# Barite Scale Formation and Injectivity Loss Models for Geothermal Systems

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Geochemistry

#### 2.1.1. Fluid Chemistry

#### 2.1.2. Equilibrium Models and Barite Scaling Potential

#### 2.1.3. Crystal Growth Kinetics

#### 2.2. Flow

#### 2.2.1. Reservoir Hydraulics

#### 2.2.2. Reactive Transport Modelling

## 3. Results

#### 3.1. Equilibrium Models

#### 3.2. Reactive Transport Models

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

Abbreviation | Description | Unit |

${c}_{i}$ | Concentration | $\mathrm{M}$ |

${c}_{i,\mathrm{eq}}$ | Concentration in equilibrium | $\mathrm{M}$ |

$\mathrm{Da}$ | Damköhler number | − |

${\gamma}_{i}$ | Activity coefficient | − |

i | Aqueous species or solid | − |

$\mathrm{IS}$ | Ionic strength | $\mathrm{M}$ |

j | Grid node | − |

J | Injectivity | ${\mathrm{m}}^{3}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}\phantom{\rule{0.166667em}{0ex}}{\mathrm{Pa}}^{-1}$ |

K | Rock permeability | ${\mathrm{m}}^{2}$ |

${K}_{0}$ | Initial rock permeability | ${\mathrm{m}}^{2}$ |

${k}_{\mathrm{p}}$ | Precipitation rate constant | $\mathrm{mol}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ |

${K}_{\mathrm{sp}}$ | Solubility constant | ${\mathrm{mol}}^{2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{kg}}^{-2}$ |

$\mathrm{LND}$ | Landau | − |

M | Aquifer thickness | $\mathrm{m}$ |

${m}_{\mathrm{Da}}$ | Da slope along the r-axis | ${\mathrm{m}}^{-1}$ |

${m}_{\mathrm{water}}$ | Water mass | $\mathrm{kg}$ |

${n}_{i}$ | Precipitation potential | $\mathrm{mol}$ |

$\mathrm{NG}$ | Neustadt-Glewe | − |

$\mathrm{NGB}$ | North German Basin | − |

P | Pressure | $\mathrm{Pa}$ |

$\varphi $ | Porosity | − |

${\varphi}_{0}$ | Initial porosity | − |

${\varphi}_{i}$ | Volume fraction | − |

Q | Flow rate | ${\mathrm{m}}^{3}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ |

r | Radial distance from well-centre | $\mathrm{m}$ |

R | Barite precipitation rate (surface area normalised) | $\mathrm{mol}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ |

${r}_{\mathrm{c}}$ | Characteristic length | $\mathrm{m}$ |

${r}_{\mathrm{e}}$ | Reach of pressure difference | $\mathrm{m}$ |

${r}_{\mathrm{w}}$ | Well radius | $\mathrm{m}$ |

${\rho}_{i}$ | Density of solid | $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-3}$ |

${\rho}_{\mathrm{s}}$ | Density of fluid | $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-3}$ |

s | Water column | $\mathrm{m}$ |

S | Specific inner rock surface | ${\mathrm{m}}^{2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-3}$ |

${S}_{i}$ | Reactive surface area | ${\mathrm{m}}^{2}$ |

$\mathrm{SF}$ | Scaling factor for reactive surface area | − |

${\mathrm{SR}}_{i}$ | Supersaturation ratio | − |

T | Temperature | ${}^{\circ}\mathrm{C}$ |

${T}_{\mathrm{inj}}$ | Injection temperature | ${}^{\circ}\mathrm{C}$ |

$\mathrm{TDS}$ | Total dissolved solids | $\mathrm{kg}$ |

$\mathrm{URG}$ | Upper Rhine Graben | − |

V | Flow constant (=Q / 2 $\pi $ M $\varphi $) | ${\mathrm{m}}^{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{s}-1$ |

${w}_{i}$ | Weight fraction | $\mathrm{kg}\phantom{\rule{0.166667em}{0ex}}{\mathrm{kg}}^{-1}$ |

${X}_{\mathrm{score}}$ | Scaling score | $\mathrm{mol}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-1}\phantom{\rule{0.166667em}{0ex}}{\mathrm{year}}^{-1}$ |

## Appendix A. Reactive Transport Simulations

#### Appendix A.1. Kinetic Rate Constant

**Table A1.**Rate constants for bulk precipitation of barite at varying conditions used for the linear regression. The parameters T and $\mathrm{IS}$ are the input factors. Comparing experimental and model rates yields ${R}_{\mathrm{adj}}^{2}=0.88$.

