ECO2N

International Journal of Greenhouse Gas Control 9 (2012) 393–401

Contents lists available at SciVerse ScienceDirect

International Journal of Greenhouse Gas Control journal homepage: www.elsevier.com/locate/ijggc

Modeling brine leakage to shallow aquifer through an open wellbore using T2WELL/ECO2N Litang Hu a , Lehua Pan b , Keni Zhang a,b,∗ a College of Water Sciences, Engineering Research Center of Groundwater Pollution Control and Remediation of Ministry of Education, Beijing Normal University, Beijing 100875, PR China b Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA

a r t i c l e

i n f o

Article history: Received 13 October 2011 Received in revised form 3 May 2012 Accepted 3 May 2012 Available online 31 May 2012 Keywords: CO2 geological storage Brine leakage Excess pore pressure (EPP) T2WELL/ECO2N Equivalent Porous Media Wellbore flow Coupled wellbore–reservoir model

a b s t r a c t The efficiency and sustainability of CO2 storage in deep saline formations depends on the integrity of the overlying caprocks. Existing oil and gas wells, which penetrate the formations, are potential leakage pathways. In this paper, T2WELL/ECO2N, a coupled wellbore–reservoir flow simulator of carbon dioxide and brine, is employed to analyze the effects of salinity and excess pore pressure (EPP) on brine leakage from an injection reservoir to a shallow fresh aquifer. The effectiveness of the Equivalent Porous Media (EPM) approach, a widely used approximation of wellbore flow in wellbore–reservoir simulations, is also evaluated. A hypothetical model is built to create test cases with EPP of 0.1 MPa, 0.5 MPa and 1.5 MPa under low-, middle-, and high-salinity. The results show that a quasi-steady-state leakage rate will be quickly established if the EPP caused by CO2 injection is higher than the threshold EPP. However, the brine salinity has an important impact on the brine leakage rate including the threshold EPP below which no leakage occurs. The leakage rate decreases with the increase of the salinity whereas the threshold EPP increases with the increase of the salinity. For the same brine salinity, the quasi-steady-state leakage rate increases with the EPP nonlinearly. The leakage rate calculated by the EPM approach is very sensitive to the equivalent permeability of the wellbore, which however, is not an intrinsic parameter of a given wellbore–aquifer system. Although the EPM approach could reproduce the dynamic leakage rate reasonably well with a fitted permeability, it could over- or underestimates the leakage rate by orders in magnitude for the same system depending on whether the true leakage rate itself is smaller or larger than that of the fitting case due to changes in the salinity and/or the EPP through an abandoned well. The dependence of the equivalent permeability on the flow rate makes the EPM approach not to be a viable method for predicting wellbore leakage except for the cases with very small leakage rates. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction Carbon dioxide capture and geological storage (CGS) is a promising technology that will allow the continued use of fossil fuels for power generation and combustion in industrial processes well into this century without putting unmanageable anthropogenic carbon dioxide (CO2 ) into the atmosphere. By far it is believed that the greatest storage capacity is in saline aquifers (Dooley et al., 2004; Bachu, 2008). However, an industrial-scale CO2 injection could cause significant pressure perturbation over basin-scale regions with a dimension of hundreds of kilometers or more (Birkholzer and Zhou, 2009; Birkholzer et al., 2009). Large-scale pressure

∗ Corresponding author at: College of Water Sciences, Engineering Research Center of Groundwater Pollution Control and Remediation of Ministry of Education, Beijing Normal University, Beijing 100875, PR China. E-mail addresses: [email protected] (L. Hu), [email protected] (L. Pan), [email protected], [email protected] (K. Zhang). 1750-5836/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijggc.2012.05.010

changes may have environmental impacts on shallow groundwater resources (Bergman and Winter, 1995; Nicot, 2008; Yamamoto et al., 2009; Zheng et al., 2009; Zhou et al., 2010), especially in the area where there exist wells due to other previous activities. Wellbores are widely recognized as the main possible leakage pathway capable of conveying CO2 or brine to groundwater resources leading to potential groundwater contamination (e.g., Apps et al., 2010; Carey et al., 2007; Gasda et al., 2004; Pan et al., 2011a; Viswanathan et al., 2008). Among the leakage risks, leakage of brine to shallow potable groundwater aquifers through open wellbores is a more likely risk because the area of overpressure is usually much larger than the free phase plume and many wellbores may be only completely plugged near the land surface. In many analytical solutions (e.g., Nordbotten et al., 2004, 2005; Celia et al., 2011), it is assumed that fluid flow use Darcy’s law and brine leakage is independent of salinity variation along the leakage pathway. However, increased gravity force due to the invasion of heavier brine into the wellbore could effectively hinder the migration of brine upward (Nicot et al., 2008; Oldenburg and Rinaldi, 2011; Birkholzer et al., 2011). In some

