Hydrogeochemical modelling of fluid–rock interactions triggered by seawater injection into oil reservoirs: Case study Miller field (UK North Sea)

Hydrogeochemical modelling of fluid–rock interactions triggered by seawater injection into oil reservoirs: Case study Miller field (UK North Sea)

Applied Geochemistry 27 (2012) 1266–1277 Contents lists available at SciVerse ScienceDirect Applied Geochemistry journal homepage: www.elsevier.com/...

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Applied Geochemistry 27 (2012) 1266–1277

Contents lists available at SciVerse ScienceDirect

Applied Geochemistry journal homepage: www.elsevier.com/locate/apgeochem

Hydrogeochemical modelling of fluid–rock interactions triggered by seawater injection into oil reservoirs: Case study Miller field (UK North Sea) Yunjiao Fu a,⇑, Wolfgang van Berk a, Hans-Martin Schulz b a b

Clausthal University of Technology, Department of Hydrogeology, Leibnizstraße 10, D-38678 Clausthal-Zellerfeld, Germany Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences, Sec. 4.3, Organic Geochemistry, Telegrafenberg, D-14473 Potsdam, Germany

a r t i c l e

i n f o

Article history: Received 22 September 2011 Accepted 3 March 2012 Available online 20 March 2012 Editorial handling by A. Bath

a b s t r a c t A hydrogeochemical model is presented and applied to quantitatively elucidate interdependent reactions among minerals and formation water–seawater mixtures at elevated levels of CO2 partial pressure. These hydrogeochemical reactions (including scale formation) occur within reservoir aquifers and wells and are driven by seawater injection. The model relies on chemical equilibrium thermodynamics and reproduces the compositional development of the produced water (formation water–seawater mixtures) of the Miller field, UK North Sea. This composition of the produced water deviates from its calculated composition, which could result solely from mixing of both the end members (formation water and seawater). This indicates the effect of hydrogeochemical reactions leading to the formation and/or the dissolution of mineral phases. A fairly good match between the modelled and measured chemical composition of produced water indicates that hydrogeochemical interactions achieve near-equilibrium conditions within the residence time of formation water–seawater mixtures at reservoir conditions. Hence the model enables identification of minerals (including scale minerals), to quantitatively reproduce and to predict their dissolution and/or formation. The modelling results indicate that admixing of seawater into formation water triggers the precipitation of Sr–Barite solid solution, CaSO4 phases and dolomite. In contrast, calcite and microcrystalline quartz are dissolved along the seawater flow path from the injection well towards the production well. Depending on the fraction of seawater admixed, interdependent reactions induce profound modifications to the aquifer mineral phase assemblage. At low levels of seawater admixture, Ba–Sr sulfate solid solution is precipitated and coupled to concurrent dissolution of calcite and microcrystalline quartz. Massive dissolution of calcite and the formation of CaSO4 phases and dolomite are triggered by intense seawater admixture. Hydrogeochemical modelling to reproduce observed compositional trends, resulting from an increase of the seawater fraction, can help (1) to explain changing production properties and (2) to predict the type and the degree of scaling depending on the content of injected seawater. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction The injection of seawater is often applied in reservoirs to increase oil production, to enhance recovery and to extend field life. Chemical incompatibility between the original formation water and injected seawater leads to scaling problems and wellbore damage (Oddo and Tomson, 1994; Bedrikovetsky et al., 2009, and references therein). One controlling factor may be high fluid velocities near the production well, which can stimulate intense mixing of formation water and seawater, and concurrent scaling (Sorbie and Mackay, 2000). Scale deposits in oil operations are often composed of Ba-, Sr- and Ca-sulfates (Oddo and Tomson, 1994, and references therein). Calcium carbonate is another common scale in oilfields and can severely impact production (e.g., Nasr-El-Din

⇑ Corresponding author. Tel.: +49 5323 72 3673; fax: +49 5323 72 2903. E-mail address: [email protected] (Y. Fu). 0883-2927/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.apgeochem.2012.03.002

et al., 2004). Yuan et al. (1994) calculated saturation indices for several scale-forming sulfate minerals and reported that the type of these scale minerals depends on the seawater fraction within the produced water: (1) BaSO4 precipitates at low seawater fractions, (2) SrSO4 forms at medium seawater fractions, and (3) CaSO4 scaling occurs at high seawater contents. Scale dissolvers have been commercially and successfully applied for many years to remove scale from oilfield equipment. Sequestering agents containing ethylenediaminetetraacetic acid (EDTA) can effectively remove Ca, Sr, Ba and Ra sulfate scales near wellbore (Rhudy, 1993). An effective method for removing and preventing CaCO3 scales is a combined acid and EDTA treatment (Shaughnessy and Kline, 1983). For Fe sulfide scaling problems mineral acids can be used (Nasr-El-Din et al., 2001). Consequently, knowledge of the exact type of scale mineral assemblages (and aquifer mineral assemblages) is a prerequisite for any effective treatment to dissolve scales.

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Fig. 1. Modelled and measured concentrations of chloride, Na, Li, Ba and Sr as well as pH in produced water versus seawater fraction for scenarios NRM_T = 393 and RM_pCO2 = 3_T = 393_W. Measured data (squares): taken from Houston (2007); Mod_NRM-line (circles with line): scenario NRM_T = 393; Mod_RM (dots): scenario RM_pCO2 = 3_T = 393_W.

The Miller oilfield has ‘‘arguably the harshest oilfield scaling regime in the North Sea’’ (Wylde et al., 2005). Barite is the dominating scale-forming mineral in most production wells, additionally celestite and calcite scales may be formed (Wylde et al., 2005). During oil production, the chemical composition of the produced water was regularly analysed for nearly 10 a (Houston, 2007). This measured compositional development of produced water resulted from interconnected hydrogeochemical processes, including scale formation that proceeded along the fluid flow path from the injection well towards the production well. Consequently, this measured compositional development of produced water can be used as the key signal to reproduce these hydrogeochemical processes. Therefore, the Miller field was chosen to quantitatively reproduce the hydrogeochemical fluid–rock interactions, which evolved in

this reservoir aquifer as a result of seawater injection. The approach is based on chemical equilibrium thermodynamics. It enables calculation of the type and the amount of minerals that are precipitated and/or dissolved, as opposed to the qualitative interpretations by Houston et al. (2007). The observed deviations of measured concentrations (sulphate, Ba, Sr, Ca, Mg, and silica) in the produced water from their concentrations, predicted from non-reactive mixing of seawater and formation water, are the key signals to be reproduced. Thereby, the aim is to test if relevant hydrogeochemical reactions can lead to equilibrium conditions along the seawater flow path from the injection well towards the production well within a reaction time of less than 2 years at reservoir conditions. If this can be demonstrated, the model enables two applications. Firstly, the interactions of mineral phases and

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Fig. 2. Modelled and measured concentrations of sulphate, Ca, Mg and dissolved silica in produced water versus seawater fraction for scenarios NRM_T = 393 and RM_pCO2 = 3_T = 393_W. Measured data (squares): taken from Houston (2007); Mod_NRM-line (circles with line): scenario NRM_T = 393; Mod_RM (dots): scenario RM_pCO2 = 3_T = 393_W.

formation water–seawater mixtures that are exposed to CO2 partial pressure (pCO2), can be resolved. Secondly, the corresponding mass transfer of mineral phases can be calculated. Reproducing the observed compositional trends, which evolve in formation water–seawater mixtures, helps to conclude on modifications to the porosity–permeability properties of reservoir aquifers, as well as on the type of scales and the degree of their severity. 2. Water injection into the Miller oilfield and hydrogeochemical consequences The Miller oilfield covers an area of 45 km2 in the deep marine setting of the South Viking Graben, Central North Sea (McClure and Brown, 1992; Haszeldine et al., 2006). The fairly constant oil–water contact in the fine- to coarse-grained reservoir sandstone is at 4190 m (Rooksby, 1991; Smalley and Warren, 1994). The present-day temperature is 393 K (Rooksby, 1991) or 413 K (Haszeldine et al., 2006) and the pressure is ca. 50 MPa (Rooksby, 1991). Sandstone in the oil-filled reservoir exhibits a higher porosity of 15–18% compared to the underlying reservoir rocks that are filled by water (14% on average; Marchand et al., 2002). The mineralogical composition of the reservoir sandstone is dominated by quartz comprising ca. 89% of the bulk rock (Marchand et al., 2002). Potassium-feldspar is the single feldspar type and comprises 1–5% of the bulk rock (Houston, 2007). Detrital clay (illite and kaolinite, ca. 3%), muscovite (ca. 1%), pyrite and rock fragments (ca. 4%) occur in minor to trace amounts (Lu et al., 2010). The rock cement is made up of calcite (up to 4.2%; Lu et al., 2010). Oil from the reservoir contains up to 20 mol% CO2 (Haszeldine et al., 2006), and CO2 contributes

Fig. 3. Modelled mineral conversion in mmol/L of produced water (mmol L1) versus seawater fraction for scenario RM_pCO2 = 3_T = 393_W. Negative and positive conversions indicate dissolution and precipitation, respectively; conversion is referred to as mineral amounts present at 0% seawater fraction.

