Analysis of Pressure Response at an Observation Well against Pressure Build-Up by Early Stage of CO2 Geological Storage Project


 To ensure a safe and stable CO2 storage, pressure responses at an observation well is expected to be an important and useful field monitoring items to estimate the CO2 storage behaviors and the aquifer parameters during and after injecting CO2, because it can detect whether the injected CO2 leaks to the ground surface or the bottom of the sea. In this study, pressure responses were simulated to present design factors such as well location and pressure transmitter of the observation well. Numerical simulations on the pressure response and the time-delay from pressure build-up after CO2 injection were conducted by considering aquifer parameters and distance from the CO2 injection well to an observation well. The measurement resolution of a pressure transmitter installed in the observation well was presented based on numerical simulation results of the pressure response against pressure build-up at the injection well and CO2 plume front propagations. Furthermore, the pressure response at an observation well was estimated by comparing the numerical simulation results with the curve of CO2 saturation and relative permeability. It was also suggested that the analytical solution can be used for the analysis of the pressure response tendency using pressure build-up and dimensionless parameters of hydraulic diffusivity. Thus, a criterion was established for selecting a pressure transducer installed at an observation well to monitor the pressure responses with sufficient accuracy and resolution, considering the distance from the injection well and the pressure build-up at the injection well, for future CCS projects.


Introduction
The average atmospheric CO2 concentration had increased from 280 ppm in industrial era to 411 ppm in May 2019 (Dlugokencky and Tans, 2019;Lake and Lomax, 2019). The average CO2 concentration is increasing continuously by more than 2 ppm/year (Metz et al., 2005). With this growth rate, it will exceed 450 ppm within the next 20 years (Li et al., 2019), and the mean global temperature will increase by over 2 °C. To mitigate the increasing rate, many intergovernmental organizations have assessed climate change and exchange technology for reducing the anthropogenic CO2 emissions (IEACHG, 2010;Metz et al., 2005;Shackley et al., 2005). In 2017, a possible framework to reduce CO2 emissions into the atmosphere had been agreed upon countries that joined COP23 (Obergassel et al., 2018).
CO2 capture and geological storage is a promising way to mitigate CO2 emissions into the atmosphere by capturing CO2 gases from relatively large industrial sources, such as power plants, and then transporting and injecting them into porous and permeable storage reservoirs. A suitable reservoir should be covered by sealing layers with very low permeability to prevent CO2 leakage from storage reservoirs to the ground surface or sea bottom. Three main underground storage reservoirs have been identified: saline aquifers, depleted oil and gas reservoirs, and unminable coal seams (Yang et al., 2010). Deep saline aquifers at depths over -800 m have been considered ideal because of their large storage capacity and broad distribution worldwide. The saline aquifers are geologic layers of permeable layers located 1,000 to 3,000 m deep and can store injected CO2 in a supercritical state under reservoir conditions. The International Energy Agency (IEA) has estimated the potential contribution of CCS in mitigating global CO2 emission to be as high as 20 % of the global emissions in 2050, which follows the most important contribution by improvement in energy efficiency (Lipponen et al., 2011). The Blue Map reduction plan has been considered necessary to continue annual geological storage of 9.5 Gt-CO2 by CCS for 45 years. Several ongoing pilots and commercial CCS projects have suggested that CO2 geological storage in deep sedimentary formations is technologically feasible (Eiken et al., 2011;Hansen et al., 2013;Tanaka et al., 2014). To make a significant contribution to the mitigations of climate change, many CCS projects with larger CO2 injection rates from an injection well need to be planned and implemented.
However, the CO2 reduction rate by CCS projects is currently limited because sufficient CCS projects have not been implemented owing to economic issues as well as social acceptance issues related to storage safety and stability.
CO2 injections induce a pressure increase in the reservoir from its original geomechanical pressure. A large CO2 injection rate can easily cause considerable pressure build-up in the bottom hole and its surrounding region in the reservoir, where activated faults through the upper sealing layers may lead to CO2 leakage (Rutqvist, 2012). Therefore, the management of the bottom hole pressure (BHP) as an induced pressure build-up will be a critical factor in the safe operation of CO2 storage. For instance, the In Salah CCS project in Algeria has shown significant geomechanical changes because of the injection pressure and site-specific geomechanical conditions. Although the injection rate of the In Salah CCS project was 1 Mt/year, the project was still shut down because of concerns about the integrity of the seal layers (Eiken et al., 2011;Goertz-Allmann et al., 2014). In the Tubåen Formation in the Snøhvit field (offshore Norway), Statoil successfully injected 1.6 Mt of CO2 from April 2008 to April 2011. However, the CO2 injection had to be stopped owing to an increase in pore pressure before reaching the full storage capacity of the Tubåen Formation (Hansen et al., 2013).
Generally, to confirm that the injected and stored CO2 is in a safe and stable condition, it is necessary to grasp the behavior of CO2 in the reservoir and to detect whether there is leakage of CO2 out of the reservoirs or not. In the Tomakomai CCS demonstration project (hereinafter Tomakomai CCS project) (Tanaka et al., 2014), five continuous monitoring items and three periodic monitoring items were operated for two aquifers at different average depths of 1,150 and 2,700 m. The continuous monitoring items are temperature and pressure in two injection wells, temperature, and pressure changes in two remote observation wells, and seismic monitoring at the ocean bottom and onshore. In contrast, the periodic monitoring items are marine environmental observations (sea water, bottom mud, and sea lives) and 2D and 3D seismic surveys. Specifically, two observation wells were drilled from onshore to the Moebetsu Formation (1,100-1,200 m in deep) and the Takinoue Formation (2,400-3,000 m in deep) to record continuous passive changes in aquifer pressure and temperature as well as CO2 saturation in each formation water. The monitoring data recorded in the observation wells can be used to detect the movement of the CO2 plume and judge the stability of stored CO2 based on comparisons with the numerical simulation results using aquifer models.
In the Tomakomai CCS project, CO2 was injected into the Moebetsu Formation in short cycles between April 6 and May 24, 2016, at an injection rate of 180 to 600 t-CO2/day and 7,163 t-CO2 were stored in cumulative amount (Sato and Horne, 2018). The original pressure of the Moebetsu Formation at the injection well was 9.3 MPa and the maximum BHP in the injection well that was recorded during the test injection was 10 MPa at an injection rate of 600 t-CO2/day, the cumulative CO2 injection was around 0.3 Mt-CO2 during the four years (Sawada et al., 2018;Tanaka et al., 2014). However, there is no pressure response was recorded in the observation well OB-2 (Tanaka et al., 2014) which was drilled about 3,000 m from the injection well in the Moebetsu Formation with installing pressure and temperature sensors. The reason for the lack of pressure response at the observation well was explained as the sensitivity of the pressure transducer is not sufficient to detect the pressure propagation from the injection well to the observation well.
Drilling a new observation well requires an additional budget and may create a new potential pathway for CO2 leakage to the surface. Therefore, the observation well and installed sensors for measuring parameters, such as distance from the CO2 injection well and the sensor sensitivity, should be suitably designed before drilling an observation well. In this study, we numerically investigated the pressure response at an observation well, induced by CO2 injection in the early stage of CO2 geological storage in a deep saline aquifer. The results can be used as reference data for designing an observation well and determining the location for installing sensors (or transmitters).

