CMTC 151516

Wellbore Leakage Model for Above-Zone Monitoring at Cranfield, MS Qing Tao, Steven L. Bryant, Tip A. Meckel and Zhiyuan Luo, The University of Texas at Austin

Copyright 2012, Carbon Management Technology Conference This paper was prepared for presentation at the Carbon Management Technology Conference held in Orlando, Florida, USA, 7–9 February 2012. This paper was selected for presentation by a CMTC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed and are subject to correction by the author(s). The material does not necessarily reflect any position of the Carbon Management Technology Conference, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Carbon Management Technology Conference is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of CMTC copyright.

Abstract Geologic storage of CO2

for atmospheric emissions reductions imposes unique requirements to document containment. Monitoring pressure in strata above the injection interval is a fit-to-purpose technique to document performance of confining system and degree of isolation provided by existing wellbore completions. Field data are collected over two-and-a-half year period during a continuous industrial-scale CO2

injection at an enhanced oil recovery (EOR) site at Cranfield Field, Mississippi. Continuous downhole high-precision pressure and temperature data were collected at a monitoring well at two depths: at the injection interval and at a selected above zone monitoring interval (AZMI). The AZMI is a prevalent non-productive sandstone above the injection zone and a thick confining system.

Pressure data show a perturbation in above zone contemporaneously with pressure elevation in injection zone, which suggests a possible interformational fluid communication via wellbore. Meanwhile temperature data maintain a linear correlation between zones with a consistent differential, which indicates negligible volumes of injection interval fluid being introduced into the AZMI. Interpretation of the data requires a physics-based transport model to illustrate the possibility of wellbore leakage and quantify the rate if leakage exists.

We model the wellbore leakage by coupling the flow in wellbore and a diffusion model in the above zone sand layer. Matching the pressure data yields an effective wellbore permeability in order of tens of darcies. This corresponds to a large flow rate along the pathway which would very likely raise the temperature in the above zone. To gain insight about the temperature response, we model the heat transfer between the fluid in wellbore and the surroundings. The heat transfer coefficient is tuned and justified by modeling the heat conduction in the formation rock. In order for the temperature in above zone to remain unaffected by that in injection zone, the flow rate should be no more than 10 g/s and the corresponding wellbore permeability not exceed a few darcies. This value is at least an order of magnitude smaller than that estimated from the pressure response. Only if the sand layer in above zone is assumed to have a closed boundary within a few hundred feet of the monitoring well can the pressure data and temperature data be made consistent. However the assumption of closed boundary is not very feasible since there is no evidence of the sand layer being closed by faults locally.

We conclude that leakage from the injection zone is very small. The observed pressure increases in the monitoring well are attributed to larger-scale geomechanical phenomena.

Introduction Carbon capture and geological storage (CCS) is a critical technology to reduce anthropogenic emissions of CO2 (IEA, 2004; IPCC, 2005). Large-volume injection of CO2 for sequestration in subsurface geologic reservoirs will typically elevate subsurface reservoir fluid pressure. Elevated pressure has the potential to impact storage integrity (Chiaramonte et al., 2008) and to cause long-term regional environmental effects (Nicot, 2008; Birkholzer et al., 2009). The concept of pressure management in the injection interval via brine extraction has been discussed and could reduce the potential for interformational communication, but does not negate the utility of pressure and temperature monitoring as a surveillance tool for evaluating containment during CCS projects.

