Analysis of Reservoir Fluid Migration in the Process of CO 2 Sequestration in a Partially Depleted Gas Reservoir

: This paper addresses problems of reservoir ﬂuid migrations in the process of CO 2 sequestration in a partially depleted petroleum reservoir. A detailed analysis of the migrations is required to obtain fundamental characteristics of a sequestration structure, including estimation of its sequestration capacity and leakage risks. The paper presents a general discussion of the relevant mechanisms and their contributions to the analysed issues. The proposed approach to solve the problems relies on the usage of numerical structure modelling and simulations of the sequestration processes on numerical models of the structure. It is applied to a selected geological structure comprising a partially depleted gas reservoir. The modelling includes key types of reservoir ﬂuid migrations: viscous multiphase transport and convection transport. It also takes into account other phenomena that affect ﬂuid migrations including injected gas solubility in the formation water and gas trapping by capillary forces. Correspondingly, the leakage risks are associated with distinct leakage pathways (beyond the structural trap, to the caprock, via activated fractures). All these cases are separately modelled and their detailed characteristics are presented and discussed. The ﬁnal results of the ﬂuid migrations and their consequences for the leakage events are discussed and some generalized conclusions are drawn from the approach employed in the study.


Introduction
The idea of gas sequestration such as CO 2 or other acid gases in geological structures is commonly considered a method of their utilization. A unique example of gas sequestration is given by the Borzęcin project described in [1][2][3][4]-the 25 year on-shore acid gas sequestration project. The study reported in this paper was performed on models of the Borzęcin structure.
Other long-lasting projects of the European contribution include the In Salah CO 2 Storage Project [5] and the Sleipner Carbon Capture and Sequestration Project [6]. Both of those projects are located at different geological settings: the In Salah Project has been reinjecting CO 2 into a fractured sandstone formation since 2004, the Sleipner Project has been reinjecting CO 2 to offshore sandstone formation since 1996. Hence, the Borzęcin Project is the longest-running on-shore sequestration project in Europe.
One of the most important aspects of CO 2 sequestration in deep geological structures refers to risks of CO 2 leakage to shallow geological formations or into the atmosphere which can damage the ecological system and caused hazards to human health. Detailed information about risk assessment procedures is presented in [7]. To asses leakage risks, it is necessary to study processes of fluid migrations within an analysed sequestration structure. There are several pathways of possible fluid migrations.
One of the most likely migration routes is to overburden rocks, which is governed by the threshold pressure. This parameter was extensively studied in experimental tests under laboratory conditions in [8]. Field studies of the leakage path-ways to overburden rocks were performed in [9] but they were limited to the natural CO 2 reservoirs and did not refer to sequestration sites.
Other possible leakage path-ways are induced faults and/or fractures. These cases were studied by D. Alexander and D. Boodlal in [10]. They considered synthetic models of saline aquifers with faults characterized by features typical for potential sequestration structures in a selected geological area. Effects of fractures on gas migration were studied by S. Yang et al. in [11] for a case of enhanced shale gas recovery employing a numerical model based on geological data of Ordos basin in China. T. Nakajima et al. [12] performed numerical simulations of CO 2 leakage along fault system at a hypothetical CCS site with the fault/fracture parameters adopted from Tertiary formations in Japan.
J.R. Brydie et al. [13] recognized the potential leakage pathway via wellbores, which may provide a direct connection between the storage formation and the surface. They performed experimental studies to assess various potential blocking agents and conducted numerical simulations to assess the upscaling requirements of the blocking process in preparation for large-scale laboratory tests and a field demonstration. Their work proves a very complex dependence of the leakage via wellbores upon detailed parameters of the wellbore technicalities, cement bonding, and other characteristics of the wellbore construction. Analogous conclusions can by drawn from the studies by B. Doherty et al. [14] where they applied a special tool to estimate well leakage as response to different scenarios representing initial well states and configurations. Consequently, the problem of leakage via wellbores requires an individual approach to each and every well operating on a sequestration structure.
