Method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs

Abstract

The method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs estimates porosity and water saturation in a porous medium, such as brine-saturated shale, as is common in carbon capture and storage reservoirs, based upon measured electrical conductivity and seismic P-wave velocity. The estimated porosity and water saturation may be used for monitoring carbon dioxide leakage from a carbon dioxide reservoir to the overlying cap rock of the region. Measured electrical conductivity and seismic P-wave velocity data are used by the present method to estimate the porosity and water saturation in the cap rock. If a decrease in water saturation in the cap rock is found, this indicates that carbon dioxide may be leaking up from the carbon dioxide reservoir. An alert signal is then generated to indicate that there may be a carbon dioxide leak.

Claims

1. A method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs, comprising the steps of: (a) setting an integer i equal to zero; (b) measuring an electrical conductivity σ and a seismic P-wave velocity V.sub.p at a cap rock location above a carbon dioxide storage reservoir; (c) calculating a porosity φ associated with the cap rock as $V_p=\sqrt{\frac{\begin{array}{c}\varphi K_a{K}_m{K}_w+\left({\varphi }_c-\varphi \right)\left(K_m+\frac{4}{3}{G}_m\right)[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+\\ K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)]\end{array}}{\begin{array}{c}{\varphi }_c\left[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)\right]\\ \left[\left(1-S_w\right){\mathrm{\varphi \rho }}_a+\left(1-\varphi \right){\rho }_m+\varphi S_w{\rho }_w\right]\end{array}}}$ where a water saturation S.sub.w of the cap rock is given by: $S_w=\frac{\sqrt{\sigma }-\left(1-\varphi \right)\sqrt{{\sigma }_m}-\varphi \sqrt{{\sigma }_a}}{\varphi \left(\sqrt{{\sigma }_w}-\sqrt{{\sigma }_a}\right)},$ wherein σ.sub.m is an electrical conductivity of a solid matrix of the cap rock, σ.sub.w is an electrical conductivity of water in the cap rock, and σ.sub.a is an electrical conductivity of air in the cap rock, K.sub.a is a bulk modulus of the air in the cap rock, K.sub.m is a bulk modulus of the solid matrix of the cap rock, K.sub.w is a bulk modulus of the water in the cap rock, φ.sub.c is a critical porosity of the cap rock, G.sub.m is a shear modulus of the solid matrix of the cap rock, ρ.sub.a is a density of the air in the cap rock, ρ.sub.m is a density of the solid matrix of the cap rock, and ρ.sub.w is a density of the water in the cap rock; (d) calculating an i-th value of the water saturation S.sub.wi of the cap rock as: $S_{\mathrm{wi}}=\frac{\sqrt{\sigma }-\left(1-\varphi \right)\sqrt{{\sigma }_m}-\varphi \sqrt{{\sigma }_a}}{\varphi \left(\sqrt{{\sigma }_w}-\sqrt{{\sigma }_a}\right)};$ (e) recording the i-th value of the water saturation S.sub.wi of the cap rock in non-transitory, computer-readable memory; and (f) if consecutive i-th values of the water saturation of the cap rock decrease, then generating an alert signal to indicate a carbon dioxide leak in the cap rock, and if the consecutive i-th values of the water saturation of the cap rock do not decrease, then setting i=i+1 and returning to step (b).