394

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

Nomenclature A C0 f F g hˇ k krˇ m M n P Pˇ q q SG Sˇ t T ud uG uL um uˇ Uˇ Vn Xˇ z

the well cross sectional area, m2 the profile parameter (or distribution coefficient), dimensionless the Fanning friction coefficient, dimensionless the mass or energy transport terms along the borehole due to advective processes, W m−1 gravitational acceleration constant, m s−2 specific enthalpy in phase ˇ, J kg−1 absolute permeability, m2 relative permeability to phase ˇ the mixture the accumulation terms of the components and energy , kg m−3 normal vector on surface element, dimensionless pressure, Pa the fluid pressure in phase ˇ, Pa the wellbore heat loss/gain per unit length of wellbore, kg m−3 s−1 source/sink terms for mass or energy components, kg m−3 s−1 saturation of gas phase, dimensionless saturation of phase ˇ, dimensionless time, s temperature, ◦ C, K drift velocity, m s−1 gas phase velocity, m s−1 liquid phase velocity, m s−1 the mixture velocity (velocity of the mixture mass center), m s−1 the Darcy’s velocity in phase ˇ, m s−1 the internal energy of phase ˇ per unit mass, J kg−1 volume of the nth grid cell, m3 mass fraction of component  in fluid phase ˇ, dimensionless distance along-wellbore coordinate (can be vertical, inclined, or horizontal), m

Greek letters ˇ viscosity, kg m−1 s−1  porosity, dimensionless  the incline angle of the wellbore, dimensionless  thermal conductivity, W K−1 m−1 G the density of gas phase, kg m−3 L the density of liquid phase, kg m−3 ∗ is the profile-adjusted average density, kg m−3 m m the density of the gas–liquid mixture, kg m−3 ˇ the density of phase ˇ, kg m−3  the momentum term caused by slip between gas and liquid phases, kg s−2 m−1 the perimeter of the cross-section, m n area of closed surface, m2 Subscripts and superscripts  the index for the components,  = 1 (H2 O), 2 (salt), 3 (CO2 ), and 4 (energy). =G for gas; =L for liquid ˇ

cases, the heavy brine even stops its continuous migration, and the system reaches a new equilibrium. Nicot (2008) presented an analytical method for calculating the threshold pressure below which a new equilibrium will be established and no continuous leakage

would occur, based on a static evaluation of the weight of brine column in the well after full invasion of brine up to the bottom of the freshwater aquifer. Using the numerical simulator TOUGH2/EOS7C, Birkholzer et al. (2011) extended the analysis to include the dynamics of the brine leakage through a wellbore as affected by the brine salinity and the excess pore pressure (EPP, defined as pore pressure minus hydrostatic pore pressure, Stauffer and Bekins, 2001), as a result of the wellbore–reservoirs interactions. Oldenburg and Rinaldi (2011) characterized brine communication through the low-permeability caprock between targeted and shallow groundwater formations and illustrated both thermal regime and salinity could affect brine leakages, resulting in the oscillating behavior of brine. However, in the above numerical analyses, the wellbore, the key component in the system, was represented as an Equivalent Porous Media so that the flow through the wellbore was assumed to obey multi-phase version of Darcy’s law. Such approximation of flow dynamics could under- or over-estimate the behaviors of the wellbore–reservoirs system, especially for the cases with a larger leakage rate. In this paper, we use the recently developed coupled wellbore–reservoir simulator of CO2 –brine system, T2WELL/ECO2N (Pan et al., 2008, 2011b) to investigate how brine leakage responses excess pore pressure (EPP) and salinity variation through a wellbore that connects a deep saline aquifer to a shallow fresh aquifer as a result of injection of CO2 into the deep saline aquifer. The model represents a typical way for brine flowing upward through an abandoned well in response of aquifer pressurization due to CO2 sequestration. We also evaluate the effectiveness and the accuracy of the Equivalent Porous Media (EPM) approach for the wellbore leakage problem as compared to openhole flow. 2. Method 2.1. The simulators T2WELL/ECO2N (Pan et al., 2008, 2011b) is incorporated into TOUGH2/ECO2N (Pruess, 2005; Pruess and Spycher, 2007) to be applicable for wellbore flow coupled to reservoir flow. The model (T2WELL/ECO2N) uses an integrated wellbore–reservoir system of CO2 –brine in which the wellbore and reservoir are two different sub-domains where flow is controlled by a standard multiphase Darcy’s law in the reservoir, and a one-dimensional Drift-Flux Model (DFM) (Shi et al., 2005) with related conservation equations in the wellbore. The mass, momentum (in terms of phase velocity), and energy equations solved in T2WELL/ECO2N for two-phase condition and three components (water, NaCl, and CO2 ) are summarized in Table 1 (see Nomenclature for definitions of all symbols used). The codes were verified with analytical solutions and have been applied to analyze various leakage and injection problems (Pan et al., 2011a,b,c). Its capacity is deemed to be enough for this study. The mixture velocity, um , in wellbore is a solution of the momentum equation: ∂ 1 ∂ (m um ) + [A(m u2m + )] A ∂z ∂t =−

∂P fm |um | um − m g cos  − 2A ∂z

(1)