A significant leakage path-way can result from migrations of a sequestrated gas beyond structural trap boundaries of the sequestration structure. This effect is a particular consequence of the injected gas plume evolution during the sequestration process. G. Zhang et al. [15] studied CO 2 plume migration and fate at Sleipner. They applied a multiphase compositional simulation model to perform a sensitivity study of various simulation results, including plume migration, to changes of fundamental structure parameters. The problem of plume migration was a subject of the study by Y. Zapata et al. [16]. They investigated CO 2 plume characteristics and determined its evolution during a 100-year injection and 200-year post-injection periods in hypothetical saline aquifers. CO 2 plume migration was a subject of the studies by Y. Diao et al. [17] performed on the Shenhua CCS demonstration project in China. That project lasted only five years (2011-2015) and employed relatively shallow saline aquifers. None of the above studies took into account any leakage path-ways other than the one beyond structural trap boundaries.
In this paper we report on the studies of the reservoir fluid migration in the long-term running process of CO 2 sequestration in the structure of the Borzęcin partially depleted gas reservoir in the context of all possible leakage pathways with the exception of leakage via wellbores, as justified above.
To this aim we employed numerical modelling of the analysed structure and simulations of the migration processes performed on the model that was calibrated against the data of 25-years' sequestration history. In general, the modelling of CO 2 sequestration in deep geological structures was performed by many groups of investigators. Such modelling may be exemplified by E.J. Mackay [18], C. Khan et al. [19], W. Szott et al. [20]. They investigated general aspects of CO 2 sequestration with possible anticipatory CO 2 enhanced gas recovery and did not study reservoir fluid migrations in the context of CO 2 leakage risks.
The model of the analysed sequestration structure was constructed and calibrated as reported in the authors' previous publications [21,22]. This paper presents an application of the existing model and its necessary extensions to analyse reservoir fluid migrations and their potential leakage via three typical leakage pathways listed above. Particular tasks concerning statistical analysis presented below were performed according to conventional computer-assisted approach [23].
The approach applied in this study does not include a coupled dynamical and geomechanical simulations, i.e., assumes small influence of the variation of geomechanical state upon the transport properties of the structure rocks. The detailed analysis of this problem is a subject of other papers by the authors. The first paper concerning the subject is [24] Other papers on this subject are in preparation.
The uniqueness of the study presented in this paper refers to: (i) a unique sequestration project of 25 years' history-that infers large amount of operational and monitoring data; (ii) a most complete analysis of fluid migrations including various leakage path-ways.

Reservoir Fluid Migrations
Significant consequences of reservoir fluid migrations during the process of gas sequestration are given by potential leakage risks outside the sequestration site. There are commonly identified as four leakage risk factors according to the following leakage pathways: • leakage beyond the structural trap, • leakage to the caprock by exceeding caprock threshold pressure, • leakage along activated fractures or other rock discontinuities, • leakage along well trajectories (deterioration of well integrity).
The first one occurs when the plume of the injected fluid migrates along the spill trajectories out of the geological structure boundaries defined by caprock local depressions. This case refers to both free phase of the injected fluid and its aqueous solution.
The second one occurs across the reservoir-caprock boundary to overburden rocks. The sealing properties of the caprock are determined primarily by the capillary threshold pressure, which arises from a pore pressure step across the reservoir-caprock boundary for primary pressure vertical distribution. For obvious reasons the actual threshold pressure is not lower than the pressure step at the highest point of the reservoir-overburden boundary.
During the process of gas sequestration in a target structure, a local pore pressure may exceed formation breakdown (fracturing) pressure that is an important characteristic of the structure rock properties. As a consequence, either original fractures can be generated or existing but closed fractures can be opened. If such fractures extend up to the structure overburden, they provide conductive channels for the injected fluid to escape from the sequestration structure.
The last leakage pathway can occur when the integrity of an injecting or monitoring well is deteriorated due to variety of reasons such as failed cement bonding or its erosion. Contrary to the previous three leakage pathways, this one depends upon the technical state of wells and specific geomechanical state of the wells and surroundings and therefore cannot be forecasted prior to well completions.