2. A computer software product that includes a non-transitory storage medium readable by a processor, the non-transitory storage medium having stored thereon a set of instructions for performing monitoring carbon dioxide leakage in carbon capture and storage reservoirs, the instructions comprising: (a) a first set of instructions which, when loaded into main memory and executed by the processor, causes the processor to set an integer i equal to zero; (b) a second set of instructions which, when loaded into main memory and executed by the processor, causes the processor to measure an electrical conductivity σ and a seismic P-wave velocity V.sub.p at a cap rock location above a carbon dioxide storage reservoir; (c) a third set of instructions which, when loaded into main memory and executed by the processor, causes the processor to calculate a porosity φ associated with the cap rock as: $V_p=\sqrt{\frac{\begin{array}{c}\varphi K_a{K}_m{K}_w+\left({\varphi }_c-\varphi \right)\left(K_m+\frac{4}{3}{G}_m\right)[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+\\ K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)]\end{array}}{\begin{array}{c}{\varphi }_c\left[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)\right]\\ \left[\left(1-S_w\right)\varphi {\rho }_a+\left(1-\varphi \right){\rho }_m+\varphi S_w{\rho }_w\right]\end{array}}}$ where a water saturation S.sub.w of the cap rock is given by: $S_w=\frac{\sqrt{\sigma }-\left(1-\varphi \right)\sqrt{{\sigma }_m}-\varphi \sqrt{{\sigma }_a}}{\varphi \left(\sqrt{{\sigma }_w}-\sqrt{{\sigma }_a}\right)}$ wherein σ.sub.m is an electrical conductivity of a solid matrix of the cap rock, σ.sub.w is an electrical conductivity of water in the cap rock, and σ.sub.a is an electrical conductivity of air in the cap rock, K.sub.a is a bulk modulus of the air in the cap rock, K.sub.m is a bulk modulus of the solid matrix of the cap rock, K.sub.w is a bulk modulus of the water in the cap rock, φ.sub.c is a critical porosity of the cap rock, G.sub.m is a shear modulus of the solid matrix of the cap rock, ρ.sub.a is a density of the air in the cap rock, ρ.sub.m is a density of the solid matrix of the cap rock, and ρ.sub.w is a density of the water in the cap rock; (d) a fourth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to calculate an i-th value of the water saturation S.sub.wi of the cap rock as: $S_{\mathrm{wi}}=\frac{\sqrt{\sigma }-\left(1-\varphi \right)\sqrt{{\sigma }_m}-\varphi \sqrt{{\sigma }_a}}{\varphi \left(\sqrt{{\sigma }_w}-\sqrt{{\sigma }_a}\right)};$ (e) a fifth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to record the i-th value of the water saturation S.sub.wi of the cap rock in non-transitory, computer-readable memory; and (f) a sixth set of instructions which, when loaded into main memory and executed by the processor, causes the processor to generate an alert signal to indicate a carbon dioxide leak in the cap rock if consecutive i-th values of the water saturation of the cap rock decrease, and to set i=i+1 and return to the second set of instructions if the consecutive i-th values of the water saturation of the cap rock do not decrease.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a block diagram illustrating system components for implementing a method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs according to the present invention.

(2) FIG. 2A is a graph comparing conductivity as a function of porosity modeled by the prior art complex refractive index method (CRIM) against other prior art techniques, including a basic arithmetic model, a harmonic model, a geometric model, the Hermance model, a self-similar model, the Hashin-Shtrikman model, Archie's law, and a modified version of Archie's law (indicated as by the “Glover” curve) for data obtained from a shale section of a well in the Gullfaks field of the North Sea.

(3) FIG. 2B is a graph comparing conductivity as a function of porosity modeled by the prior art complex refractive index method (CRIM) against other prior art techniques, including a basic arithmetic model, a harmonic model, a geometric model, the Hermance model, a self-similar model, the Hashin-Shtrikman model, Archie's law, and a modified version of Archie's law (indicated as by the “Glover” curve) for data obtained from a sandy section of the same well as in FIG. 2A.

(4) FIG. 3 is a three-dimensional plot of electrical conductance as a function of porosity and brine saturation modelled by the prior art complex refractive index method (CRIM) for a typical brine-saturated shale.

(5) FIG. 4 is a three-dimensional plot for P-wave velocity as a function of porosity and brine saturation for a typical brine-saturated shale.

(6) FIG. 5 is a three-dimensional plot of inverted porosity as a function of measured P-wave velocity and electrical conductance generated by the method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs according to the present invention.

(7) FIG. 6 is a three-dimensional plot of inverted brine-saturation as a function of measured P-wave velocity and electrical conductance generated by the method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs according to the present invention.

(8) Similar reference characters denote corresponding features consistently throughout the attached drawings.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

(9) The method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs estimates porosity and water saturation in a porous medium, such as brine-saturated shale commonly found in carbon capture and storage (CCS) reservoirs, based upon measured electrical conductivity (σ) and seismic P-wave velocity (V.sub.p). The estimated porosity and water saturation may be used for monitoring carbon dioxide (CO.sub.2) leakage from a carbon dioxide reservoir to the overlying cap rock of the region. Controlled source electromagnetic (CSEM) surveying is performed repeatedly at close intervals over the carbon dioxide reservoir to measure the electrical conductivity in the cap rock. A seismic survey is performed right after each CSEM survey in order to measure the P-wave velocity in the cap rock at the same locations where the electrical conductivities were measured. The measured electrical conductivity and seismic P-wave velocity data is then used by the method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs to estimate the porosity and water saturation in the cap rock. If a decrease in water saturation in the cap rock is found, corresponding to sequential measurements, this indicates an increase in gas saturation, which indicates that carbon dioxide may be leaking up from the carbon dioxide reservoir. An alert signal is then generated to indicate that there may be a carbon dioxide leak.