∗2 )[(C − 1)u + u ]2 where the term  = (SG /(1 − SG ))(G L m /m m 0 d is caused by slip between the two phases. It is noted that the formula for phase velocity in porous media (Table 1), Darcy’s law, can be seen as a special case of Eq. (1) that (1) the fluid velocity is so small that the acceleration components of the pressure drop (left hand side of the equation) can be ignored

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

395

Table 1 Equations solved in T2WELL/ECO2N. Description

Equation

Conservation of mass and energy

d dt

Mass accumulation

M =



Vn 

M  dVn =





 n

Sˇ ˇ Xˇ ,

F  · n d n +

 Vn

q dVn

 = 1, 2 and 3

ˇ

Mass flux

F =

Xˇ ˇ uˇ ,  = 1, 2 and 3

ˇ

Porous media Energy flux

F = −∇ T +

 hˇ ˇ uˇ ,  = 4 ˇ

Energy accumulation

M  = (1 − ϕ)R CR T + ϕ

 ˇ Sˇ Uˇ ,  = 4 ˇ

Phase velocity

k

uˇ = −k rˇ (∇ Pˇ − ˇ g) ˇ

Wellbore

∂ ∂z



F  = − ∂T − ∂z

Energy accumulation

M =

Phase velocity

L m ∗ um + ∗ ud m m (1 − SG C0 )m SG G uL = um − ud ∗ ∗ (1 − SG )m (1 − SG )m



1 A

 

Energy flux

ˇ

ˇ Sˇ Uˇ +

Aˇ Sˇ uˇ 1 2 u 2 ˇ



hˇ +

u2

ˇ

2

  −

(Sˇ ˇ uˇ g cos ) − q ,  = 4

ˇ

, =4

ˇ

uG = C0

as compared to the friction component (the 2nd term on the right hand side) and (2) the friction component is linearly proportional to the fluid velocity, if the porous media is considered as a bundle of capillary tubes conceptually (Bear, 1972). In many simulations of leakage through wellbores (Birkholzer et al., 2011), the Equivalent Porous Media (EPM) approach is used to simulate the flow in wellbore, and the wellbore is also represented as a porous medium but with a very high permeability and a porosity of 1. So the phase velocity can be calculated according to the same formula for porous media (the Darcy’s law) shown in Table 1, even though the flow status is far away from the above two conditions. T2WELL/ECO2N has an option to turn off the wellbore model so that the code will behave just like TOUGH2/ECO2N and the wellbore will be treated as an equivalent porous medium (i.e., the EPM approach).

model and van Genuchten function (Pruess et al., 1999) are used to calculate relative permeability and capillary pressure, respectively. To evaluate the impact of pressurization related to CO2 storage in the brine formation, the system is subjected to an instantaneous pressure change at the outer boundary (i.e., at R = 2000 m) of the storage reservoir and assumed to be constant over 10 days (Table 4). The instantaneous pressure change imposed at the boundary propagates to the well, causes a slightly delayed pressurization there, and starts pushing dense brine up the wellbore. The model is under non-isothermal conditions and the heat flow between the flowing wellbore and the surrounding formation (both sand and mudstone) as well as within the formations is simulated numerically since all formations are discretized along the entire length of the wellbore. Neither dissolved nor free phase CO2 exists in the system for simplicity.

2.2. Model setup A hypothetical two-aquifer and one wellbore system are established. The deep saline aquifer is classified into three layers for hypothetical studies. The shallow fresh water aquifer extends to about 700 m below ground surface (bgs). In this study, we will assume the deep saline aquifer as a single uniform layer from 2200 m to 2300 m bgs and the shallow fresh aquifer as a single uniform, unconfined aquifer, which are separated by a thick mudstone formation (1500 m). A hypothetical passive (existing, other than the injection well) wellbore with a diameter of 0.12 m goes through both aquifers (fully perforated) as well as the mudstone formation (perfectly cased). However, the wellbore is sealed at surface (wellhead) and well casing in contacting with the mudstone formation is assumed to allow only the heat exchange between wellbore and the surrounding mudstone (i.e., no mass flux there). A radially symmetric vertical mesh was developed with considerable grid refinement near the well (horizontal direction, nodal spacing from 0.12 m to 14 m) and near formation interfaces (vertical direction, nodal spacing from 1.0 m to 74 m) (see Fig. 1). The radius of the model domain is 2000 m. The system configurations and parameters used in the simulations are summarized in Tables 2 and 3. The model domain is initially in hydrostatic equilibrium with a linear distribution of temperature and salinity along the depth. Van Genuchten–Mualem

Fig. 1. Radial-symmetric model grid for dynamic simulations.

