Background
=========
During the injection of carbon dioxide (CO2), the fluid density within the injection pipe could vary significantly along the well in response to pressure and temperature variations, thus affecting the CO2 injection rate at the reservoir depth. Among other reasons, understanding the behavior of CO2 flow through injection and monitoring wells is crucial because: (i) CO2 flow through the injection wells is the linking step between transport and storage (Nimtz et al., 2010); (ii) the adopted injection strategy may affect significantly the energy consumption and efficiency of CO2 geological storage (Vilarrasa et al., 2013); (iii) design and control of the operation both at pilot and industrial scale. Flow of CO2 in non-isothermal wells involves solving the partial differential equations (PDE) that express energy, mass and momentum conservation. These PDEs are coupled through equations of state (EOS) governing fluid and thermodynamic properties (Lu and Connell, 2014; Silva, 2015).

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/CO_2_injection_1_54cf598d21.png" alt=""/>
 <figcaption>Figure 1. Injection conditions of CO2 at the wellhead may play a major role on the flow behavior through the wellbore. The density and the injection rate reached at the bottomhole are key factors affecting the performance and efficiency of CO2 geological storage.</figcaption>
</figure>


Modeling CO2 injection
===========================
A one-dimensional (1D) model for non-isothermal single-phase flow of CO2 through injection wells was developed in Comsol Multiphysics and applied to evaluate different injection modes and hypothetical CO2 injection scenarios (Silva, 2015). The implementation methodology follows the approach of Lu and Connell (2014), in which the flow equations are based on the averaged-flow model (Hasan and Kabir, 2002). This model can be used for the assessment of several injection modes by comparing different operating conditions at the wellhead, which can represent hypothetical scenarios of CO2 pre-conditioning at surface.

Energy consumption
===============
The energy consumption due to surface conditioning operations varies for each injection mode and can be roughly estimated by the difference of specific enthalpy between wellhead and storage vessel conditions (Vilarrasa et al., 2013). The table below shows the energy consumption for seven CO2 injection conditions at the wellhead: gas, gas and liquid near the critical point (CP), supercritical (SC) (8 and 10 MPa), liquid at high p and T, liquid at low p and T (storage vessel at 2.0 MPa and -20 ºC; injection flowrate of 1.0 kg/s). As suggested by the CO2 phase diagram, the compression work is higher when injecting CO2 in gas-phase, near critical and SC conditions at the wellhead. On the contrary, injecting CO2 in liquid-phase reduces substantially the energy consumption because pumping/compression is easier and heating is minor.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/CO_2_injection_2_23431ce081.png" alt=""/>
 <figcaption>Figure 2. CO2 phase diagram. Traditionally, pipeline transportation is done in liquid phase and geological storage stays in supercritical conditions. The color dots and numbers represent 7 injection conditions at the wellhead, each with an associated compression work (see the table) (VC stands for vessel conditions).</figcaption>
</figure>

Flow behavior through the well
========================
As petroleum and geothermal engineers well know, the injection/extraction conditions at the wellhead can have a significant impact on the flow behaviour through the wellbore. The same occurs during the CO2 geological storage. The figure below shows the temperature, pressure, velocity and density profiles obtained in steady state for each injection mode. Injecting gaseous CO2 causes very low densities through the wellbore. CO2 injection in gaseous near the CP and SC (8 MPa) conditions increase density but at the bottom this is still lower than 600 kg/m3. By contrast, injecting liquid near the CP and SC (10 MPa) conditions lead to higher bottomhole densities, comparable to those reached by injecting liquid CO2. Higher CO2 densities are advantageous because are closer to the density of the resident brine, which reduce buoyancy effects in the reservoir and the potential risks of caprock failure and subsequent CO2 leakages.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/CO_2_injection_3_9f6625bc95.png" alt=""/>
 <figcaption>Figure 3. Comparison of different injection modes (Table 1): temperature (a), pressure (b), velocity (c), and density (d) profiles in steady state.</figcaption>
</figure>

Note that the fluid within the injection pipe tends to equilibrate with the geothermal gradient. Transient simulations reveal that steady state is reached faster by injecting at higher pressures. In particular, steady state flow conditions are obtained after 1 hour when injecting SC CO2 at the wellhead. By contrast, operational equilibrium is reached only after 100 days by injecting gaseous or liquid CO2 at low pressure (see the video below).