(10) It should be understood that the calculations of the present method can be performed by any suitable computer system, such as that diagrammatically shown in FIG. 1. Data is entered into the system 100 via any suitable type of user interface 116, and can be stored in memory 112, which can be any suitable type of computer readable and programmable memory and is preferably a non-transitory, computer readable storage medium. Calculations are performed by a processor 114, which can be any suitable type of computer processor, and can be displayed to the user on display 118, which can be any suitable type of computer display. The electrical conductivity σ and seismic P-wave velocity V.sub.p are fed to the system by any suitable type of electrical conductivity sensor 120, such as a CSEM system or the like, and by any suitable type of seismic P-wave velocity sensor 122.

(11) The processor 114 can be associated with or incorporated into any suitable type of computing device, for example, a personal computer, a programmable logic controller (PLC), or an application specific integrated circuit (ASIC). The display 118, the processor 114, the memory 112 and any associated computer readable recording media are in communication with one another by any suitable type of data bus, as is well known in the art.

(12) Examples of computer-readable recording media include non-transitory storage media, a magnetic recording apparatus, an optical disk, a magneto-optical disk, and/or a semiconductor memory (for example, RAM, ROM, etc.). Examples of magnetic recording apparatus that can be used in addition to memory 112, or in place of memory 112, include a hard disk device (HDD), a flexible disk (FD), and a magnetic tape (MT). Examples of the optical disk include a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc-Read Only Memory), and a CD-R (Recordable)/RW. It should be understood that non-transitory computer-readable storage media include all computer-readable media, with the sole exception being a transitory, propagating signal.

(13) Although several models have been proposed to explain the relation between V.sub.P, φ and S.sub.w in porous media, the Gassmann model is the most commonly used among these models for low-frequency (less than 100 Hz) seismic studies. The Gassmann model is appropriate for CCS because V.sub.P measured from surface seismic reflection surveys has frequencies that fall within this range. In this model, the bulk (K.sub.s) and shear (G.sub.s) moduli of the saturated material are given by:

(14) $\begin{array}{cc}\frac{K_S}{K_m-K_s}=\frac{K_d}{K_m-K_d}+\frac{K_f}{\varphi \left(K_m-K_f\right)}& \left(17\right)\\ G_s=G_d,& \left(18\right)\end{array}$
where K.sub.m, K.sub.d and K.sub.f are the bulk moduli of the mineral making up the rock, the dry rock, and the pore fluid, respectively, and G.sub.d is the shear modulus of the dry rock. The pore-fluid bulk modulus of an air-water mixture is given by Wood's formula as:

(15) $\begin{array}{cc}\frac{1}{K_f}=\frac{S_w}{K_w}+\frac{\left(1-S_w\right)}{K_a},& \left(19\right)\end{array}$
where K.sub.w and K.sub.a are the bulk moduli of the pore water and air, respectively. The dry-rock bulk and shear moduli can be approximated by the following linear relations in the porosity range φ≦φ.sub.c:

(16) $\begin{array}{cc}{K}_d=K_m\left(1-\frac{\varphi }{{\varphi }_c}\right)& \left(20\right)\\ G_d=G_m\left(1-\frac{\varphi }{{\varphi }_c}\right),& \left(21\right)\end{array}$
where G.sub.m is the shear modulus of the mineral making up the rock and φ.sub.c is the critical porosity of the rock. The critical porosity of a porous medium is the porosity at which the medium changes its mechanical behavior from a medium in which the mineral grains are load-bearing to a suspension in which the fluid phase is load-bearing. The typical critical porosity for shales is φ.sub.c=0.4. For a multi-mineral rock matrix, K.sub.m and G.sub.m can be estimated using Hill's average of the Voigt and Reuss bounds as:

(17) $\begin{array}{cc}{K}_m=\frac{1}{2}\times \left[\underset{i}{.Math.}\left(p_i\times K_i\right)+\underset{i}{.Math.}\left(\frac{p_i}{K_i}\right)\right]& \left(22\right)\\ G_m=\frac{1}{2}\times \left[\underset{i}{.Math.}\left(p_i\times G_i\right)+\underset{i}{.Math.}\left(\frac{p_i}{G_i}\right)\right],& \left(23\right)\end{array}$
where p.sub.i, K.sub.i, and G.sub.i are the fractional volume, the bulk, and shear moduli of the i-th mineral phase of the rock matrix.

