Reserves estimation methods for prospect evaluation with 3D CSEM data
Daniel Baltar1* and Friedrich Roth,1 explain how 3D controlled-source electromagnetic data can reduce volumetric uncertainty in the reserves estimation process of prospect evaluation.
R eserves are among the key pieces of information used in prospect evaluation. The estimation of reserves is typically done in a probabilistic way in order to account for the large uncertainties in the parameters
that determine the reserves. The largest source of uncertainty in the reserves estimation is usually the net rock volume of the reservoir, which is the product of reservoir area and net pay thickness. The controlled-source electromagnetic (CSEM) method is sensitive to the net rock volume and the reservoir resistivity, thus making it an excellent exploration tool capable of reducing the volumetric uncertainty. We present two methods that include 3D CSEM inversion data in the net rock volume evaluation and the reserves estima-tion process. The first method deals with a case where a resistivity anomaly is recovered at the prospect location; the second method handles a case where no resistivity anomaly is detected. Both methods are easily integrated into common probabilistic reserves estimation processes.
BackgroundEstimating reserves is fundamental to the economic evalua-tion of exploration prospects. The probability of economic success Pe assigned to a prospect is given by the product of the probability Pg of discovering a flowable hydrocarbon (HC) accumulation and the probability PMEFS of the discov-ered accumulation being greater than the minimum econom-ic field size (MEFS) quantified in recoverable reserves (RR):
Pe = Pg * PMEFS = Pg * P(RR > MEFS) (1)
(Rose 2001).
It is standard industry practice to calculate Pg by evaluating a number of independent geologic chance factors associated
with the components of a petroleum system that are required for a hydrocarbon accumulation to exist, i.e., source, reser-voir, etc. The calculation of PMEFS requires generation of a prospect reserves distribution to which the economic thresh-old can be applied. The reserves distribution is obtained from a statistical evaluation of the reserves equation:
RR=A * ΔZ * Φ * (1-Sw) * Rf/Boi . (2)
Here A is the reservoir area, ΔZ is the net pay thickness, Φ is the porosity, Sw is the water saturation, Rf is the recovery factor, and Boi is the formation volume factor. The product of reservoir area and net pay thickness defines the net rock volume: NRV = A * ΔZ.
CSEM has the capability to influence both the prob-ability of geologic success Pg and the probability of an economic discovery PMEFS, leading to better informed explo-ration decision-making. Due to the strong sensitivity of formation resistivity to hydrocarbon saturation, CSEM is a very good direct hydrocarbon indicator (DHI) and thus can be used to update Pg, e.g. using Bayesian risk modification (Buland et al., 2011), based on CSEM anomaly and data quality characteristics in analogy to seismic amplitude risk analysis (Roden et al. 2005). The impact of CSEM on the prospect reserves distribution results from its sensitivity to the net rock volume. The CSEM response of a hydrocarbon accumulation is not a local scattering phenomenum, but a partially guided wave response the strength of which depends on the volume of resistive reservoir rock (area x thickness).
Hydrocarbon exploration is an activity in which uncertainties are generally high. Table 1 lists typical uncertainties in recoverable reserves for different explo-ration scenarios (Rose, 2001). Uncertainty is meas-ured by the P10/P90 ratio of the reserves distribution.
Development well Step-out/extension
Wildcat in known productive trend
Wildcat in proven trend
Wildcat in new play or new basin
P10/P90 ratio 2.2-7.0 5-25 10-120 55-220 120-650
Table 1 Characteristic uncertainty ranges for different hydrocarbon exploration scenarios; taken from Rose (2001).
HC-saturated formation resistivity scenarios on the well log scale that would be consistent with the inversion result. These scenarios can be calculated from the transverse resistance equivalence principle, as will be derived below. All resistivities considered in the derivation are vertical resistivities.
Transverse resistance is the integral of resistivity over depth. We define the anomalous transverse resistance (ATR) of the reservoir as the amount of transverse resistance above the value that would exist if no hydrocarbons were present:
. (3)
Here, ΔR is the resistivity anomaly due to hydrocarbons at the well log scale. The ATR represents the cumulative resis-tivity contrast over the pay zone (Figure 2).
