Assessing uncertainty on Net-to-gross at the Appraisal Stage: Application to a West Africa Deep-Water Reservoir

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1 Assessing uncertainty on Net-to-gross at the Appraisal Stage: Application to a West Africa Deep-Water Reservoir Amisha Maharaja April 25, 2006 Abstract A large data set is available from a deep-water reservoir offshore West Coast of Africa. The objective of this study is to assess the uncertainty about the net-to-gross (NTG) ratio of this reservoir by mimicking appraisal stage conditions. Early stratigraphic interpretation is retained and two different depositional facies scenarios are considered. The structural setting is well-known, hence the uncertainty about the geological scenario is mostly related to facies distribution. A prior NTG distribution is obtained from a database of analog reservoirs. Four wells, those available at appraisal stage, and acoustic impedance data are retained for the uncertainty study. The NTG uncertainty workflow is carried out using two different geological scenarios to update the prior NTG distribution into two posterior distributions. The posteriors obtained from using the two geological scenarios are similar because the two scenarios are not very different from the perspective of NTG uncertainty. Both scenarios are conditioned to the same set of data and the same prior NTG distribution was used, which further diminishes the difference between the two scenarios. The impact of additional data is investigated by conducting the study with one well and then repeating it each time a new well is added. With each additional well the posterior NTG distribution becomes narrower, which implies that additional data is reducing the uncertainty interval. The posterior NTG distribution with twenty-eight wells, which provide a good coverage of the reservoir, is very narrow and has a mean comparable to the mean of the posterior with the four appraisal stage wells. This suggests that the pay zones in this reservoir are not localized vertically. 1 Introduction Hydrocarbon exploration is a risky business. Apart from the economical and geo-political factors, early estimates about the reserves is a major source of uncertainty. In expensive, deepwater reservoirs it is crucial to know very early the distribution of hydrocarbon in place (HIP) in the reservoir before expensive development costs are committed. The uncertainty about the gross reservoir volume has the first order impact on the HIP calculations. The volume uncertainty, however, is related to seismic data processing and interpretation, which falls outside the scope of this research. We assert that the net-to-gross (NTG) ratio of a hydrocarbon reservoir has the next crucial impact on the HIP calculations. A workflow, based on Bayesian framework, was proposed by Caumon et al. (2004) to assess 1

2 uncertainty about the NTG ratio. This workflow identifies (a) the geological scenario, (b) prior NTG distribution and (c) the quantitative data themselves as the major sources of uncertainty related to NTG. In this paper we apply this workflow to a real reservoir from off-shore West Coast of Africa (WCA). The reservoir will be refered to as the WCA reservoir in the paper. The goal is to use only the data available at the appraisal stage, assess the uncertainty about the NTG and compare the results with the NTG obtained from a dense well data set from the same reservoir. First we recall the basic framework of the workflow. Next, we describe in section 2 the two alternative geological scenarios, the prior NTG distribution and the available quantitative data. We aim to study the impact of geological scenario, the impact of introducing additional well data and the impact of using seismic data on the posterior NTG distribution. The results are discussed in section 4 and we draw some conclusions in section Review of methodology Net-to-Gross is defined as the ratio of volume of reservoir quality rock to total rock volume in the reservoir. By definition this is a global parameter and it has no replicate. Some researchers have used spatial boostrap as a way to assess uncertainty about the NTG estimate by randomizing the well data location and re-sampling from stochastic realizations (Journel, 1993; Norris et al., 1993; Bitanov and Journel, 2004). However, stochastic simulation requires a model of spatial variability and a prior knowledge of NTG value, both of which are highly uncertain. Caumon et al. (2004) realized this problem and proposed to randomize both, the geological scenario and the prior global NTG value. We denote the uncertain geological scenario by S, with s k, k = 1,...,K being its realizations. At the appraisal stage, if the geological setting is poorly understood, it is essential to consider different geological scenarios that fit all available data until some could be eliminated by subsequently acquired data. The prior global NTG value is also casted as a random variable (RV) denoted A. The true, but unknown, NTG value of the reservoir is a realization of this RV. The quantitative data are treated as a realization of the RV data, denoted D. Spatial bootstrap addresses the uncertainty about the observed data. By framing the problem in this manner, Caumon et al. (2004) ask the question, what is the uncertainty about the global NTG value given the observed data and geological interpretation. Since it is not practical to compute the likelihood of all available data, we retain the NTG estimate, A, as a summary of the data. The proposed workflow is summarized in (Figure 1). Refer to Caumon et al. (2004) for details on the theoretical foundations of this workflow. Associated with each geological scenario, S = s k, is a prior distribution of NTG values, P(A S = s k ), see Figure 1, Panel A. This prior distribution would be typically drawn from the company prior expertise about this type of geological scenario. To update this distribution into a posterior distribution given a NTG estimate, P(A S = s k, A = a 0 ), the workflow proceeds as follows: 2