<figure className="image">
<StrapiVideo width="725" height="395" src="/uploads/CO_2_Transient_Continuous_Injection_4_d8bd68f492.mp4" type="video/mp4"/>
 <figcaption>Evolution of the temperature (top left), pressure (top right), velocity (bottom left) and density (bottom right) profiles through the wellbore. Steady state is reached after 1 hour and 100 days, when CO2 is injected SC (blue line, 40 ºC and 10 MPa) and liquid (red line, -10 ºC and 5 MPa), respectively.</figcaption>
</figure>


Fluctuating injection regime
=====================
Injecting CO2 at variable flowrate can help to increase considerably the density of CO2 at the bottomhole. A fluctuating injection regime was defined by a piecewise function in Comsol (see the figure below), such that the total mass of injected CO2 during 100 days is equal to the mass injected at a constant rate of 1.0 kg/s in the same period (8640 ton of CO2).

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/CO_2_injection_5_c998b1ad3c.png" alt=""/>
 <figcaption>Figure 4. Fluctuating CO2 injection regime.</figcaption>
</figure>

The video below shows that an average density increase of about 18% is obtained at the bottomhole, despite there are periods in which CO2 heating due to the friction within the injection pipe can induce a notorious density reduction. Nevertheless, it has been demonstrated that a fluctuating injection regime can enhance CO2 dissolution into the resident brine of the storage aquifer (Hidalgo and Carrera, 2009). Therefore, the present simulation shows that this injection mode has the double advantage of reducing the pressure within the reservoir and improving the efficiency of CO2 storage.

<figure className="image">
<StrapiVideo width="725" height="395" src="/uploads/CO_2_Continuous_Vs_Fluctuating_Injection6_587ec412f2.mp4" type="video/mp4"/>
 <figcaption>Continuous (blue line) versus fluctuating (red line) CO2 injection. Evolution of the temperature (top left), pressure (top right), velocity (bottom left) and density (bottom left) profiles through the wellbore (CO2 is injected SC at 40 ºC and 8 MPa).</figcaption>
</figure>

Pressure-controlled injection
======================
Pressure-controlled injection may be more realistic operating conditions. Still, it provides a way for coupling models of CO2 flow through the well and multiphase flow and transport of CO2 through the geological formations (reservoir and caprock). Nevertheless, pressure-controlled injection causes variable mass injection flowrates, which can reduce substantially the storage efficiency. A comparison between the steady state temperature, pressure, velocity and density profiles obtained under flowrate-controlled injection and pressure-controlled injection with a constant reservoir pressure of 10 MPa is presented in the figure below. Due to the lower heating (a) and the higher pressures (b) developed through the injection string, the CO2 density increases significantly under pressure-controlled injection (d). However, the higher density is compensated by a reduction of the injected mass of CO2. The velocities decrease in more than one order of magnitude (c), which results in a total injected mass of CO2 of about 1322 ton in 100 days.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/CO_2_injection_7_a3fb90eebc.png" alt=""/>
 <figcaption>Figure 5. Flowrate-controlled versus pressure-controlled injection: temperature (a), pressure (b), velocity (c), and density (d) profiles in steady state. CO2 is injected SC at 40 ºC and 8 MPa.</figcaption>
</figure>

The situation can be even worse when considering the effect of a dynamic reservoir pressure. The increase of the reservoir pressure due to the evolution of a CO2–rich phase within the storage formation reduces the injection rate. However, the CO2 densities through the injection well are substantially increased, as a consequence of the stronger cooling of the well. This is due to the lower velocities that allow CO2 to exchange heat with the surrounding for longer times.