28 mol% to the gas released from the oil (Baines and Worden, 2004). No gas cap is developed, however (Rooksby, 1991). The production of oil began in March 1995 with an almost simultaneous start-up of seawater injection into the reservoir aquifer at an injection well ca. 2.5 km away from one typical production well. In total, roughly 1.9  1011 L of formation water– seawater mixtures were produced from all wells during ca.10 a, with typical rates of 3.8  105 L/day (Houston et al., 2007). The migration time of the injected seawater arriving at the (typical)

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production well can be inferred from changes in the Cl concentrations monitored in the (typical) production well, and is ca. 600 days (Houston et al., 2007). The chemical composition of produced water from each well in the Miller field was analysed almost daily over a period of ca. 10 a (Houston et al., 2007). The Cl concentration of the produced water strongly decreases after 600–700 days of seawater injection, compared to the high Cl concentration in the formation water (ca. 42,000 mg L1 on average; Fig. 1 in Houston et al., 2007). As a result, a continuous increase in the fraction of seawater admixed into the formation water through time is signified by the linear decreasing Cl concentration in the produced water. Contemporaneously, the measured concentrations of other components (sulphate, barium, strontium, calcium, magnesium, silica) in the produced water vary non-linearly (Figs. 2–4 in Houston et al., 2007). Consequently, Houston et al. (2007) suggest that precipitation and dissolution of mineral phases induce the observed deviations. These measured concentrations deviate from the concentrations predicted from non-reactive mixing of seawater and formation water as indicated by Cl concentrations (Figs. 2–4 in Houston et al., 2007; Figs. 1–3). Non-reactive mixing considers the effects of formation water– seawater mixing on the total dissolved concentrations (ctoti) which exclusively result from mixing; hydrogeochemical interactions are not considered by non-reactive mixing.

3. Modelling concept and setup Mixing of formation water and seawater in a porous sandstone matrix is simulated by a closed batch-mixing reactor that is exposed to the reservoir temperature (393 K or 413 K) and to a preassigned pCO2. The modelling concept considers a reactor with a total volume of 7.1 L and a pore volume of 1.0 L (14% porosity). The pore volume is filled with a mixture of formation water and seawater with defined fractions. A series of 11 identical reactors enables consideration of seawater fractions ranging from 0% to 100%. The starting conditions of the seawater injection are represented by original formation water that fills the pore space provided by the batch reactor. A primary mineral phase assemblage (calcite, kaolinite, microcrystalline quartz with and without K-feldspar; Table 1 and Table A.1 in the Supplementary material) occupies the remaining 6.1 L of the total reactor volume. Quartz is

considered as a non-reactive phase although it is the major mineral phase present in the reservoir sandstone. Conceptually, microcrystalline quartz is the (meta-stable) SiO2(s) mineral phase that equilibrates with fluids at reservoir conditions (for details see Section 3.3). Ion exchange equilibria are not considered by the model due to a lack of data about the type of ion exchangers and their capacity. In addition, surface complexation is excluded due to the fact that Fe(III) hydrous oxides have not been described as a major or minor component of the reservoir rocks. Within the first modelling step (prior to the mixing of formation water and seawater), this primary phase assemblage is equilibrated with the original formation water and pCO2 setup starting conditions. The pre-assigned potential secondary phases are barite, witherite, celestite, strontianite, solid solution Sr–Barite (BaxSr(1x)SO4), dolomite, and anhydrite (Table 1). These secondary mineral phases are not present at the beginning of the equilibrium calculations, but are allowed to precipitate from aqueous solutions at saturation during the model run. Within the second modelling step, 1.0 L of a formation water–seawater mixture is equilibrated with the primary mineral phase assemblage and pCO2; secondary phases are allowed to form. Conceptually, modification of the chemical composition of the pore water from the original formation water (within the first modelling step) into formation water–seawater mixtures is the driving force for establishing a new equilibrium species distribution among minerals and fluids. Consequently, dissolution and/or precipitation of mineral phases and coupled reactions are induced. The modelling results provide (1) the composition of the aqueous solution at equilibrium (pH, concentrations of chloride, Li, Na, Ba, Sr, sulphate, Ca, Mg and dissolved silica will be presented) and (2) the type and amount of mineral phases precipitated or dissolved. The evaluation of the modelled aqueous species distribution at equilibrium is based on the comparison of (1) separately calculated concentrations in formation water–seawater mixtures resulting from non-reactive mixing, and (2) measured concentrations in formation water–seawater mixtures produced from the Miller field (Houston, 2007). These double-tracked calculations are important to evaluate the effects of formation water–seawater mixing on the total dissolved concentration of elements or components, which are restricted to pure, non-reactive mixing without consideration of any hydrogeochemical equilibrium interactions among minerals, aqueous solution and gas (heterogeneous reactions). In contrast, association and dissociation equilibrium reactions of aqueous

Table 1 Pre-assigned mineral phase assemblage (primary phases), potential secondary phases, solubility constants (log K for 298 K and 0.1 MPa) and the amount of phases at starting conditions in the modelling reactors.

Primary phase

Secondary phase

Gas phase a b c d

Reaction

log Ka

SiO2 + 2H2O = H4SiO4 KAlSi3 O8 þ 8H2 O ¼ Kþ þ AlðOHÞ 4 þ 3H4 SiO4 Al2Si2O5(OH)4 + 6H+ = 2Al3+ + 2H4SiO4 + H2O

3.857 20.573 7.435 8.48

Amount (wt.%)

(mol)

Microquartzb K-feldspar Kaolinite Calcite

0.01 3 1.5 2.1

0.03 2.04 1.1 3.97

Quartz

89

280

CaCO3 ¼ Ca2þ þ CO2 3 SiO2 + 2H2O = H4SiO4

Dolomite

0

0

CaMgðCO3 Þ2 ¼ Ca2þ þ Mg2þ þ 2CO2 3

Strontianite

0

0

SrCO3 ¼ Ba2þ þ CO2 3

9.271

Witherite

0

0

BaCO3 ¼ Ba2þ þ CO2 3

8.562

Barite

0

0

BaSO4 ¼ Ba2þ þ SO2 4

9.97

Celestite

0

0

SrSO4 ¼ Sr2þ þ SO2 4

Sr–Barite

0

0

Bax Srð1xÞ SO4 ¼ xBa2þ þ ð1  xÞSr2þ þ SO2 4

Gypsum

0

0

CaSO4 : 2H2 O ¼ Ca2þ þ SO2 4 þ 2H2 O

4.58

Anhydrite

0

0

CaSO4 ¼ Ca2þ þ SO2 4

4.36

CO2(g) = CO2(aq)

1.468

CO2(g)

d

3 MPa

From Wateq4f.dat database (Parkhurst and Appelo, 1999) except for microquartz. Re-calculated from data reported by Azaroual et al. (1997). Calculated by PHREEQC utilizing log K of barite and celestite. Pre-assigned carbon dioxide partial pressure.