Aquifer model for CO2 injection and storage
As shown in Fig. 1, a cylindrical grid system with (r, φ, z) coordinates was used to construct the reservoir model. The pressure and CO2 saturation distributions were simulated by injecting CO2 from an injection well located at r=0 m into an aquifer with radius rw. It was assumed that the aquifer had uniform porosity and permeability in horizontal and vertical directions. Its outer boundary at r=re is defined as an open boundary that the pressure is equal to the initial pressure. There is no-flow across the top and bottom boundaries. A typical aquifer model was simulated by setting rw=0.1 m and re=10 km.
The meshing of the aquifer in the r and z directions is shown in Fig. 2. The grid blocks consist of 1,000×1×10 grid cells in the (r, φ, z) directions, of which 200 grid-cells were set between r=0.1-400 m, and 800 grid-cells between r=400-10,000 m. The reservoir consists of 10 layers with a constant spacing of 10 m in the vertical direction. CO2 was injected from the injector into horizontal layers connecting to the aquifer by three types of perforations. The radial distance from the observation well to the injection well, rm, was assumed to be in the range of 1,000 to 5,000 m. The pressure changes in the aquifer blocks connected to the aquifer at r=rm were considered as the pressure responses at the bottom of the observation well connected to the aquifer. Numerical simulations were conducted using the compositional reservoir simulator CMG-STARS TM .  The simulation parameters set for the base model are listed in Table 1. In the case of the Moebetsu Formation in the Tomakomai CCS project, the range of horizontal permeability was estimated as k=0.98×10 -15 -980×10 -15 m 2 (=1-1,000 md) from the geophysical measurements, and k=363×10 -15 m 2 (=370 md) based on the fall-off test using the injection well after drilling. In addition, the porosity was measured as ϕ=0.20-0.40 by a laboratory core test and the excavation result was ϕ=0.12-0.42 (Tanaka et al., 2014). In this simulation, the uniform permeability in the horizontal direction was also set as k=363×10 -15 m 2 , and the ratio of vertical permeability (ky) to horizontal permeability (k) was ky/k=0.1.
The porosity ϕ=0.30 was used for the base simulations. In the present simulations, assuming the ground surface temperature was 15 ℃ and geothermal gradient as 2.5-2.75 ℃/100 m, the targeted aquifer temperature was 40-42.5 ℃, and the CO2 injection temperature was specified as 40 ℃. Therefore, the injected CO2 was similar to the isothermal process. No geochemical reactions or mineralization were considered because a short period of fewer than 200 day was considered for simulation. Table 1 Aquifer parameters and CO2 injection well set in the base model (Garimella et al., 2019;Sawada et al., 2018;Tanaka et al., 2017)   Relative permeability was modeled based on the Brooks-Corey-Burdine model (Garimella et al., 2019) and is expressed by following Eqs.
(1) to (3), as follows: where Se is the effective saturation; krw and krg are the aqueous and gas phase relative permeability respectively; Sl is the aqueous phase saturation; Slr and Sgr are the aqueous and gas phase residual saturations respectively, and λ (-) is the pore size distribution index. In the present simulations, Swr=20 %, Sgr=5 %, and λ=0.5. The relative permeability curves are shown in Fig. 3. Based on the curves, the remaining water saturation after displacement of CO2 gas is almost Sw≈65 %, which means that the CO2 gas saturation becomes Sg≈35 % in an aquifer except near the well.