Meckel and Hovorka (2009 and 2010) have deployed above-zone pressure and temperature monitoring during a continuous CO2

injection to test the sensitivity of this approach for documentation of integrity of the confining system in an area of numerous well completions. The Southeast Regional Carbon Sequestration Partnership (SECARB) Phase 2 field project is conducted at Cranfield Field in southwest Mississippi by the Gulf Coast Carbon Center at the Texas Bureau of Economic Geology. This location provides a unique opportunity to monitor large-scale (105-106

metric tons) CO2 injection in

2 CMTC 151516

an anticline structure at 3 km depth. Carbon dioxide from the natural geologic accumulation at Jackson Dome (near Jackson, MS) is transported 160 km via pipeline to Cranfield and has been injected continuously in supercritical phase since July 2008 to support enhanced oil recovery. Pressure and temperature monitoring began two weeks prior to injection initiation and has been essentially continuous throughout the ongoing injection. A total of eight injection wells, six production wells, and one dedicated observation well have been involved in the experiment.

The injection interval constitutes the lowermost 18 m of the basal sandstone of the middle Cretaceous Lower Tuscaloosa Formation (Devery, 1980; Werren et al., 1990; Mancini and Puckett, 2005)

at a depth of 3117 m (~10,300 feet). The facies

receiving the carbon dioxide are fluvial conglomerates and sandstones with porosities averaging 20-25% and have heterogeneous permeabilities in the tens to a few hundreds of md (determined from well tests and core data). Immediately above the regional confining system and 112 m above the injection zone, the Above Zone Monitoring Interval (AZMI) is a prevalent non-productive brine-saturated ~100 md sandstone. The permeability of this formation was evaluated from a standard 12-hour pressure drawdown (3 MPa; 447 psia, 31 bar) and 13-hour pressure buildup test in the observation well. Two sets of pressure/temperature gauges were installed on tubing, one set adjacent to the injection zone and the other adjacent to the AZMI.

The continuous time series of field data recorded at 10 minute intervals is presented in Fig. 1 (Meckel and Hovorka, 2010). Pressure in the injection zone reached a maximum of 8.8 MPa (1280 psi) higher than initial pre-injection conditions, while the pressure in the AZMI has increased 0.7 MPa (100 psi) (Fig. 1, top). Temperature data (Fig. 1, middle) in both zones recover from gauge installation to distinct baselines, maintaining a linear correlation with a consistent ~5 °C differential. The sustained large pressure differential of >8 MPa between the injection zone and the AZMI is a first order indication that the confining layer and the wellbores penetrating it are isolating the injection zone. The small increase in AZMI pressure is nevertheless interesting, especially since the temperature difference between the formations is not disturbed. One of the possibilities to account for this behavior is slow fluid leakage along the monitoring well itself (Fig. 2). In this work we model the leakage behavior, and apply it to the observed pressure and temperature data to estimate the effective permeability of the leakage pathway. The results enable us to determine the plausibility of a wellbore leak as the cause of the increase in AZMI pressure.

Modeling Pressure Response We model the pressure response before the CO2 plume reaches the monitoring well. Pressure measurement starts from the beginning of July 2008. The data series used here ends in August 2010, a time period of two years and two months (Fig. 3). The pressure in the injection zone (Pinj) is elevated due to CO2 injection elsewhere. This imposes a potential gradient for formation fluid (brine) along the wellbore. If the wellbore is not properly zonal isolated, leakage of brine at a rate qwell could happen (Fig. 4). We consider an effective permeability (kwell) of the leakage pathway (Huerta et al., 2009; Tao et al., 2010a). The leaking fluid reaches the sand above the confining layer and migrates into it. By coupling the fluid migration along the wellbore and into the sand layer, we are able to estimate the effective permeability of the leakage pathway. The estimate requires a boundary condition on the sand layer. Here we consider two limiting cases: open boundary at which the pressure is equal to the initial pressure of the layer at infinity (worst case, in that the leakage rate is largest) and closed boundary (best case, in that leakage rate is smallest).