T | $\mathbf{IS}$ | ${log}_{10}{\mathit{k}}_{\mathbf{p},\mathbf{exp}}$${}^{\mathbf{a}}$ | ${log}_{10}{\mathit{k}}_{\mathbf{p},\mathbf{model}}$ |
---|---|---|---|

${}^{\circ}\mathrm{C}$ | $\mathrm{mol}\phantom{\rule{0.166667em}{0ex}}{\mathrm{kgw}}^{-1}\phantom{\rule{0.166667em}{0ex}}\mathrm{NaCl}$ | $\mathrm{mol}\phantom{\rule{0.166667em}{0ex}}{\mathrm{m}}^{-2}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ | |

25 | $0.0$ | $-8.46$ | $-8.21$ |

25 | $0.1$ | $-7.62$ | $-7.99$ |

25 | $1.0$ | $-7.60$ | $-7.51$ |

25 | $1.5$ | $-7.55$ | $-7.36$ |

60 | $0.1$ | $-7.22$ | $-7.09$ |

60 | $0.7$ | $-6.60$ | $-6.73$ |

60 | $1.0$ | $-6.54$ | $-6.62$ |

60 | $1.5$ | $-6.52$ | $-6.46$ |

25 | $1.0$ | $-7.40$ | $-7.51$ |

#### Appendix A.2. Governing Equations and Analytical Solution

**Figure A1.**(top) The decline of the flow velocity along the r-axis due to the diverging flow; and (bottom) the comparison of the analytical and numerical solutions for solving Equation (A7). The solid line and dots represents the analytical and numerical solution, respectively.

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**Figure 1.**(

**a**) Schematic diagram of a geothermal doublet, showing the core technical installations consisting of a production and an injection well, as well as a heat exchanger. Brine temperature (T) and pressure (P) change along the flow path. Scalings at the injection site clog the pores, which results in reduced injectivity. (

**b**) Fluid temperatures at respective depths for the test cases Neustadt-Glewe (NG), Landau (LND) as well as for the hypothetical sites in the North German Basin (NGB) and the Upper Rhine Graben (URG) (Table 1). The dashed line represents the average geothermal gradient for Germany [15].

**Figure 2.**Model predictions of barite solubility using phreeqc and the Pitzer database at ambient/vapour pressure (solid lines) and $50\phantom{\rule{0.166667em}{0ex}}\mathrm{MPa}$ (dashed lines) for various temperatures and $\mathrm{NaCl}$-contents. The markers represent experimental values from Blount [16] (circles) and Templeton [17] (crosses).

**Figure 4.**Dimensionless cases for the radial diverging flow scheme with Damköhler number (

**a**) ranging 0–1 (solid), 0–10 (dashed) and 0–100 (dash-dotted) along the normalised horizontal flow axis. (

**b**) Corresponding normalised steady-state solute concentration.

**Figure 5.**(

**a**) Barite saturation according to reducing temperature for the various geothermal cases. ${\mathrm{SR}}_{\mathrm{barite}}=1$ represents equilibrium with respect to barite. (

**b**) The associated precipitation potential in units of millimoles per produced cubic metre of formation fluid. At respective reservoir conditions, the values are zero since equilibrium is assumed to be the initial state. The solid lines assume system pressures ($1\phantom{\rule{0.166667em}{0ex}}\mathrm{MPa}$) and the dashed lines assume the respective reservoir pressures. The dotted vertical lines indicate the assumed injection temperature (${T}_{\mathrm{inj}}$).