Linearized radial flow equation and estimation solution
Assuming porous media is viscous-dominated and there is no turbulent flow, the flow in porous media can be described by Darcy's law for a single incompressible fluid phase that is shown in Eq. (4) (Hubbert, 1953): where q is the vector of the volumetric flow rate; k (m 2 ) is permeability; µ (Pa·s) and ρ (kg/m 3 ) are the viscosity and density of the reservoir fluid; g is the gravitational acceleration vector directed downwards; p is the hydraulic gradient. Without considering gravity in the vicinity of an injection well, the governing equation on pressure p (Pa) for onedimensional radial linearized flow, assuming a constant compressibility in the aquifer is given as (Wu and Pan, 2005): where η (m 2 /s) is hydraulic diffusivity; ϕ is reservoir porosity; µ (Pa·s) is reservoir fluid viscosity; Ct=Cr+Cf (Pa -1 ) is the total value of rock compressibility (Cr) and reservoir fluid compressibility (Cf), and t (s) is elapsed time from the start of CO2 injection. The hydraulic diffusivity, η, is a hydraulic parameter that controls the unsteady pressure transient.
The pressure build-up in an injection well, defined as pi, under the general steady-state radial flow is proportional to the fluid injection rate q (m 3 /s), while it is inversely proportional to the transmissivity (or permeability-thickness product) Κ=k·H (m 3 ), which is product of the horizontal permeability k and the reservoir thickness H(m) (Dietz, 1965).
The transmissivity K expresses the flow capacity and ability in aquifers and reservoirs. The radial flow solution for the steady-state (∂p/∂t=0) in Eq. (6) is given by the following equation (IEACHG, 2010;Van Everdingen and Hurst, 1949): where re (m) is the effective reservoir radius, which is the extent from the injection well to the reservoir boundary where the pressure is equal to the initial hydrostatic pressure; and rw (m) is the injection well radius.
Assuming that the reservoir fluid is uniform and uncompressible (Cf =0 and ρ=const.), a typical solution of radial transient flow can be expressed as (Goode and Thambynayagam, 1987): The pressure response at the observation well at r=rm, ∆p (Pa) can be estimated by: The pressure calculated by Eq. (8) is roughly equal to the pressure changes between build-up and fall-off at r=rm.
The transient condition is applicable only if the pressure response in the aquifer is assumed to be not affected by the presence of the outer boundary; thus, the reservoir appears infinite in extent. In this study, a constant pressure boundary was assumed to be close to an aquifer with enough radius. Therefore, it is possible to use this equation to estimate the rough pressure response at the observation well. The distance from the CO2 injection well to the observation well (r=rm) is the critical parameter that controls the magnitude of the pressure response at the observation well, which is affected by the CO2 injection rate and amount from the injection well and the aquifer parameters. According to Eq. (7), the magnitude of the response pressure is directly proportional to the injection rate, q, and injection period, while the transmission delay time is inversely proportional to the hydraulic diffusivity of the aquifer. The pressure response is almost inversely proportional to distance rm.

Analysis method
The initial pressure of the aquifer was set as p0=10 MPa in the present simulations. The BHP in the injection well is equal to p0+pi. The pressure response and distribution of CO2 saturation in the aquifer were simulated for a constant CO2 mass injection rate qm (t-CO2/day) as shown in Fig. 5.
When the injection well is shut-in after the CO2 injection for a period, ti, the pressure response of the observation well changes and has a peak value ∆pmax, which is recorded after the delay time, ∆tmax from the shut-in of the injection well.
A pressure response ∆pmax is sensitive to the magnitude of pressure build-up pi. Therefore, it is expected that the ratio of both pressures defined as: is not sensitive to injection rate q. Simulations were carried out to investigate the pressure response and the delay time of the peak pressure in the observation well by comparing the CO2 plume front position extending to the outer ward.
In the present simulations, the CO2 injection rate q was controlled according to the BHP, which must be less than the threshold capillary pressure and sufficiently less than the fracture pressure of the caprock or upper sealing layer. The maximum BHP has been set as 90% of the threshold capillary pressure (12.6 MPa=14.0 MPa×0.9) measured for the Moebetsu Formation (Osiptsov, 2017). In the base model, the CO2 mass injection rate was set as qm=600 t-CO2/day (q=3.744 m 3 -std/s, ρCO2=1.855 kg/m 3 at the surface condition). The injection period in the base model was assumed to be ti=100 day, and the distributions of the pressure response and CO2 saturation were simulated until t=1,000 day from the start of CO2 injection.

