Can we overcome thermo-elastic limits on CO 2 injection rates in horizontal wells?

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1 Available online at Energy Procedia 37 (213 ) GHG-11 Can we overcome thermo-elastic limits on CO 2 injection rates in horizontal wells? Abstract Zhiyuan Luo and Steven Bryant* Department of Petroleum and Geosystems Engineering, he University of exas at Austin, Austin, X 78712, USA Large-scale CO 2 sequestration projects will be prone to thermally induced tures at injectors, because CO 2 delivered by pipeline will enter the storage formation significantly cooler than reservoir temperature at typical large injection rates. Fracturing will influence plume migration and may be forbidden by regulators, so it is important to be able to predict its onset, especially since it occurs at pressures below the nominal ture gradient. Reducing the injection pressure by constructing horizontal wells does not obviate this limitation. Based on ture initiation criterion and heat transfer model between wellbore fluid and formation, this work provides a simple tool for evaluating this tendency and strategies to avoid it in horizontal wells. 213 he Authors. Published by by Elsevier Ltd. Ltd. Selection and/or peer-review under responsibility of of GHG GHG Keywords: horizontal injector; thermoelastic stress; turing, injection rate 1. Introduction Large-scale geological CO 2 storage requires high injection rate for economic considerations. Horizontal injectors have large injectivities and are thus attractive for meeting this requirement. On the other hand, considerations of risk lead toward smaller injection rates. Large rates impose large injection pressures, which can exceed the ture pressure for the rock. As tures are potential conduits for leakage, they may not be permitted by regulators for sequestration projects. Moreover, at large injection rates the temperature of the injected CO 2 will be less than formation temperature. he thermo-elastic stress in the wellbore surrounding formation rocks induced by this temperature difference can greatly reduce critical pressure for turing, reducting the maximum injection rate [1]. his limitation can be severe (one to two orders of magnitude reduction) for a horizontal injection well, thereby largely canceling the high injectivity benefit of a horizontal well. An example of thermoelastic impact on * Corresponding author. el.: ; fax: address: steven_bryant@mail.utexas.edu he Authors. Published by Elsevier Ltd. Selection and/or peer-review under responsibility of GHG doi:.16/j.egypro

2 33 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) turing is CO 2 injection well KB-53z at In Salah, Algeria. he temperature difference at bottomhole is about 4 o C at 165 m depth (from surface), corresponding to about 14 MPa thermoelastic stress (assuming a typical coefficient of thermoelasticity of K -1 ). he nominal ture pressure is 3 MPa so accounting for thermoelastic stress reduces the ture pressure to 16 MPa. Avoiding turing the injector would thus impose a severe limitation on injection rate, even in the horizontal well. In this work, we have studied several options to overcome this limitation and increase maximum injection rate. he evaluation relies on a steady-state heat transfer model for wellbore fluid with overall heat transfer coefficient depending on injection rate [2]. he model accounts for the decreasing flow rate within the perforated horizontal section and yields the CO 2 temperature profile along the horizontal well. his temperature profile enables evaluating ture initiation criteria for horizontal wellbores for different injection strategies. An analytical solution is possible for certain boundary conditions, and it shows that the Stanton number (ratio of heat transfer to advective heat transport) in the vertical section of the well and the wellhead temperature of CO 2 control the maximum injection rate. Among the controllable factors, depth of storage formation (D) and wellhead temperature of injected CO 2 ( wh ) are the two most important, with strong non-linear effects on maximum injection rate. 2. Modeling Approach In this section, we first introduce the model used to calculate temperature profile along horizontal wellbore, then the ture criterion with thermoelastic influence emperature profile of horizontal wellbore As shown in Fig. 1, the wellbore is separated to a vertical and a horizontal segment with different models. emperature difference between wellbore fluid and surrounding formations exists in both segments. Steady-state assumption is applied for fluid flow in entire wellbore. emperature of the heel of horizontal segment Wellhead CO 2 injection rate is assumed equal to the bottomhole temperature of vertical wellbore model [3]. his is reasonable for Earth wells constructed with a small build radius formations between segments. By introducing the improved z L D model with heat transfer coefficient as a function x of mass injection rate [2], we have temperature res CO 2 in difference at the heel of horizontal wellbore, wellbore CO 2 in vertical section of wellbore ( ) 1 R heel wh e (x) oe x Figure 1. Sketch of horizontal CO 2 injection well with uniform flux into formation m/ L G g/ cp where D is a dimensionless wh 2 rud temperature gradient, w is the Stanton number in vertical section of wellbore, a cpm dimensionless ratio of the rate of heat transfer to the rate of advective transport of enthalpy, and D is the vertical depth of the heel of the horizontal section. Here, we use Heel res.8 U.795m (1)