396

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

Table 2 Properties of simulation cases. Parameter

Unit

Value

Comment

All rock units Porosity Thermal conductivity Heat capacity Pore compressibility

– W/(m K) J/(kg K) Pa−1

0.3 2.51 1000 0

Pore compressibility is not considered in this simple model

Injection formation Permeability

m2

10−12

Isotropic

Mudstone formation Permeability

m2

10−18

Isotropic

Shallow aquifer Permeability

m2

10−12

Isotropic

Well properties Well radius Porosity Maximum C0 Roughness Thermal conductivity

m – – – W/(m K)

0.12 1.0 1.2 0.000046 2.51

For wellbore connection with adjacent formations

Table 3 Model initial and boundary conditions (base case). Boundary conditions Top of shallow aquifer

Bottom of injection formation Top and bottom of well Lateral boundary at R = 2000 m Initial conditions Temperature Salinity Pressure

Fluid density

Fixed pressure: P = atmospheric (unconfined aquifer) Fixed temperature: T = 8 ◦ C Fixed salinity: S = 0 mg/L Closed boundary for fluid and dissolved salt Fixed temperature: T = 77 ◦ C Closed boundary for fluid, mass, and heat (i.e., wellbore is assumed to be plugged at the land surface) Fixed pressure, temperature, and salinity (in freshwater aquifer and the mudstone formation, equal to initial condition; in the injection formation, equal to the prescribed conditions for each case) Thermally stratified system with geothermal gradient of 30 ◦ C/km Compositionally stratified system with linear variation of salinity from top of shallow aquifer (0 mg/L) to bottom of brine formation (scenarios include 5%, 10% and 15%) Hydrostatic equilibrium calculated from running simulation model to steady state (i.e., considering temperature, salinity, and density effects on pressure), excess pore pressure at Lateral boundary of reservoir (R = 2000 m) is set as 0.1 MPa, 0.5 MPa and 1.5 MPa Depends on initial temperature, salinity, and pressure distribution

3. Results The results show that a small EPP (e.g., 0.1 MPa) can only send a short-lived brine leakage to the shallow fresh aquifer for all three cases of different salinities (Fig. 2a). Because the EPP is balanced by the increased fluid density in the wellbore, the system basically attains a new equilibrium with effective EPP and no further flow through the wellbore occurs. This can be seen in Fig. 3a where the brine invasion, as marked by the salinity increase from the initial condition, stops at various depths below the bottom of the fresh aquifer (700 m), depending on the salinity. Because only a shortlived brine leakage to the shallow fresh aquifer in the wellbore after

10 days with a small EPP (0.1 MPa) is formed, less brine enters into the shallow fresh aquifer and the salt concentration difference in high salinity scenario is lower than that in the middle and low salinity scenarios (Fig. 3a). Correspondingly, the peak of the flow rate is also lower for the higher salinity brine (Fig. 2a). Noticeably, the only fluid leaving the wellbore and entering the freshwater aquifer is the displaced water initially in the well, which presumably will minimally impact water quality in the shallow aquifer because of low salinity. At an excess pore pressure of 0.5 MPa, only the high-salinity (15% by mass) brine could stop sustained leakage (Fig. 2b). The quasi-steady-state leakage flow rates are 11.5 kg/s and 17.8 kg/s

Table 4 Basic scenarios set. Scenario name

Scenario set

The EPM method

The T2WELL method

Salinity

Excess pore pressure (EPP)

Low EPM, dP = 0.1 MPa Low EPM, dP = 0.5 MPa Low EPM, dP = 1.5 MPa

Low T2WELL, dP = 0.1 MPa Low T2WELL, dP = 0.5 MPa Low T2WELL, dP = 1.5 MPa

5%

0.1 MPa 0.5 MPa 1.5 MPa

Mid EPM, dP = 0.1 MPa Mid EPM, dP = 0.5 MPa Mid EPM, dP = 1.5 MPa

Mid T2WELL, dP = 0.1 MPa Mid T2WELL, dP = 0.5 MPa Mid T2WELL, dP = 1.5 MPa

10%

0.1 MPa 0.5 MPa 1.5 MPa

High EPM, dP = 0.1 MPa High EPM, dP = 0.5 MPa High EPM, dP = 1.5 MPa

High T2WELL, dP = 0.1 MPa High T2WELL, dP = 0.5 MPa High T2WELL, dP = 1.5 MPa

15%

0.1 MPa 0.5 MPa 1.5 MPa

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

397

Fig. 3. The difference profile between the end and the initial salinity in the wellbore after 10 days by T2WELL model. (a) dP = 0.1 MPa; (b) dP = 0.5 MPa; (c) dP = 1.5 MPa.

Fig. 2. Evolution of flow rate in wellbore at the bottom of the freshwater aquifer, for the low-, middle- and high- salinity case (dP refers to the EPP boundary condition in the brine reservoir; Low means the low salinity; Mid means the middle salinity; High means the high salinity). (a) dP = 0.1 MPa; (b) dP = 0.5 MPa; (c) dP = 1.5 MPa.

for 10% salinity and 5% salinity, respectively. Such differences in leakage flow rate are caused by the difference in brine salinity. The hydrostatic pressure gradient of the heavier brine is higher leading to less effective EPP to drive flow at a given over-pressure. Interestingly, the brine invasion through the wellbore reaches up to the depth of 108.5, 522.5, and 700.5 m below surface for the low, the mid, and the high salinity cases, respectively (Fig. 3b). The depth of 700 m is the bottom of the shallow aquifer, which means that the EPP of 0.5 MPa is almost the threshold pressure perturbation for the high salinity case (given the 1500 m distance between the shallow aquifer and the deep saline reservoir). Similarly for the low salinity case, 0.1 MPa EPP is close to the threshold pressure perturbation