Flow along the wellbore is given by Darcy’s law,

well annuwell

k Aqμ

= − ∇Φ (1)

where qwell is flow rate along the wellbore, Aannu is wellbore annular area and Φ is the potential of fluid whose gradient is given by,

p g zρ∇Φ =∇ − ∇ (2) where z is the depth, ρ is formation fluid density, assumed to be constant. The cross section available for flow, A, is taken to be the annulus between inner and outer casings. Open boundary in sand layer. Flow in the sand layer is modeled as radial flow starting from the outer radius of the wellbore. The properties of the sand layer and wellbore are summarized in Table 1. We first consider a limiting case of open boundary at outer end of the sand layer. The flow in sand layer is described by the radial diffusion equation,

1 t

sand

cp prr r r k t

φμ∂ ∂ ∂⎛ ⎞ =⎜ ⎟∂ ∂ ∂⎝ ⎠ (3)

The diffusion equation can be solved analytically by using dimensionless variables:

CMTC 151516 3

2

2 (

sandD

t w

sand iD

Dw

k ttc rk h p pp

qBrrr

φμπ

μ

=

−=

=

) (4)

Eq. (3) in dimensionless form is given by,

1 D DD

D D D D

p prr r r t

⎛ ⎞∂ ∂∂=⎜ ⎟∂ ∂ ∂⎝ ⎠ (5)

The solution of Eq. (5) is given by, 21( , ) ( )

2D

D D DD

rp r t Eit

= − (6)

By equalizing the flow rates along the wellbore (qwell) and through the sand layer (qsand) (Fig. 4), and using pressure profile in the injection zone as input, we can calculate the pressure profile in the above zone using the approach described above. Comparing the pressure profile with the measured pressure in the above zone, we can estimate the effective permeability by visually fitting the calculated and measured above zone pressure (Fig. 5). A reasonable fit is obtained with an effective permeability kwell of approximately 70 Darcy and a constant pressure far from the wellbore. This scenario is very unlikely, since a typical leaky wellbore has a permeability in the range of md to μd (Tao et al., 2010b). If kwell is set to smaller values, e.g. 1 D or 1md, there is no pressure response in the above zone (Fig. 6) because the smaller amount of fluid entering the above zone is not enough to build up pressure in the sand layer if it has an open boundary at the other end. Closed boundary in sand layer. We consider the other limiting case that the sand layer has a closed boundary at a fixed distance from the monitoring well. In this case the sand layer is modeled as a closed cylindrical tank with a far field radius re. Mass balance under constant fluid density in closed sand layer gives:

welldV qdt

= (7)

where V is fluid volume in sand layer, qwell is volumetric flow rate into the sand layer from the leaking wellbore. The fluid accumulation causes pressure in the sand layer to increase, given by,

tdV dpcVdt dt

= (8)

where ct is the total compressibility in sand layer. Coupling Eq. (7) and (8) with wellbore flow Eq. (1) and (2), we calculate the pressure in the above zone with time.

Comparing with the measured pressure, a good match is obtained with an effective wellbore permeability of 50 md and a far field drainage radius re is 100 ft (Fig. 7).

The sand layer boundary re plays a very important role in determining wellbore permeability under the closed boundary condition. It is instructive to vary re and see how it affects the corresponding permeability (Fig. 8). With the increase of re by 10 times, the permeability will increase by 100 times. This is because the rate of fluid accumulation in the sand layer qwell has a linear relationship with wellbore permeability, while the rate of accumulation dV/dt increases with the square of re. It is also clear that when re gets large enough (thousands feet), the effective permeability is equivalent to that in the open boundary case. Modeling Temperature Response The measurements in Fig. 1 show that the temperature in the above zone is not perturbed relative to the temperature in the injection zone. This does not necessarily imply that fluid is not flowing from injection zone to above zone, however. As fluid flows along the wellbore it will lose enthalpy due to heat transfer with the surroundings. If the flow rate is small and there is sufficiently rapid heat exchange between fluid and surroundings, the temperature in the above zone might not be affected by the flow from the injection zone. In this section we describe a simple analytical model that calculates the flow rate below which the above-zone temperature is not perturbed. We can then estimate the wellbore permeability to which this flow rate corresponds and compare with that from the pressure response model.