3 The prior NTG distribution is discretized into M classes resulting in M realizations of the NTG, a 1,...,a M (Figure 1, Panel B). Corresponding to each class of NTG, L realizations of the reservoir facies are generated using some simulation algorithm, preferably one that utilizes multiple-point statistics because it is better at honoring the data patterns found in the geological scenario. Freezing the seismic data and initial drilling strategy, N sets of synthetic wells are sampled from the L realizations by randomizing the well locations. This provides N L realizations of the NTG estimate, a 1,...,a NL. From this distribution the likelihood of observing the initial best NTG estimate for the given class of true NTG and given geological scenario, P(A = a 0 A = a m, S = s k ), is obtained (Figure 1, Panel C). Bayes inversion is then used to obtain the probability of the true NTG being in that class given the observed NTG estimate and geological scenario, P(A = a m A = a 0, S = s k) (Equation 1). P(A = a m A = a 0, S = s k ) = P(A = a 0 A = a m, S = s k ) P(A = A m S = s k ) P(A = a 0 S = s k) (1) The denominator P(A = a 0 S = s k) is obtained by applying the total probability rule (2). P(A = a 0 S = s k ) = M m=1 P(A = a 0 A = a m, S = s k ) P(A = a m S = s k ) (2) This procedure, when repeated for each class of true NTG, gives the posterior distribution of true NTG given the initial NTG estimate for a given geological scenario, P(A = a m A = a 0, S = s k) (Figure 1, Panel D). If desired, the probability distribution for the true NTG given initial best estimate, P(A = a m A = a 0 ), can be obtained using the total probability rule (3). P(A = a m A = a 0) = K k=1 P(A = a m A = a 0, S = s k ) P(S = s k ) (3) Assigning a prior probability P(S = s k ) to a geological scenario is necessarily a subjective task. A convenient alternative to using expert knowledge is to assume each scenario to be equally likely, which might be reasonable in sparse data situation. To summarize, Caumon et al. (2004) considered three jointly related sources of uncertainty: the geological scenario S, the true NTG value A, and the global NTG estimate A obtained from the available data. Seismic data, the well-to-seismic calibration algorithm, and the initial drilling strategy are frozen throughout, however these can be randomized in a broader study. 3