3.98 17.09

6.63c

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species (homogenous reactions including H+-transfer) are considered. Consequently, the total dissolved component concentration (ctoti) is unaffected by the ‘‘non-reactive mixing’’ process, and merely the component’s species distribution is altered. A negative deviation of the modelled equilibrium concentrations from the non-reactive mixing trend indicates that elements have been removed from the aqueous solution (formation water–seawater mixture) by precipitation of certain mineral phases. In contrast, modelled equilibrium concentrations, which are higher than the concentrations calculated by non-reactive mixing, indicate dissolution of a certain solid phase or phases, and a release of components in the formation water–seawater mixture. The PHREEQC computer code (Parkhurst and Appelo, 1999) was used as the modelling tool. It is applied to calculate equilibrium species distribution among aqueous solutions, gas partial pressures, and primary and secondary mineral phases. Equilibrium species distribution and coupled mass transfer to achieve equilibrium are calculated by applying homogenous and heterogeneous massaction equations, and related temperature-dependent equilibrium constants. Equilibrium species distribution is characterised in terms of molalities and activities of aqueous species, pH levels and the type and amount of solid phases dissolved or precipitated, as well as the amount of CO2(g) that is dissolved or outgases. The PHREEQC computer code is based on the fundamental laws of conservation of mass and charge (for details on the applied chemical and mathematical basics see Parkhurst and Appelo, 1999). The PHREEQC computer code and its Wateq4f.dat database apply activity coefficients for charged species calculated according to the Davies equation or to the extended or WATEQ Debye–Hückel equation. The Wateq4f.dat database uses these three equations and selects the most suitable equation depending on the available data for each dissolved species. Activity coefficients for most uncharged 0 speciesðaqÞ are calculated by the Setchenow equation considering ionic strength and a parameter (bi) with a value of 0.1 (for details see Parkhurst and Appelo, 1999). If the WATEQ Debye–Hückel equation is used, activity calculations are valid for ionic strengths of <0.7 molal. In NaCl-dominated systems, the calculations may be reliable at higher ionic strengths (Parkhurst and Appelo, 1999). Due to the fact that the WATEQ Debye–Hückel equation is only used for a small number of species in the Wateq4f.dat database, the validity of this approach is limited. Temperature effects on equilibrium constants are considered by using PHREEQC’s ‘‘analytical expressions’’ or the ‘‘standard enthalpy of reaction’’ (used in the van’t Hoff expression; Table A.1 in the Supplementary material). With the exception of microcrystalline quartz, all equilibrium reactions for solids and CO2(g), their corresponding equilibrium constants and their temperature dependence are taken from the thermodynamic database Wateq4f.dat (provided by Parkhurst and Appelo (1999); Table 2 and Table A.1 in the Supplementary material). Control of the total pressure (not pCO2) over solubility equilibria of solid phases, as well as of aqueous species distribution, is not considered by PHREEQC, and calculations are performed at a fixed total pressure of 0.1 MPa. To evaluate the effect of total pressure, an additional modelling scenario is performed by using equilibrium constants for the primary and secondary mineral phases calculated by SUPCRT92 and the DPRONS92.dat dataset (Johnson et al., 1992; Table A.2 in the Supplementary material).

interactions with some minerals (dissolved or precipitated) containing specific elements. With this method, the type and the amount of minerals, dissolved and/or precipitated, cannot be determined and calculated. Yuan and Todd (1991) and Yuan et al. (1994) presented a model for the quantitative prediction of scaling tendencies of Ba, Sr and Ca sulfates. Bethke (2008) suggested a similar model using the Geochemist’s Workbench computer code and discussed the possible formation of sulfate solid solution phases and applied the model to formation waters in different oilfields. Both models are restricted to calculate scales comprising pure sulfate minerals, and suppress the formation of possible different scale minerals (e.g., carbonates and/or sulfides) as well as sulfate solid solution phases. These modelling approaches are focused on a selected part of the complete hydrogeochemical system. The dissolution of primary minerals is excluded, but could induce more intensive scale formation or conversely create secondary porosity and permeability within the reservoir aquifer. In contrast to the present modelling approach, all the above-mentioned alternative approaches only consider parts of the complex web of water–rock interactions in reservoirs.

3.2. Chemical composition of seawater and formation water Information about the actual chemical composition of the injected seawater is lacking. The present-day seawater composition given by Parkhurst and Appelo (1999; Example 1) is taken as the model seawater, but dissolved molecular O2 is excluded (Table 2) assuming that the seawater is anoxic prior to injection. N(5)-, N(-3)-, and U concentrations (given by Parkhurst and Appelo (1999); Example 1) are ignored because N and U are not involved in the modelling phase assemblages. In addition, concentrations of Ba, Sr, Al and Li, which are lacking in the seawater composition presented by Parkhurst and

Table 2 Seawater composition excluding nitrate, nitrite, uranium, and dissolved oxygen (Parkhurst and Appelo, 1999; Example 1) and formation water composition prior to seawater injection (Lu et al., 2010; original data from Smalley and Warren, 1994). PHREEQC notation

pH pe Temperatureb units Density (Kg/L) Calcium Magnesium Sodium Potassium Iron Manganese Silica, as SiO2 Chloride Alkalinity, as HCO 3 Sulfate, as SO2 4 Barium Strontium Lithium Aluminum Zinc

3.1. Alternative approaches a

Houston (2007) calculated the compositional development of the produced water resulting solely from mixing of formation water and seawater depending on the seawater fraction. Hydrogeochemical reactions of any type are not considered in Houston’s calculation. Deviations of this calculated compositional development from the measured data in the Miller field indicate hydrogeochemical

Concentration Seawater

Formation water

Ca Mg Na K Fe Mn Si Cl Alkalinity S(6)

8.22 8.451 4 ppm 1.023 412.3 1291.8 10768 399.1 0.002 0.0002 4.28 19353 41.682 2712

7.5 n.a.a 120 ppm 1.055 307 82 25898 1399 1 n.a. 70c 41767 2221 4

Ba Sr Li Al Zn

0.02d 8d 0.17e 0.001e n.a.

643 39 28e 1f 0.4f

pH pe temp ppm

Not analyzed. Given in °C (equivalent to 277 K or 393 K, respectively). c Measured concentration at 0% seawater fraction (corresponds to Houston, 2007). d Mean concentration from Turekian (1968) and Bearman (1989). e According to Turekian (1968). f Mean concentration in the seawater fraction range from 0% to 1.58% according to Houston (2007). b

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Appelo (1999; Example 1), are included in accordance with Turekian (1968) and Bearman (1989). The formation water composition used in the model is characterised by high Na+ and Cl concentrations of 25,898 and 41,767 ppm (sample no. 5 in Lu et al. (2010); original data from Smalley and Warren (1994); Table 2). Additional data on dissolved silica, Sr, Li and Al concentrations are taken from Houston (2007) to compile a complete formation water dataset that is consistent with the seawater compositional parameters (Table 2). 3.3. Mineral phase assemblage The mineralogical composition of the reservoir rock is dominated by quartz. Several samples from varying reservoir depths display microcrystalline quartz coatings on quartz grain surfaces which were identified by scanning electron microscope studies (Houston, 2007). However, the exact grain size of ‘‘microcrystalline quartz’’ is not reported by Houston (2007). Azaroual et al. (1997) evaluated the behaviour of aqueous silica in basinal solutions with respect to different SiO2(s) polymorph phases. The authors concluded from calculated and measured dissolved SiO2(aq) activities that the concentrations of dissolved SiO2(aq) measured in brines of the Paris basin (Dogger; ca. 330 K to 360 K) are probably controlled by equilibration with a microcrystalline quartz phase characterised by a grain size of ca. 0.02 lm. Moreover, the authors provide calculated SiO2(aq) activities at equilibrium with the microcrystalline quartz at elevated temperature (393 K) that are very close to the activities of dissolved SiO2(aq) measured in the formation water of the Miller field. It is assumed (1) that microcrystalline quartz is the SiO2 solid phase to equilibrate with formation water–seawater mixtures at reservoir conditions, and (2) that this SiO2(s) phase is characterised by a solubility according to Azaroual et al. (1997). Within this context the equilibrium constant of microcrystalline quartz was re-calculated