The plateau temperature in the injection zone is 126.6°C (260°F) and that in the above zone is 121.6°C (251°F) (Fig. 1). Assume the temperature in the wellbore tubing where the gauges are equals to the surrounding temperature. The geothermal gradient is given by,

4 CMTC 151516

126.6 121.6 0.045 C / m111.8

G −= = °

(9) Computational model. Luo and Bryant (2010a, b) modeled the heat conduction between fluid in wellbore and the surroundings. The analytical solution is given by,

2

0 0( ) ( )2 2 2 2

zR

injp p

g R GR g R GRT z T T e T Gzc c

β

β β β β−

= − − + + − + + (10)

where Tinj is temperature in the injection zone, To is temperature at a reference depth, cp is specific heat capacity, G is geothermal gradient, R is wellbore radius, z is distance from the reference depth, and β is dimensionless ratio of the rate of heat transfer to the rate of advective transport of enthalpy, given as,

w

p

UAc m

β =& (11)

where Aw is cross-sectional area of the wellbore, is mass flow rate and U is heat transfer coefficient between fluid and wellbore, in unit of W/m2·K.

m&

To utilize the model for our purpose (Fig. 9), we neglect the gravitional term in Eq. (10) since the distance z between zones is small. T0 corresponds to Tabove in Fig. 4 and is set to the surrounding temperature in above zone. To fit the need for our problem that the flow is in the annulus instead of well tubing, we calculate a pseudo wellbore radius R based on equivalent cross-sectional area described as,

2 2 2 0.1 mo iR r r Rπ π π= − ⇒ = (12) where R is pseudo wellbore radius, ro is radius of outer casing and ri is radius of inner casing.

This assumption underestimates the heat flow because the heat transfer surface area is decreased by a factor of ro/R=1.4. By varying the mass flow rate , the temperature in the above zone varies (Fig. 10). Under small flow rate, the temperature in the above zone is not perturbed by the rising brine because it equilibrates to the geothermal gradient. On the other hand at large flow rate, the fluid arriving at the above-zone gauge has not cooled off at all, and the above-zone gauge will read the same temperature as the injection zone. Here we seek the largest flow rate that does not perturb the temperature.

m&

Heat transfer coefficient. The heat transfer coefficient U significantly affects the estimation of the threshold flow rate for perturbing the above-zone temperature (Fig. 10). Larger heat transfer coefficient will shift the curve to the right hand side and yield a larger flow rate. An empirical estimate of heat transfer coefficient between wellbore and surrounding formations is in the magnitude of tens W/m2·K (Luo and Bryant, 2010b). A good way to verify its value is to compare the heat transfer from wellbore to formation with conductive heat transfer through the rock formation away from the well. To build this model, we assume a large enough flow rate (102 kg/s) along the well which yields a uniform temperature (Tw=Tinj) between the injection and above zone. Assume 1-D radial steady state heat conduction in the rock formation from near wellbore to far field (Fig. 11). This assumption is valid only if the radial heat flux is small compared with geothermal flux so that the vertical temperature distribution is not affected by the radial flux. Hence an essential step will be to compare the heat flux in radial direction and in vertical direction.

The steady state heat diffusion equation is given by,

1 0Trr r r∂ ∂⎛ ⎞ =⎜ ⎟∂ ∂⎝ ⎠ (13)

with B.C.,

;

w er r w r r eT T T= == = T (14)

where Te is the far field temperature, assumed to be geothermal temperature at the mean depth. The solution of the above differential equation is,

( )ln lnln ( )

e ww w

e w

T TT rr r−

= − r T+ (15)

The radial and geothermal heat flows are given by Fourier’s law,

q kA T= − ⋅∇ (16) where k is the thermal conductivity of rock, in unit of W/m·K, A is cross-sectional area perpendicular to heat flow direction, ∇T is temperature gradient.