**Figure 6.**Reactive transport simulation results for the NGB cases. (

**a**,

**c**,

**e**) Distribution of porosity change per year for steady-state. (

**b**,

**d**,

**f**) Resulting relative, effective permeability loss (Equation (14)) based on the porosity–permeability relationship (Equation (13)) over the course of ten years. The lines represent respective scenarios.

**Figure 7.**Reactive transport simulation results for the URG cases. (

**a**,

**c**,

**e**) Distribution of porosity change per year for steady-state. (

**b**,

**d**,

**f**) Resulting relative, effective permeability loss (Equation (14)) based on the porosity–permeability relationship (Equation (13)) over the course of ten years. The lines represent respective scenarios.

**Figure 8.**Effective permeability loss after ten years of injecting barite supersaturated fluids into the reservoir. T is the injection temperature, Q is the flow rate and R is the precipitation rate. Note that the connecting dashed lines are only plotted to help distinguish the cases from each other.

**Figure 9.**Scaling score plotted against injectivity loss per year as calculated from reactive transport simulations for the considered geothermal cases and different scenarios (Table 4). The dashed line is a linear regression without intercept. Using Equation (15) for ${X}_{\mathrm{score}}$, the slope is $2.89\xb7{10}^{-5}$ and ${R}^{2}=0.96$.

**Table 1.**Physicochemical parameters (upper part) and chemical composition (lower part) of the considered geothermal fluids. Measured chemical compositions are taken from given literature and converted from ($\mathrm{mg}/\mathrm{L}$) to ($\mathrm{M}$) using calculated solution densities. Reservoir chemical compositions have been calculated to achieve thermodynamic equilibrium with respect to quartz, barite, anhydrite, celesite and calcite at respective reservoir conditions, using the measured values as the basis. ${\mathrm{Cl}}^{-}$ has been additionally adjusted to achieve charge balance.

Parameter | Unit | NGBa ${}^{\mathbf{a}}$ | NGBb ${}^{\mathbf{a}}$ | NG ${}^{\mathbf{b},\mathbf{c}}$ | URGa ${}^{\mathbf{a}}$ | URGb ${}^{\mathbf{a}}$ | LND ${}^{\mathbf{d}}$ | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Measured | Reservoir | Measured | Reservoir | Measured | Reservoir | Measured | Reservoir | Measured | Reservoir | Measured | Reservoir | ||

T | ${}^{\circ}\mathrm{C}$ | 25 | 95 | 25 | 110 | 25 | 98 | 25 | 120 | 25 | 155 | 25 | 160 |

P${}^{\mathrm{e}}$ | $\mathrm{MPa}$ | 0.1 | 20 | 0.1 | 30 | 0.1 | 23 | 0.1 | 20 | 0.1 | 30 | 0.1 | 30 |

${\rho}_{\mathrm{s}}$${}^{\mathrm{f}}$ | $\frac{\mathrm{kg}}{{\mathrm{m}}^{3}}$ | 1130 | 1110 | 1190 | 1150 | 1150 | 1110 | 1050 | 1000 | 1080 | 1010 | 1070 | 996 |

$\mathrm{pH}$ | − | 5.60 | 5.33 | 6.00 | 4.91 | 5.20 | 5.64 | 5.80 | 5.66 | 5.50 | 5.28 | 5.15 | 5.41 |

$\mathrm{IS}$ | $\mathrm{M}$ | 4.05 | 4.00 | 6.21 | 6.11 | 4.50 | 4.48 | 1.37 | 1.32 | 2.29 | 2.31 | 2.05 | 2.01 |

${\mathrm{Ba}}^{2+}/{\mathrm{SO}}_{4}^{2-}$ | − | NA | 3.42 $\times {10}^{-3}$ | NA | 2.89 $\times {10}^{-2}$ | 8.33 $\times {10}^{-3}$ | 5.47 $\times {10}^{-3}$ | NA | 3.19 $\times {10}^{-3}$ | NA | 2.64 $\times {10}^{-2}$ | 6.38 $\times {10}^{-2}$ | 3.62 $\times {10}^{-2}$ |