Analysis of the reservoir fluid migrations resulting in potential leakage events can be obviously performed with the application of numerical structure modelling and simulations of various key reservoir processes taking place during gas sequestration projects. This approach may be realised in both feasibility studies, monitoring, and long-term relaxation phases of such projects. Its basic result includes estimations of the analysed structure sequestration capacity defined as maximum total injection volume avoiding leakage events.
The sequestration capacity strongly depends upon various groups of factors. The first one includes reservoir and fluid properties: • geological properties of the structure (size and shape of structural trap, effective pore volume, absolute permeability and its anisotropy, formation breakdown «fracturing» pressure, caprock threshold pressure, reservoir water distributions, reservoir temperature and pressure, presence, and activity of surrounding and underlying aquifers), • thermodynamic state of reservoir fluids (single-phase vs. multi-phase state, interphase tension), • transport properties of the original reservoir fluid and its mixture with injected CO 2 (miscible vs. immiscible displacement, effective phase permeabilities), • other properties (CO 2 solubility in water, CO 2 reactivity with rock minerals).

•
The other includes operation and technical parameters of a sequestration project: • number and location of injection wells, • depth of completion intervals (relative to the reservoir fluid distribution), • contribution of injection wells in a total injection stream, • injection rates.
The rest of the paper presents the application of the numerical modelling and simulation approach to an example of a geological structure primarily containing a reservoir natural gas that is partially depleted.

Structure Modelling
The analysed geological structure includes the natural gas field located in the southern part of the Pre-Sudetian Monocline, Poland [21]. It forms an anticline with two local uprisings. The structure includes the Zechstein anhydrites and salt formation over the Basal limestone formation on top of the Rotliegend sandstone formation. The Basal limestone horizon and the Rotliegend sandstone horizon are hydrodynamically connected while the Zechstein horizon forms a caprock of the former. The natural gas zone is limited by the underlying water.
A simulation model of the structure was constructed and calibrated [21]. A geological model was generated based on standard input data including structural maps of the above listed formations. An example of the structural map of the Basal limestone top is shown in Figure 1 that also defines a vertical cross section line A-A'. A basic parametric model of the structure was constructed based on standard input data sources including geophysical logs, laboratory measurements of well core samples, etc. Those data were used to generate lithological, stratigraphic, and geophysical structures for all tested wells. For spatial distributions of key geological parameters (porosity, permeability, net-to-gross thickness ratio), a variographic analysis was applied. The resulting variogram (spherical type) and its parameters (sill, range values) were used to conditionally simulate (by sequential gaussian simulation) stochastic realizations of all parameter distributions [25]. The effects of fine-scale features [26] and their influence on rock deformations [27] were considered as those of higher order and postponed to future studies.    Based on the geological model a dynamical simulation model of the structure was constructed [19] that included the original gas-bearing zone surrounded by an active water-bearing zone.
The dynamical model was complemented with initial gas and water saturation distributions consistent with measured data and complying hydrostatic conditions and an original water-gas contact depth. Resulting gas saturation distribution is presented in   A standard Corey type dependences upon fluid saturations were adopted for relative permeabilities used in the model.
The simulation model of the analysed structure was formulated as a compositional one for the variations of the reservoir gas composition to be reconstructed and monitored. To this aim the Peng-Robinson equation of state and standard Lorentz-Bray-Clark viscosity correlation were applied and six parameter (three hydrocarbon components: C 1 , C 2 , C 3+ , and three nonhydrocarbon components: N 2 , CO 2 , H 2 S) gas composition was assumed. The initial gas composition is given in Table 1. Reservoir brine properties applied in the model consist of: density (1100 kg/m 3 ), salinity (150 g/L), formation volume factor: (1.011 Rm 3 /Sm 3 @ 154.8 bar, 46.8 • C), compressibility (4.5 × 10 −5 1/bar), viscosity (0.66 cP, @ 154.8 bar, 46.8 • C), viscosibility (6 × 10 −5 1/bar).
In addition, CO 2 solubility in the reservoir brine was taken into account based on the laboratory measurements [28] shown together with interpolating curves in Figure 7. The dynamical model was complemented with basic well data (localizations, trajectories, radii, completion intervals). The complete model of the structure used the format of Eclipse simulator by Schlumberger ® .