Fig. 5 Schematic diagram of defined variables
Pressure build-up at the injection well and pressure response at the observation well

Effect of perforation scheme for injecting CO2
The CO2 injection well was assumed to be a vertical well. As different perforation schemes will lead to a difference in pressure build-up at the well, the effects of the perforation scheme on the CO2 injectivity were discussed. As shown in Fig. 6, some previous studies used different simulation models with several perforation points and locations for CO2 injection (Chadwick et al., 2009;Cinar et al., 2008). In this study, the multiple perforation scheme using 10 holes perforated in the center of each layer ( Fig. 6 (a)) was used. Chadwick (2009) Figure 7 shows the pressure build-up at the injection well with different perforation schemes for CO2 injection using the same injection rate. It can be seen that the injection with one perforation point will lead to a significant pressure build-up in the first hour of injection, which is more than twice that of all the perforations ( Fig. 6 (a)). In the multiple perforation scheme, a larger contact area with the reservoir results in a smaller pressure build-up and less stress on the sealing layer for the same injection rate. Furthermore, only one block in the vertical direction may not be rigorous to study the pressure build-up. If the pressure gradient of the reservoir is not considered, the calculated BHP may be overestimated. Therefore, in this study, a multiple perforation scheme was used in the simulations to ensure a safe injection with a smaller pressure build-up at the well.

Fig. 7
Numerical simulation results on pressure build-up of the injection well obtained with different perforation methods of the CO2 injection well using CMG-STARS TM

Pressure build-up and bottom-hole pressure
To study the pressure build-up at the CO2 injection well, an injection scheme based on the base model for injection rate qm=600 t-CO2/day and continuous injection for 100 day (ti=100 day) was simulated compared with the case of injecting saline water that is the same with the reservoir fluid. The injection rates of injecting CO2 and saline water were the same in the reservoir condition.
After the start of injecting CO2 into the aquifer, CO2 saturation around the injection well increased with replacing saline water. Therefore, with increasing CO2 saturation, the viscosity μ of the aquifer fluid, especially around the injection well, gradually changed from the viscosity of saline-water (μbrine≈6×10 -10 Pa·s) to that of supercritical-CO2 viscosity (μCO2≈0.429×10 -10 Pa·s). As shown in Fig. 8, a decrease in the transient pressure after a pressure build-up of 350 kPa was observed during CO2 injection at a constant injection rate, while the pressure build-up during saline water injection gradually increased. However, in the early stage of CO2 geological storage, the magnitude of pressure buildup (≈350 kPa) is similar even if different fluids are injected, because the CO2 storage area is limited around the well; moreover, CO2 saturation is also limited to less than 35 %, based on the relative permeability curves shown in Fig. 3, when CO2 dissolution into saline water is neglected. Therefore, the pressure change (≈50 kPa) during the CO2 injection period (100 day) is not proportional to the fluid viscosity, even if the viscosity of CO2 is less than 10 % of the viscosity of saline water. Thus, using the viscosity of saline water in Eq. (6) instead of that of CO2 shows a more realistic estimation of the pressure build-up in the aquifer at the initial injection stage. However, the pressure build-up estimated by Eq. (6) using the viscosity of saline water is slightly overestimated than that of CO2. This difference can also be explained by the equation presented by Cinar et al. (Cinar et al., 2008;IEACHG, 2010). They modified Eq. (6). by introducing the relative permeability of CO2. However, introducing CO2 relative permeability is another complicated question as CO2 relative permeability changes with continuous injection, adding more uncertain variables. In this study, the viscosity of saline water is used to estimate the rough pressure build-up using Eq. (6). In the present simulations, the radial flow consisting of saline water and CO2 was calculated considering the relative permeability curves for each fraction. Therefore, physical property changes in the blocks including multi-phase flow were simulated automatically in the present simulations using CMG-STARS TM . Figure 9 shows the cross-sectional simulation results for the r and z axes of CO2 saturation and CO2 plume flux vectors at t=10, 50, 100, and 200 day after the start of CO2 injection. The CO2 plume expands mainly as a radial flow, because the horizontal permeability, k, or hydraulic diffusivity, η, is 10 times larger than that of the vertical value. The buoyancy force on unit CO2 volume (roughly 4,000 kN/CO2-m 3 ) induces vertical CO2 convection flow, because of the density difference between injected supercritical CO2 (≈600 kg/m 3 ) and saline water (=1,030 kg/m 3 ) in the aquifer. Therefore, the top layer of the aquifer shows the largest expanding CO2 seepage flow velocity with the farthest CO2 plume front. The red arrows in Fig. 9 show the flow velocity vectors. It is clear that the CO2 plume diffuses mainly in the radial direction during the CO2 injection period, while the convection in the vertical direction is much slower.
After the injection well was shut-in, the driving pressure in the horizontal direction gradually vanished with fall-off pressure, and the vertical buoyancy flow becomes prominent. At the end of CO2 injection, the CO2 saturation around the injection well is about 70 %-80 %, and it decreases with the distance from the injection well, with a sharp decrease to 0 % around the plume front. After the injection is stopped, the CO2 pattern continues to expand, and the CO2 saturation next to the injection well decreases over time. When ti=100 day, the CO2 saturation around the injection well decreases to approximately Sc=50 %-60 % at t=200 day.
We defined the CO2 plume front position at the top layer, rp, where the CO2 saturation is Sc=10 %. As shown in Fig.   10, the plume front is observed at rp=84 m on the 100 th day. Figure 10 shows the CO2 plume front position, rp, before and after stopping CO2 injection at t=100 day (=ti). The CO2 plume front position, rp, expands almost proportionally to t 0.5 for 0<t<100 day. After the injection well was shut-in at t>100 day, the CO2 front slowly expands proportionally to 0.1t by buoyancy force on the CO2 plume.  The numerical simulation results of the base model for the distributions of the reservoir pressure change from the initial aquifer pressure (p(r)-p0) and CO2 saturation (Sc(r)) at t=50 and 100 day are shown in Fig. 11.