CMTC 151516 5

Literatures give the thermal conductivity of clay saturated with brine to be 0.6~2.5 W/m·K and that of saturated sand to be 2~4 W/m·K. Thus for our calculation we take k = 2 W/m·K.

Heat flow rate in both radial and vertical direction (geothermal) change with the far field radius re (Fig. 12). The heat flow rate in radial direction decreases slightly with re while that in vertical direction increases with re. The radial heat flow does not vary dramatically with re because the decrease in temperature gradient is compensated by the increase in flow cross-sectional area. When re is large enough (greater than 102 m), the geothermal heat flow is substantially larger than radial heat flow. Hence the temperature distribution is not perturbed and the assumption of 1-D radial heat flow is applicable. Within the reasonable range of re (>102 m), the radial heat flow rate is in hundreds of watts (Fig. 12).

The rate of heat transfer from the fluid in the wellbore to the formation is given by,

transfer sq UA= ⋅ΔT (17) where U is heat transfer coefficient, As is heat transfer surface area and ΔT is the temperature difference between the fluid in wellbore and the formation.

Coupling Eq. (17) with Eq. (10) and (11) yields the rate of heat transfer qtransfer versus the rate of mass flow along the wellbore qwell at different heat transfer coefficient (Fig. 13). The curves converge when qwell is small because heat is transferred sufficiently fast from fluid to surroundings even under low heat transfer coefficient U. At large mass flow rates, the temperature of the rising fluid becomes constant and the heat flow rate is simply proportional to the heat transfer coefficient as Eq. (17) illustrates.

Recall that a radial heat flow rate of hundreds of watts occurs under high mass flow rate. Suppose the rate of heat transfer from fluid to formation qtransfer is equivalent to the radial heat flow rate in formation rock qradial (that corresponds to a few hundred watts in Fig. 12). We interpret from Fig. 13 that a heat transfer coefficient in the range of 1 to 10 W/m2·K is most likely a good estimate.

Wellbore permeability. We consider the maximum flow rate from injection zone to above zone that does not raise the temperature in above zone under the heat transfer coefficient in the range of 1 to 10 W/m2·K. Figure 10 indicates the threshold under limiting case U=10 W/m2·K is between 10-3 and 10-2 kg/sand that under U=1 W/m2·K is between 10-4 and 10-

3 kg/s. Hence the threshold flow rate should be in the rage of 10-4 and 10-2 kg/s. Consider the limiting flow rate of 10-2 kg/s and utilize the measured pressure in the injection and above zones (Fig. 3). We estimate the effective permeability of the leakage pathway by Darcy equation (Eq. (1)). Pressure measurement at each time yields an effective permeability, and therefore a permeability distribution is obtained by incorporating the two-year-and-two-month measurement history (Fig. 14). The distribution shows a most probable value of wellbore permeability to be several darcies. Since flow rate is proportional to effective permeability, the other limiting case of flow rate of 10-4 kg/s yields one-hundred-time smaller permeabilities, in which the most probable value is in tenth darcy. Thus a reasonable range of wellbore effectiver permeability interpreted from the temperature profile is in tenth to several darcies.

The permeability estimated from the temperature response is at least an order of magnitude lower than that from the pressure response (70 D) under open-boundary sand layer, and thus they are not consistent with eath other. Meanwhile the permeability estimated under a closed-boundary sand layer could be in the same range as that from temperature response if and only if the far field radius re is less than a few hundred feet (Fig. 8). However field evidence shows that the sand layer is very unlikely to be closed within a few hundred feet. The permeabilities estimated from both pressure response and temperature response are summarized in Table 2. Conclusion We model the wellbore leakage of the monitoring well based on the pressure and temperature response between above zone and injection zone. The effective permeability estimated from the pressure response is in tens of darcies. This corresponds to a large flow rate and will raise the temperature in the above zone. However field measurement shows the temperature in above zone is not affected by that in injection zone. This corresponds to a flow rate no more than hundredth kg/s and a wellbore permeability not exceeding a few darcies. It is substantially lower than that estimated from pressure response. If the sand layer in above zone has a closed boundary within a radius of hundreds feet, the estimated wellbore permeability is equal to or less than several darcies, which is in the same magnitude to that estimated from temperature response. However this assumption is not very feasible geologically. Therefore we conclude that wellbore leakage is not likely in the monitoring well. The observed pressure communication could possibly be caused by other mechanism, e.g. geomechanical effect.