4 2 Information available at appraisal stage 2.1 Geological scenarios At the appraisal stage the degree of uncertainty about the geological setting depends on several factors. If the reservoir is located in a frontier basin the uncertainty tends to be much higher as opposed to a mature basin where the geological setting is known with greater confidence. In deep-water settings the quality of seismic data also plays a big role. Wellimaged seimic data can significantly reduce the uncertainty about the structural setting and, in exceptionally good cases, even the facies types can be deduced from the seismic amplitude slices. Conversely, poorly imaged seismic data can lead to higher uncertainty about both, the reservoir boundaries and the facies types. In most cases the quality of seismic data falls somewhere in between these two extremes. In the WCA reservoir the seismic data quality is sufficiently good to identify the structural setting with a high degree of confidence. It is determined to be a Slope-Valley (SV) system from the very get-go. However, the internal complexity of this SV system has increased with time as the seismic data was better interpreted. It is observed that the greater the number of mapped geobodies, the smaller the gross reservoir volume, and consequently the smaller the OOIP. For this study we retain the appraisal stage stratigraphic architecture as shown in Figure 2. Figure 2(a) shows a schematic of the reservoir boundaries interpreted from the seismic data and Figure 2(b) shows the corresponding reservoir grid. The entire workflow is limited to this domain. The depositional facies within the SV region, however, cannot be easily inferred from the seismic data. Since the structural setting is known in this case, the uncertainty about geological setting boils down to the uncertainty about the type and distribution of the depositional facies. This facies uncertainty is expressed through different training images (Ti). From well-log analysis four depositional facies were identified. The NTG ratio within these facies are given in Table 1. Facies 1, which has the lowest NTG, is the background facies. Facies 4, with the highest NTG, is interpreted as channels and it is the main reservoir rock. The Tis can be divided into two families depending on how facies 3 and 4 are characterized. In the first family of scenarios, facies 2 with 47.3 percent NTG is characterized as poor quality channels, and facies 3 with 63.0 percent NTG is considered as intermediate quality channels (Figure 3). In the second set of scenarios, facies 2 and facies 3 have been interpreted as poor and intermediate quality lobes respectively (Figure 4). The within-family scenarios differ from one another with respect to channel widths, width-to-depth ratio, and channel sinuosity. To study the impact of geological scenario, one representative Ti is retained from each of the two family of Tis. Figure 5 shows these two scenarios. 2.2 Prior knowledge of net-to-gross distribution A prior NTG distribution for the WCA reservoir is obtained using a database of analog reservoirs. This distribution is shown in Figure 7. The bounds of the distribution, [0.06, 0.61], specify the minimum and maximum NTG values expected to be found in a reservoir 4

5 like the WCA reservoir. In the Bayesian framework adopted in this workflow the bounds of the posterior distribution cannot be greater than those of the prior distribution, hence it is advisable to choose a conservative (i.e. wide) prior distribution. Note that the prior distribution is defined independently from the actual data from the WCA reservoir. It is obtained by pooling together information from other reservoirs that are deemed analogous to the WCA reservoir; hence it is truly a prior in the Bayesian sense. The goal of the workflow is to update this prior distribution taking account of actual quantitative data available on the WCA reservoir. In the analog database system used for this study, the reservoirs are classified at the system scale and not based on the depositional facies. In the WCA reservoir since the structural style is unambiguously determined to be Slope Valley, only one prior NTG distribution was available for the different facies scenarios. Ideally, each geological scenario should have a different prior NTG distribution. Since the prior NTG distribution is independent from the local reservoir data, it does not change as new data becomes available. However, if the interpretation of the geological scenario changes as a result of new data, then a new prior distribution may have to be considered. 2.3 Well and seismic data The WCA reservoir has been in production for a few years and about 28 wells are available which provide a good coverage of the reservoir (Figure 6(a)). The wells are marked with the order they were drilled, which makes it possible to study the impact of additional data on NTG uncertainty. At the appraisal stage only four wells were available, which we retain for this study (Figure 6(b)). Four different facies are deduced from the well-log data, but the interpretation of these four facies varies from one geological scenario to the other (see section 2.1). Each facies has a constant NTG value, which is same for all geological scenarios, see Table 1. Here NTG is defined as volume fraction of sand. Facies number NTG value (%) Table 1: Within-facies NTG values Seismic amplitude and four derived seismic attributes are available for this area. These attributes are acoustic impedance and Vshale values obtained from three different calibration techniques. To determine which attribute is the most informative in terms of discriminating between facies we compute, from the colocated facies-seismic data pairs along the wells, the likelihood of observing a particular seismic datum value given a facies value. The lesser the overlap between the likelihood histograms of different facies, the better the discrimination power. Amongst the seismic attributes provided, acoustic impedance was retained as the best discriminator of facies (Figure 8). We observe that impedance discriminates reasonably facies 1 from the others. However, the discrimination amongst facies 2, 3 and 4 is not significant. The Vshale attribute does not discriminate well the facies as seen 5