The uncertainty is particularly high in frontier exploration and for new play concepts. It is therefore important to use all available information to reduce the uncertainty as much as possible to be able to focus the exploratory drilling on the prospects with the highest probability of economic success and maximize the risked prospect portfolio value.
It is well known that most of the uncertainty in the recov-erable reserves can be attributed to the uncertainty in the net rock volume. Thus given a CSEM favourable setting, the CSEM volume sensitivity can result in significant uncertainty reduction on the reserve estimation. This makes CSEM a very attractive ‘companion’ to seismic for prospect evaluation.
We present statistical evaluation methods for estimat-ing reserves that use anisotropic 3D CSEM inversion data to reduce uncertainty. The methods were developed to easily integrate into common probabilistic reserves estimation processes.
We will distinguish between the case where the 3D CSEM inversion reconstructed a resistivity anomaly at the prospect location and the case where no anomaly has been reconstructed. In the presence of a CSEM anomaly, a Monte Carlo simulation is run that uses the transverse resistance equivalence principle to interpret the CSEM anomaly in terms of net pay thickness and reservoir area, resulting in a net rock volume probability distribution. This distribution can then be used in a standard Monte Carlo simulation for recoverable reserves based on equation (2). In the absence of a CSEM anomaly, 3D forward modelling is used to establish maximum non-detectable target cases, which are then used to condition a standard Monte Carlo simulation for recoverable reserves.
We start by describing the evaluation method for the CSEM anomaly case. The method has been applied to real commercial exploration projects, but for reasons of com-mercial confidentiality, we simulate an exploration case using the widely published CSEM data from the Troll West oil province (TWOP) in the Norwegian North Sea to illustrate the capability for reducing the uncertainty measured as the P10/P90 ratio for the net rock volume, and compare the resulting probability distribution to the actual net rock volume. We then elaborate on the evaluation method used in the absence of a CSEM anomaly and show how it truncates the high end of the recoverable reserves distribution.
CSEM anomaly evaluation using the transverse resistance equivalence principleMarine CSEM is a low-frequency technique. Unconstrained CSEM inversion therefore has a resolution that is typi-cally above the reservoir thickness (Figure 1). A hydrocarbon related resistivity anomaly in a CSEM inversion result is an upscaled (‘averaged’) version of the resistivity anomaly at the well log scale.
In case the only piece of available data is the CSEM inversion result, there are an infinite number of net pay and
Figure 1 A hydrocarbon related resistivity anomaly in a 3D CSEM inversion result is an upscaled version of the resistivity anomaly at the well log scale. The transverse resistance equivalence can be used to interpret the CSEM anomaly at the well log scale. Example from Yuan et al. (2009).
Figure 2 The anomalous transverse resistance (ATR) of the reservoir describes the cumulative resistivity contrast due to hydrocarbons, i.e., the green shaded area under the resistivity log curve. It is calculated by integrating the resistivity contrast over the pay zone.
Assuming the background resistivity Rbg is known, equa-tions (7) and (8) allow for calculating pairs of R and ΔZ that are consistent with the CSEM resistivity trace. This is illustrated in Figure 3. If the average pay resistivity R was known, the net pay ΔZ could be calculated from the CSEM net-to-gross relationship. This, however, is not the case in exploration. As we will show in the next section, a good way to deal with lacking information and uncertainties is to run a Monte Carlo simulation using the CSEM inversion result as input.So far we have only considered a single resistivity trace, i.e., the 1D case. It is straightforward to extend the analysis to the full 3D CSEM inversion model. In this case, the averaging over the anomaly results in an average CSEM resistivity map (Figure 5), which may then be interpreted in terms of equa-tions (7) and (8), i.e., we iterate over each cell in an area of interest to achieve a full net rock volume calculation.
