3.2Time-Lapse Geophysical Data Response

3.1

3.2Time-lapse geophysical data response

Primary Subsurface Decision Variable (): Existence of CO2/brine plume in shallow aquifer due to leakage from deep C02 storage reservoir via an abandoned wellbore:
Subsurface Earth models (z(s)): 5 geologic parameters varied: correlation coefficient in x and z direction, permeability of sand and clay facies (geologic units), and sand volume fraction
Decision alternatives (a): Given that this groundwater is used for irrigation, which crop should be planted: a more profitable crop (corn) or more salt-tolerant (wheat)?
Information Considered to make decision variable interpretation (): electrical resistivity
3 different survey acquisition geometries (as location of leak is deemed unknown)
2 different acquisition times: time=0 years and time=50 years since start of CO2 injection

Geologic sequestration of CO2 is a possible mitigation technique to address global climate change (Benson & Surles, 2006). Possible subsurface receptors of this CO2 are depleted gas and oil fields (Jenkins et al., 2012). Two important unknowns when monitoring CO2 sequestration operations will be: did a leak occur and if it did, where did the leak occur? This example considers the possibility of CO2 and accompanying brine leaking from a deep, depleted oil field into a shallow aquifer that is used as a source of irrigation water. The considered conduit of leakage is an abandoned wellbore that connects the deep reservoir to the surface; Watson & Bachu (2009) estimate that 4.5% of abandoned wellbores pose a risk of leakage. Therefore, the prior uncertainty of a leak occurring is . For all details of this work, please see Trainor-Guitton et al., (2013).

Southwest Kansas has depleted oil fields that could be potential geologic storage sites of CO2. The High Plains Aquifer lies above these oilfields and is extremely vital to the agricultural economy. The largest economic consequence of changing groundwater chemistry due to a combined CO2 and brine intrusion would be to the irrigated crops, of which corn is the most profitable and ubiquitous. Corn is sensitive to the salinity of the irrigation water as demonstrated in Table 3, which shows the total dissolved solids (TDS) concentrations in mg/L concentration that result in crop yield reductions of 10%, 25%, and 50% (Ayers, 1977). Table 3 also shows the TDS levels that will result in the same crop yield reductions for wheat. These concentrations are much higher than for corn, illustrating that wheat is much more tolerant to saline water. Figure 5 demonstrates the decision tree of this example. The value outcomes are based on revenues and costs for 100 acres of each crop (Dumler et al., 2011; Dumler & Shoup, 2011).

Table 3: Crop Yield Reduction as function of Salinity (modified from Ayers(1977))

Crop Yield Reduction / 0% / 10% / 25% / 50%
Corn / 700TDS / 1088TDS / 1600TDS / 2500TDS
Wheat / 2560 TDS / 3130 TDS / 5120 TDS / 6960TDS

Figure 5: Decision tree for Example 1: principal uncertainty is if a plume of 2,000 mg/L exists in agricultural aquifer due to CO2/brine leakage. Value outcomes based on 100 acres of each crop (Dumler, Brien, & Martin, K., 2011; Dumler&Shoup, 2011)

To represent the range of possible contamination, an uncertainty quantification (UQ) analysis provided a dataset of 714, 3D groundwater samples which assume an abandoned well is a source of leakage. The UQ study is based on a section of the High Plains Aquifer in southwest Kansas and was performed to see how 9 different subsurface and leakage parameters would determine the existence and/or extent of contamination to the shallow aquifer (Mansoor et al., 2012; Sun et al., 2013). See Table 4 for the ranges sampled for the 5 subsurface heterogeneity parameters and the other hydrogeologic parameters varied (scaling of leakage rates, brine concentration, etc.). On each sample, groundwater fate and transport was simulated for 100 years, assuming 50 years of CO2 injection into the deeper reservoir.