Acknowledgement This material is based upon work supported as part of the Center for Frontiers of Subsurface Energy Security (CFSES), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Award Number DE-SC0001114. The study was conducted as part of the Southeastern Regional Carbon Sequestration Partnership’s (SECARB) Phase II research project funded by the U.S. Department of Energy’s National Energy Technology Laboratory (DOE/NETL) under DE-FC26-05NT42590, and managed by Southern States Energy Board

6 CMTC 151516

(SSEB). We are also grateful to the sponsors of the Geologic CO2 Storage Joint Industry Project at UT-Austin: BP, Chevron, ConocoPhillips, ExxonMobil, Foundation CMG, Halliburton/Landmark Graphics, Luminant, Shell and Statoil. References Birkholzer, J.T., Zhou, Q., and Tsang, C-F., 2009. Large-scale impact of CO2 storage in deep saline aquifers: a sensitivity study on pressure

response in stratified systems, Int. J. of Greenhouse Gas Control, 3(2): 181-194. Chiaramonte, L., Zoback, M., Friedmann, J., and Stamp, V., 2008. Seal integrity and feasibility of CO2 sequestration in the Teapot Dome

EOR pilot: geomechanical site characterization, Env. Geo., 54(8): 1667-1675. Devery, D.M., 1980. Lower Tuscaloosa of southern Mississippi, Miss. Geol., 1(2): 6-7. Huerta, N.J., Checkai, D.A., Bryant, S.L., 2009. Utilizing sustained casing pressure analog to provide parameters to study CO2 leakage

rates along a wellbore. SPE 126700, presented at SPE International Conference on CO2 Capture, Storage, and Utilization. San Diego, California, USA, 2-4 November 2009.

IEA (International Energy Agency), 2004. Prospects for CO2 Capture and Storage. IEA/OECD, Paris, France. IPCC (Intergovernmental Panel on Climate Change), 2005. Special Report on Carbon Dioxide Capture and Storage, (Metz, B., Davidson,

O., de Coninck, H., Loos, M., Mayer, L., eds.) Cambridge University Press, Cambridge, UK, and New York, NY, USA. Luo, Z. and Bryant, S.L., 2010a. Influence of Thermo-Elastic Stress on Fracture Initiation During CO2 Injection and Storage. Proc. 10th

Int. Conf. Greenhouse Gas Control Technologies, Amsterdam, the Netherlands, 19-23 September 2010. CD ROM, Elsevier. Luo, Z. and Bryant, S.L., 2010b. Influence of Thermo-Elastic Stress on CO2 Injection Induced Fractures During Storage. SPE 139719,

presented at SPE International Conference on CO2 Capture, Storage, and Utilization held in New Orleans, Louisiana, USA, 10–12 November 2010.

Mancini, E.A., and Puckett, T.M., 2005. Jurassic and Cretaceous transgressive-regressive (T-R) cycles, northern Gulf of Mexico, USA, Stratigraphy, 2(1): 31-48.

Meckel, T.A., and Hovorka S.D., 2009. Results of continuous downhole monitoring (PDG) at a field-scale CO2 demonstration project,

Cranfield, MS. SPE 127087, presented at the SPE International Conference on CO2 Capture, Storage, and Utilization held in San

Diego, California, 4-9 November, 2009. Meckel T.A. and Hovorka S.D., 2010. Above-Zone Pressure Monitoring as a Surveillance Tool for Carbon Sequestration Projects. SPE

139720, presented at the SPE International Conference on CO2 Capture, Storage, and Utilization, New Orleans, Louisiana, USA, 10–12 November 2010.