Conclusions
==========
Wellhead conditions of CO2 below the critical point cause low fluid densities through the injection pipe. Conversely, injecting liquid CO2 or CO2 at high pressure helps to increase the density at the bottomhole, which has added benefits for the efficiency and security of the geological storage. Moreover, steady state is reached faster by injecting at high pressures. Higher densities at the bottomhole can also be achieved by a fluctuating injection regime, which also has the advantage of enhancing the CO2 storage efficiency. Pressure-controlled injection may induce high densities as well, although at a reduced injected mass of CO2. It is concluded that CO2 injection conditions should be tuned considering a balance between optimal storage densities and the stability of the operation.

Acknowledgements
==============
The support received from the MINECO (Torres Quevedo Programme) and the European Social Fund is very much acknowledged.

References
==========
*Hasan, A.R. and Kabir, C.S.*, 2002. **Fluid flow and heat transfer in wellbores. **SPE Richardson, TX, USA.

*Hidalgo, J. and Carrera, J.* 2009.** Effect of dispersion on the onset of convection during CO2 sequestration, **Journal of Fluid Mechanics, 640, 441-452.

*Lu, M. and Connell, L.D.,* 2014. **The transient behaviour of CO2 flow with phase transition in injection wells during geological storage,** Journal of Petroleum Science and Engineering, 124, 7-18.

*Nimtz, M., Klatt, M., Wiese, B., Kühn, M. and Krautz, H.J., *2010. **Modelling of the CO2 process- and transport chain in CCS systems-Examination of transport and storage processes, **Chemie der Erde, 70, 185-192.

*Silva, O.,* 2015. **Non-isothermal flow of CO2 in injection wells: evaluation of different injection modes.** Comsol Conference 2015, Grenoble, https://www.comsol.it/2015-user-presentations/geophysics-and-geomechanics

*Vilarrasa, V., Silva, O., Carrera, J. and Olivella, S., *2013. **Liquid CO2 injection for geological storage in deep saline aquifers,** International Journal of Greenhouse Gas Control, 14, 84-96.

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Injection conditions of CO2 at the wellhead may play a major role on the flow behavior through the wellbore. 

Non-isothermal flow of CO2 in injection wells: evaluation of different injection modes

Background
=============
Accidental oil spills in aquatic environments are a recurring problem in the oil and gas industry and have severe ecological, social and economic consequences.

There are several oil spill clean-up techniques, such as skimming, in-situ burning, biodegradation, hydrophobic meshes, etc. Hydrophobic meshes are generally made of stainless steel and coated with a hydrophobic and oleophilic material. They act as a filter: the oil passes through the mesh, while water is retained outside.

Hydrophobic meshes are still at an early development stage but offer many advantages: they are clean, can be operated continuously, require low energy input, present good recovery capacities and recover pure oil, which allows to recycle the spilled oil. The only disadvantage is the operation depth: when a hydrophobic mesh is submerged below its breakthrough pressure depth, water will intrude and contaminate the recovered oil.

 
Conceptual Model
=============
The model presented here conceptualizes a hydrophobic mesh as a porous medium. The model is based on the black oil model, which is extensively used for oil reservoir simulations, and solves multi-phase flow in porous media. In this case there are two phases: water and oil (air was not included in the model).

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/multiphse_flow_hydrophobic_mesh_02_6776f441dd.png" alt=""/>
 <figcaption>Conceptual model of a hydrophobic mesh. At the left boundary there is an oil-water mixture at hydrostatic pressure, and at the right boundary oil at atmospheric pressure.</figcaption>
</figure>

The governing equations consist on a system of two partial differential equations, one for each phase.