(Fig. 3a). Although the brine starts to leak from the wellbore to surrounding formation after it reaches the bottom of the shallow aquifer, it continues to move upward to a higher elevation through the leaking wellbore. The height of such invasion is inversely proportional to the brine salinity (Fig. 3b). For the low salinity case, the invaded brine almost reaches the top of the wellbore (about 108.5 m below the surface, shown in Fig. 3b). As EPP is increased to 1.5 MPa, quasi-steady-state leakage flow occurs for all salinity (Fig. 2c). The leakage rate varies from 27.8 kg/s (high salinity) to 31.5 kg/s (low salinity). Correspondingly, the fronts of the invaded brine for all salinity cases are above the bottom of the shallow aquifer (Fig. 3c). However, only for the low salinity case, the front reaches the top of the wellbore (the sealer at land surface), mainly because, in the low salinity case, the (inverse) buoying force induced by the density difference between the surrounding fresh water and the invaded brine is relatively small so that the fast moving brine is able to flow upward further along the leaking wellbore driven by the inertia momentum. This phenomenon can be further revealed by the plot of salinity versus time at a depth of 700 m within wellbore (Fig. 4a–c) and contour map of the salinity (mass fraction of salt) over the entire profile (Fig. 5). For all salinity scenarios in Fig. 4a and the high salinity scenario in Fig. 4b, the salinity at a depth of 700 m within wellbore arrives a peak in 4 days and then decreases to a constant value. However, for the other scenarios in Fig. 4b and scenarios in Fig. 4c, salinity at the depth of

398

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

Fig. 4. Change of salinity with time at the depth of 700 m within the wellbore (a) dP = 0.1 MPa; (b) dP = 0.5 MPa; (c) dP = 1.5 MPa.

700 m increases in 2 days and arrives an equilibrium state. Under low salinity (Fig. 5e and f), the plume in the shallow aquifer occurs more like a fountain (i.e., concentrated around the leaking wellbore) whereas the plume of brine tends to spread more widely for the cases of higher salinity. Fig. 6a–f shows contour map of temperature after 10 days of the EPP of 0.5 MPa and 1.5 MPa under low, middle and high salinity to demonstrate the non-isothermal conditions. When temperature is changed, the density, viscosity and related fluid properties will be changed accordingly in the model. In other words, the effects of temperature difference on the leakage flow are fully accounted for in these simulations. In these simulations, diffusion between the fresh water and the invaded brine is not considered. The diffusion process could reduce the salt concentration difference between these two fluids. Fig. 7 shows the brine leakage rate at the bottom of the shallow aquifer as a function of the EPP in reservoir at different salinity levels. In general, if the EPP is less than certain threshold values (for example, 0.5 MPa in high salinity scenario), no sustained leakage would occur. If the EPP is higher than the threshold value, the leakage rate is proportional to the EPP. However, the relationship is not linear. In high salinity scenario, at values just greater than 0.5 MPa, the leakage rates increase quickly with the EPP. The rate of increase decreases markedly after 10 kg/s is reached. This change of leakage rate response to the EPP could be contributed to the change in flow status from laminar flow to turbulent flow. As implied in the momentum equation (1), the resistance to flow through wellbore would be roughly proportional to the square of velocity in turbulent

Fig. 5. Contour map of salinity along radial distance and wellbore after 10 days of the EPP of 0.5 MPa and 1.5 MPa. (a) High T2WELL, dP = 0.5 MPa; (b) High T2WELL, dP = 1.5 MPa; (c) Mid T2WELL, dP = 0.5 MPa; (d) Mid T2WELL, dP = 1.5 MPa; (e) Low T2WELL, dP = 0.5 MPa; (f) Low T2WELL, dP = 1.5 MPa.

status as compared to that of the resistance that can be approximated as only proportional to the velocity itself under laminar flow conditions. For example, the Reynolds number is 2.15 × 105 in the entire length of the wellbore (Fig. 8) indicating a turbulent condition when the leakage rate is 9.07 kg/s (5% salinity and 0.2 MPa EPP). Fig. 9 shows a response surface of the brine leakage rate to brine salinity and excess pore pressure. For either fixed salinity or fixed EPP, the response in the leakage rate to the other factor is not linear. However, the almost parallel and straight contour lines (especially in the high EPP end) indicate that the effects on the leakage rate caused by the salinity and by the EPP, respectively, are linearly correlated. 4. Discussions Although flow in an open wellbore is usually not expected to obey the Darcy’s law, the Equivalent Porous Media (EPM) approach is widely used to simulate the wellbore flow as a convenient approximation, especially if it is involving reservoir simulations (Birkholzer et al., 2011). Battistelli et al. (2011) used both the EPM and the conventional wellbore flow model and made a comparison of the two approaches. However, the effectiveness of the EPM approach for simulate the flow in wellbore is rarely evaluated. For

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

399

Fig. 8. Change of brine flow rate and the Reynolds number within the wells under 0.2 MPa EPP and 5% salinity scenarios after 10 days.