The simulation model of the structure was calibrated based upon the gas reservoir operational data [4]. Examples of the calibration results are given in: Figures 8-10 as bottomhole pressures, water-gas ratios, and CO 2 concentrations of the produced gas in Well W4, respectively.   The calibration process concluded with a satisfactory match of the model results to the measured data and resulted in several modifications of model parameters including: the division of the model into three partially separated regions (western, central, and eastern ones as shown in Figure 11) required to match three different measured pressure trends as presented in Figure 12; transmissibilities between these regions; their effective pore volumes; characteristic parameters of underlying aquifers; global vertical to horizontal permeability anisotropy; local transport properties in several well drainage zones.

Sequestration Capacity
The calibrated model of the structure is used for the detailed analysis of processes taking place during the sequestration project resulting, among others, in the estimation of the sequestration capacity. This value depends upon and requires the adoption of several technical assumption of the sequestration project. The key assumption refers to the well system applied to the injection phase of the project. For the analysed structure the well system includes 17 wells shown in Figure 13. Additional assumptions include: • completion of the injection wells in aquifers underlying the gas cap, • maximum injection rates of an individual well, q g,inj,max = 400,000 Nm 3 /d, • maximum bottomhole injection pressure, P bhp,max = 200 bar.
While fulfilling these assumptions, varying total CO 2 injection scenarios were tested against the following risk determinants: • no leakage of the injected CO 2 beyond the structural trap, • maximum pressure in the structure volume below the formation damage (fracturing) pressure, • maximum pressure step across the reservoir-caprock boundary below the displacement threshold pressure.
The scenarios differ in injection schedules and in contributions of the individual injection wells to the total injection stream. As a result of the optimization process taking into account the above criteria, a simulation scenario was determined for which the amount of CO 2 injected into the structure was maximized. Thus, the sequestration capacity was found to be 135% of the OGIP (original gas in place) and the injection phase lasted 8 years and 5 months.
The maximum local pressure was localized along the trajectory of an injection well. Its value was 108% of the initial pressure in the reservoir and was significantly lower than the fracturing pressure of the structure rocks. Therefore, there is no risk of gas leakage through the fracture into the overburden.
Another risk factor for gas leakage related to the displacement threshold pressure was analysed by the estimation of the pressure step across the reservoir-caprock boundary that reached its maximum value at the end of the injection phase and at the highest point of the structure and did not exceed the threshold pressure.

CO 2 Sequestration Forecasts vs. Total Injection
Additional scenarios were performed to study the effects of increased total injection upon the sequestration process. In general, total injection volumes exceeding the sequestration capacity resulted in violating any of the three leakage criteria related to and listed in the "Leakage pathways" chapter above. Below, the three cases were studied separately, one at a time.
The case of the leakage beyond the structural trap boundaries was investigated in four scenarios differing in the total injection volumes relative to the sequestration capacity found earlier. Figure 14 shows the leakage volume as a function of time for the scenarios of the total injections equal to 128%, 154%, 180%, and 205% of the sequestration capacity for the subsequent four scenarios respectively. It is worth noting that leakage prolongs a long time (up to 100 years) after the injection phase is finished. The amount of total leakage after 100 years was 0.002%, 0.06%, 0.42%, 1.25% of the sequestration capacity CO 2 volume, for the four scenarios, respectively. The size of the leakage and its time evolution were influenced by: • increased total injection volume and, consequently, an increased pressure difference across the storage zone and surrounding water-bearing horizons causes the migration of the injected CO 2 in the free phase beyond the trap boundaries, • equalization of gas saturations (flows inside the storage zone) in the relaxation phase with a simultaneous slow pressure drop in some regions due to the pressure equalization process (and a consequent decrease in the amount of CO 2 dissolved in the brine) increases the volume of the mobile gas that migrates beyond the trap boundaries.