Oil Mass Balance:

$$
\phi \frac{\partial S_o}{\partial P_c}\frac{\partial P_c}{\partial t} + \nabla \cdot \left(\lambda_o \mathbf{k} \left(\nabla P_c - \nabla P_w \right) \right) = 0
$$

Water Mass Balance:

$$
-\phi \frac{\partial S_o}{\partial P_c}\frac{\partial P_c}{\partial t} - \nabla \cdot \left(\lambda_w \mathbf{k} \left(\nabla P_w \right) \right) = 0
$$

The system of equations is solved for the water pressure, Pw, and the capillary pressure, Pc. is the porosity of the mesh, So the oil saturation, k the permeability of the mesh and λw and λo refer to water and oil phase mobilities, respectively. The porosity and permeability depend on the dimensions of the mesh, which are the coated wire radius and pore radius. The phase mobilities depend on fluid properties and retention properties of the mesh.

Implementation in Comsol
====================
The model was implemented in Comsol Multiphysics using a 1D geometry and the coefficient form PDE interface.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/multiphse_flow_hydrophobic_mesh_03_7bdfa2c4b5.png" alt=""/>
 <figcaption>Implementation of the hydrophobic mesh model with the coefficient form PDE interface</figcaption>
</figure>

The water and capillary pressures were defined at the boundaries with Dirichlet boundary conditions. The initial condition in the mesh is full oil saturation.

In the Figure below, one can see the typical behavior of a hydrophobic mesh. At low depths there is only oil flowing through the mesh, with higher fluxes at higher depths, until the breakthrough pressure is reached at a depth of 0.7 m. Then the water flux increases, contaminating the recovered oil.


<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/multiphse_flow_hydrophobic_mesh_04_d0f2bc6737.png" alt=""/>
 <figcaption>Oil and water fluxes within a hydrophobic mesh as a function of mesh depth.</figcaption>
</figure>


App development with Comsol Application Builder
=======================================
Once the Comsol model was developed, the Comsol Application Builder feature was applied to create a practical and user-friendly tool tailored for mesh designers and/or operators.

The App allows the user to set the main parameters that define the system, such as mesh, oil and water properties, and retention function parameters.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/multiphse_flow_hydrophobic_mesh_05_322d2751a3.png" alt=""/>
 <figcaption>“Set Parameters” window of the Hydrophobic Mesh App.</figcaption>
</figure>


Once the parameters are introduced, analysis of the mesh can be facilitated through different studies e.g. breakthrough and pore analysis.

The “Breakthrough Analysis” window allows to determine the depth at which water breakthrough occurs. Oil and water fluxes, oil saturation and water fractional flow can be obtained following the definition of pore radius of the mesh and operational depth interval.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/multiphse_flow_hydrophobic_mesh_06_33d67319c2.png" alt=""/>
 <figcaption>“Breakthrough Analysis” window of the Hydrophobic Mesh App.</figcaption>
</figure>


The “Pore Analysis” window, on the other hand, can be used to determine an optimum mesh pore radius. Wider mesh pores enhance both water content and oil fluxes. Hence, the optimum mesh size must be chosen in such a way to maximize oil flux while maintaining a low water content. In this window one can compare both variables for a set of depths and pore radiuses.

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/multiphse_flow_hydrophobic_mesh_07_237e474eba.png" alt=""/>
 <figcaption>“Pore Analysis” window of the Hydrophobic Mesh App.</figcaption>
</figure>


Summary and Conclusions
========================
Hydrophobic meshes offer many advantages when it comes to oil spill clean-ups. This project shows that these meshes can be modelled as porous media with multiphase flow.

The model offers a good understanding of how these meshes work, and can be a useful tool for researchers, designers and users.

Acknowledgements
================
This project has been made possible thanks to the CRUE-CEPYME scholarship of Banco Santander. I would like to express my gratitude to Orlando Silva and Jorge Molinero for the help received during this project.

References
=========
[1] **COMSOL Multiphysics. COMSOL Multiphysics® Reference Guide Version 5.1; COMSOL AB**: 2015.

[2] **COMSOL Multiphysics. Introduction to Application Builder Version 5.0; COMSOL AB**: 2014.

[3] *Deng, D., Prendergast, D.P., MacFarlane, J., Bagatin, R., Stellacci, F., Gschwend, P.M.* (2013). **Hydrophobic Meshes for Oil Spill Recovery Devices**. Applied Materials and Interfaces 5 pp. 774-781.

