DKJStartApplication of multi-well analytical models to maximize geological CO2 storage in brine formations

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 63 (2014) 3563 – 3567

GHGT-12

Application of multi-well analytical models to maximize geological CO2 storage in brine formations Seyyed A. Hosseini a,* ,Seunghee Kim b ,Mehdi Zeidouni c a

The University of Texas at Austin, University Station, Box X, Austin, TX 78713 Western New England University, 1215 Wilbraham Road, Springfield, MA 01119 c Louisiana State University, 2127 Patrick F. Taylor Hall, Baton Rouge, LA 70803

b

Abstract

Injection of CO2 emissions from industrial units into geological formations would require many storage sites and each storage site would require multiple injection wells to inject high volumes of CO2. Although multi-well injection of CO2 in brine formations increases the injection rate but this increase is not linear with respect to the number of injection wells. This is because of the well-known pressure interference effect. Ideally there is an optimum number of injection wells and injection rates (for each individual well) that would maximize the project net present value based on some economic assumptions. In this study we are using our new tool (Enhanced Analytical Simulation Tool or EASiTool) to investigate this concept for both open and closed boundary aquifers. Also with tornado charts we will show how sensitive our capacity estimations are to the input parameters of the analytical models. © Published by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license © 2014 2013The TheAuthors. Authors. Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of GHGT. Peer-review under responsibility of the Organizing Committee of GHGT-12 Keywords: Pressure interference; geological CO2 storage; storage capacity; optimal injection rate.

* Corresponding author. Tel.: +1-512-739-6212; fax: +1-5122-471-0140. E-mail address: [email protected]

1876-6102 © 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Peer-review under responsibility of the Organizing Committee of GHGT-12 doi:10.1016/j.egypro.2014.11.385

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1. Introduction To meet the need of massive CO2 sequestration into geological formations multi-well injection scenarios are expected to be employed in the field. As part of our ongoing work to develop an enhanced simulation tool for CO2 storage capacity estimation (EASiTool), using an inversion algorithm we compute the distribution of injection rates in multi-well injection scenarios so all the injection wells will have the same bottom hole pressure at the end of injection period i.e. reach the maximum allowable injection pressure at the end of injection period. In addition, EASiTool has capability to optimize the number of injection wells based on the given injection time period and a simple NPV analysis based on simple term such as drilling cost, operation cost, monitoring cost and assuming a tax credit for stored CO2. In our models we use analytical models for two-phase flow while considering partial miscibility and the principle of superposition to model scenarios with more than one well both in closed and open boundary conditions. Our model is a combination of studies done by researchers [1-4]. There have been other efforts to find reduced order models to investigate multi-well injection scenarios [5]. Our results show that assigning optimized injection rates, in which injection rate is smallest for wells in the center of reservoir and larger away from the center, yields higher total injection rate than assigning identical injection rate for all injection wells for a given maximum allowable pressure limit. Moreover, gap in the total injection rate between optimized injection rates and same injection rates widens as the number of wells increases (Figure 1). Total injection rate [ton/day]

20000

15000

10000

5000

0 0

20

40

60

80

100

Number of wells

Fig. 1 Total injection rate with respect to the number of injection wells. Note: line with triangular markers - constant injection rate is identically applied, and line with circular markers - constant injection rate is non-identically but optimally applied to injection wells. Reservoir size is 10km*15km and pressure limit is ¨P=5.8MPa. Initial pressure and temperature is P=10MPa and T=40°C.

This computation model will be useful in determining the optimum number of injection wells as well as optimizing allocation of injection rates to maximize the storage capacity. We will demonstrate the results for both open and close boundary conditions. 2. Optimal flow rate determination Superposition technique is used to find a distribution of pressure build-up for a multi-well scenario [3-4]. For an infinite-boundary condition with a number of wells Nw, normalized bottom-hole pressure of a reference well PwD is: PwD