Further analysis of the total CO 2 leakage beyond the trap boundaries as a function of the storage capacity filling for t = 10, 50, 100 years since the injection start ( Figure 15) allowed to formulate the following conclusions: • the amount of the total leakage significantly increases in cases where more than 154% of the sequestration capacity has been injected, • in the case of the total injection volume up to 154% of the sequestration capacity, the rate of CO 2 leakage from the storage zone does not vary with time, • in the case of the total injection volume above 180% of the sequestration capacity, most of the outflow beyond the trap boundaries occurs in the first 50 years, when a highpressure difference is observed between the storage zone and the surrounding aquifers. The identification of the sites where gas leaks beyond the storage zone is available with the analysis of free-phase gas saturation in the top layer of the storage zone and in vertical sections of the structure. An example of data for such an analysis is presented in Figure 16 for the scenario in which the total injection volume equals 205% of the sequestration capacity. From these data it can be concluded that during the injection phase of the sequestration project the leakage beyond the storage zone occurs near the wells, i.e., in the south-eastern part of the reservoir, and then during relaxation phase of the sequestration project-along quite different routes i.e., in the northern, north-western and south-western parts of the reservoir. This analysis not only allows to identify the most critical places of potential gas leakage but also to optimize the contribution of individual wells to the total injected gas stream to reduce the leakage.
Below, the simulation of the other two leakage paths are presented and discussed in detail. The dimensionality of the models applied to simulate them was selected the smallest ones that are sufficient to model each of them. Therefore, it is a 1D model for leakage to the caprock by exceeding threshold pressure and a 2D model for leakage via a fracture.

1D Model of CO 2 Migration in the Overburden Due to Exceeding Displacement Threshold Pressure
In order to investigate processes of injected gas leakage to the overburden and to estimate leakage quantities, a one-dimensional simulation model was applied taking into account detailed characteristics of the overburden.
For these purposes, a high-resolution 1D model was constructed including a storage zone together with an extended overburden zone (with the total thickness above 1000 m) including anhydrite and rock salt horizons as shown in the most left part of Figure 17. The detailed parametric model was based upon the stratigraphic data presented in Table 2.  The model adopted the estimated displacement threshold pressure of the caprock (P th = 9.25 bar). Two ensembles of several scenarios each were investigated differing in initial pressures at the storage zone top corresponding to various exceeding of the threshold pressure and in the pressure, boundary conditions at the storage zone top-this pressure was either kept constant or naturally decreasing according to the steady depletion of the storage zone by the leakage effects. The ensemble no. 1 included scenarios with the storage zone initial pressure of P ini1,s = 165.68 bar, which is equivalent to exceeding the threshold pressure by 12 bar. The Ensemble no. 2 included scenarios with the storage zone initial pressure of P ini1,s = 170.68 bar, which is equivalent to exceeding the threshold pressure by 17 bar. An example of simulation results in terms of a leaked gas distribution across the overburden for a scenario from the Ensemble no. 2 is shown in Figure 17. Similar results were obtained for other scenarios of this ensemble and they will be presented and discussed below. Results in Figure 17 are described below: • during gas migration through the anhydrite, the main factor determining the relatively small migration velocity is the low absolute permeability of the rock, • a secondary factor affecting the velocity of the gas migration is the pressure at the top of the storage zone (the bottom of the overburden), • during gas migration through the anhydrite, it reaches saturation, S g~2 6%, which determines its effective phase permeability, • after reaching the rock salt horizon, gas migration is faster due to their larger absolute permeability, • in the rock salt horizon, gas migration becomes effective at relatively low gas saturation due to small critical gas saturation S gcr = 10%, • decrease of gas saturation in the anhydrite formations to the value of S g~1 8% after 500 years since the end of injection results from the fast migration of gas through the rock salt horizon and the decrease of the pressure at the top of the storage zone.

Ensemble Approach to Study CO 2 Migration in the Overburden of Uncertain Properties
Since the main parameters of the overburden rocks, such as the absolute permeability of young rock salts and anhydrite (YRS&A-rocks with relatively low permeabilities), and the old rock salts (ORS-rocks with relatively high permeability) were known with high uncertainty, therefore an ensemble approach was applied to study the influence of these parameters upon the results of leaked gas migration in the overburden. The uncertain parameters were assumed to vary within a selected range of values for a selected probability distribution. The list of these parameters include: • absolute permeability of young rock salts and anhydrite (YRS&A), • absolute permeability of old rock salts (ORS), • maximum gas relative permeability (K rgmax ), • critical saturation for gas (S gcr ), • critical saturation for water (S wcr ), • threshold pressure (P th ).