Table 4: Parameter ranges

Parameter / Wellbore Leakage Model
Sand volume fraction / 0.35 to 0.65
Correlation length in X-direction / 200 to 2500 m
Correlation length in Z-direction / 0.50 to 25.00 m
van Genuchten α in clay (related to the inverse of the air entry suction) / -5.50 to -4.14 m-1
Permeability in sand / 10-12 to 10-9 m2
Permeability in clay / 10-18 to 10-15 m2
CO2 leakage flux scaling parameter / 0 to 1.0
Brine leakage flux scaling parameter / 0 to 1.0
Brine concentration / 0.3-3moles/kg

Our decision variable indicates whether a plume exists (i=1) or does not exist (i=2), where a plume is defined as the area or volume of the aquifer that exceeds the maximum contamination level (mcl) of TDS (EPA, 2010). Here, plumes of 2,000 mg/L or higher results in an economic loss when planting corn, and therefore is the threshold considered to define the decision variable . The concentration of total dissolved solids at the 50 year time step for each sample is evaluated to determine if a plume exists or not:

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The samples of the UQ study represent 4.5% of the total event space since the well acts as a leakage source from the deeper CO2 storage reservoir in all S=714 simulations. Not all samples resulted in a plume of 2,000 mg/L. No plume is expected when no leak has occurred. Thus, the probabilities of a plume or no plume occurring (branches in Figure 5) is calculated by:

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For the case of 2,000 mg/L, and . Using these uncertainties along with the value outcomes of Figure 5 in Equations 4 and 5, and . Therefore, the value of perfect information (VOIperfect) is (see Table 5).

Table 5: Value of Imperfect Information (VOIimperfect) for 3 Different Electrode Locations

Electrode Location
(Middle Electrode Distance from Leaking Well) / Vprior =$32,744 / VOIperfect = $420
Vimperfect(mcl=2000) / VOIimperfect(mcl=2000)
Surface (400m) / $32,530 / $200
Surface & Borehole (400m & 210m) / $32,560 / $240
Surface (1500m) / $32,340 / $20

2D Electrical Resistivity

From the vantage point of the farmers, knowledge of the existence of a high salinity plume in the groundwater would be useful before the choice of crop is determined. A remote-sensing technique would be preferable to well sampling, as the wells are expensive and only sample one lateral position. A remote-sensing device could detect the plume before it reaches the well. Two factors make this situation favorable for electrical resistivity: the target (the plume) is electrically conductive and the aquifer depth is 240m (relatively shallow). Dissolved CO2 will result in dissociated hydrogen ions, which will increase the ionic conductivity of the groundwater (Carroll et al., 2009). Brine will also increase the ionic conductivity with dissociated sodium and chloride ions.

An electrical resistivity survey uses surface and/or borehole electrodes to induce electrical current into the subsurface in order to estimate the electrical resistivity of the underlying media (Daily et al., 1992; Ramirez et al., 2003). Two electrode pairs alternate between acting as the current electrodes and potential electrodes which results in a large number of measurements. The bulk resistivity of a homogeneous half-space can be calculated using a form of Ohm’s Law

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since the locations of the four electrodes (r) are known and the amount of current input into the ground () and the voltage difference (V) between the two potential electrodes are measured. Each measurement, known as a transfer resistance (V/I), will have a different depth of investigation due to the separation of four electrodes used in this measurement.

Different geometries and depths of plumes will influence the reliability of electrical resistivity to accurately detect the existence of a leak. A significant benefit of utilizing the UQ study samples is that one can capture a comprehensive set of conditions where false positives and false negatives may occur. This is accomplished by simulating the electrical resistivity response on all the 714 UQ samples. First, the geochemical variables must be translated into electrical resistivity (or its inverse: conductivity).

To calculate the ionic conductivity of the pore water for every simulation sample , we follow Hearst et al. (2000). Rock physics relationships are used to estimate the bulk rock electrical resistivity using the porosity of the media and the calculated pore water conductivity (Archie, 1942; de Lima & Sharma, 1990). Therefore, we compute and include the bulk electrical resistivity (Ω-m) and the associated transfer resistances for time=50 years as attributes of vector (Equation 1). Figure 6 displays two properties associated with sample 275: total dissolved solids (equivalent to mg/L concentration) at time = 50 years and the factor change in electrical resistivity from time = 50 years relative to time=0 years.