Fig. 11
Numerical simulation results of pressure response vs. CO2 saturation at different distances from the injection well It can be seen that pressure changes and CO2 saturation distributions are correlated in the region of CO2 saturation Sc>35 %, while only a pressure change is observed in the region (r>100 m) with a CO2 saturation Sc≈0. Assuming the position of the CO2 plume front defined by Sc=10 %, the pressure transmitting speed is two orders of magnitude higher than that of the CO2 plume front, because the pressure change is observed without CO2 saturation change. Figure 12 shows the simulation results of pressure build-up, pi at the CO2 injection well for injection rate, qm, compared with the estimated line calculated using Eq. (6) by assuming the viscosity of saline water, as discussed in the previous section. The pressure build-up does not show a significant linear relationship with injection rate. As discussed previously, this can be explained by the changing CO2 saturation around the injection well, since the relative permeability changes with CO2 saturation. The simulation results show that the linearity between pi and qm is better and closer to the values estimated by Eq. (6) with a low injection rate qm<600 t-CO2/day than that with a large injection rate qm>1,500 t-CO2/day. This is because the higher injection rate results in a faster change in CO2 saturation around the injection well. We confirmed that the pressure build-up can be correctly estimated using saline water viscosity can be corrected by using the viscosity of saline water to be 65 % because the CO2 saturation around the injection well is close to 35 %.

Pressure fall-off at the CO2 injection well
Opening or shutting off a well causes pressure changes in the CO2 injection well. The CCS projects including fall-off data after shut-in can be used to study the aquifer state (Escobar and Montealegre, 2008). When the BHP vs. time plots are measured with sufficient precision after the well shut-in, the aquifer in-situ permeability and well skin factor can be estimated by analyzing the data. This is similar to the well-testing method widely used in petroleum reservoir engineering. Without considering the skin factor the pressure fall-off function in the injection well is expressed by the radial transient flow equation (Eq. (7)). The pressure p0 should be modified to the instantaneous BHP when the injection well is shut in. Because qμ/(4πkH) can be treated as a constant if the injection rate q is constant, the hydraulic diffusivity η can be considered the main parameter controlling the fall-off curve.
In contrast to the traditional method of analyzing pressure fall-off lines, the pressure fall-off time is defined in this study to analyze reservoir conditions and pressure transients. As shown in Fig. 14, t0.75 and t0.25 are defined as the elapsed times to reach 75% and 25% pressure reductions from the build-up pressure after the well shut-in. The pressure fall-off time is defined as (t0.75-t0.25), which shows the period the pressure falls off 50% of the built-up pressure.
In the case of CO2 injection in the Moebetsu Formation, Tomakomai CCS project, some pressure fall-off data were recorded after shutting the well, and the fall-off time (t0.75-t0.25) was analyzed at about 5 day based on the BHP data.
The numerical simulation results for the fall-off time (t0.75-t0.25) vs. hydraulic diffusivity η for the base model are shown in Fig. 15, which includes the results of different porosities (0.1, 0.2, and 0.3) and permeabilities k (=98×10 -15 -1,960×10 -15 m 2 ). As the fall-off time for the Moebetsu Formation (dotted line in Fig. 15) was 5 day, the hydraulic diffusivity range of the Moebetsu Formation can be estimated as η=2-4 m 2 /s from the simulation results of (t0.75-t0.25) and hydraulic diffusivity. As the transmissivity of the Moebetsu Formation was matched as K=2.7×10 -11 m 3 in the last section, and the thickness is between H=100-200 m, porosity ϕ=0.2-0.4; therefore, the matrix rock compressibility of the Moebetsu Formation is estimated as Cr=0.14×10 -9 -1.11×10 -9 Pa -1 . This means that the rock compressibility set as Cr=0.9×10 -9 Pa -1 is within the reasonable range compared with the Moebetsu Formation.