2 Nw 1 O § · 1 ln(tD )  0.80908  Sa  1 ¦ qDi g Ei ¨¨  rDi ¸¸ 2 2 i1 Ow © 4KD3tD ¹

(1)

where tD is normalized time, Sa is apparent skin associated with the two-phase flow, qDi is relative injection rate with തതത തതതത respect to the reference well, (ߣ ௚ ) is gas mobility in gas zone, (ߣ௪ ) is endpoint brine mobility, rDi is normalized radius, and Ei is Exponential integral function. For a closed-boundary condition, normalized bottom-hole pressure is:

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Seyyed A. Hosseini et al. / Energy Procedia 63 (2014) 3563 – 3567

S PwD 

PwD

N w 1

¦q i 1

S PwD

Di

ª 1 Og § O g K D 3t D § r 2 · 1 Og § r2 · r 2 ·º Ei ¨¨  Di ¸¸  Ei ¨¨  eD ¸¸  2 exp¨¨  eD ¸¸» « 2 Ow reD © 4K D3t D ¹¼» ¬« 2 Ow © 4K D3t D ¹ 2 Ow © 4K D3t D ¹

2 2 O § O · § · 1 ln(tD )  0.80908  Sa  1 g Ei ¨¨  reD ¸¸  2 g KD32tD exp¨¨  reD ¸¸ 2 2 Ow © 4KD3t D ¹ Ow reD © 4K D3t D ¹

(2)

and reD denotes formation external boundary radius divided by well-bore radius re/rw. While calculating bottom-hole pressure given constant injection rate is straightforward, determining constant injection rates for a given pressure limit in a reversed way requires some computational effort. We revisit Equation (1) to express pressure buildup ¨P as a result of injection from the reference well and other surrounding wells: 2Shk k rg

Pg

'P

N 1 r2 · ½ ref 1 w i Og §¨ ­1 Ei ¨  Di ¸¸ ® ln(t D )  0.80908  S a ¾q  ¦ q 2 i 1 Ow © 4K D3t D ¹ ¿ ¯2

(3)

Then Equation (3) can be rearranged into a matrix computation ‫ܣ‬Ӗ ή ܺത ൌ ‫ܤ‬ത where matrix A consists of coefficients for each flow rate, vector X is unknown flow rates, and vector B contains the left-hand side term in Equation (3). For example, for a 3-wells system, the matrix computation is written as: ª1 « ln(t D )  0.80908  S a «2 « 1 Og § r 2 · Ei ¨¨  D 21 ¸¸ «  « 2 Ow © 4K D3t D ¹ « 1O § r2 · g «  Ei ¨¨  D31 ¸¸ «¬ 2 Ow © 4K D3t D ¹



1 Og § rD212 · ¸ Ei ¨  2 Ow ¨© 4K D 3t D ¸¹

1 ln(t D )  0.80908  S a 2 1 Og § rD232 · ¸  Ei ¨  2 Ow ¨© 4K D 3t D ¸¹

º » » ­ q1 ½ »° 2 ° » ®q ¾ »° 3 ° » ¯q ¿ 1 ln(t D )  0.80908  Sa » 2 »¼ 1 Og § rD213 · ¸ Ei ¨  2 Ow ¨© 4K D3t D ¸¹ 2 1 Og § rD 23 · ¸  Ei ¨  2 Ow ¨© 4K D3t D ¸¹



½ ­ 2Shk k rg 'P ° ° P g ° ° °° °° 2Shk k rg 'P ¾ ® P g ° ° ° ° 2Shk k rg 'P ° ° °¿ °¯ P g

(4)

ିଵ ή ‫ܤ‬ ധധധധധ ത . However, Then the flow rate is obtained by inversing the systems of equation to recover the vectorܺത ൌ ‫ܣ‬ apparent skin Sa in matrix A varies with flow rate q. So we start with initial assumption for flow rates, and iterate until convergence. There is analytical solution for inverse problem when only one well exists [6]. This process is repeated until the error between former and new flow rate falls below a threshold. Matrix computation for the closed-boundary condition is also constructed in the same way by rearranging Equation (2) into a matrix computation.

3. Case study We verified the analytical models with numerical simulations of CMG-GEM. In one scenario we used 24 equally spaced injection wells to inject CO2 into an aquifer of size of 10 km by 15 km for 1000 days (Figure 2).