Figure 6: Sample 275. Longest mcl = 500 mg/L plume (of 714 simulations). No plume at mcl = 2000 mg/L. Top panel shows total dissolved solids (TDS). Bottom panel shows resistivity ratio (time=50 years/ time=0)

Recall that the location of the leak is considered to be unknown. Figure 7 demonstrates the three possible electrical resistivity survey scenarios that are considered to test the sensitivity of the technique at different distances to the plume. The first (demonstrated in red) is a 1,200 m line of surface-based of electrodes, where the westernmost electrode is 200 m upstream of the leaking well. The line consists of 120 electrodes. The length of 1,200 m was chosen based on the depth of the aquifer, as it will provide the necessary depth of investigation. The second survey geometry includes 11 borehole electrodes (in addition to the 120 surface electrodes) located 250 m downstream of the leak. The last survey scenario shifts the 1,200 m line of surface electrodes downstream (away from the leak) by 1,100 m. The distance of the closest electrode to the leaky well is 900 m (no overlap as in the first survey scenario). This distance was chosen based on the average well spacing of the area of interest of the High Plains aquifer, such that the position of the electrode line is equidistance between the hypothetical leaking well and a neighboring well.

Figure 7: Three electrode configurations. (1) Red: 120 surface electrodes straddling leaking well. (2) Red and purple: straddling electrodes plus 11 borehole electrodes200 m downstream of leaky well. (3) Green: surface electrodes 900 m downstream of leaky well

Since the electrode lines only span the x-axis of the aquifer grid, 2D slices of the 3D aquifer simulation results are extracted, representing the plane made by the x-axis and z-axis. This profile captures the effect that regional flow will have on any pH/TDS plume.

Leak Diagnostic

Electrical resistance measurements were computed for all samples of at 0 and 50 years (function represents forward geophysical calculation).

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3% random Gaussian noise was added to each of the transfer resistance predictions to simulate realistic field measurements (LaBrecque & Daily, 2008; LaBrecque et al., 1996).

Typically, these transfer resistances would be used in geophysical inversion () to estimate the resistivity structure of the earth; however, geophysical inversion can be computationally intensive for one set of field measurements. Thus, it is computationally expensive to perform inversion for all resistivity profiles. Considering the decision variable, the goal is to use the transfer resistance measurements to determine if a leak has occurred and resulted in a plume, not to know the spatial structure of the plume; we follow the approach of Daily et al. (2004) and borrow their mean of logarithmic ratios (MLR) as a leak diagnostic metric

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wheren is the number of measurements taken on each sample, rktime is the kth transfer resistance at year = time, and rk0 is the transfer resistance at year = 0. A MLR is calculated for each aquifer realization s, and this is used as an interpretation of electrical resistivity detecting aconductive plume, represented by . The index j represents the J discrete bins of the MLR values.

The 714 calculated MLR’s only represent leak events (estimated as 4.5% of the event space). Therefore, 15,153 “synthetic” MLR’s (representing non-leak events) are generated by utilizing the statistics of the MLR’s calculated from non-plume simulations (mcl<500 mg/L). These synthetic MLR’s include the effects of noise added to the transfer resistances.

The data reliability of the electrical resistivity technique can be calculated by comparing MLR’s () to the plume existence (red) or non-existence (green)

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The reliability in the top plot in Figure 8 is for the surface electrode configuration straddling the leaky well. The information posterior

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is the bottom plot of Figure 8. In general, MLR’s < 0.001 indicate that no plume (green) is present while MRS’s > 0.002 are indicative of a plume (red). The range between 0.001 and 0.002 demonstrate ambiguity in the electrical resistivity message: the probability of a plume existing is comparable to it not existing. This exhibits the imperfectness of the electrical resistivity measurement.

Figure 8: (a) Data reliability and (b) information pre-posterior for mcl = 2000 mg/L at time = 50 years

There is an obvious deviation around MLR = 0.002. This is due to sample 275, which has the longest plume at threshold mcl ≥ 500 mg/L (for all 714 samples), but no plume for mcl ≥ 2000 mg/L (see Figure 6). The electrodes have a high sensitivity to the resistivity change of the long, lower concentration plume, but sample 275 does not contain concentrations greater than 1,000 mg/L at 50 years. Therefore, sample 275 represents a situation where the message from the information will not uniquely identify if a plume of 2,000 mg/L exists.