Fig. 6. Contour map of temperature along radial distance and wellbore after 10 days of the EPP of 0.5 MPa and 1.5 MPa. (a) High T2WELL, dP = 0.5 MPa; (b) High T2WELL, dP = 1.5 MPa; (c) Mid T2WELL, dP = 0.5 MPa; (d) Mid T2WELL, dP = 1.5 MPa; (e) Low T2WELL, dP = 0.5 MPa; (f) Low T2WELL, dP = 1.5 MPa.

example, the important model parameter such as permeability can fairly be considered as an intrinsic parameter for a given porous medium which can be obtained from laboratory or field experiments and is believed to be independent of the fluid properties or

Fig. 7. Responses of the brine leakage rate after 10 days to the EPP under the effect of salinity.

flow status (e.g. velocity, phase composition, or fluid density). But in the case of wellbore, this parameter is just an “equivalent” permeability which is not an intrinsic parameter of a given wellbore. While researchers often use high permeability for the wellbore, it is hard to know what value is proper for a given problem. The equivalent permeability can be computed as function, among the others, of friction factor, of fluid viscosity, and flow rate. This means an ‘equivalent permeability’ does exist only for steady state flow with minimal variations of Reynolds number, fluid viscosity and flow rate along the wellbore. In reality, it is even a question whether a “proper” value exists or not. Meanwhile, as shown in Fig. 7, the equivalent permeability has a big impact on the simulated leakage rates by the EPM approach. For the same case (low salinity and 0.5 MPa EPP), if the equivalent permeability of 10−8 m2 (taken from Birkholzer et al., 2011) is used for the wellbore, the predicted leakage rate (Fig. 10) would be smaller by orders of magnitude than the predicted leakage rate using the DFM model in which the proper momentum equation is solved. By fitting the final leakage rate (at the 10th day), we obtain the equivalent permeability of 3.16 × 10−6 m2 . With this fitted permeability, the simulated leakage rate curve using EPM approach is quite close to the one calculated using T2WELL (Fig. 10). In other words, if we could find the proper equivalent permeability for the wellbore, the EPM approach could effectively simulate the leakage dynamics at least in terms of the temporal variations of the leakage rate. However, the question is whether or not the fitted permeability is a fixed parameter of the given wellbore like that of a given porous medium. To investigate this problem, we did more simulations with the fitted equivalent permeability by varying either the

Fig. 9. Contour map of brine leakage rate with the EPP and salinity.

400

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

Fig. 10. Fitting of the value of equivalent permeability in the wellbore with cases 0.5 MPa pressure rise and low salinity.

EPP or the salinity of the brine from the above base case. Fig. 11 shows the quasi-steady-state leakage rates as a function of the varied EPPs for the same wellbore–reservoir system with the same salinity. While the EPM approach does a good job only in the low leakage rate range (or low EPP range), it overestimates the leakage rate in the high leakage rate range (Fig. 11). Such overestimation increases with the EPP and is about 1.56 times under the low salinity scenario at the EPP of 1.5 MPa. Basically, the EPM approach predicts a straight response line, which is rooted in the underlying Darcy’s law where the flow rate is linearly proportional to the effective pressure gradient (sum of gravity and pressure gradient). Such a linear relationship is a good approximation only if the flow rate is small. Otherwise, the momentum equation (1) should be used to describe the flow dynamics instead. Note that, here, we obtain the equivalent permeability by fitting the leakage rate at the EPP of 0.5 MPa which is relatively close to the low end. If the fitting point had been selected toward the high end of the EPP (e.g., 1.5 MPa), we would expect the EPM approach to underestimate the leakage rates at lower EPP. Because the density gradient needed to be overcome is proportional to the salinity of brine for a given wellbore length, the effective EPP will decrease as the salinity increases. As expected, a linear response of the leakage rate to the increase of the salinity (Fig. 12) is not always the case if the full wellbore model based on the momentum equation (1). In short, the EPM approach is not a viable method for predicting the leakage through an open wellbore caused by CO2 injection simply because the so-called equivalent permeability also depends on the leakage rate (or velocity) itself except for those cases with

Fig. 11. Response in 10 days’ leakage rate to the EPP under the effects of 5%, 10%, and 15% salinity.