3 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) an empirical correlation regressed from Cranfield measurements with injection rate between and ton/d [2]. We assume the extrapolation of this correlation is valid for injection rate from to 2, ton/d (Fig. 2a). he exponent of.8 in Eq. 1 makes the Stanton number a weak function of injection rate at large rates, and has a fairly narrow range from.2 to 1 for injection rates greater than ton/d (Fig. 2b) U W/m 2 K Measurements Extrapolation U.8.795m v Injection Rate (ton/d) (a) Injection Rate (ton/d) Figure 2. (a) heat transfer coefficient as a power law function of injection rate by regression of Cranfield measurements from to ton/d (b) Stanton number of -meter deep vertical section of the well versus mass injection rate based on correlation in (a) In horizontal segment, fluid flux from wellbore into formation is assumed uniform along the perforated zone if wellbore is not too rough [1]. Hence, bottomhole pressure in the horizontal well is constant. Bottomhole pressure is calculated by [4] with effective viscosity as used in [3]. o describe the steady state balance between advection of heat along the wellbore and radial transfer of heat from the surroundings into the wellbore, we use the equation: (b) d dx 2 ru w R cpm( x) (2) As flow rate within the wellbore decreases from heel to toe, the heat transfer coefficient also decreases according to the above empirical correlation (Eq. (1)). As U has the format of U.8 bm c, Eq. (2) can be written as, d 2 rwb R 2 rwc R dx.2.2 c (1 / ) cpm (1 x / L) pm x L (3) By solving Eq. (3), we have 2 rcl w cpm 5 rbl w.8 D R wh D D 2 p ( x ) ( x) (1 x ) 1 e exp (1 x ) 1 c m (4)

4 332 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) hermo-elastic stress and its impact on criterion of turing he criterion for turing of horizontal well is different from that of vertical well, as ture surface occurs on Shmin Svplane or SHmax Svplane rather than on Shmin SHmax plane. In this study, to simplify the problem and emphasize the influence of thermo-elastic stress, we assume the formation is in a normal stress region (S v >S Hmax >S hmin ) with isotropic horizontal stress distribution ( Shmin SHmax S h ). For illustration in this paper we use the relationship between minimum horizontal stress and depth from US Gulf Coast data [5], Sh.53D.46( PP Pn) D < 35m (5) where P p is pore pressure (MPa) and P n is hydrostatic pressure (MPa) at depth D (m). In this article, we assume the pore pressure is normal (P p = P n ). For the vertical stress, we assume the overburden is 2. g/cm 3, and S v increases about 2 MPa/km. herefore, in this article, the critical ture pressure for horizontal wellbore is P / 9.8 / 6 Sh Sv Pp s D D D s (6) where s is rock tensile strength. By considering thermo-elastic effect, the turing criterion is modified as, P P 3Sh Sv Pp s (7) where E is thermoelastic stress. 1 v Eq. (7) means that the turing criterion pressure along entire wellbore is smaller than the nominal value and the smallest value occurs at the heel of wellbore (Fig. 3). he zone where wellbore pressure exceeds critical ture pressure ( Pwf P ) is deemed unsafe for perforation because tures would initiate there. Here we add a safety factor of.5 MPa to this constraint, i.e. we require Pwf P Results and Discussions P Nominal P ( ) x 1 D Figure 3. Profile of difference between reservoir temperature and CO 2 in horizontal section of wellbore (black curve), ture criterion pressure that accounts for thermoelastic stress (blue curve) and nominal ture pressure (orange line) vs dimensionless distance along horizontal wellbore. Optimizations are carried out to overcome the impact of thermoelastic effect and thus to increase maximum injection rate that does not initiate tures. As shown below, the non-linear relationship between maximum injection rate, storage depth and CO 2 temperature at wellhead plays a key role. Parameters used in the analysis are listed in able 1 except otherwise specified. able 1 Conditions for Injection Well