(18) The P-wave velocity in the rock at any porosity or saturation is given by:

(19) $\begin{array}{cc}{V}_p=\sqrt{\frac{K_s+\frac{4}{3}{G}_s}{{\rho }_s}},& \left(24\right)\end{array}$
where ρ.sub.s is the density of the saturated rock, given by:
ρ.sub.s=(1−φ)ρ.sub.m+φ(1−S.sub.w)ρ.sub.a+φS.sub.wρ.sub.w,  (25)
where ρ.sub.m, ρ.sub.w and ρ.sub.a are the densities of the mineral making up the rock, pore water, and air, respectively. The final form of V.sub.p (φ, S.sub.w) is given as:

(20) $\begin{array}{cc}{V}_p=\sqrt{\frac{\begin{array}{c}\varphi K_a{K}_m{K}_w+\left({\varphi }_c-\varphi \right)\left(K_m+\frac{4}{3}{G}_m\right)[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+\\ K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)]\end{array}}{\begin{array}{c}{\varphi }_c\left[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)\right]\\ \left[\left(1-S_w\right){\mathrm{\varphi \rho }}_a+\left(1-\varphi \right){\rho }_m+\varphi S_w{\rho }_w\right]\end{array}}.}& \left(26\right)\end{array}$

(21) FIG. 4 shows a plot of V.sub.P in equation (26) as a function of φ and S.sub.w in a typical brine-saturated shale. It should be noted that this formulation is valid only from rock porosities from zero to the critical porosity of the rock, since the rock will behave like a suspension beyond this porosity and another formulation is required to estimate V.sub.P (e.g., Wood's formula).

(22) The method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs includes the following steps: (a) setting an integer i equal to zero; (b) measuring an electrical conductivity σ and a seismic P-wave velocity V.sub.p at a cap rock location above a carbon dioxide storage reservoir; (c) calculating a porosity φ associated with the cap rock as:

(23) $V_p=\sqrt{\frac{\begin{array}{c}\varphi K_a{K}_m{K}_w+\left({\varphi }_c-\varphi \right)\left(K_m+\frac{4}{3}{G}_m\right)[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+\\ K_a\left(\left(1-{\varphi }_c\right)K_w+{\varphi }_c{K}_m{S}_w\right)]\end{array}}{\begin{array}{c}{\varphi }_c[{\varphi }_c{K}_m{K}_w\left(1-S_w\right)+K_a\left(\left(1-{\varphi }_c{K}_m{S}_w\right)\right]\\ \left[\left(1-S_w\right){\mathrm{\varphi \rho }}_a+\left(1-\varphi \right){\rho }_m+\varphi S_w{\rho }_w\right]\end{array}}}$
where a water saturation S.sub.w of the cap rock is given by:

(24) $S_w=\frac{\sqrt{\sigma }-\left(1-\varphi \right)\sqrt{{\sigma }_m}-\varphi \sqrt{{\sigma }_a}}{\varphi \left(\sqrt{{\sigma }_w}-\sqrt{{\sigma }_a}\right)};$
where σ.sub.m is an electrical conductivity of a solid matrix of the cap rock, σ.sub.w is an electrical conductivity of water in the cap rock, and σ.sub.a is an electrical conductivity of air in the cap rock, K.sub.a is a bulk modulus of the air in the cap rock, K.sub.m is a bulk modulus of the solid matrix of the cap rock, K.sub.w is a bulk modulus of the water in the cap rock, φ.sub.c is a critical porosity of the cap rock, G.sub.m is a shear modulus of the solid matrix of the cap rock, ρ.sub.a is a density of the air in the cap rock, ρ.sub.m is a density of the solid matrix of the cap rock, and ρ.sub.w is a density of the water in the cap rock; (d) calculating an i-th value of the water saturation S.sub.wi of the cap rock as:

(25) 0$S_{\mathrm{wi}}=\frac{\sqrt{\sigma }-\left(1-\varphi \right)\sqrt{{\sigma }_m}-\varphi \sqrt{{\sigma }_a}}{\varphi \left(\sqrt{{\sigma }_w}-\sqrt{{\sigma }_a}\right)};$
(e) recording the i-th value of the water saturation S.sub.wi of the cap rock in non-transitory, computer-readable memory; and (f) if consecutive i-th values of the water saturation of the cap rock decrease, then generating an alert signal to indicate a carbon dioxide leak in the cap rock, and if the consecutive i-th values of the water saturation of the cap rock do not decrease, then setting i=i+1 and returning to step (b).