${\mathrm{K}}^{+}$ | $\mathrm{M}$ | 2.06 $\times {10}^{-2}$ | 2.06 $\times {10}^{-2}$ | 2.87 $\times {10}^{-2}$ | 2.87 $\times {10}^{-2}$ | 2.24 $\times {10}^{-2}$ | 2.24 $\times {10}^{-2}$ | 7.88 $\times {10}^{-2}$ | 7.88 $\times {10}^{-2}$ | 1.33 $\times {10}^{-1}$ | 1.33 $\times {10}^{-1}$ | 1.06 $\times {10}^{-1}$ | 1.06 $\times {10}^{-1}$ |

${\mathrm{Na}}^{+}$ | 3.08 | 3.08 | 4.87 | 4.87 | 3.54 | 3.54 | 8.94 $\times {10}^{-1}$ | 8.94 $\times {10}^{-1}$ | 1.59 | 1.59 | 1.27 | 1.27 | |

${\mathrm{Ca}}^{2+}$ | 2.11 $\times {10}^{-1}$ | 2.15 $\times {10}^{-1}$ | 3.49 $\times {10}^{-1}$ | 3.47 $\times {10}^{-1}$ | 2.33 $\times {10}^{-1}$ | 2.37 $\times {10}^{-1}$ | 1.03 $\times {10}^{-1}$ | 1.04 $\times {10}^{-1}$ | 1.82 $\times {10}^{-1}$ | 1.77 $\times {10}^{-1}$ | 1.99 $\times {10}^{-1}$ | 1.96 $\times {10}^{-1}$ | |

${\mathrm{Mg}}^{2+}$ | 7.53 $\times {10}^{-2}$ | 7.53 $\times {10}^{-2}$ | 4.61 $\times {10}^{-2}$ | 4.61 $\times {10}^{-2}$ | 6.43 $\times {10}^{-2}$ | 6.43 $\times {10}^{-2}$ | 4.23 $\times {10}^{-3}$ | 4.23 $\times {10}^{-3}$ | 4.29 $\times {10}^{-3}$ | 4.29 $\times {10}^{-3}$ | 3.25 $\times {10}^{-3}$ | 3.25 $\times {10}^{-3}$ | |

${\mathrm{Sr}}^{2+}$ | 5.53 $\times {10}^{-3}$ | 3.38 $\times {10}^{-3}$ | 8.57 $\times {10}^{-3}$ | 5.70 $\times {10}^{-3}$ | 5.61 $\times {10}^{-3}$ | 3.80 $\times {10}^{-3}$ | 2.58 $\times {10}^{-3}$ | 2.70 $\times {10}^{-3}$ | 4.16 $\times {10}^{-3}$ | 8.83 $\times {10}^{-3}$ | 5.09 $\times {10}^{-3}$ | 1.06 $\times {10}^{-2}$ | |

${\mathrm{Ba}}^{2+}$ | NA | 2.71 $\times {10}^{-5}$ | NA | 1.30 $\times {10}^{-4}$ | 4.43 $\times {10}^{-5}$ | 3.77 $\times {10}^{-5}$ | NA | 1.89 $\times {10}^{-5}$ | NA | 9.53 $\times {10}^{-5}$ | 8.69 $\times {10}^{-5}$ | 1.10 $\times {10}^{-4}$ | |

${\mathrm{Fe}}^{2+/3+}$ | 1.73 $\times {10}^{-3}$ | 1.73 $\times {10}^{-3}$ | 2.61 $\times {10}^{-3}$ | 2.61 $\times {10}^{-3}$ | 1.26 $\times {10}^{-3}$ | 1.26 $\times {10}^{-3}$ | 1.84 $\times {10}^{-3}$ | 1.84 $\times {10}^{-3}$ | 3.73 $\times {10}^{-3}$ | 3.73 $\times {10}^{-3}$ | 4.03 $\times {10}^{-4}$ | 4.03 $\times {10}^{-4}$ | |

${\mathrm{Cl}}^{-}$ | 3.79 | 3.67 | 5.85 | 5.69 | 4.19 | 4.15 | 1.30 | 1.18 | 2.06 | 2.10 | 1.88 | 1.79 | |