5 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) From Fig. 2b we know decreases with increasing injection rate at fixed r w, D, c p. We select four values of (2, 1,.5,.229) by changing injection rate ( ton/d, ton/d, 48 ton/d and 113 ton/d) in Fig. 4 and Fig. 8 to investigate its influence on the temperature difference profile along horizontal wellbore. For each case, the largest temperature difference occurs at the heel of horizontal wellbore ( =, Fig. 4a). In Fig. 4b, at wh = 15 o C, we see the entire horizontal wellbore has bottomhole pressure more than.5 MPa below ture criterion pressure ( P ) with =2 ( ton/d). By increasing injection rates as shown in Fig 4b, we find bottomhole pressure scarcely increases, reflecting the large injectivity of the well. However P declines drastically. herefore, the intersections of Wellhead temperature, wh 15 C Earth surface temperature, 2 C Geothermal gradient, G 3 C/km Wellbore radius, r w.1 m E 2 GPa v.35 hermoelasticity coefficient, K -1 Heat transfer coefficient, U W/m 2 K Formation thickness, h 4 m Formation permeability, k H md Formation depth, D m Effective iscosity, eff 17-5 Drainage radius, r eh m Mean density of CO 2 8 kg/m 3 Mean heat capacity of CO 2 25 J Length of horizontal well, L m Formation factor, B 1. P and Pwf move toward the toe of the horizontal section. Fig. 4b indicates that tures would initiate in the first half of the wellbore for 1 and in almost the entire wellbore for.5. ( o C) wh =15 o C v =.5 v =1 v =2 P( ) (MPa) wh =15 o C P, v =.5 P, v =1 P, v =2.5 MPa (a) (b) Figure 4. (a) emperature difference along horizontal wellbore at various Stanton number for a m deep vertical section of the well: =2 ( ton/d); =1 (292.9 ton/d); =.5 (48 ton/d). (b) Fracture pressure along horizontal wellbore at various Stanton number at depth m. Solid curves indicate ture criteria pressures and dash lines are wellbore pressures corresponding to each injection rate. For =2 ( ton/d) the entire horizontal section has bottomhole pressure more than.5 MPa below ture pressure. For larger flow rates, the injection pressure exceeds ture pressure for much of the wellbore length Effect of partial perforation We can diminish influence of by perforating only between the toe and some location intermediate between toe and heel. In effect, this strategy uses the part of the horizontal wellbore between heel and the beginning of the perforations as a heat exchanger to warm up CO 2 before it flows into the formation. For example, by only perforating last half of horizontal wellbore, we can increase maximum injection rate about three times from ton/d in the fully perforated wellbore (Fig. 4b) to ton/d, as indicated in Fig. 5. he larger injection rate is still below large-scale commercial sequestration requirements and does not exploit the large injectivity of the well. herefore this approach would need to be combined with other approaches discussed below to be feasible.

6 334 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) Effect of depth Deeper formations have larger ture pressures, according to Eq. 6. Although the reservoir temperature also increases with depth, the difference between reservoir temperature and wellbore fluid temperature approaches constant at sufficiently large depths [3]. hus the thermoelastic stress makes a smaller contribution to the ture pressure in deeper formations. From Fig. 6, we can see maximum injection rate is an exponential function of depth, which implies the maximum injection rate can increase from 55 ton/d to 15 ton/d by selecting various depth formations for storage from 8m to 26m. However, this approach is limited by many geological factors and the cost for deep drilling and completion. P( ) (MPa) P, v =1, full perf P, v =1, partial perf P wf Margin Pressure.5MPa Injection Rate (ton/d) Depth (m) Figure 5. Optimization to prevent turing by partial perforation. By starting perforation from =.5, at the same injection rate, bottomhole pressure of perforated portion of horizontal wellbore (black line) is lower than ture criterion with a.5 MPa margin (red dashed line). In effect the horizontal section < <.5 is used as a heat exchanger and the remaining section to inject CO 2 into the formation. Figure 6. Optimization to prevent turing in horizontal wellbore by selecting deep storage formation. Maximum injection rate increases rapidly with formation depth (other parameters being constant) because thermoelastic stress becomes smaller compared to nominal ture pressure Effect of pre-heating By pre-heating CO 2 to 4 o C from 15 o C at the wellhead, as shown in Fig. 7a, at large injection rate ( =.229, 11,3 ton/d) at the heel is less than o C. Correspondingly, in Fig. 7b, it demonstrates 11,3 ton/d is a safe injection rate: the entire bottomhole pressure profile is.5 MPa below ture criterion. he behavior of in Fig. 7a is counterintuitive: larger injection rate can have a smaller temperature difference and thus larger ture pressure. he reason is illustrated in Fig. 8, which shows the temperature difference at heel of horizontal well varies non-monotonically with flow rate when the wellhead temperature is 4 o C (green curve). he physical reason is as follows. First, the more the CO 2 is pre-heated, the deeper the intersection between the geothermal profile and the adiabatic profile, as shown in Fig. 9. his means the CO 2 is losing heat to the surroundings in most of the well. Large flow rates are advantageous in this situation because the CO 2 loses less heat and arrives at the bottom of the hole warmer, as shown in Fig. 9a. he opposite is the case when the geothermal/adiabatic intersection is shallow: the CO 2 is gaining heat from the surroundings in most of the well, and small flow rates enable greater heat gain, so that the CO 2 arrives warmer at the bottom of the hole. his situation applies when wh =3 o C (Fig. 9b) or 15 o C, and consequently the corresponding trend of with flow rate is monotonic in Fig. 8.