CSEM anomaly evaluation under uncertaintyWe use a Monte Carlo method to handle the uncertainties in the evaluation of the CSEM anomaly. To do this, we must associate a random variable with a probability distribution to each source of uncertainty in the calculation. For net rock volume calculations from an average resistivity map obtained from a 3D CSEM inversion model, the main uncertainties and corresponding random variables are the following:n What is the background resistivity value? Variable: Rbg
n What resistivity values must be considered anomalous? Variable: Rcutoff
n What is the average pay resistivity? Variable: R
Suitable distributions for Rbg and Rcutoff should be defined based on the average CSEM resistivity map itself. The R distribution must be obtained from nearby wells, analogues, or other a priori information.
The Monte Carlo algorithm (Figure 4) draws a random value for each of the above variables. The algorithm then iterates over all cells of the input map with average resistivity value Rcsem above Rcutoff and calculates their contributions to the total net rock volume for the given combination of Rbg
Given a 1D resistivity trace extracted from a 3D CSEM inversion model, the transverse resistance equivalence princi-ple (Constable, 2010) suggests that
, (4)
where ΔRcsem refers to the resistivity anomaly owing to hydrocarbons in the CSEM resistivity trace. In other words, the cumulative resistivity contrast of the CSEM resistivity trace and that of the resistivity well log are equal.
Equation (4) can be rewritten in terms of average resistivities as
. (5)
Here denotes the averaging operator, ΔZcsem is the thick-ness of the CSEM anomaly in the CSEM resistivity trace and ΔZ is the actual thickness of the hydrocarbon charged reser-voir interval, i.e. the net pay thickness required to evaluate the reserve equation (2).
Given a relatively uniform background resistivity varia-tion over the depth interval of interest defined by the CSEM anomaly, equation (5) can be simplified to
, (6)
where Rcsem is the average value of the CSEM resistivity trace over the CSEM anomaly interval, R is the average hydrocar-bon charged reservoir resistivity over the pay zone and Rbg is the average background resistivity.
Equation 6 can be rearranged to yield an expression for the “CSEM” net-to-gross ratio
, (7)
which links the CSEM anomaly thickness ΔZcsem to the net pay thickness ΔZ according to
. (8)
Figure 3 A CSEM resistivity trace extracted from a 3D CSEM inversion result can be linked to average pay resistivity R and net pay thickness ∆Z via the transverse resistance equivalence principle.
order to simulate an exploration setting. We only used the reservoir top horizon from seismic and the results from an unconstrained anisotropic 3D CSEM inversion.
The following steps were followed to generate the input to the Monte Carlo simulation:(1) Identify the CSEM anomaly in section view.(2) Create two surfaces, one above the CSEM anomaly and
one below by shifting the top reservoir horizon up and down respectively. (Figure 5)
(3) Generate a map of the average CSEM resistivity Rcsem by averaging the vertical resistivity from the 3D CSEM inversion model between the two surfaces created in step 2. (Figure 5)
(4) Calculate a thickness map of the averaging operator by taking the difference between the two surfaces created in step 2. In this case, the thickness was constant, but the algorithm equally applies to a laterally varying thickness. The thickness map serves to define the thickness of the CSEM anomaly, ΔZcsem in equation (8).
(5) Define distributions for the background resistivity Rbg and the cut-off resistivity Rcutoff from the average CSEM resistivity map generated in step 3.
The Monte Carlo simulation tested possible reservoir scenarios using the following resistivity ranges: 10 Ωm < R < 100 Ωm, 2.6 Ωm < Rbg < 3.2 Ωm, 3.3 Ωm < Rcutoff < 4.7 Ωm. To keep things simple, uniform probability distributions were chosen. Note that the range for the pay resistivity R is very large since no well data were used to constrain this variable. The limits for the Rbg and Rcutoff variables were chosen based on histograms derived from the average CSEM resistivity map.
and R. The steps are repeated many times and a cumulative probability distribution for the net rock volume is generated.