(26) In step (c), the nonlinear equation in φ results in two real solutions. Checking the validity of the solutions using known models showed that only one of the solutions consistently gave the correct porosities of tested model, which is used as the value φ(σ, V.sub.P, K.sub.m, K.sub.w, K.sub.a, G.sub.m, φ.sub.c, ρ.sub.m, ρ.sub.w, ρ.sub.a, σ.sub.m, σ.sub.w, σ.sub.a). The other solution was found to always give the wrong porosity values, and is thus neglected.

(27) The calculated inverted φ(σ, V.sub.P, K.sub.m, K.sub.w, K.sub.a, G.sub.m, φ.sub.c, ρ.sub.m, ρ.sub.w, ρ.sub.a, σ.sub.m, σ.sub.w, σ.sub.a) from step (c) and the inverted S.sub.wi(σ, V.sub.P, K.sub.m, K.sub.w, K.sub.a, G.sub.m, φ.sub.c, ρ.sub.m, ρ.sub.w, ρ.sub.a, σ.sub.m, σ.sub.w, σ.sub.a) from step (d) for the case of a brine-saturated shale using the values in Table 1 for the mineral and pore-fluid properties are shown in FIGS. 5 and 6, respectively. The method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs has been applied to 17 σ-V.sub.p well-log measurements in a shale section of a vertical well from the Gullfaks field of the North Sea, which was fully saturated with brine. Table 2 provides a list of these σ-V.sub.P measurements.

(28) TABLE-US-00002 TABLE 2 σ-V.sub.P Measurements of Shale Section Measured V.sub.P (km/s) Measured σ (S/m) Lithology 2.90 1.52 Shale 2.80 1.51 Shale 2.79 1.53 Shale 2.79 1.52 Shale 2.70 1.51 Shale 2.70 1.48 Shale 2.63 1.55 Shale 2.70 1.54 Shale 2.61 1.60 Shale 2.59 1.50 Shale 2.60 1.42 Shale 2.40 2.12 Shale 2.41 2.20 Shale 2.38 2.30 Shale 2.41 2.35 Shale 2.42 2.21 Shale 2.50 2.40 Shale

(29) Table 3 shows the well-log porosities measured in this depth interval alongside those estimated by the present method of monitoring carbon dioxide leakage in carbon capture and storage reservoirs, with absolute errors shown in the rightmost column. The absolute errors lie between 0.5% and 25% with a mean of 7.35% and a standard deviation of 7.33%. The points with relatively high error may be attributed to local heterogeneities within this shale interval caused by different matrix and/or fluid properties than those used for the inversion.

(30) TABLE-US-00003 TABLE 3 Comparison Between Measured and Estimated Porosities Measured φ Estimated φ Absolute Error (%) 0.221 0.229 3.8 0.222 0.228 2.8 0.224 0.231 2.9 0.241 0.229 4.8 0.242 0.228 5.7 0.254 0.225 11.6 0.261 0.233 10.8 0.272 0.232 14.8 0.274 0.239 12.9 0.282 0.227 19.5 0.292 0.217 25.6 0.300 0.294 1.8 0.301 0.302 0.5 0.31 0.312 0.7 0.312 0.317 1.6 0.313 0.303 3.1 0.315 0.322 2.1

(31) Table 4 shows the water saturation values measured in this depth interval alongside those estimated by the present method, with absolute errors in the rightmost column. The absolute errors lie between 0.002% and 0.004% with a mean of 0.003% and a standard deviation of 0.0005%.

(32) TABLE-US-00004 TABLE 4 Comparison Between Measured and Estimated Water Saturations Measured S.sub.w Estimated S.sub.w Absolute Error (%) 1.0 1.00004 0.004 1.0 1.00004 0.004 1.0 1.00004 0.004 1.0 1.00004 0.004 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00002 0.002 1.0 1.00002 0.002 1.0 1.00002 0.002 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00003 0.003 1.0 1.00003 0.003

(33) With the exception of a few samples with relatively high errors, the present method estimated rock porosity within this formation very well. The high-error porosities are clustered in the middle of this shale section, which might be explained by a layer having matrix and/or fluid properties that are slightly different from those used for the inversion. If this is the case, then the background parameters have to be adjusted accordingly. The water saturation results demonstrate much higher accuracy, although readings with a wider range of water saturations are required to confirm this result.

(34) It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.