${\mathrm{Br}}^{-}$ | 4.04 $\times {10}^{-3}$ | 4.04 $\times {10}^{-3}$ | 6.73 $\times {10}^{-3}$ | 6.73 $\times {10}^{-3}$ | 5.30 $\times {10}^{-3}$ | 5.30 $\times {10}^{-3}$ | 1.29 $\times {10}^{-3}$ | 1.29 $\times {10}^{-3}$ | 2.61 $\times {10}^{-3}$ | 2.61 $\times {10}^{-3}$ | 2.84 $\times {10}^{-3}$ | 2.84 $\times {10}^{-3}$ | |

${\mathrm{SO}}_{4}^{2-}$ | 5.04 $\times {10}^{-3}$ | 7.91 $\times {10}^{-3}$ | 7.58 $\times {10}^{-3}$ | 4.49 $\times {10}^{-3}$ | 5.31 $\times {10}^{-3}$ | 6.89 $\times {10}^{-3}$ | 3.74 $\times {10}^{-3}$ | 5.93 $\times {10}^{-3}$ | 3.26 $\times {10}^{-3}$ | 3.61 $\times {10}^{-3}$ | 1.36 $\times {10}^{-3}$ | 3.02 $\times {10}^{-3}$ | |

${\mathrm{HCO}}_{3}^{-}$ | 3.97 $\times {10}^{-3}$ | 3.61 $\times {10}^{-3}$ | 5.97 $\times {10}^{-3}$ | 4.10 $\times {10}^{-3}$ | 7.11 $\times {10}^{-4}$ | 8.32 $\times {10}^{-4}$ | 4.21 $\times {10}^{-3}$ | 4.04 $\times {10}^{-3}$ | 7.69 $\times {10}^{-3}$ | 7.42 $\times {10}^{-3}$ | 4.01 $\times {10}^{-3}$ | 4.14 $\times {10}^{-3}$ | |

${\mathrm{SiO}}_{2}$ | NA | 4.15 $\times {10}^{-4}$ | NA | 4.25 $\times {10}^{-4}$ | NA | 4.16 $\times {10}^{-4}$ | NA | 1.09 $\times {10}^{-3}$ | NA | 1.89 $\times {10}^{-3}$ | 2.75 $\times {10}^{-3}$ | 2.12 $\times {10}^{-3}$ |

**Table 2.**Hydraulic parameters of a potential hydrothermal reservoir taken from Franz et al. [52].

${\mathit{r}}_{\mathbf{w}}\phantom{\rule{0.166667em}{0ex}}\left(\mathbf{m}\right)$ | $\mathit{Q}\phantom{\rule{0.166667em}{0ex}}\left({\mathbf{m}}^{3}\phantom{\rule{0.166667em}{0ex}}{\mathbf{h}}^{-1}\right)$ | $\mathit{K}\left(\mathbf{mD}\right)$ | $\mathit{M}\left(\mathbf{m}\right)$ | $\mathit{\varphi}\phantom{\rule{0.166667em}{0ex}}(-)$ |
---|---|---|---|---|

0.22 | 100 | 500 | 20 | 0.2 |

**Table 3.**Varied parameters in the respective scenarios for a one-at-a-time sensitivity analysis. Decreasing Q and ${w}_{\mathrm{barite}}$ corresponds to decreasing flow velocity and precipitation rate, respectively.

Scenario | Parameter | Value | Unit |
---|---|---|---|

$T+10{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | T | 65 | ${}^{\circ}\mathrm{C}$ |

$T-10{\phantom{\rule{0.166667em}{0ex}}}^{\circ}\mathrm{C}$ | T | 45 | ${}^{\circ}\mathrm{C}$ |

$Q/2$ | Q | 50 | ${\mathrm{m}}^{3}\phantom{\rule{0.166667em}{0ex}}{\mathrm{h}}^{-1}$ |

$R/10$ | ${w}_{\mathrm{barite}}$ | 0.01 | − |

**Table 4.**Summary of results of the equilibrium calculations and the reactive transport simulations for all considered geothermal cases and scenarios. Further, the developed empirical scaling score ${X}_{\mathrm{score}}$ is shown (Equation (15)).