The first two parameters were modified by multiplicative factors: MF_YRS&A and MF_ORS for YRS&A and ORS, respectively, and their probability distributions were of logarithmic-triangular type. The remaining parameters were directly modified with triangular probability distributions. The detailed data of the parameter reliability are given in Table 3. Based on the assumed variability of input parameters and the initial pressure at the bottom of the underburden two ensembles were generated with the multiplicity of n = 729 cases (scenarios).
Basic simulation results of the ensemble cases in the form of CO 2 leakage as function of total injection volume (related to the sequestration capacity) for Ensemble no. 1 (P ini1,s = 165.68 bar) is the amount of leakage after 500 years from the end of gas injection. It ranges from 0.13% to 0.40% of sequestration capacity, while for Ensemble no. 2 (P ini2,s = 170.68 bar), the amount of leakage ranges from 0.23 to 0.55% (Figure 18). For the above forecasts, a distance of the gas front position from the overburden bottom ranges from 9 to 33 m (for Ensemble no. 1 with initial pressure P ini1,s = 165.68 bar at the bottom boundary of the overburden). The same quantity varies between 12 and 39 m for Ensemble no. 2 with initial pressure P ini2,s = 170.68 bar as shown in Figure 19. Step-like variation of the distance results from the finite resolution (0.5 m) of the model vertical structure.
The statistical analysis for both ensembles is presented in Figures 20 and 21 for CO 2 leakage and distance of CO 2 migration in the overburden, respectively. It contains histograms of the results discussed above together with their cumulative distribution functions of the simulation results after 500 years from the end of gas injection. Based on these results the following conclusions can be made: • both the values of the total CO 2 leakage and the distances between the gas front position from the overburden bottom are smaller for Ensemble no. • the difference of the results for the distances between the gas front location and the overburden bottom between the two ensembles is smaller than the analogous difference of the results for the total leakage between the two ensembles.

2D Model of CO 2 Migration in the Overburden via Induced Fractures
The last case of the CO 2 migration in the overburden refers to CO 2 leakage via induced fractures. For the study of this migration 2D models of the structure vertical cross-section were constructed with vertical resolution of 0.5 m. The data from Table 2 were implemented into the parametric model with a uniform distribution in horizontal layers. Figure 22 presents a detailed layer structure of the overburden used in the 2D model for this case. For the purposes of studying the gas migration to the overburden within induced macro-fractures, three simulation models were constructed. They differed in the properties of a macro-fractures as follow: For each of the above models, the initial pressure at the reservoir top/overburden bottom was assumed to be, P ini = 170.68 bar.
Another unknown factor that was used in scenario of the models described above was the height of the resulting fracture. For the sake of simplicity, it was assumed that the fracture is formed in the entire thickness of separated formations, therefore, for each model, three Sub-scenarios were considered where the induced fracture extends up to: lower anhydrite (LA), 2.