So far, we have assumed that the ATR estimated by the CSEM inversion is a good approximation of the actual anomalous transverse resistance of the reservoir. Following the derivation in the previous section, it is obvious that when the ATR is under- or overestimated, the net rock volume will be under- or overestimated in proportion to the error in the ATR.
CSEM inversion will typically underestimate the ATR of the reservoir slightly. This can be accounted for in the Monte Carlo simulation by introducing an extra random variable describing the uncertainty in the estimated ATR. This is especially important when the CSEM sensitivity to the target interval is low, e.g., for deep exploration objectives. The extra random variable will naturally increase the uncertainty of the resulting net rock volume probability distribution (P10/P90 ratio). The uncertainty can be reduced by calibrating the ATR estimation by 3D forward modelling and synthetic data inversion for a representative target embedded in the background resistivity model obtained from the 3D inversion of the measured CSEM survey data.
Application to the Troll West oil provinceWe demonstrate the performance of net rock volume esti-mation on the Troll West oil province (TWOP) over which a full-azimuth 3D CSEM survey was acquired in 2008 (Gabrielsen et al., 2009). Anisotropic 3D inversion of the survey data has been reported by Morten et al. (2009).
No prior information about the pay resistivity, the net pay thickness, and the reservoir area was assumed in
Figure 4 Monte Carlo algorithm for generating a net rock volume distribution from a CSEM anomaly.
Figure 5 Generation of an average resistivity map from a 3D CSEM inversion model (vertical resistivity). The contours mark the top of the averaging window, which starts 400 m above the top reservoir horizon and ends 300 m below it. The inversion result is from the Troll West oil province (TWOP).
mud line), geologic setting (e.g., water depth, overburden resistivity), and acquisition parameters (e.g., source current amplitude and frequencies, available offset range, receiver sensitivity, ambient noise). If the geologic setting and acqui-sition parameters are defined, the CSEM sensitivity can be established for assumed target characteristics by 3D forward modelling. Such modelling is best performed using the back-ground resistivity model obtained by anisotropic 3D inver-sion of the measured CSEM survey data.
As a result of the transverse resistance equivalence principle, it makes sense to analyse the CSEM sensitivity as a function of ATR for a given reservoir area. An example of such modelling is shown in Figure 7. The reservoir is located 2200 m below mud line and has been modelled for three different reservoir areas: 10, 30, and 75 km2. For each area, a number of ATR values have been considered to generate a sensitivity curve. The displayed sensitivity metric is the nor-malized magnitude versus offset (NMvO) attribute expressed as a percentage for the offset and frequency combination that maximises the target response. Similar sensitivity curves can be generated for other sensitivity metrics, e.g., the hardware dependent sensitivity metric described in Barker et al. (2012).
Detection criterionFor the NMvO sensitivity metric, it is common to assume a limit of 10% for reliable target detection and imag-ing. It is well known that the detectability depends on the geologic complexity and the quality of the CSEM data. Thus, for some CSEM surveys (e.g., shallow water surveys), the NMvO detection criterion may have to be adjusted.
Given a NMvO detection criterion of 10%, the sensitivity curves of Figure 7 can be used to establish the minimum ATR detected reliably for each modelled reservoir area, which we will call ATR10. The dependence of ATR10 on reservoir area A can be represented by fitting the functional
ATR10(A) = ATR10inf + r/(A-A0) (8)
50,000 Monte Carlo samples were produced. The resulting cumulative probability distribution for the net rock volume is shown in Figure 6 together with the actual volume defined by the top reservoir horizon and the known oil-water contact (OWC). The distribution is relatively narrow with a P10/P90 ratio of less than six, which is in the order of uncertainties typical for development or near-field exploration (see Table 1). The actual net rock volume coincides with the 60th percentile.
Other information such as analogues or seismic interpreta-tion could be used to condition the distribution, e.g., the higher end of the rock volume distribution could probably be ruled out using seismic interpretation. By cross-plotting the Monte Carlo input variables against the resulting net rock volume samples, we found the main controlling factor in the net rock volume estimation to be the average pay resistivity R.