7 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) ( o C) wh =4 o C v =.229 v =1 v =2 P( ) (MPa) wh =4 o C P, v =.229 P, v =1 P, v =2.5 MPa Margin Pressure (a) Figure 7. (a) At wh = 4 o C, the temperature difference between formation and injected fluid at the heel of horizontal wellbore is between 7 o C and o C, much smaller than when wh = 15 o C, especially for < 1 (cf. corresponding profiles in Fig. 4a). For sufficiently large injection rate (small ), is even smaller than that of lower injection rate (see text). (b) Optimization to prevent turing by increasing wellhead temperature of injected CO 2. Counterintuitively, large injection rate ( =.229, 11,3 ton/d) has higher threshold pressure for turing than smaller injection rates ( =1, 292 ton/d; =2, ton/d), because the warmed CO 2 loses less heat to shallow formations (cf Fig. 8). Dash lines are wellbore pressures corresponding to each injection rate. he effect of pre-heating on maximum injection rate is non-linear with depth of storage formation, Fig.. For shallow formations, pre-heating to values below a threshold would provide little benefit. he threshold is about 35 o C at m and about 25 o C at 15 m. However, pre-heating sufficiently beyond the threshold temperature, in these cases to about 4 o C, largely eliminates the negative influence of thermoelastic effect. For formations of intermediate depth (2 m) even a small amount of pre-heating provides a notable increase in injection rate. For deep formations (3 m) the thermoelastic stress is small compared to the nominal ture pressure and preheating has correspondingly modest effect on the maximum injection rate. 4. Conclusions hermoelastic stress can substantially reduce injection rates in horizontal wells if induced tures are prohibited. Simple models of flow, heat transfer and turing criterion for vertical and horizontal sections of the wellbore and for the CO 2 storage formation enable analysis and optimization of strategies to overcome the thermoelastic limitation. Partial perforation can increase injection rate several times by making the first portion of the horizontal well function as a heat exchanger for the CO 2. For gradients typical of the US Gulf Coast, the nominal ture pressure increases faster with depth than does thermoelastic stress. herefore, much larger safe injection rates are possible in deeper storage formations. Preheating CO 2 over a threshold wellhead temperature before injection is most beneficial in formations of intermediate depth. A threshold level of preheating is necessary in shallow formations, but above this threshold the thermoelastic effect is almost eliminated. he benefit of pre-heating declines in deeper formations because the thermoelastic effect itself declines. = R - heel (b) v wh =15 o C wh =3 o C wh =4 o C Increasing Injection Rate Figure 8. emperature difference at heel of horizontal well at m depth versus Stanton number of vertical section of the well at different wellhead temperature. he nonmonotonic behavior at wh=4 o C provides great benefit to reduce impact of thermo-elastic stress and recover the high injection rate capacity of horizontal injector.

8 336 Zhiyuan Luo and Steven Bryant / Energy Procedia 37 ( 213 ) z (m) ( o C) Geothermal 6 2 v =.229 v =1 4 6 v =2 Adiabatic z (m) ( o C) Geothermal 6 2 v =.229 v =1 4 6 v =2 Adiabatic 8 8 (a) wh =4 o C (b) wh =3 o C Figure 9(a) emperature profile in vertical section of wellbore of wh=4 o C. At large injection rate ( =.229, with 11,3 ton/d), BH is even higher than at low injection rates ( =1, with ton/d and =2, with ton/d). At large injection rate the temperature profile approaches the adiabatic limit. his leads to the non-monotonic trend in Fig. 8. (b) When wh=3 o C, as injection rate increases the temperature difference at m increases, hence the monotonic profile in Fig. 8. Injection Rate (ton/d) D=m D=15m D=2m D=3m Figure. Optimization of maximum injection rate by preheating CO 2 to wh for formations at different depths. For shallow storage formations, preheating has little benefit until wh exceeds a threshold value, beyond which the safe injection rate increases rapidly (blue and red curves); for deeper formations, any amount of preheating is beneficial (green curve). At wh = 4 o C, the disadvantage of a shallow formation (cf. Fig 6) is almost entirely compensated wh ( o C) Acknowledgement We are grateful to the sponsors of Geologic CO 2 Storage Industrial Associates Project at he University of exas at Austin: BP, Chevron, ExxonMobil, Foundation CMG, Halliburton/Landmark Graphics, Luminant, Shell, Statoil and the USGS. References [1] -elastic stress on turing a horizontal injector during geological CO 2 PE , Canadian Unconventional Resources Conference held in Calgary, Canada, November, 211 [2] - 11, Kyoto, Japan [3] Luo, Z. and Bryant, S.L., Influence of hermo-elastic Stress on CO 2 Injection Induced Fractures During Storage, SPE , International Conference on CO 2 Capture, Storage, and Utilization held in New Orleans, Louisiana, USA, 12 November 2 [4] Joshi, A., Horizontal Well echnology, PennWell Books, [5] Fjaer, E., Holt, R.M. and Horsrud, P. Petroleum Related Rock Mechanics, 2nd ed., Elsevier Science, 28.