The rates and total CO 2 leakage volumes to the overburden rocks obtained as results of the simulations on the above Model I are presented in Figures 23-25 for Sub-scenario 1, Subscenario 2, and Sub-scenario 3, respectively. These results can be summarized as follow: • for the shortest fracture (Sub-scenario 1) its conductivity does not affect the rate and total leakage volume, while for the longer fractures (Sub-scenario 2 and Sub-scenario 3), the larger the conductivity the larger the leakage, • for Model III (assuming a decrease of the pressure at the reservoir top/overburden bottom according to the steady depletion of the storage zone by the leakage effects) the outflow rate decreases with time due to the ever-lower pressure gradient between the fracture and the overburden, • for Models I and Models II (assuming constant pressure at the reservoir top/overburden bottom over time) the leakage rate decreases for the first 70 years (LA fracture), while in the following years the leakage rate begins to increase, which is related to the movement of the gas front, resulting in an increase in gas saturation in subsequent layers, and which in turn causes an increase in phase permeability for gas (resistance drop), • for the shortest fracture (Sub-scenario 1), its conductivity does not affect the results, while in the case of further extending fractures (Sub-scenario 2 and Sub-scenario 3) their conductivities have significant impacts on the leakage rate which increases with the fracture extension.   The detailed analysis of gas migration in the overburden due to the gas leakage from the sequestration zone via an induced fracture is based upon the studies of the evolution of gas distributions obtained from the simulation predictions performed on three models introduced above. As an example, the results of Sub-scenario 3 (for the longest-range fracture extended across lower anhydrite, old rock salt, and upper anhydrite formations) are presented in Figures 26-28) for Model I, Model II, and Model III, respectively. This analysis can be summarized as follows: • gas migration through the main dolomite formations of the sequestration zone is much faster than its subsequence migration through the Lower Anhydrite, Old Rock Salt, Upper Anhydrite formations of the overburden due to a very low permeability of the latter-as a consequence the gas migration in this part of the overburden is confined to the vertical, upward movement within the fracture with no horizontal spread, • when the gas reaches the Main Dolomite formation of low thickness and increased permeability it migrates horizontally within this formation, • as a consequence of this horizontal migration, further gas upward migration is horizontally spread even though it takes place in low permeability formations (  Figure 27. However, the overall pattern of the gas migration in Model III is similar to the pattern of the former models, • the infinite conductivity fracture is completely filled with gas during the total simulation period and along the complete fracture length and reveals no pressure gradient, • in contrary, the case of the finite conductivity fracture results in gas saturation varying with the fracture hight and changing its value between 15% at the dolomite formations and 1.5% at the anhydrite formations. This indicates a noticeable inflow of formation water into the fracture.

Summary
Numerical simulations of dynamical phenomena taking place during the project of CO 2 sequestration in a partially depleted reservoir gas give a unique opportunity to study reservoir fluid migrations in both the sequestration zone and in the overburden of that zone in case of CO 2 leakage from the sequestration zone to the overburden. Key types of reservoir fluid migrations include: viscous multiphase transport (mobile injected CO 2 in free phase or hypocritical phase, mobile formation water with dissolved CO 2 ) in porous and naturally fractured media driven by the pressure potential gradient; convection transport due to differences of local fluid densities (downward movement of formation water with dissolved CO 2 ). The viscous transport is limited by the adhesive phenomena generating immobile phases as a fracture of the free or hypocritical phases. In addition, the injected CO 2 migration is affected by chemical reactions of aquas CO 2 with metal cations. All the above effects, that determine actual migrations of reservoir fluids including the injected CO 2 , are modelled in the numerical simulation approach to analyse the process of CO 2 sequestration in partially depleted petroleum reservoirs.
A sequestration capacity being a fundamental characteristic property of the sequestration structure results from a maximum injection volume for which reservoir fluid migrations are constrained to the sequestration zone or, equivalently, no leakage effects occur. Reservoir fluid migrations can generate one of the following, commonly identified four types of leakage risks associated with leakage pathways: • leakage beyond the structural trap, • leakage to the caprock by exceeding caprock threshold pressure, • leakage along activated fractures or other rock discontinuities, • leakage along well trajectories (deterioration of well integrity).
In this study the numerical approach with all its advantages was applied to realistic structure of a partially depleted gas reservoir located in the southern part of the Pre-Sudetian Monocline of Poland. A model of this structure was constructed and calibrated against the multi-year history of gas production from the reservoir and acid gas sequestration to the underlying water formations. The sequestration capacity of the structure was determined taking account all the leakage risks by including the above-described migration phenomena and accepting several technical constrains (system of injection wells, their location and completion, maximum allowable injection rates, maximum bottomhole injection pressure). In addition, the following structure characteristics are found significant for the sequestration process simulations: spill points of the analysed structure trap, formation damage (fracturing) pressure, displacement threshold pressure across the reservoir-caprock boundary. The leakage risk associated with deteriorations of injection well integrities was not considered in the above studies as it is an individual feature of injection wells and it cannot be predicted in a deterministic way.