Pressure response at observation wells
In this section, the pressure responses at a hypothetical observation well located at a range of radial distance rm=1,000 -5,000 m from the injection well are discussed based on the simulation results by comparing the values estimated using Eq. (8). The maximum value of pressure response is defined as ∆pmax, which is recorded at the observation well (r=rm) after continuous CO2 injection for ti=100 day in each injection scheme. Figure 16 shows the numerical simulation results of the pressure response at the observation well located at rm=1,000, 3,000 and 5,000 m against the CO2 injection qm=600 t-CO2/day for ti=100 day (base model). The pressure of the observation well increases gradually during the injection period, which is different from the pressure build-up of the injection well. This is because the pressure build-up in the vicinity of the injection well (less than r=100 m) is influenced by both CO2 and saline water flows, while the pressure disturbance around the observation well far from the injection well is not influenced by the difference in viscosities of CO2 and saline water. After the injection well is shut-in (t>ti), the observation well pressure draws a curve similar to the pressure fall-off of the injection well. It can also be seen that there is a time delay between the injection well shut-in to the peak pressure response of the observation well, and this delay time becomes larger as the distance from the injection well increases. The peak value of the pressure response, ∆pmax becomes smaller and broader, and the peak time recorded at the observation well, ∆tmax, increases with increasing distance from the injection well, rm. For example, ∆pmax=57 kPa at rm=1,000 m becomes more than twice (∆pmax=25 kPa) at rm=3,000 m.
The analytical solution obtained with Eq. (10) is less than the simulation results. The difference between the results increases as the radial distance between the injection well and observation wells increase, because the value estimated by Eq. (10) can only be applied for a rough estimation. In this simulation study, the injection period was assumed to be ti=100 day, and the peak pressure response at the observation well can be detected after dozens of days.

Fig. 17
Numerical simulation results of the pressure response at the observation wells vs. CO2 mass injection rate qm (t-CO2/day)

The pressure ratio of the injection well and observation well Single CO2 injection with pressure build-up and fall-off
To avoid the error in the absolute magnitude of the pressure response at the observation well, we introduced the parameter R, which is the ratio of the pressure build-up (BHP) pi and the maximum value of pressure response ∆pmax. Injection rate, q m (t-CO 2 /day) Both the pressure build-up at the injection well and the pressure response at the observation wells have almost linear relationships with the injection rate, qm<600 t-CO2/day. This ratio can be used for determining the pressure response at the observation wells based on the pressure build-up, because the ratio R=∆pmax/pi is not sensitive to the mass injection rate, qm. In addition, the term qμw/(4πkH) in Eq. (7) can be treated as a constant if the mass injection rate qm is a constant. Therefore, the value of R is proportional to the injection period and hydraulic diffusivity but inversely proportional to the square of the radial distance from the well, while it is not as sensitive to the CO2 mass injection rate qm. The rough value of R can be estimated by the following equation where hydraulic diffusivity, η, is defined by Eq. (5).
where Ct is equal to rock compressibility because fluid is assumed to be incompressible (Cf=0); re=10,000 m is the effective reservoir radius, and rw=0.1 m is the radius of the injection well. Equation (11) shows that R consists of a logarithmic function of time t, aquifer area up to the inner area of the observation well radius (πrm 2 ), and hydraulic diffusivity, η. Assuming that the observation well response to the peak pressure value occurs at the moment the injection well is shut-in, the time t in Eq. (11) is replaced with ti.
The numerical simulations of R using CMG-STARS TM were performed for the base model with the horizontal permeability range from k=196×10 -15 -784×10 -15 m 2 (=200-800 md), the observation well location rm=1,000-5,000 m, and different injection periods ti=50-300 day; the porosity and compressibility of the porous media were considered constant (ϕ=0.30 and Ct =1.4×10 -9 Pa -1 ). A sensitive study of hydraulic diffusivity η was also carried out by setting the constant injection rate qm=600 t-CO2/day. The simulation results of R compared with values calculated by Eq. (11) are shown in Fig. 18. It can be seen that the pressure ratio R shows an almost logarithmic function of ηt/rm 2 . However, there is a slight difference between the values of R for different permeabilities, especially when ηt/rm 2 >10. Because there is a time delay between the injection well shut-in and the observation well response to the peak pressure value, the time t of the simulation results shown in Fig.18 was considered as t=ti+Δtmax. Δtmax is defined as the time delay from the shut-in time at the injection well to the time observation well attains the peak pressure (Fig. 5). Thus, the pressure response at the observation well calculated by Eq. (11) is underestimated compared with the numerical simulation; however, both plots of R vs. ηt/rm 2 have a similar relationship expressed by the logarithmic function. It can also be seen that Eq. (11) is more suitable for a high-permeability aquifer as an aquifer with a larger permeability has a shorter time delay, and the simulation results of R will be closer to the value calculated by Eq. (11). This logarithmic function can help us deduce an evolution of the pressure at the observation well at different distances rm, at different times according to the injection well pressure build-up of field data. The hydraulic diffusivity η was evaluated by the pressure fall-off lines after the shut-in. Therefore, the observation well location can be designed at an appropriate location, and a pressure transmitter with suitable pressure resolution can be selected for pressure monitoring.
An empirical equation based on the simulation results in Fig. 18 was summarized without considering the time delay Δtmax, and it is given by: The pressure ratio at an observation will have a big variation at different permeability aquifer conditions. Eq. (12) can be applied to the Tomakomai CCS project, and it can also be applied to other CCS projects with the pressure ratio ηt/rm 2 <10. In addition, a specific analysis of the pressure ratios against different variables can be performed to make a relatively more accurate assessment for a planned CCS project in the future.