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Fig. 2 Pressure distribution in brine aquifer with 24 injection wells. Pressure increase is 5.4-6.1 MPa versus designed value of 5.8 MPa.

The output of the models is the injection rates of each individual well such that bottom hole pressure at all wells will be around 15.8 MPa i.e. maximum allowable injection pressure (initial reservoir pressure is 10MPa). (Table 1) Table 1— Injection rate of individual wells designed to increase the bottom hole pressure of all well by 5.8 MPA in 1000 days. Notice the symmetry in the results. Boundary Infinite Closed Infinite Closed Well Number

Q [kg/day]

Q [kg/day]

Well Number

Q [kg/day]

Q [kg/day]

1

1152200

394650

13

874040

302790

2

831000

288000

14

528180

187240

3

734160

255070

15

431650

154050

4

734160

255070

16

431650

154050

5

831000

288000

17

528180

187240

6

1152200

394650

18

874040

302790

7

874040

302790

19

1152200

394650

8

528180

187240

20

831000

288000

9

431650

154050

21

734160

255070

10

431650

154050

22

734160

255070

11

528180

187240

23

831000

288000

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874040

12

302790

24

1152200

394650

16.0

17.0

15.0

16.0 Well Bottom-hole Pressure (MPa)

Well Bottom-hole Pressure (MPa)

Based on our results bottom hole pressure increased 5-5.8 MPa in all the wells in open boundary condition (Figure 3a) and 5.4-6.1 MPa in closed boundary condition (Figure 3b). Total estimated capacity in 3 years of injection was 18.2 and 6.3 million tone of CO2 in open and closed boundary conditions, respectively. Capacity in closed boundary condition is about %35 of open boundary condition. Obviously capacity would be bigger if we run the simulations for longer times.

14.0

13.0

12.0

11.0

10.0

15.0

14.0

13.0

12.0

11.0

2000-7

2001-1

2001-7

Time (Date)

(a)

2002-1

2002-7

10.0

2000-7

2001-1

2001-7

2002-1

2002-7

Time (Date)

(b)

Fig. 3 Bottom hole pressure of 24 wells in (a) open boundary condition scenario (b) closed boundary condition scenario. All the well have 5 to 5.8 MPa increase in their BHP in 1000 days.

4. Conclusions In this study we showed that for any given formation with multiple injection wells there is an optimal injection rate distribution that can maximize the storage capacity. Note that we are still injecting at constant rate but different at individual wells, more injection on the boundaries and less at the middle of reservoir. This optimal rate could be found for both open and closed boundary aquifers. Acknowledgements This work was funded by the Gulf Coast Carbon Center at the Bureau of Economic Geology (BEG) and the U.S. Department of Energy, NETL, under contract number DE-FE0009301. Modeling work done by CMG software package provided to us free of charge. References [1] Mathias, SA, Gluyas, JG, Gonzalez Martinez de Miguel, GJ, Hosseini, SA. Role of partial miscibility on pressure buildup due to constant rate injection of CO2 into closed and open brine aquifers. Water Resources Research 2011. v. 47, W12525, doi:10.1029/2011WR011051. [2] Hosseini, SA, Mathias, SA, Javadpour, F. Analytical model for CO2 injection into brine aquifers containing residual CH4. Transport in Porous Media 2012. v. 94, p. 795௅815. [3] Azizi, E, Cinar, Y. A new mathematical model for predicting CO2 injectivity, Energy Procedia 2013. 37, 3250-3258. [4] Azizi,E, Cinar,Y. Approximate analytical solutions for CO2 injectivity into saline formations, SPE Revervoir Evaluation and Engineering 2013. 123-133. SPE 165575 [5] Pooladi-Darvisha, M, Moghdam, S, Xu, D. Multiwell injectivity for storage of CO2 in aquifers. Energy Procedia 2011. 4, 4252-4259. [6] Mathias, SA, Roberts, AW. A Lambert W function solution for estimating sustainable injection rates for storage of CO2 in brine aquifers. IJGGC 2013. 17: 546-548