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): 982-593.

Tao, Q., Checkai, D.A., Huerta, N.J. and Bryant, S.L., 2010a. Model to Predict CO2 Leakage Rates Along a Wellbore. SPE 135483, presented at SPE Annual Technical Conference and Exhibition held in Florence, Italy, 20-22 September 2010.

Tao, Q., Checkai, D.A., and Bryant, S.L., 2010b. Permeability Estimation for Potential CO2 Leakage Paths in Wells Using a Sustained-Casing-Pressure Model. SPE 139576, presented at SPE International Conference on CO2 Capture, Storage & Utilization held in New Orleans, Louisiana, USA, 10–12 November 2010.

Werren, E.G., Shew, R.D., Adams, E.R., and Stancliffe, R.J., 1990. Meander-belt reservoir geology, mid-dip Tuscaloosa, Little Creek Field, Mississippi, In: Barwis, J.H., McPherson, J.G., and Studlick, J.R., eds., Sandstone Petroleum Reservoirs, Springer-Verlag, New York, NY, pp. 85-107.

Table 1—Inputs in the well leak model of Figure 4

Parameter Units Value Above zone sand layer Thickness

ft

18

Permeability md 100

Porosity - 0.28

Drainage radius ft 100

Ambient pressure psi 4400

Viscosity of formation fluid cp 0.44

Total compressibility psi-1 6×10-6 Wellbore Inner casing diameter in 7

Outer casing diameter in 10.75 Depth to above zone gauge ft 9859.4

Depth to injection zone gauge ft 10226.1

CMTC 151516 7

Table 2—Summary of wellbore permeability Computation basis

Boundary of sand layer Permeability Reason for not plausible

Pressure response

Open 70 darcy Large flow rate will raise temperature in the above zone

Closed md to hundreds darcies depending on re

Geologically very unlikely to have a closed boundary within a few hundred feet radius

Temperature response -- tenth to several darcies

Permeability substantially lower than that estimated from pressure response

Fig. 1— Plot of over 2 years of continuously recorded pressure and temperature data for the CO2 injection interval and overlying above-zone monitor interval (AZMI) (Meckel and Hovorka, 2010). Top: Pressure data for both intervals; note different vertical pressure scales. Pressure in the injection zone reached a maximum on January 4, 2010, 8.8 MPa higher than initial pre-injection conditions. Pressure increase in the AZMI has increased <0.7 MPa. The sustained pressure differential (> 8 MPa) indicates first-order isolation across the geologic confining system and existing (new and historic) wellbore completions between the two zones. Middle: Temperature data for both intervals. Temperature data support first-order isolation as both zones recover to distinct baselines, maintaining a linear correlation with a consistent differential of ~5 °C (~8.8 °F). Bottom: Surface measurement of casing and tubing pressure. The arrival of CO2 is seen as the reversal in trend in the tubing pressure curve after July 2010.

8 CMTC 151516

Confining layer

Permeable layer

Possible leakage path

Fig. 2— CO2 injected into underground formation and migrate through permeable layers. This would cause elevated pressure in the injection zone. Brine migration could happen along the wellbore (monitoring well) if there is not proper zonal isolation.

0 100 200 300 400 500 600 700 8004200

4400

4600

4800

5000

5200

5400

5600

5800

t (days)

Pre

ssur

e (p

si)

Pinj

Pabove

Fig. 3— Pressure profiles in the injection zone (Pinj) and the above zone (Pabove) before CO2 breaks through in the monitoring well. Data extracted and rescaled from Fig. 1.