Reserves estimation in the absence of a CSEM anomalyIn the early days of CSEM for hydrocarbon exploration, the absence of a CSEM anomaly was often equated with ‘no hydrocarbons’. This simplified interpretation, however, does not account for the volume sensitivity of CSEM. In other words, the absence of a CSEM anomaly can only be used to conclude that any hydrocarbon accumulation must be smaller than the detection limit of CSEM for this particular geologic setting and acquisition. By modelling the CSEM sensitivity and defining a detection threshold, it is possible to test whether a specific reservoir case is consistent or incon-sistent with the CSEM observation, i.e., that no anomaly was reconstructed by 3D CSEM inversion. Such test in turn can be used to condition a standard Monte Carlo simulation for recoverable reserves.
CSEM sensitivityThe sensitivity of CSEM data to a hydrocarbon accumula-tion is known to be a function of target characteristics (e.g., reservoir area, net pay thickness, pay resistivity, depth below
Figure 6 Troll West oil province example: Estimated cumulative probability dis-tribution for the net rock volume. The reference volume calculated from the reservoir top and OWC coincides with the 60th percentile. The P10/P90 ratio is less than six, which is low by common exploration standards.
equation (2), which include the reservoir area A and the net pay thickness ΔZ. In addition, for each reservoir scenario, the average pay resistivity R and background resistivity Rbg needs to be established in order to calculate the correspond-ing ATR, ATR = ΔZ * (R-Rbg). As before, these resistivity values need to be vertical resistivities. The algorithm works according to the scheme outlined in Figure 9.
There are a number of ways in which the average pay resistivity R and the background resistivity Rbg can be intro-duced into the calculation. The probability distribution for Rbg can be derived from the 3D CSEM inversion model or nearby well control. The probability distribution for R can be obtained from analogues for which well data are avail-able. Alternatively, pay resistivity can be calculated from the porosity distribution and saturation distribution using an Archie-like saturation equation and additional input distributions defining the remaining Archie parameters such as pore water resistivity, cementation exponent, etc. Both approaches require a proper evaluation of expected
to the ATR10 samples as exemplified in Figure 8. Here, ATR10inf is the ATR10 value for an infinite reservoir area estimated from 1D modelling, A0 defines the minimum theoretical reservoir area detectable by CSEM and r is a curvature parameter. For the example case considered, the fitting parameters are ATR10inf = 540 Ωm2, A0 = 5.7 km2 and r = 2,000 Ωm2km2. Hydrocarbon accumulations with ATR and reservoir area above this curve are most likely to be detected by CSEM, while those accumulations falling below the curve are more likely to remain undetected.
Reserves estimationIn the absence of a CSEM anomaly, possible existing hydro-carbon accumulations are most likely to be below the ATR10 curve defined above. Therefore it makes sense to use this information in the reserves estimation.
This can again be achieved through a Monte Carlo simulation. The algorithm uses the usual probability distri-butions for the reservoir parameters entering the reserves
Figure 7 CSEM sensitivity curves obtained by 3D forward modelling: Maximum NMvO as a function of ATR for different reservoir areas. The prospect is located 2,200 m below mud line. Assuming a 10% NMvO detection criterion, the ATR threshold at which the NMvO value drops below 10% can be estimated for each reservoir area. This threshold is called ATR10. The forward modelling uses the background resistivity model obtained by anisotropic 3D inversion of the meas-ured CSEM survey data.
transverse resistance for all Monte Carlo samples. The sam-ples corresponding to large reservoir area and/or high ATR (red dots) have been removed as they would have produced an anomaly in the 3D CSEM inversion result. Since large areas and high ATR are more likely to be associated with high recoverable reserves, we are removing mostly large fields from the recoverable reserves distribution. Therefore one would expect a large impact at the high end of the distribution (P10) and a smaller impact at the lower end of the distribution (P90). Figure 10 shows that this is exactly what happens: The P10 reserves are reduced by about 40%, whereas the P90 reserves are only reduced by 23%. The resulting reduction in expected (average) reserves is fairly significant, about 38% from 104 MMbbl to 64 MMbbl. The uncertainty in the reserves as quantified by the P10/P90 ratio is reduced from 18 to 14.
electrical anisotropy in order to obtain meaningful vertical resistivity values.