Fig. 12. Response in 10 days’ leakage rate to the salinity under 0.1, 0.5, 1.5 MPa EPP between T2WELL results and EPM results with the best fitted permeability.

very small leakage rates. As a result, the conclusions about the leakage risk of a given wellbore–reservoir system deduced from such analyses could be problematic and misleading. Although the results presented here are limited to single phase brine leakage, we would expect that the under- or over-estimation of the leakage rates by the EPM approach could be larger and more complicated if two phase (CO2 –brine) flow condition occurs in the leaking wellbore. 5. Conclusions We have used a coupled wellbore–reservoir model (T2WELL/ECO2N) to analyze the problem of brine leakage to a shallow aquifer through an open wellbore due to the excess pore pressure in a deep saline aquifer as a result of CO2 injection. Our hypothetical wellbore–reservoir system comprises a vertical wellbore and two aquifers which are separated by a thick mudstone formation (1500 m in thickness). The wellbore is assumed to go through all formations but be only screened to two aquifers, a shallow freshwater aquifer (700 m in thickness) and a deep saline aquifer (2200–2300 m below ground surface). Salinity has an important influence on the brine leakage rate because it directly reduces the effective pressure gradient that drives the brine upward. In some low excess pore pressure cases (e.g., 0.1 MPa), the salinity effect could effectively stop the leakage up the wellbore. As a result, the wellbore–reservoir system reaches a new equilibrium and only a portion of less harmful water in the wellbore that is displaced by the invaded brine enters the freshwater aquifer. The height of the invasion brine is inversely proportional to the salinity of the brine for the given EPP. The threshold pressure perturbation, below which no sustainable leakage would occur, increases with the salinity for a given wellbore–reservoir system. When the excess pore pressure caused by CO2 injection is higher than the threshold pressure perturbation, a quasi-steadystate leakage rate will be quickly established. The leakage rate responds to the effective EPP (above the threshold pressure perturbation) nonlinearly (at a reduced rate as EPP increases). This is because the resistance to the flow through wellbore (e.g., the friction) is proportional to the square of the fluid velocity. Although the Equivalent Porous Media approach is a convenient approximation for simulation of wellbore flow and might work in some limited cases, it is not a reliable approach, especially if one expects high leakage rate could occur. It may over or under estimate the leakage rate for a given wellbore–reservoir system depending on what value of the equivalent permeability for the wellbore is used as well as how far the current EPP is away from the value under which the equivalent permeability was obtained. This is because the underlying Darcy’s law is not suitable for describing

L. Hu et al. / International Journal of Greenhouse Gas Control 9 (2012) 393–401

open wellbore flow. As a result, the conclusions about the leakage risk of a given wellbore–reservoir system deduced from analyses based on EPM approach could be problematic and misleading. Note that, although the results presented here are limited to single phase brine leakage, we would expect that the under- or over-estimation of the leakage rates by the EPM approach could be larger and more complicated if two phase (CO2 –brine) flow condition occurs in the leaking wellbore, which would be a good topic for future works. Acknowledgements This research is in part supported by the National Nature Science Foundation of China (Grant Nos. 41072178 and 40872159) and the Fundamental Research Funds for the Central Universities (No. 105560GK), by the CO2 Capture Project (CCP) of the Joint Industry Program (JIP), by the National Risk Assessment Partnership through the Assistant Secretary for Fossil Energy, Office of Sequestration, Hydrogen, and Clean Coal Fuels, National Energy Technology Laboratory (NETL), and by Lawrence Berkeley National Laboratory under Department of Energy Contract No. DE-AC02-05CH11231. The authors thank four anonymous reviewers and associate editor for their helpful comments and substantial editing that led to a significant improvement in the paper. References Apps, J.A., Zheng, L., Zhang, Y., Xu, T., Birkholzer, J.T., 2010. Evaluation of potential changes in groundwater quality in response to CO2 leakage from deep geologic storage. Transport in Porous Media 82 (1), 215–246. Bachu, S., 2008. CO2 storage in geological media: role, means, status and barriers to deployment. Progress in Energy and Combustion Science 34 (2), 254–273. Battistelli, A., Ceragioli, P., Marcolini, M., 2011. Injection of acid gas mixtures in sour oil reservoirs: analysis of near-wellbore processes with coupled modelling of well and reservoir flow. Transport in Porous Media 90 (S1), 233–251. Bear, J., 1972. Dynamics of Fluids in Porous Media. American Elsevier Publishing Company, Inc., New York. Bergman, M., Winter, E.M., 1995. Disposal of carbon dioxide in aquifers in the U.S. Energy Conversion and Management 36 (6–9), 523–526. Birkholzer, J.T., Nicot, J.P., Oldenburg, C.M., Zhou, Q.L., Kraemer, S., Bandilla, K., 2011. Brine flow up a well caused by pressure perturbation from geologic carbon sequestration: static and dynamic evaluations. International Journal of Greenhouse Gas Control 5 (4), 850–861. Birkholzer, J.T., Zhou, Q., 2009. Basin-scale hydrogeologic impacts of CO2 storage: capacity and regulatory implications. International Journal of Greenhouse Gas Control 3 (6), 745–756. Birkholzer, J.T., Zhou, Q., Tsang, C.F., 2009. Large-scale impact of CO2 storage in deep saline aquifers: a sensitivity study on the pressure response in stratified systems. International Journal of Greenhouse Gas Control 3 (2), 181–194. Carey, J.W., Wigand, M., Chipera, S.J., WoldeGabriel, G., Pawar, R., Lichtner, P.C., Wehner, S.C., Raines, M.A., Guthrie, G.D., 2007. Analysis and performance of oil well cement with 30 years of CO2 exposure from SACROC unit, west Texas, USA. International Journal of Greenhouse Gas Control 1 (1), 75–85.