CMTC 151516 9

Sand

Cen

terli

ne o

f wel

lbor

eAnnulus

Leakage path (cement) has effective permeability kwell

Above monitoring zone, Pabove

Injection zone, Plnj

qsand

qwell

re

Fig. 4— Schematic of leakage model. Fluid leaks from the injection zone along the wellbore cement to the above monitoring zone. It accumulates and migrates through the sand layer in the above zone sand layer. Primary unknown is the effective permeability kwell of the leakage path.

0 100 200 300 400 500 600 700 8004380

4400

4420

4440

4460

4480

4500

4520

4540

t (days)

Pre

ssur

e (p

si)

Pabove-model

Pabove-data

Fig. 5— A reasonable fit between the calculated pressure (red) and measured pressure (blue) in the above zone is obtained when the effective permeability of the leakage pathway is set to 70 D and the sand layer has a constant pressure boundary 100 ft from the monitoring well.

10 CMTC 151516

0 100 200 300 400 500 600 700 8004380

4400

4420

4440

4460

4480

4500

4520

4540

t (days)

Pre

ssur

e (p

si)

Pdata

kw ell = 70 D

kw ell = 1 D

kw ell = 1 mD

Fig. 6— Pressure response in the above zone under different wellbore permeability when the sand layer has an open far-field boundary. Fitting the measured pressure requires a very large value of kwell, and smaller permeabilities (1D and 1md) exhibit negligible pressure response in the above zone.

0 100 200 300 400 500 600 700 8004380

4400

4420

4440

4460

4480

4500

4520

4540

4560

t (days)

Abo

ve z

one

pres

sure

(ps

i)

Pmodel

Pdata

Fig. 7— Calculated pressure under closed-boundary sand layer (red) and measured above zone pressure. A good match between them yields an estimate of the wellbore permeability for an assumed drainage radius (distance to the closed boundary). In this particular case, far-field radius of sand layer re assumed to be 100 ft, the permeability kwell is assumed to be 50 md.

CMTC 151516 11

101

102

103

104

10-2

100

102

104

106

re (ft)

k (m

d)

Fig. 8— Effective wellbore permeability needed to fit observed pressure response increases with the square of the far field radius of sand layer under closed-boundary condition.

Fig. 9— Heat conduction between the fluid flowing along a leaky wellbore and the surroundings.

12 CMTC 151516

10-4

10-3

10-2

10-1

100

101

102

121

122

123

124

125

126

127

qw ell (kg/s)

T abov

e (o C

)

U = 1 W/m2K

U = 10 W/m2K

U = 100 W/m2K

Fig. 10— Temperature in the above zone varies with flow rate along the leaky wellbore. For small flow rate, the temperature is not perturbed; for large flow rate, the temperature approaches that of the injection zone. Larger heat transfer coefficient shifts the curve to the right, so that the threshold flow rate which perturbs the above-zone temperature increases.

Fig. 11— Heat flow in radial direction due to temperature gradient between near wellbore and far field formation and in vertical direction due to geothermal gradient.

100

101

102

103

104

10-2

100

102

104

106

108

re (m)

q (W

)

qradial

qgeothermal

Fig. 12— Heat flow rate in radial direction (qradial) decreases slightly with re while that in vertical direction (qgeothermal) increases with re. When re is large (greater than 102 m), the qgeothermal is substantially larger than qradial.

CMTC 151516 13

10-4

10-2

100

102

100

101

102

103

104

105

qw ell (kg/s)

q tran

sfer

(W

)

U = 1 W/m2K

U = 10 W/m2K

U = 100 W/m2K

Fig. 13— Rate of heat transfer qtransfer versus rate of mass flowqwell at different heat transfer coefficient U. The curves converge when the mass flow rate is low. At high mass flow rate, qtransfer increases with the increase of U.

3 3.5 4 4.5 5 5.5 60

100

200

300

400

500

log(k) (md)

Cou

nt

Fig. 14— Wellbore permeability distribution based on the two-year-and-two-month measurement of pressure. Limiting case of flow rate 10-2 kg/s is estimated from the temperature response. The most probable permeability value is in several darcies.