ExampleLet us return to the prospect associated with the sensitivity curves of Figure 7 and impose a NMvO detection criterion of 10%. The reservoir parameter distributions for this pros-pect are given by the P10 and P90 values in Table 2. All distributions are assumed to be log normal. Figure 10 shows the recoverable reserves distribution generated by Monte Carlo simulation with and without CSEM conditioning. For the sake of simplicity, we have chosen to input the pay resistivity data directly instead of deriving it from a satura-tion equation.
The Monte Carlo simulation was run for 100,000 iterations. Figure 11 shows the reservoir area and anomalous
Figure 9 Monte Carlo algorithm for reserves esti-mation in the absence of a CSEM anomaly.
Figure 8 Reservoir area and ATR combinations that generate a 10% NMvO. The three points have been picked from the modelled sensitivity curves of Figure 7 and the curve was obtained by fitting the points with the functional of equation (8). Reservoir cases above the curve will generate a NMvO > 10%; reservoir cases below the curve generate a NMvO < 10%. The prospect is located 2200 m below mud line.
We presented two methods for reserves estimation incor-porating anisotropic 3D CSEM inversion data to effectively reduce the uncertainty associated with the net rock volume. The first method applies when the 3D CSEM inversion reconstructed a resistivity anomaly at the prospect loca-tion; the second method is used in the absence of a CSEM anomaly. Both algorithms are implemented as Monte Carlo simulations and are straightforward to integrate into existing probabilistic reserve estimation processes.
The examples studied demonstrate that the uncertainty reduction resulting from the use of 3D CSEM information can be quite large. For the simulated exploration case in the Troll West oil province, the observed CSEM anomaly resulted in a P10/P90 ratio for the net rock volume below six, which is extremely low by common exploration standards.
ConclusionsCSEM is sensitive to the reservoir area, net pay thickness, and pay resistivity. Two of these variables, reservoir area and net pay thickness, constitute the main uncertainty in the reserves calculation for a prospect: the net reservoir rock volume. This fact makes CSEM a very useful exploration tool for reducing the uncertainty in the estimated recover-able reserves.
Figure 11 Reservoir area and anomalous transverse resistance for all Monte Carlo samples used to generate the recoverable reserves distributions of Figure 10. When using CSEM information, the samples corresponding to large reservoir area and/or high ATR (red dots) have been removed as they are expected to produce an anomaly in the 3D CSEM inversion result; the samples marked by blue dots are kept.
Variable P90 P10
Area [km2] 5 50
Thickness [m] 15 65
Porosity 0.23 0.33
HC saturation 0.5 0.75
Recovery factor 0.1 0.2
FVF 1.2 1.4
Rbg [Ωm] 2.15 2.5
R [Ωm] 10 50
Table 2 Inputs to the Monte Carlo simulation resulting in the recoverable reserves distributions of Figure 10.
Figure 10 Recoverable reserves distribution in the absence of a CSEM anomaly generated by Monte Carlo simulation with and without CSEM conditioning. The larger fields are more likely to be detected by CSEM and thus the high end of the distribution is more affected by the CSEM result than the lower end. The prospect is located 2200 m below mud line. The reservoir parameter distributions and other input to the Monte Carlo simulation are taken from Table 2.
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In the negative case, i.e., absence of a CSEM anomaly, the impact on reserves in terms of P10/P90 ratio will generally not be that strong, but the P10 and average reserves can experience a significant reduction after the inclusion of the 3D CSEM information (~40% for the example studied).
Both results suggest that 3D CSEM can have a major impact on the estimated reserves and their uncertainty, which can lead to a great improvement in the prospect evaluation and decision-making.
AcknowledgementsWe would like to thank Mårten Blixt from Blueback Reservoir for the interesting discussions about the algorithms and its implementation.
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