401

Celia, M.A., Nordbotten, J.M., Court, B., Dobossy, M., Bachu, S., 2011. Field-scale application of a semi-analytical model for estimation of CO2 and brine leakage along old wells. International Journal of Greenhouse Gas Control 5 (2), 257–269. Dooley, J.J., Kim, S.H., Edmonds, J.A., Friedman, S.J., Wise, M.A., 2004. A first-order global geological CO2 -storage potential supply curve and its application in a global integrated assessment model. In: Proceedings 7th International Conference of Greenhouse Gas Control Technologies, Vancouver, Canada, September 2004. Gasda, S.E., Bachu, S., Celia, M.A., 2004. The potential for CO2 leakage from storage sites in geological media: analysis of well distribution in mature sedimentary basins? Environmental Geology 46 (6–7), 707–720. Nicot, J.-P., 2008. Evaluation of large-scale CO2 storage on fresh-water sections of aquifers: an example from the Texas Gulf Coast Basin. International Journal of Greenhouse Gas Control 2 (4), 582–593. Nordbotten, J.M., Celia, M.A., Bachu, S., 2004. Analytical solutions for leakage rates through abandoned wells. Water Resources Research 40 (4), W04204, http://dx.doi.org/10.1029/2003WR002997. Nordbotten, J.M., Celia, M.A., Bachu, S., Dahle, H.K., 2005. Semianalytical solution for CO2 leakage through an abandoned well. Environmental Science & Technology 39 (2), 602–611. Oldenburg, C.M., Rinaldi, A., 2011. Buoyancy effects on upward brine displacement caused by CO2 injection. Transport in Porous Media 87 (2), 525–540. Pan, L.H., Oldenburg, C.M., Pruess, K., Wu, Y.S., 2011a. Transient CO2 leakage and injection in wellbore–reservoir systems for geologic carbon sequestration. Greenhouse Gases: Science and Technology 1 (4), 335–350. Pan, L., Oldenburg, C.M., Wu, Y.S., Pruess, K., 2008. Wellbore flow model for carbon dioxide and brine. In: Energy Procedia, GHGT9 Conference, Washington, DC, LBNL-1416E. Pan, L., Oldenburg, C.M., Wu, Y.S., Pruess, K., 2011b. T2WELL/ECO2N Version 1.0: Multiphase and non-isothermal model for coupled wellbore–reservoir flow of carbon dioxide and variable salinity water. LBNL Report, Berkeley, CA, LBNL4291E, 57 pp. Pan, L.H., Webb, S.W., Oldenburg, C.M., 2011c. Analytical solution for two-phase flow in a wellbore using the drift-flux model. Advances in Water Resources 34 (12), 1656–1665. Pruess, K., 2005. ECO2N: A TOUGH2 Fluid Property Module for Mixtures of Water, NaCl, and CO2 . Research Report, Lawrence Berkeley National Laboratory, Berkeley, CA, LBNL-57952. Pruess, K., Oldenburg, C.M., Moridis, G.J., 1999. TOUGH2 User’s Guide Version 2.0. Lawrence Berkeley National Laboratory Report, LBNL-43134. Pruess, K., Spycher, N., 2007. ECO2N: a fluid property module for the TOUGH2 code for studies of CO2 storage in saline formations. Energy Conversion and Management 48 (6), 1761–1767. Shi, H., Holmes, J.A., Durlofsky, L.J., Aziz, K., Diaz, L.R., Alkaya, B., Oddie, G., 2005. Drift-flux modeling of two-phase flow in wellbores. SPE Journal 10 (1), 24–33. Stauffer, P., Bekins, B.A., 2001. Modeling consolidation and dewatering near the toe of the northern Barbados accretionary complex. Journal of Geophysical Research 106 (B4), 6369–6383. Viswanathan, H.S., Pawar, R.J., Stauffer, P.H., Kaszuba, J.P., Carey, J.W., Olsen, S.C., Keating, G.N., Kavetski, D., Guthrie, G.D., 2008. Development of a hybrid process and system model for the assessment of wellbore leakage at a geologic CO2 sequestration site. Environmental Science & Technology 42 (19), 7280–7286. Yamamoto, H., Zhang, K., Karasaki, K., Marui, A., Uehara, H., Nishikawa, N., 2009. Numerical investigation concerning the impact of CO2 geologic storage on regional groundwater flow. International Journal of Greenhouse Gas Control 3 (5), 586–599. Zheng, Apps, L., Zhang, J.A., Xu, Y., Birkholzer, T., 2009. On mobilization of lead and arsenic in groundwater in response to CO2 leakage from deep geological storage. Chemical Geology 268 (3–4), 281–297. Zhou, Q., Birkholzer, J.T., Mehnert, E., Lin, Y.-F., Zhang, K., 2010. Modeling basin- and plume-scale processes of CO2 storage for full-scale deployment. Ground Water 48 (4), 494–514.