Fig. 18
Numerical simulation results of pressure ratio R for different permeabilities (q=600 t-CO2/day, ti=100 day, According to the simulation results of pressure build-up at the CO2 injection well and pressure response at the observation well, it is expected that the pressure ratio R increases with increasing injection period because the pressure build-up at the injection well pi decreases with increasing CO2 injection period ti. In contrast, the response pressure at the observation well ∆pmax becomes higher. Figure 19 shows the numerical simulation results of the pressure ratio R for different injection periods from ti=50-300 day. The higher response pressure can be monitored by increasing the injection period because R increases with ti.  Fig. 18, there is a small difference between the values of R for different permeabilities, especially when ηt/rm 2 >10. Figure 20 more intuitively reflects the pressure ratio change with the increasing radial distance from the injection well. The pressure ratio, R, changes faster when the radial distance from the injection well is larger. However, as the upper limit pressure response at the observation well is small, it is easy to estimate the pressure for choosing an effective pressure sensor. In the Tomakomai CCS project, the observation well OB-2 was drilled at rm≈3,000 m from the injection well to monitor the pressure change caused by CO2 injection. The present simulation result for qm=600 t-CO2/day and ti=100 day shows that R=0.09 at rm=3,000 m.

Fig. 20
Pressure ratio vs radial distance from the injection well (ti=100 day) for the base model

A case of multiple CO2 injections
For the Tomakomai CCS project, the CO2 injection pattern in the early stage of the project comprised a series of injections with multiple pressure build-ups and fall-offs. The CO2 injection status was tested to check the pressure build-up against the injection rate in the early stage of CO2 injection. A model case used to investigate the pressure response by multiple CO2 injections is shown in Fig. 21. The multiple injection model includes six cycles with ti=100 day as injection period and ts=30 day as shut-in period based on the Tomakomai CCS project (Singh, 2018). The parameters set in the numerical simulation were the same as those for the single injection model (Table 1).
The simulation results of pressure build-up at the injection well and pressure response at the observation well are shown in Fig. 22. The pressure responses of the observation wells located 3,000 m away from the injection well are shown in Fig. 22. The first CO2 injection cycle is the same as the single injection case (base case) until the second cycle starts. It can be seen that each injection causes a pressure response peak at the observation well and draws down in the injection well, similar to the pressure fall-off in the case of single build-up and fall-off. The BHP in the injection well shows a slight drop due to the changing CO2 saturation and fluid viscosity around the injection well as discussed for the single build-up and fall-off case. The pressure build-up in each injection decreases, while the pressure response ∆pmax in each corresponding injection at the observation well gradually increases. The reservoir flow around the injection well turns to a steady state after injecting a large amount of CO2 into the reservoir in a single cycle. As is shown in Fig. 22, the case of multiple CO2 injections shows a broader pressure response. Figure 23 shows the pressure response at the observation wells and the pressure ratio for the distance rm=3,000 m from the injection well. The peak pressure value at the observation well turns to be a stable value, which is similar to the pressure build-up at an injection well. Thus, the pressure ratio also approaches to a stable value. This is more convenient for determining a reliable pressure ratio in the simulation study.

Delay time of the pressure response at the observation well
Even if the injection well is shut-in and returns to the initial pressure, the pressure transmitted in the aquifer continues moving to the outer ward with depleting its amplitude. Figure 24 shows the numerical simulation results of time delay ∆tmax in the aquifer with the horizontal permeability range from k=196×10 -15 -784×10 -15 m 2 (=200-800 md) at the observation wells with different radial distances (rm=1,000 to 5,000 m) from the injection well. As discussed above, fluid flow transmits faster in a high-permeability aquifer, and the pressure transmitting speed is two orders of magnitude higher than that of the CO2 plume. The time delay ∆tmax is proportional to the distance from the injection well and inversely proportional to the aquifer permeability. The time delay ∆tmax increases exponentially with increasing radial distance rm. For example, the time delay value for an observation well located at the radial distance rm=1,000 m occurs the peak pressure value on the day of shut-in of the injection well, while it takes about t=37 day to detect a peak pressure response from an observation well located at a radial distance rm=5,000 m for a reservoir with permeability k=196×10 -15 m 2 . The pressure response at the observation well shows a pressure peak that is almost proportional to the pressure buildup at the injection well. The delay time, Δtmax, as defined in Fig. 5, was found to be the peak value on the curve of p(rm) vs. t for rm=1,000-5,000 m and permeability k=196×10 -15 -784×10 -15 (=200-800 md). The simulation results of Δtmax vs. rm 2 /η are summarized in Fig. 25. It can be seen that the time delay Δtmax is almost linearly proportional to rm 2 /η, which is inversely proportional to the horizontal permeability, k. The relationship can be summarized as follows: The time delay Δtmax can be used as a reference parameter to assess the hydraulic transmission capacity of aquifers.