The information posterior is used to calculate the value with imperfect information (Equation 8). The same process is repeated for the two other electrode configurations. The three values of imperfect information (VOIimperfect) for the three configurations are summarized in Table 5. As expected, all are less than VOIperfect : the VOIimperfect range from 5-55% of the VOIperfect value. Also, the configuration that includes borehole electrodes has the highest value and the configuration farthest from the leak (downstream surface electrodes) has the lowest. This is expected given that the strength of the electrical resistivity signal will increase when electrodes are placed in-situ (e.g. the borehole) and the signal will drop with increasing distance from the target (Equation 12).

Summary: CO2 Leak Example

A leak diagnostic (MLR) was introduced to assess if the electrical resistivity technique can achieve a holistic measure of how well ER data will indicate the existence of plume.
Simulated electrical response on all 714 UQ samples.
Avoided geophysical inversion (computationally expensive for 714 datasets).
Imperfectness of electrical resistivity was captured with the MLR diagnostic.
The electrical resistivity response to larger but lower concentration plumes can be equivalent to the response of higher concentrated plumes. This creates false positives and affects the information reliability.
Ambiguity in the message at MLR’s between 0.001 and 0.002: similar probabilities are assigned for plume and no plume.
Decision alternative is not spatial.
A possible decision could be where (if at all) the aquifer requires remediation due to the CO2/brine leak. However, after conferring with local agriculturists regarding how they currently address issues of the salinity of irrigation water, crop rotation was chosen as the decision alternative.

3.3Equivalent Collocated Geophysical Inversions and Geologic Observations

Aquifer vulnerability: removal of contaminate sources at critical locations

Primary Subsurface Decision Variable (): Surface-locations that act as entry points into aquifer
Subsurface Earth models (z(s)): Depositional system: buried glacial valley
18 training images: capturing different dimensions of buried valleys
10 realizations each for S=180 subsurface models
Decision alternatives (a): Which farms should be compensated to not use fertilizers?
Information Considered to interpret decision variable (): existing time-domain electromagnetics collocated with drillers logs (subjective lithology information)

This example is inspired by a Northern European situation, where the populace relies solely on its groundwater resources for drinking water. The aquifers have been compromised by surface-sourced contaminants due to agricultural activities. Contamination will continue to be a threat until the crops or farms that are located at entry points into the aquifer are identified and the source of contamination removed. The key uncertainty (surface locations that allow contaminants to enter the aquifer) is related to the geologic depositional system. For this location, it is buried glacial valleys, which present overlapping and cross-cutting, sinuous features (Figure 9). A reasonable assumption is that the buried valley facies are filled with sand and represent high volume aquifers; sand facies are therefore assigned a high permeability value. Conversely, the non-valley or background facies are assumed to be aquitards and are assigned a low permeability value. The details of this example can be found in Trainor-Guitton et al. (2013).

Figure 9: Plane-view of network of buried valleys; darker to lighter representing older to younger buried valley generations (Jørgensen&Sandersen, 2006)

For this example, 18 training images are generated to represent the model uncertainty of the buried valley length, width and thickness dimensions. Figure 10a demonstrates two of these training images. Ten Earth models are generated for each training image (examples shown in Figure 10b). As seen in Figure 9, the network of connected buried valleys is complex; ‘‘significant parts of the recharge area may therefore lie at relatively large distances from the valley [which represents the deep aquifer]’’ (Sandersen & Jørgensen, 2003). Thus, contamination can be transported kilometers from its surficial entry point into a deep aquifer. Therefore, the dynamic response or transport of surface-borne contaminants into the aquifer is the decision variable .

Figure 10: ) Two examples of training images used to represent patterns of glacial, buried valleys b) Examples of models or samples generated from these training images

Aquifer vulnerability, the decision variable, is determined by placing a tracer on the surface of all Earth models , simulating the groundwater flow and transport (), and tracking the volume of aquifer affected by entry at each surface location .

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Figure 11 is an example vulnerability map resulting from one individual model via flow simulation. The magnitude of vulnerability reflects the volume of aquifer affected from entering at that surface location.