SiO2ðMicroquartzÞ þ 2H2 O ¼ H4 SiO4 logK ¼ 3:857 ðfor 298 K and 0:1 MPaÞ

ð1aÞ

and its temperature dependence (temperature T in K)

logK ¼ 96:13þ0:0311T 1 434:06T 1 41:02logT 1 559298:3T 2

ð1bÞ

and added this new solid phase ‘‘Microquartz’’ was added to the thermodynamic database (Table 1 and Table A.1 in the Supplementary material). The authors are aware that the microcrystalline

quartz coatings on quartz grain surfaces observed in the Miller field’s reservoir rocks probably display grain sizes diverging from those given by Azaroual et al. (1997; 0.02 lm), and that their solubility can be affected by grain size. However, it was assumed that the solubility of these microcrystalline quartz coatings on quartz grain surfaces is represented by Eqs. (1a) and (1b), respectively. Potassium-feldspar is the single proven feldspar phase, but it is significantly corroded (Houston, 2007). This feldspar provides carbonic acid buffering capacity, and consequently can control pore water pH levels at high pCO2 (van Berk et al., 2009). By activating its carbonic acid buffering capacity, K-feldspar will be consumed. Conceptually, it is assumed that K-feldspar (or its reactive fraction) exposed to the formation water is completely removed by dissolution from the reservoir rock filled by formation water. This process is assumed to be driven by CO2, as the Miller field’s oil contains up to 20 mol% CO2, and CO2 contributes 28 mol% to the gas released from the oil (see Section 2). Although K-feldspar has been detected, it is excluded from the mineral phase assemblage of the modelling reactors that represent the Miller field’s reservoir rock filled by formation water. Nevertheless, one alternative modelling scenario considers K-feldspar as a primary mineral phase to test its effect on the equilibrium species distribution. Kaolinite is chosen as the primary clay mineral phase in the model. Although also detected by Houston (2007), illite is excluded from the list of potential secondary phases due to relatively unfavourable formation kinetics at temperatures <110–140 °C (Smith and Ehrenberg, 1989). Authigenic calcite cement occurs in the reservoir sandstones at relatively shallow burial depths and exhibits dissolution features (Houston, 2007). Thus, calcite is chosen as a primary phase (Table 1). The seawater injected into the reservoir is characterised by a relatively high Mg concentration. Intense CO2 and Mg supply may induce the formation of secondary dolomite from formation water–seawater mixtures. In analogy to dolomite, strontianite and witherite are chosen as potential secondary carbonate mineral phases to form (Table 1), because of the high concentrations of Sr and Ba in the formation water prior to seawater injection (Table 2). The Wateq4f.dat database used in the study includes two types of dolomite – ‘‘dolomite’’ and ‘‘dolomite(d)’’ (disordered dolomite). The phase ‘‘dolomite’’ is used in all of the modelling scenarios. The effect of disordered dolomite on chemical composition of formation water–seawater mixtures is also tested. The sulphate concentration of seawater is much higher (2712 ppm) than in the formation water (4 ppm; Table 2). In contrast to the SO4-rich seawater, the concentrations of Ba and Sr are

Table 3 Modelling scenarios. Model type

NRM NRM_T = 393 RM_pCO2 = 3_T = 393_W RM_pCO2 = 3_T = 413_W RM_pCO2 = 3_T = 373_W RM_pCO2 = 0.3_T = 393_W RM_pCO2 = 30_T = 393_W RM_pCO2 = 3_T = 393_W_Gy RM_pCO2 = 3_T = 393_W_Qz RM_pCO2 = 3_T = 393_W_Kfs RM_pCO2 = 3_T = 393_S

pCO2 (MPa)

T (K)

RM

W

x x x x x x x x x x

Data base

3 3 3 0.3 30 3 3 3 3

393 413 373 393 393 393 393 393 393

Mineral assemblage

S

x x x x x x x x x

SiO2 phases

Silicates

Carbonates

MQ

Kfs

Ka

Cc

Do

St

Wi

Ba

Ce

SrBa

An

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x x x x x

x x x x x

Qz

x x x x x x x x

Modelling results Figure

x x

x

Sulfates Gy

x x x x

1, 2 1, 2, 3 S.1, S.2 S.1, S.2 S.3, S.4 S.3, S.4 S.5, S.6 S.7, S.8 S.9, S.10 S.11, S.12

NRM: non-reactive mixing (hydrogeochemical interactions are unconsidered); RM: reactive mixing (hydrogeochemical interactions are considered); T: temperature; W: Wateq4f database provided by Parkhurst and Appelo (1999); S: solubility constants of solid phases calculated by SUPCRT92 and its DPRONS92.dat dataset (Johnson et al., 1992); MQ: microquartz; Qz: quartz; Kfs: K-feldspar; Ka: kaolinite; Cc: calcite; Do: dolomite; St: strontianite; Wi: witherite; Ba: barite; Ce: celestite; Sr-Ba: Sr–Barite; An: anhydrite; Gy: gypsum.

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high in the formation water (643 ppm, and 39 ppm, respectively). Conceptually, the mixing of seawater and formation water may allow the formation of the secondary sulfate phases: barite (BaSO4), celestite (SrSO4) and anhydrite (CaSO4) or gypsum (CaSO42H2O), respectively. Hence, barite, celestite and anhydrite (alternatively gypsum) were pre-assigned as potential secondary phases (Tables 1 and 3). Barium sulfate is often accompanied by SrSO4 to form a Sr–Barite solid solution

Bax Srð1xÞ SO4 ¼ xBa2þ þ ð1  xÞSr2þ þ SO2 4

ð2Þ

that is often reported to occur as a result of scaling processes in formation water or basinal brines (Gordon et al., 1954; Todd and Yuan, 1992). The modelling phase assemblage includes secondary solid solution Sr–Barite that is composed of barite and celestite and is treated as an ideal solid solution (Table 1). Pyrite is excluded from the modelling, although it occurs in minor amounts in the Miller field; preliminary modelling results indicate that pyrite exerts no effect on pore water composition. Sulfide-containing scale mineral phases have not been detected in the Miller field. Additionally, the concentrations of aqueous S(II) species have not been reported (Houston, 2007). Thus, sulfate reduction to sulfide and consequently the precipitation of sulfidecontaining minerals are not considered by the models. The missing sulfide may result from a limited ‘‘electron donor supply’’ from the oil leg compared to a typical seawater injection rate of 3.8  105 L per day. In other words, there is no direct contact of the formation water–seawater mixing zone and the oil–water contact, and the (potential) flux of electron donors leaves the mass conversion of (potential) sulfate reduction nearly unaffected. Measured pCO2 data are lacking for the Miller field. The various pCO2 levels are thereby pre-assigned for alternative modelling scenarios considering a total reservoir pressure of ca. 50 MPa (Table 3).

(2) pCO2 (in MPa units; ‘‘pCO2 = 3’’), (3) temperature (T in K; ‘‘393’’), (4) origin of solubility constants for solid phases (‘‘W’’ indicates the Wateq4f.dat database; ‘‘S’’ representing solubility constants of solid phases calculated by the SUPCRT92 code), (5) gypsum as the secondary phase instead of anhydrite (‘‘Gy’’), (6) quartz as the primary SiO2(s) solid phase replacing microcrystalline quartz (‘‘Qz’’), and (7) K-feldspar (‘‘Kfs’’) is included in the primary mineral phase assemblage. The results from the modelling scenarios NRM_T = 393 and RM_pCO2 = 3_T = 393_W will be discussed in Sections 4.1 and 4.2 while the results from all other modelling scenarios (Table 3) will be Appendix in the Supplementary material, but will be discussed (Section 5.1). In total, the results of nine different RM scenarios will be discussed. PHREEQC input files are formatted for copy and paste to run with the PhreeqcWin tool (Supplementary Tables 1–10). PHREEQC calculates the concentration of species(aq) in molal units (mol kgw1) and the measured concentrations of species(aq) in the produced water are given in molar units (mol L1; Appendix V in Houston, 2007). The modelled concentrations are re-calculated from the molal unit to the molar unit, and compared with measured concentrations of species(aq). Assuming that the density of the produced water depends exclusively on the concentration of Na+ and Cl ions, a simplified conversion factor from mol kgw1 to mol L1 is calculated for 393 K. At seawater fractions of 0%, 10%, 40%, 50%, 60%, 90%, and 100%, the modelled concentration of species(aq) in produced water (given in molal units) are multiplied by 0.93 to get molar units; at seawater fractions of 20%, 30% and 70%, the conversion factor is 0.92 (0.94 at 80%). 4.1. Non-reactive mixing scenario NRM_T = 393