Design of observation wells for CO2 geological storage
Observation wells are drilled to observe the aquifer with CO2 storage. It is assumed that temperature and pressure gauges are installed in the bottom hole for continuous monitoring of the aquifer. They are used to detect the CO2 plume front development and verify that the injected CO2 had not leaked into shallower strata (Metz et al., 2005).
Most of the observation wells are used to monitor the CO2 plume front position (Hu et al., 2015;Mathieson et al., 2011). rate 78 t-CO2/day) respectively (Liebscher et al., 2013). If the distance between the observation wells and the injection well is extremely small, it can detect the CO2 plume front development. However, according to some in situ experience, the greatest risk of CO2 leakage for any geological storage project is associated with old wells and observation wells.
Thus, an observation well located at a small distance from the injection well also creates a new potential pathway for CO2 leakage to the sublayers, limiting the CO2 injectivity.
In this section, pressure responses at an observation well are analyzed to discuss the effect of the radial distance from the injection well (rm>1,000 m) and the pressure sensor resolution installed in it. Table 2 shows the simulation results of the pressure at the observation well range with different radial distances from the injection well. For example, in the case of the observation well distance is equal to rm=3,000 m, the minimum sensitivity of the pressure transmitter needs approximately 1 kPa order under the absolute pressure (or pressure resistance) of 10 to 11 MPa to obtain an accuracy of 2 digits. However, in the case of the minimum sensitivity is 10 kPa order, the well distance required should be lesser than rm=1,000 m.
The pressure build-up of the Tomakomai CCS project is about 450 kPa, and the observation well OB-2 is drilled with a distance rm=3,000 m from the injection well, according to the calculation, the maximum pressure value might be Δpmax=27 and 35 kPa is expected after t=50 and 100 day injection respectively. The specific resolution of the pressure Hydraulic diffusivity, m 2 /s) transmitter installed in the observation well at rm=3,000 m is required to be less than 1 kPa that is a tough specification under absolute pressure 10 to 11 MPa to analyze aquifer permeability characteristics.

Conclusion
In this study, numerical simulations on pressure responses at injection and observation wells for CO2 geological storage in a deep saline aquifer were done for CO2 injection rate and aquifer characteristics, such as permeability or transmissibility and hydronic diffusivity. The pressure responses and their time delay at the observation well become base data to check whether the aquifer model is enough reasonable to simulate the CO2 storage. If the pressure measurement result at the observation well in the early stage of the CO2 storage project matches the numerical prediction result using the aquifer simulation model, it can be one of the data proofing accuracies of the simulation model. Especially, the pressure ratio of the pressure response at the observation against a pressure build-up and falloff at the injection well has been predicted as the judgment index of pressure change that is mainly related to the distance between injection and observation wells, but not sensitive to the injection rate. Therefore, it is essential to determine the location of the observation well and select a pressure transmitter with a reasonable resolution to measure the pressure response induced by the pressure build-up. The comparison of the simulation results and the actual measured results at the observation well provides whether the wide-area aquifer modeling used for the simulation is enough to correct or not. The results can be summarized as follows: 1. The pressure build-up pi is proportional to q/K (q: CO2 injection rate, K: transmissivity), and gradually tends to be saturated and maintains a slight dropping rate with increasing CO2 saturation around the injection well due to decreasing reservoir fluids viscosity. The equation (6) for steady-state flow can be used for a rough estimation of the pressure build-up of the injection well by assuming saline water saturated in the aquifer.
2. The numerical simulation results of pressure build-up, and fall-off at the injection well were analyzed by comparing the field data of the Tomakomai CCS project, the transmissivity of the Moebetsu Formation targeted in the project was estimated roughly as =2.7×10 -11 m 3 and the hydraulic diffusivity of the reservoir is η=2-4 m 2 /s. Therefore, assuming that the permeability of the Moebetsu Formation is k=13510 -15 -27010 -15 m 2 and the porosity is ϕ=0.20-0.40, and the rock matrix compressibility of the Moebetsu Formation is estimated as Cr=0.14×10 -9 -1.11×10 -9 Pa -1 .
3. The radius of the CO2 plume top front expands approximately proportionally to t 1/2 before t<ti =100 day, and after shut-in of the injection well at t=ti, the top front is slowly expanding with proportionality to 0.1t due to buoyancy force on the CO2 plume.
The numerical simulation results on the pressure ratio R defined as the corresponding response pressure peak at the observation well (∆pmax) overpressure build-up in the injection well (pi ) were analyzed, and a rough estimation value of R at the observation well location (r=rm) has been presented as max 2 = =(0.0425-0.06) ln 0.809 In the case of six cycles of CO2 injections of 100 day injection and 30 day shut-in, R for each response pressure peak at the observation well shows an almost same value as that of the single injection case.

5.
The time of Δtmax from shut-in to the time observing the response pressure peak at the observation well is directly proportional to the radial distance from the injection well (rm) and inversely proportional to the hydraulic diffusivity of the aquifer (η), but it is not sensitive to the injection rate (q).
6. The peak value of pressure response at the observation well at a radial distance from the injection well of rm=3,000 m was simulated as 27-35 kPa for the pressure build-up of 0.45 MPa at the injection well. The specific resolution of the pressure transmitter set in the observation well at rm=3,000 m must be less than 1 kPa to get two or more valid digits.

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Not applicable Figure 1 Schematic aquifer model Injection well perforation schemes used in previous studies; (a) multiple perforations, (b) single perforation hole at the top used by Chadwick (2009) (Chadwick et al., 2009), (c) single perforation hole at a position used by Cinar et al (2008) (Cinar et al., 2008) Figure 7