[4] *Diaz-Viera, M.A., Lopez-Falcon, D.A., Moctezuma-Berthier, A., Ortiz-Tapia, A. *(2008). **COMSOL implementation of a multiphase fluid flow model in porous media**. Proceedings of the COMSOL conference 2008 Boston.

[5] *Song, J., Huang, S., Lu, Y., Bu, X., Mates, J. E., Ghosh, A., ..., Megaridis, C. M.* (2014). **Self-Driven One-Step Oil Removal from Oil Spill on Water via Selective-Wettability Steel Mesh**. Applied Materials and Interfaces 6 pp. 19858-19865.

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Comsol model and app to simulate the operation of hydrophobic and oleophilic meshes. These meshes are a new and promising technique to remove oil spills from aquatic environments.

Multiphase flow in Hydrophobic Meshes: Comsol model and app

The challenge
===========
 

As part of the pre-injection assessment of a geological storage, it is essential to estimate the mass of CO2 to be immobilized under different trapping mechanisms, which are:

1. **Structural trapping** of free-phase CO2 in geological traps.
2. **Capillary trapping** of small bubbles of CO2 gas that are retained in the porous space by capillary forces.
3. Trapping by CO2 **dissolution** into the resident brine.

**Mineral trapping **by precipitation of carbonated minerals into the porous space.


<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/Co2_migration_saline_figure_1_45f24064c3.png" alt=""/>
 <figcaption>Evolution of the CO2 dissolved in liquid phase</figcaption>
</figure>


 
A Multiphysics approach
===========
 

This is a multiphysics and multiscale problem. For that reason, we opted for Comsol Multiphysics (www.comsol.com) to build up a multiphase transport model that considers miscibility between CO2 and the native brine. Structural, capillarity and dissolution process are taken into account.

 

Results
===========

The injected CO2 gas forms a bubble that moves upwards and accumulates under the anticline caprock. While the CO2 plume moves, small bubbles of CO2 gas are retained in the porous space by capillary forces at the tail of the CO2 plume. At the CO2 /brine interface, CO2 slowly dissolves into the resident brine. The CO2 -enriched brine is denser than the resident water and tends to sink leading to the formation of gravity fingers. The resulting convective flow facilitates a faster dissolution of CO2 bubble. With the numerical model we can assess the storage capacity of the anticline/syncline system by quantifying the mass of CO2 captured for the different mechanisms and its temporal evolution.

 

<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/Co2_migration_saline_figure_2_4a283f2e3c.png" alt=""/>
 <figcaption>Temporal evolution of the computed contribution (%) of the three considered trapping mechanisms</figcaption>
</figure>


 

Just changing the location of the injection well affects the contribution of the different trapping mechanisms. For example, in Figure 3, we see how the free-phase CO2 diminishes faster for a well located at the syncline (well C). In that case, the longer CO2 footprint results in a more efficient capillary and dissolution trapping increasing the storage security.

 
<figure className="image">
 <StrapiImage className="mx-auto" src="/uploads/Co2_migration_saline_figure_3_f714b6f73b.png" alt=""/>
 <figcaption>Temporal evolution of the free-phase CO2 for three different well locations: Well A located at the anticline axis, Well B located between the anticline and the syncline and Well C located at the right syncline flank. </figcaption>
</figure>

 

Acknowledgements
===========
This work has been funded by the 7FP EC project CarbFix and has been conducted at Amphos 21 in collaboration with Albert Nardi and Fidel Grandia. Their contributions are gratefully acknowledged.

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In this post, we blog about the capture and storage of CO2 in deep geological formations,  one of the proposed solutions to reduce CO2 emissions to the atmosphere

Multiphase-flow

Non-isothermal flow of CO2 in injection wells: evaluation of different injection modes

Multiphase flow in Hydrophobic Meshes: Comsol model and app

Modeling CO2 migration in a saline aquifer