4. Modelling scenarios and results One separate modelling scenario considers the effects of formation water–seawater mixing on total dissolved concentrations of elements or components (ctoti) resulting exclusively from nonreactive mixing (NRM). Heterogeneous reactions among aqueous solution, solid phases and gas are not considered in this scenario. In contrast, homogenous equilibrium reactions are included. These reactions are triggered by mixing and lead to the association and dissociation of aqueous species (NRM modelling scenario; Table 3). The reactive mixing scenarios (RMs), on the other hand, consider combined mixing and concurrent equilibrium reaction effects (including solubility equilibria of solid phases and pCO2) and apply various pre-assigned modelling conditions (e.g., varying pCO2 or temperature). Both models NRM and RM implement identical mixing fractions of formation water and seawater. The RM scenarios take account of (1) varying temperature (393 K, 373 K and 413 K), (2) varying pCO2 (3.0, 0.3 and 30 MPa), (3) solubility constants for solid phases from different origins (Wateq4f.dat database, Parkhurst and Appelo, 1999; or calculated by the SUPCRT92 code with its DPRONS92 database, Johnson et al., 1992), and (4) different mineral phase assemblages (quartz substitutes microcrystalline quartz; with and without K-feldspar; gypsum replaces anhydrite). The parameter values tested are presented in Table 3. Scenarios names (e.g., RM_pCO2 = 3_T = 393_W_Gy) indicate: (1) the model type (‘‘RM’’),

The scenario NRM_T = 393 is calculated to evaluate the nonreactive mixing effects on the chemical composition of formation water–seawater mixtures. Within this scenario, the formation water is merely diluted by increasing the fraction of seawater (from 0% to 10%, and up to 100%). Basic assumptions for calculations are: (1) a constant chemical composition of the injected seawater, (2) a constant chemical composition of the formation water,  and (3) non-reactive behaviour of total dissolved ClðaqÞ -ions. In  other words, ClðaqÞ -ions participate in none of the heterogeneous equilibrium reactions. The modelling results of the NRM scenario show that measured Cl concentrations in formation water–seawater mixtures produced from the reservoir reflect the seawater fraction and display a linear decrease with the increasing fraction of seawater (a trend named ‘‘Mod_NRM-line’’ of chloride).The modelled compositional, non-reactive evolution of formation water–seawater mixtures is linearly dependent on the fraction of seawater (Mod_NRM-lines of Na, Li, Ba, Sr, sulphate, Ca, Mg and dissolved silica in Figs. 1 and 2). Modelled (‘‘non-reactive’’) pH values range from 7.5 to 6.9 (Fig. 1); note that pH data measured in produced formation water–seawater mixtures have not been reported by Houston (2007). 4.2. Reactive mixing scenario RM_pCO2 = 3_T = 393_W The temperature measured in formation water is 393 K (Smalley and Warren, 1994; Lu et al., 2010). It is assumed (1) that formation water–seawater mixtures equilibrate at 393 K within less than 2 years (the mean residence time of seawater) and (2) that the measured chemical composition of the produced water (Houston, 2007) is unaffected by sampling and represents the original reservoir conditions (393 K and ca. 50 MPa). The pre-assigned pCO2 level to

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fraction are similar to the trend and (partly) the range of the measured ctotSr2+ in produced water (ranging from 0.45 to 0.09 mmol L1). In addition to Sr–Barite, a concurrent precipitation of anhydrite is triggered by intense injection of seawater (seawater fractions >70%; Fig. 3 and Table 4). The modelled total sulphate concentration (ctotsulphate) trend negatively deviates from the NRM scenario (Fig. 2), but quite closely matches the measured trend at seawater fractions up to 80%. Calcium, liberated due to calcite dissolution (0.0–31.5 mmol L1; Fig. 3 and Table 4), is accessible for the precipitation of Ca-bearing minerals (anhydrite and dolomite) at seawater fraction >70% and >80%, respectively. According to this, intensive seawater admixtures lead to a strong increase in modelled total Ca concentrations (ctotCa2+, ranging from 7.37 to 16.3 mmol L1; Fig. 2). In contrast to Ca, the modelled trend of total Mg concentration (ctotMg2+) in equilibrium with the ‘‘dolomite’’ phase and the absolute concentrations are not in good accordance with the measured concentrations (Fig. 2). ‘‘Dolomite(d)’’ included in the Wateq4f.dat database is characterised by a slightly higher solubility compared to the ‘‘dolomite’’ phase used in scenario RM_pCO2 = 3_T = 393_W. The modelling results in equilibrium with the ‘‘dolomite(d)’’ phase display higher ctotMg2+ compared to the measured Mg concentrations and the concentrations modelled considering the ‘‘dolomite’’ phase (details not presented here). The discrepancy between modelled and measured ctotMg2+ indicates (1) that either the presented modelling approach with the chosen dolomite solubility at 0.1 MPa is not capable of calculating dolomite formation correctly or (2) that additional (still non-identified) Mg-bearing secondary mineral phases are absent in the model. The trend of dissolved total silica concentration (ctotSiO2) measured in the produced formation water–seawater mixtures differs significantly from the NRM scenario and indicates the release of dissolved silica from silicate phases at equilibrium (Fig. 2). The ctotSiO2 in the RM scenario remain almost constant, evolve almost independently of the seawater fraction, and are similar to the measured ctotSiO2 (slightly lower). The low dissolved ctotSiO2 in seawater causes increasing amounts of dissolving microquartz (0.1– 1.2 mmol L1 microquartz dissolved; Fig. 3) at raised seawater fractions. This leads to a pronounced deviation of measured and modelled ctotSiO2 from their NRM-line (Fig. 2). In comparison to the microquartz dissolution, the conversion of kaolinite due to seawater injection is negligible (dissolution is less than 107 mol L1).

equilibrate in formation water–seawater mixtures and the mineral phase assemblage is 3.0 MPa. The scenario RM_pCO2 = 3_T = 393_W is the basic scenario; alternative scenarios will consider different pCO2 levels and temperature conditions or various phase assemblages (Fig S1 to S12 in the Supplementary material). The modelled compositional devolvement of produced water in response to increasing admixture of seawater into formation water is illustrated in Figs. 1 and 2 for pH values and total dissolved concentrations of different components, and is compared with NRMlines as well as with measured concentrations (if available). Chloride-, Na+- or Li+-bearing minerals (e.g., albite) are excluded from the mineral phase assemblage. Hence, calculated total concentrations of chloride, Na and Li (including all their charged or uncharged, free or complex species; labelled as ctotCl, ctotNa+ and ctotLi+) for the NRM and RM scenarios linearly decrease versus the increasing seawater fraction, just as the measured concentrations (Fig. 1). Consequently, modelled and measured concentrations of Li and Na provide additional signals of the admixed seawater fraction in the Miller field formation water. A constant pCO2 of 3 MPa and equilibration between fluids and mineral phases clearly change the produced water composition versus seawater fraction compared to NRM-lines, except for concentrations of chloride, Na and Li. Comparison of the NRM-line pH level to the modelled pH level for reactive-mixing (ranging from 5.3 to 5.1, Fig. 1) reveals that H+-transfer reactions are significantly involved at elevated temperature and pCO2 conditions. Modelled total Ba concentrations (ctotBa2+) in the produced water, responding to increasing seawater fraction, strongly deviate from the Ba NRM-line (Fig. 1). Reactive admixture of seawater leads to decreasing ctotBa2+ (ranging from 4.6 to <0.01 mmol L1), which are markedly lower than the ctotBa2+ in the NRM scenario. The modelled and measured ctotBa2+ and their trends versus increasing seawater fraction are similar. Decreased Ba concentrations correspond to the formation of equivalent amounts of newly formed Sr–Barite (from 0.6 to 4.2 mmol L1; Fig. 3; Table 4). This precipitate is characterised by varying chemical compositions ranging from nearly pure barite (Ba0.999Sr0.001SO4) at low seawater fraction to Ba0.88Sr0.12SO4 at high seawater content. As a consequence of the Sr–Barite formation, reactive admixture of seawater into formation water leads to decreasing ctotSr2+ (total Sr concentration; ranging from 0.44 to 0.05 mmol L1), which negatively deviate from the appropriate Sr NRM-line (Fig. 1). The absolute level of modelled ctotSr2+ and its trend versus the seawater