When the sequestration capacity of the structure is exceeded by the injected volume then one or more of the above leakage pathways become effective in the following sequence with the increasing injection volume: beyond the structural trap, to the caprock by exceeding threshold pressure, along activated fracture. For the detailed studies of the migration processes leading to the above leakages, they were investigated separately, one at a time.
In the case of the leakage beyond the structural trap, it is found to extend to the future far beyond the end of an injection phase, i.e., the leakage is observed during the long-time (above 100 years) of a relaxation phase. The total leakage volume strongly depends upon the difference between the sequestration capacity and the actual injection volume. In case of the analysed structure, exceeding the sequestration capacity by 105% results in the total leakage of 1.25% of the sequestration capacity after 100 years of the sequestration project. The analysis of the simulation results also provides an information about the leaked CO 2 spatial distribution beyond the structural trap.
In the case of the leakage to the overburden caused by the pressure step across the sequestration zone-caprock boundary to exceed displacement threshold pressure, in general, depends upon the injected volume (maximum pressure at the sequestration zone top) and transport properties of the overburden formations. While the effect of the total injected volume upon the leakage volume is obvious, then the leaked gas migration in the overburden is significantly dependent upon the detailed properties of individual overburden formations. As the properties of overburden formations are known with typically large uncertainties, such are the simulation results of the total leakage volume. In the case of the analysed structure, the most influential, fundamental properties (absolute permeability, maximum gas relative permeability, critical gas and water saturation, threshold pressure) of the overburden formations were identified and assumed to be known with uncertainties of approx. 30% and to follow triangular or log-triangular distribution functions. The simulation results for the total CO 2 leakage (after 500 years of the sequestration project) to the overburden followed the probability distribution of the normal type with the expected values from 2.7 ‰ to 3.9 ‰ (for the pressure step at the sequestration zone-caprock boundary exceeding the threshold pressure by 12 bars and 17 bars, respectively) of the sequestration capacity and with the standard deviation of 0.6 ‰ of the sequestration capacity. The analogous simulation results for the migration distance of the CO 2 to the overburden followed a probability distribution resembling the normal distribution but with a positive skewness and with the expected values from 4.75 m to 5.75 m with the standard deviation of approximate 1 m.
In the case of the leakage to the overburden caused by a macro-fracture induced by the actual pore pressure exceeding formation damage pressure the CO 2 migration in the overburden depends upon the initial pressure in the sequestration zone, extension, and transport properties of the macro-fracture in the overburden and transport properties of the overburden formations. While the independence upon the first two factors is obvious, the effects of the macro-fracture and overburden properties are strongly dependent upon the relative relations of the properties and the sequence of the formations. In the case of the analysed structure, the CO 2 migration in the overburden is basically limited to the 2D plane of the fracture interior. This rule results from a typical large disproportion of fracture permeability and matrix permeability in the overburden. If this disproportion is smaller than the CO 2 migration can accept a 3D character as it is the case of the analysed structure at the dolomite, large permeability formation to be followed by the anhydrite, low permeability formation. Unexpectedly, in this case, the migration processes weakly depend upon the transmissibility of the macro-fracture.

Conclusions
The studies presented in this paper and concerning the analysis of reservoir fluid migration in the process of CO 2 sequestration in a partially depleted gas reservoir prove usefulness and necessity of the sequestration project modelling in the quantitative characterization of the project. As shown for the analysed case, a detailed description of the reservoir fluid migration corresponding to the injected gas leakage beyond the sequestration zone are strongly dependent upon the details of the geological properties of the structure and cannot be easily deduced from the overall description of the structure. This conclusion implies necessity of the usage of reliable simulation models of the sequestration site and its surrounding. Such models can be constructed only based upon the detailed characterization of the sequestration structure and the complete set of the historical data of the structure functioning including monitoring measurements of the sequestration process and thus improve their reliability and validity.
In particular, this conclusion concerns a long-term leakage risk analysis due to prolonged processes of the leaked gas migration from the sequestration zone to the structural overburden. Only the long-term simulation modelling of a sequestration project is a unique source of information necessary to assess consequences of the leakage.