown how these alterations and the sills themselves influence location of stress accumulations in a basin and thus may contribute to changes in fracture and fault permeability. All these factors have implications for the petroleum system and the results are summarized as follows: • Conductive thermal effects of sills significantly influence the diagenetic processes in sedimentary basins.

•
The effect of magmatic intrusions on the diagenetic processes depends on the depth at which the magmatic sills intrude. Maximum diagenetic changes occur at different temperatures for the different processes. For sills to influence the transition of opal A to opal CT they must intrude at depths >1500 m.

•
Sill thickness influences the size of the diagenetically altered area, particularly where clusters of sills are closely spaced. • Sills and diagenetically modified areas influence location of stress accumulations and may contribute to initiation of fault movement and opening of fractures. As fractures and faults can act as conduits for fluid flow, sills and areas modified by diagenesis may therefore contribute to increased permeability. • A thorough case study is required to determine the sill's specific effect on diagenetic processes and stress accumulations in the Vøring Basin and other volcanic basins. This is now made possible with the work done in this study.