Table 4 Modelled mineral conversion versus seawater fraction for scenario RM_pCO2 = 3_T = 393_W. Seawater fraction (%) 10

20

30

40

50

60

70

80

90

100

3.01 0.0 0.49 0.0 +3.24

4.16 0.0 0.61 0.0 +2.72

5.38 0.0 0.74 0.0 +2.20

6.97 +1.12 0.86 0.01 +1.66

15.21 +5.61 0.99 +3.39 +1.12

23.36 +10.07 1.11 +6.74 +0.57

31.46 +14.50 1.24 +10.05 0.0

1.1e4 0.0 1.1e5 0.0 +1.7e4 +4.6e5

1.5e–4 0.0 1.4e5 0.0 +1.4e4 2.6e5

2.0e4 0.0 1.7e5 0.0 +1.1e4 1.0e4

2.6e4 +5.1e5 2.0e5 +8.4e7 +8.6e5 1.4e4

5.6e4 +2.6e4 2.2e5 +2.2e4 +5.8e5 5.0e5

8.6e4 +4.6e4 2.5e5 +4.3e4 +2.9e5 +3.7e5

1.2e3 +6.7e4 2.8e5 +6.5e4 0.0 +1.2e4

a

Mass conversion (mmol per litre of produced water) Calcite 0.32 0.96 1.94 Anhydrite 0.0 0.0 0.0 Microquartz 0.12 0.25 0.37 Dolomite 0.0 0.0 0.0 Sr–Barite +2.91 +4.15 +3.74 Volume conversion Calcite Anhydrite Microquartzc Dolomite Sr–Barited Sum (l l1)e a b c d e

(litre per litre of produced water)a,b 1.2e5 3.5e5 7.2e5 0.0 0.0 0.0 2.8e6 5.6e6 8.3e6 0.0 0.0 0.0 +1.5e4 +2.2e4 +1.9e4 +1.4e4 +1.7e4 +1.1e4

Negative conversion () indicates dissolution and positive conversion (+) indicates precipitation relative to the mass or volume of minerals at 0% seawater fraction. q(calcite) = 2.71 kg L1, q(anhydrite) = 2.96 kg L1, q(dolomite) = 2.872 kg L1 according to Dean (2001). q: Mineral density. Based on the assumption that q(microquartz) equals to q(quartz) of 2.648 kg L1 according to Dean (2001). Based on the assumption that q the density of barium sulfate dominated Sr–Barite equals to the density of pure barite (4.5 kg L1 according to Dean, 2001). Equals to the sum of volumetric mineral conversion in litre per produced water litre.

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In summary, the amount of newly formed Sr–Barite is highest at ca. 20% of seawater fraction, but Sr–Barite is precipitated from all formation water–seawater mixtures (Table 4). In contrast, anhydrite and dolomite formation is restricted to elevated levels of seawater fractions (>70%). Calcite and microcrystalline quartz are dissolved in all formation water–seawater mixtures, but the amounts dissolved increase constantly with increasing seawater fraction. The mass of newly formed minerals can be as high as 14.5 mmol of anhydrite/L of produced water, whereas 31.5 mmol of calcite/L of produced water were dissolved. In terms of volumetric considerations, 0.67 mL of anhydrite was precipitated and 1.16 mL of calcite were dissolved/L of produced water. An overall volumetric balance reveals that the volume of newly formed Sr– Barite, dolomite and anhydrite overcompensates for the volume of dissolved calcite and microcrystalline quartz at low to medium seawater fractions (10–40%), but also at high seawater fractions (90% and 100%). It is important to note that up to 0.14 mL of additional pore space/L of produced water is generated at medium to high seawater fractions (50–80%). Formation of secondary Sr–Barite prevails at ca. 20% of seawater fraction (0.22 mL/L of produced water). The concurrent dissolution of calcite plus microcrystalline quartz (0.05 mL/L of produced water) is insufficient to compensate for the loss of pore space, which can be occupied by newly formed Sr–Barite during the transient stage of seawater injection (seawater fraction <100%). The transient character of these interactions is restricted to both interconnected formation water–seawater mixing areas along the seawater flow paths and time spans of seawater injection with seawater fractions of ca. 20%. The dissolution of calcite and microcrystalline quartz (1.19 mL/ L of produced seawater) is overcompensated by the precipitation of anhydrite and dolomite (1.31 mL/L of produced seawater) at steady state conditions after 2 years of seawater injection, when merely pure seawater is produced. A (net) volume of 0.12 mL of secondary anhydrite plus dolomite (precipitated from 1.0 L of seawater) seals the pore space of an aquifer section, which provides a total volume of 7.1 L and a pore volume of 1.0 L (at 14% porosity).

5. Discussion 5.1. Modelling results Seawater injection into the Miller field’s reservoir aquifer can trigger a complex web of hydrogeochemical reactions evolving into a multi-component and multi-phase system. Simultaneously occurring reactions are inter-related due to the reaction products and reactants that are involved in different steps of this complex weblike process. The presented model approach quantitatively reproduces this hydrogeochemical web by evaluating and comparing modelling results with measured data. The evolving measured concentrations of chloride, Na, Li, Ba, Sr, sulphate, Ca, Mg, and dissolved silica are the signals that are produced by a complex web of inter-related hydrogeochemical reactions which are triggered by the admixture of seawater into formation water under reservoir conditions. Calculations using the basic and most probable modelling scenario RM_pCO2 = 3_T = 393_W create a reasonable agreement between the modelled and the measured chemical composition of produced water. It follows that Sr–Barite, Casulphate, dolomite, calcite, microcrystalline quartz and CO2(g) are the key phases involved in the process web analysed. Calculated ctotCl, ctotNa+ and ctotLi+ linearly decrease with increasing seawater fraction, just as the measured data. Modelled ctotBa2+, ctotSr2+, ctotsulphate and ctotCa2+ and their dependence on the seawater fraction are in good agreement with the measured concentrations. In contrast, modelled ctotMg2+ is noticeably higher than the measured concentra-