Scenario | ${\mathit{n}}_{\mathbf{barite}}$ | ${\mathit{m}}_{\mathbf{Da}}$ | Loss | ${\mathit{X}}_{\mathbf{score}}$ | |
---|---|---|---|---|---|

Case | $\left(\frac{\mathbf{mmol}}{{\mathbf{m}}^{3}}\right)$ | $\left(\frac{1}{\mathbf{m}}\right)$ | $\left(\frac{1}{\mathbf{year}}\right)$ | $\left({10}^{-4}\phantom{\rule{0.166667em}{0ex}}\frac{\mathbf{mol}}{\mathbf{m}\phantom{\rule{0.166667em}{0ex}}\mathbf{year}}\right)$ | |

NGBa | Base | 16 | 4.4 | 0.018 | 6.1 |

NGBa | $T+10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 16 | 5.6 | 0.018 | 7.9 |

NGBa | $T-10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 16 | 3.3 | 0.016 | 4.7 |

NGBa | $Q/2$ | 16 | 8.7 | 0.016 | 6.1 |

NGBa | $R/10$ | 16 | 0.43 | 0.0026 | 0.61 |

NGBb | Base | 87 | 2.8 | 0.064 | 22 |

NGBb | $T+10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 87 | 3.6 | 0.069 | 27 |

NGBb | $T-10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 87 | 2.1 | 0.056 | 16 |

NGBb | $Q/2$ | 87 | 5.6 | 0.06 | 22 |

NGBb | $R/10$ | 87 | 0.28 | 0.01 | 2.1 |

NG | Base | 23 | 4.1 | 0.024 | 8.3 |

NG | $T+10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 23 | 5.3 | 0.025 | 11 |

NG | $T-10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 23 | 3.2 | 0.022 | 6.4 |

NG | $Q/2$ | 23 | 8.2 | 0.022 | 8.3 |

NG | $R/10$ | 23 | 0.41 | 0.0036 | 0.83 |

URGa | Base | 12 | 1.6 | 0.0057 | 1.7 |

URGa | $T+10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 12 | 2.3 | 0.0066 | 2.4 |

URGa | $T-10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 12 | 1.2 | 0.0048 | 1.2 |

URGa | $Q/2$ | 12 | 3.3 | 0.0051 | 1.7 |

URGa | $R/10$ | 12 | 0.16 | 0.0008 | 0.17 |

URGb | Base | 74 | 1.1 | 0.024 | 6.9 |

URGb | $T+10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 74 | 1.4 | 0.029 | 9.2 |

URGb | $T-10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 74 | 0.79 | 0.02 | 5.1 |

URGb | $Q/2$ | 74 | 2.1 | 0.022 | 6.9 |

URGb | $R/10$ | 74 | 0.11 | 0.0034 | 0.69 |

LND | Base | 85 | 0.8 | 0.022 | 6 |

LND | $T+10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 85 | 1 | 0.026 | 7.8 |

LND | $T-10\phantom{\rule{0.166667em}{0ex}}{}^{\circ}C$ | 85 | 0.58 | 0.018 | 4.3 |

LND | $Q/2$ | 85 | 1.6 | 0.02 | 6 |

LND | $R/10$ | 85 | 0.08 | 0.003 | 0.6 |

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**MDPI and ACS Style**

Tranter, M.; De Lucia, M.; Wolfgramm, M.; Kühn, M.
Barite Scale Formation and Injectivity Loss Models for Geothermal Systems. *Water* **2020**, *12*, 3078.
https://doi.org/10.3390/w12113078

**AMA Style**

Tranter M, De Lucia M, Wolfgramm M, Kühn M.
Barite Scale Formation and Injectivity Loss Models for Geothermal Systems. *Water*. 2020; 12(11):3078.
https://doi.org/10.3390/w12113078

**Chicago/Turabian Style**

Tranter, Morgan, Marco De Lucia, Markus Wolfgramm, and Michael Kühn.
2020. "Barite Scale Formation and Injectivity Loss Models for Geothermal Systems" *Water* 12, no. 11: 3078.
https://doi.org/10.3390/w12113078