tions at most seawater fractions (>20%). The calculated level of ctotSiO2(aq) is slightly lower than the measured concentration, whereas the measured concentration trend at various seawater fractions is reproduced by the calculated compositional development of produced water. Temperature affects the compositional development of the produced water, especially the concentrations of Ca, Mg and silica (Figs. S1 and S12 in the Supplementary material). High temperature leads to low ctotCa2+. In contrast, high modelled ctotMg2+ and ctotSiO2 occur at the highest temperature. Partial pressure of CO2 also has a strong effect on the chemical composition of the produced water (Figs. S3 and S4 in the Supplementary material). Low pCO2 levels result in high pH levels and induce (1) low ctotBa2+ owing to the formation of witherite, and (2) low ctotCa2+ and low ctotMg2+ due to intensive dolomite precipitation. Moreover, temperature controls CO2 solubility, and consequently influences species concentrations at equilibrium with mineral phase assemblages. Laboratory experiments show that changes in temperature and pCO2 levels have marked effects on scale formation and scaling rate (Moghadasi et al., 2003; Merdhah and Yassin, 2009). The modelling results emphasise that temperature and pCO2 affect the type and amount of minerals dissolved and precipitated (for details see Appendices in the Supplementary material). Determination of the reservoir temperature in contrast to the temperature of the mixing zone during or after seawater injection is a common reservoir engineering task. Results of a hydrogeochemical model in comparison with measured data can overcome this challenge. Such an approach can help to quantify the temperature and pCO2 conditions, at which equilibration of fluids and mineral phases has occurred. The modelling results reveal that the temperature and pressure, which modify the measured chemical composition of the produced water in the Miller oilfield, are probably in the range of 393–413 K and ca. 3 MPa pCO2, respectively (Figs. 1, 2 and Figs. S1 and S12 in the Supplementary material). In comparison to the basic and most probable scenario, the alternative scenario RM_pCO2 = 3_T = 393_W_Gy considers gypsum instead of anhydrite as the secondary CaSO4 phase. The equilibration with gypsum or anhydrite affects modelled ctotsulphate and the type of precipitated sulfate minerals (Figs. S5 and S6 in the Supplementary material). The trend of ctotsulphate versus the increasing seawater fraction at equilibrium with gypsum is identical to the NRM-line, which reflects gypsum undersaturation at any seawater fraction. The broad range and the limited number of measured ctotsulphate at higher seawater fractions (>80%) do not allow specifying whether any new CaSO4 phase is formed. The modelled ctotSiO2 is controlled by the dissolution of SiO2(s) and depends exclusively on the SiO2(s) solid phase (Figs. S7 and S8 in the Supplementary material). The modelled ctotSiO2 at equilibrium with quartz is lower than the ctotSiO2 at equilibrium with microquartz, as well as the measured ctotSiO2 value itself. It follows that microquartz, rather than quartz, is more probably equilibrating with the formation water–seawater mixtures. The clear mismatch between the measured data and the modelled results of scenario RM_pCO2 = 3_T = 393_W_Kfs (for detailed Appendix in the Supplementary material) reveals that K-Feldspar is excluded from the equilibration among the fluids and the mineral phase assemblage. Consequently, it can be assumed that (1) either that the reactive parts of K-feldspar, which were exposed to the formation water–seawater mixture, were completely dissolved prior to seawater injection, (2) or/and that the K-feldspar occurrence (ca. 3% of bulk rock; Marchand et al., 2002) is restricted to the oil column. Dissolution of K-feldspar is a proven process due to organic–inorganic interactions, which occur within the water leg and which are triggered by oil degradation (van Berk et al., 2009). Further CO2 addition, either by oil degradation or by CO2

Y. Fu et al. / Applied Geochemistry 27 (2012) 1266–1277

injection for CO2 sequestration, will neither lead (1) to K-feldspar dissolution below the oil water contact in the Miller oilfield, nor (2) to concurrent pH-buffering, or (3) to calcite or dolomite precipitation. The formation water in the Miller field is characterised by high Ba and Sr concentrations. Both elements are known to be commonly incorporated in silicate structures, such as feldspars (especially for K-feldspars), or substitute for Ca in plagioclases and calcite (Puchelt, 1978; Stueber, 1978). Release of Ba and Sr, owing to dissolution of K-feldspar or of calcite, can result in high concentrations in formation water and lead to scaling by precipitation of Ba- and Sr-bearing sulfate minerals. Anorthite provides a higher CO2-buffering capacity compared to K-feldspar (van Berk et al., 2009) and consequently could be completely dissolved prior to K-feldspar in the Miller field. This may explain the fact that plagioclase has not been detected in the Miller field’s reservoir rock filled by formation water. Overall, high Ba and Sr concentrations might suggest strong dissolution of K-feldspar and calcite, or even plagioclase. 5.2. Limitations of modelling The calculations of the most probable scenario RM_pCO2 = 3_T = 393_W ignore the effect of total pressure (differing from 0.1 MPa) on equilibrium constants. The results of scenario RM_pCO2 = 3_T = 393_S show that a reproduction of the measured concentrations is not possible with solubility constants calculated by SUPCRT at reservoir conditions (for detailed results see Fig. S9 in the Supplementary material). Witherite formation occurs and controlls the modelled Ba concentration when the SUPCTR’s thermodynamic database DPRONS92.dat (Johnson et al., 1992) is applied. Precipitation of witherite in a hydrogeochemical model has broad implications, as it directly affects the concentration of the other components that are involved in the complex web of interrelated reactions. The equilibrium solubility constants of witherite calculated by SUPCTR92 and DPRONS92.dat are log K(298 K/0.1 MPa) = 13.325 and log K(393 K/50 MPa) = 12.271, respectively (Table A.2 in the Supplementary material). In contrast, the Wateq4f.dat database provided by Parkhurst and Appelo (1999) considers a log K(298 K/0.1 MPa) = 8.562 (Table 1), which represents a significantly higher solubility compared to log K(298 K/0.1 MPa) = 13.325 (SUPCTR92 and DPRONS92.dat). Millero et al. (1984) presented a solubility constant for witherite of log K(298 K/0.1 MPa) = 8.56 (±0.04; at infinite dilution), which is in good agreement with the Wateq4f’s log K. Moreover, Busenberg and Plummer (1986) calculated a nearly identical log K(298 K/0.1 MPa) = 8.5617. The calculation of log K for elevated temperature and pressure conditions via SUPCRT and DPRONS92.dat is based on the log K at 298 K and 0.1 MPa. In summary, it seems reasonable that the failure to reproduce the measured data by modelling the effect of elevated pressure conditions in scenario RM_pCO2 = 3_T = 393_S is caused by SUPCRT’s incorrect solubility constant for witherite. Subsequently, this incorrect solubility constant also significantly affects the calculated concentration of other components involved within the complex web of inter-related reactions. The following two examples may illustrate the influence of elevated pressure on solubility constants of minerals involved in the model. Blount (1977) published experimental determinations of barite solubility in 0.2 molal NaCl solutions at 50 MPa and in a temperature field ranging from 373 K to 523 K, which display good agreement with the data calculated by García (2005). Accordingly, ca. 1.1  104 mol kgw1 of barite are dissolved in 0.2 molal NaCl at 393 K and 50 MPa (Miller field’s reservoir conditions). The equilibrium calculations are based on the PHREEQC code and the Wateq4f.dat database, and reveal that 8.2  105 mol kgw1 of barite are dissolved in 0.2 molal NaCl to achieve solubility equilibrium

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at 393 K and 0.1 MPa. A difference of ca. 2.8  105 mol kgw1 BaSO4 (equivalent to ca. 3.8 mg L1 ctotBa2+) results by ignoring the effect of pressure on barite solubility. Azaroual et al. (1997) calculated aqueous silica activities at equilibrium with quartz at 373 K and 5 MPa and 50 MPa, respectively. The difference in aqueous silica activities to be at equilibrium with quartz at 50 MPa and at 5 MPa is merely ca. 10% of the equilibrium activity at 50 MPa, which is the range of tolerable analytical inaccuracy. In addition, Table A.2 in the Supplementary material has solubility constants for the mineral phases involved in the model, which are calculated by using the SUPCRT92 code and its DPRONS92.dat database. This compilation allows a comparison of log K values, which are calculated for the same pressure (50 MPa), but for different temperatures (393 K and 298 K). Moreover, log K values have been calculated for the same temperature (298 K), but for a different total pressure (0.1 and 50 MPa, respectively). This complex data set (e.g., for barite) eveals that the effect of a temperature difference of 95 K on the solubility constant (K(50MPa/393 K) minus K(50MPa/298 K) = 3.3  1010 mol2 l2) is more pronounced than the effect of a difference in total pressure of 49.9 MPa (K(50 MPa/298 K) minus K(0.1 MPa/298 10 mol2 l2). Similarly to barite, the effect of the same K) = 1.8  10 temperature difference on anhydrite’s solubility constant (K(50 MPa/ 4 mol2 l2) tops the pressure 298 K) minus K(50 MPa/393 K) = 1.3  10 effect (K(50 MPa/298 K) minus K(0.1 MPa/298 K) = 0.8  104 mol2 l2), and applies to all other minerals within the model presented (Table A.2 in the Supplementary material). Many (isocoulombic) homogenous actions are often found to be insensitive to pressure changes at constant temperature (ca. <250 °C; Wesolowski et al., 2004). Thus, a pressure effect on aqueous species distribution is neglected in this study, although proven for equilibrium constants of association and dissociation equilibrium reactions of aqueous species. The modelling approach presented includes the assumption that the activity of each pure end-member component of the Sr– Barite solid solution phase is equal to its mole fraction in the solid solution (ideal behaviour). The degree of non-ideality in a solid solution sulfate phase that contains barite and celestite may be considered as low, due to very similar crystal lattice structures (Becker et al., 2000). In other words, it is assumed that the mixing enthalpies and entropies of solid-solution Sr–Barite formation are insignificant with regard to its composition. The effect of non-ideality on the calculated equilibrium composition of Sr–Barite, however, is undefined in the model. The results of the most probable modelling scenario RM_pCO2 = 3_T = 393_W show reasonable accordance between modelled and measured concentration trends in eight inter-related dissolved components (chloride, Na, Li, Ba, Sr, sulphate, Ca and dissolved silica). The trend and the absolute level of modelled ctotMg2+ in all of the scenarios, however, are not in good agreement with the measured concentrations (Figs. 2 and 3 and Figs. S1, S3 S5, S7, S9 and S11 in the Supplementary material). This mismatch suggests (1) that dolomite formation cannot be correctly calculated with the thermodynamic databases chosen in the study, or (2) that other unidentified Mg minerals control ctotMg2+ in the produced water. The PHREEQC computer code and its Wateq4f.dat database apply activity coefficients that are calculated according to the Davies equation or to the extended or WATEQ Debye–Hückel equation. If the WATEQ Debye–Hückel equation is used, calculated activity coefficients may be reliable at ionic strengths exceeding 0.7 mol kgw1 for Na+ and Cldominated solutions (Parkhurst and Appelo, 1999), for example the produced water from the Miller field. But this approach is invalid for species whose mean salt activity-coefficients are undefined in the Wateq4f.dat database, such as Ba2+ (for more details see Parkhurst and Appelo, 1999). The Pitzer.dat database (Parkhurst and Appelo, 1999) was chosen to test the effects of high ionic strength on modelled chemical composition

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of the produced water. This database was used to calculate two of the modelling scenarios RM_pCO2 = 3_T = 393_W and RM_pCO2 = 3_T = 393_W_Gy (Appendix in the Supplementary material). The modelling results calculated by the Pitzer.dat and by the Wateq4f. dat database, respectively, indicate that the Wateq4f.dat database enables a better accordance with the measured data. The basic assumption of the presented study is that the measured chemical composition of the produced water represents the original reservoir conditions (393 K and ca. 50 MPa) and is unaffected by sampling. Artificial effects (e.g., CO2 outgassing) may have influenced the chemical composition of the produced water, but these effects are difficult to quantify.

6. Conclusions and implications It is reasonable to attribute accordance between the modelled (most probable modelling scenario RM_pCO2 = 3_T = 393_W) and measured concentration trends of five inter-related dissolved components (Ba, Sr, sulphate, Ca, and dissolved silica), even allowing for several modelling limitations (Section 5.2). This scenario includes specific reactions between Sr–Barite, anhydrite, dolomite, calcite, microcrystalline quartz, CO2(g), and formation water–seawater mixtures, which achieve near-equilibrium conditions. Consequently, the model reasonably enables us (1) quantitatively assessing the chemical composition of the produced water, (2) identifying the types of minerals that are dissolved or precipitated, and (3) roughly estimating the quantities of these minerals at defined seawater fractions. The type and the amount of minerals dissolved or precipitated as well as the net change in the total volume of minerals involved depend on the seawater fraction. At low seawater fractions Sr–Barite, an almost pure BaSO4, is most intensively precipitated (results from the most probable scenario). If the seawater fraction is higher than 20%, the amount of Sr–Barite decreases with the increasing seawater fraction. Simultaneously, the Sr content of Sr–Barite increases. At high seawater fractions (>70%), CaSO4 dominates the sulfate mineral assemblages, and co-exists with newly formed dolomite. Microquartz and calcite are dissolved at all seawater fractions. Correspondingly, different seawater fractions cause pore volume enhancement or pore volume reduction at equilibrium. Reservoir porosity increases at levels between 40% and 80% admixed seawater, whereas porosity is reduced at lower and higher seawater fractions. The modelling results indicate that the simulated hydrogeochemical processes, including scale formation, almost reach equilibrium at reservoir conditions in the siliciclastic reservoir, the Miller field. Therefore, the model can be applied for oilfields where the injected seawater will maintain the reservoir pressure and where formation waters vary in their chemical composition, e.g. in their concentrations of Ba2+, Sr2+, Ca2+ and CO2 3 . Moreover, this model can also be applied for carbonate oil reservoirs like Ghawar, where CaCO3 was the most common scale encountered with small amounts of Ca/Sr sulfates (Raju and Nasr-El-Din, 2004). Additionally, sulfide scaling problems are known in oil reservoirs like the Elgin/Franklin field (Dyer et al., 2006) and in a carbonate reservoir in Saudi Arabia (Nasr-El-Din et al., 2001). Such scaling results from sulphate reduction in produced water or by generation of H2S(g) from reservoirs, and can also be modelled by means of addition of reducing agents or H2S(g) in the model. The modelling results suggest that K-feldspar is excluded from equilibration with the formation water–seawater mixtures. Consequently, added CO2 will not be sequestered as carbonate by pH buffering resulting from K-feldspar dissolution due to the lack of reactive K-feldspar.

Oilfield scaling is not the only issue of interest in the context of waterflooding. Recent research is focused on the technology of low salinity waterflooding to enhance oil recovery (Gamage and Thyne, 2011 and references therein). Low salinity waterflooding can shift reservoir wettability from weakly towards water wet. This results from dissolution of anhydrite and associated release of dolomite crystals and of other fine-grained material from pore surfaces (Pu et al., 2010). In this context, the model can be applied to predict whether processes improving oil recovery (e.g., anhydrite dissolution) can occur during low salinity waterflooding. Moreover, attachment of organic ligands on clay mineral surfaces can also change reservoir wettability and correspondingly enhance oil recovery owing to low salinity waterflooding (Lager et al., 2008). Such phenomena can be modelled by PHREEQC, if the PHREEQC’s database could be extended by quantitative, experimental data for the multi-component exchange of organic ligands on clay mineral surfaces. In summary, hydrogeochemical modelling of equilibrium and irreversible reactions is a reasonable tool to quantify the effects of chemical incompatibilities between original formation water and injected water. The target-oriented application of hydrogeochemical models can help to prevent pore plugging, scaling and wellbore damage. Beyond that the application offers pre-injection solutions such as the definition of the optimal type of injection water (e.g., seawater, produced water, formation water from a different reservoir formation, low salinity water) or a hydrogeochemical evaluation for an effective scale treatment. A deeper hydrogeochemical understanding is a basic prerequisite for application and interpretation as the simultaneous multi-component interactions in a reservoir are complex. Such hydrogeochemical batch models (e.g., the presented modelling scenario RM_pCO2 = 3_T = 393_W) provide first insights into possible effects on the porosity–permeability properties of reservoir rocks due to dissolution of primary mineral phases or precipitation of secondary phases. The presented reproduction of the observed compositional trends in formation water–seawater mixtures thus offers a possibility of developing predictive tools for better reservoir management of oilfields using water injection. Any interpretation, evaluation and/or application of the modelling results should take into account that the model merely consists of simple batch-mixing reactors, because geohydraulic data of water flow in the Miller field (e.g., apparent flow velocity, dispersivity, etc.) are unavailable. Consequently, effects on reservoir properties evolving in time and space, which are triggered by the flow of injected seawater, are not considered in this study. Flow of seawater or of formation water–seawater mixtures through the aquifer leads to a multiple exchange of pore water in the observed course of time. Consequently, a dramatically increased influence of pore plugging by precipitated minerals or the generation of secondary porosity, which are not considered by the simple batch modelling, could be triggered by multiple pore water exchange. Therefore, a coupling of a 3-dimensional flow model with the hydrogeochemical equilibrium model would improve predictions of the temporal and spatial consequences of interconnected flow and reaction processes, such as changes in the permeability and porosity properties of reservoirs.

Acknowledgements We thank the reviewers Dr. Stephanie Houston and Dr. María José Gimeno, and the Associate Editor Dr. Adrian Bath for their comments that helped to substantially improve the manuscript. We are also grateful to Prof. Ron Fuge for his helpful and constructive comments.

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