6 from the seismic likelihoods (Figure 9). For this study we retain the acoustic impedance (AI) for NTG computations. 3 NTG estimation At an appraisal stage wells are few and they tend to be preferentially located. This is true for the WCA reservoir (Figure 6(b)), hence the NTG estimate retained from the four clustered wells might not be representative of the entire reservoir. Seismic data, on the other hand, informs the entire area. If seismic is informative and properly calibrated with the reservoir facies, then a seismic-based NTG estimate would be closer to the true reservoir NTG value. Several techniques for integrating seismic data with facies exists in literature (Fournier and Derain, 1995; Goovaerts, 1997; Caers and Ma, 2002; Strebelle et al., 2002). The major stumbling block for many of these techniques is that they might not be robust in sparse data situation such as this. A simpler, but robust method, would be more suitable for this situation. Bayes inversion, as used by (Bitanov and Journel, 2004), is retained to calibrate seismic data with facies in this paper. Note that the conceptual framework presented here does not call for any specific calibration technique. Essentially in the Bayes inversion method, the colocated facies-impedance pairs are used to compute the likelihood of observing impedance values given a facies category, P(S = s j F = f i ). The facies proportions computed from wells are used as the prior facies proportion, P(F = f i ). For each facies category, Bayes inversion is then applied at each grid location, u, to compute the probability of observing a facies category given the observed impedance value at that location (Equation 4). Here, n refers to the number of facies and m is the total number of classes into which the seismic data is discretized when computing its likelihood probability from the well data. In Equation 4, P(F = f i ) is the proportion of facies i from the wells. Hence, Equation 4 can be interpreted as the update of well facies proportions using seismic data. P(F(u) = f i S(u) = s j ) = P(S = s j F = f i ) P(F = f i ) ; i = 1,...,n; j = 1,...,m P(S = s j ) (4) By performing Bayes inversion at each grid location for the n facies categories we get n facies probability 3D maps; the average of these 3D maps is the updated proportion p i for each facies i (Equation 5). p i = n P(F = f i (u) S = s j (u) ) (5) i=1 If the calibration is properly done and the seismic data are informative, we expect that these updated proportions would be more representative of the true facies proportions in the reservoir than the well facies proportions. Table 2 gives the proportions of the four facies from wells and the updated proportions after integrating acoustic impedance with the well facies data. Notice that the proportion of facies 4, which is has highest NTG ratio has gone down, while that of facies 1, which is the low NTG background facies has gone up. This implies 6

7 Facies number Well propotions Updated proportions Table 2: Facies proportions observed along the wells and after integrating well data with acoustic impedance data. that the initial wells were preferentially located in higher pay zone. Without the correction induced by seismic data the reservoir NTG would be over estimated from the sole well data. Equation 6 is used to compute NTG by combining the updated facies proportions p i and the within-facies NTG values n i given in Table 1 under the constraint that the proportions sum to one. a = (p i n i ) ; pi = 1 (6) The well NTG estimate and the updated NTG estimate after integrating acoustic impedance data are given in Table 3. Data NTG estimate 4 wells wells + AI Table 3: NTG estimate from wells and after integrating well and acoustic impedance data. Consider the reverse situation when the global NTG value and the within-facies NTG values n i are known and we need to compute the proportion of each facies. In the two facies case Equation 6 is sufficient to compute the facies proportions because we have two unknowns and two constraints. However, for more than two facies we have fewer constraints than unknowns and it is not possible to compute facies proportions unless additional constraints are introduced to match the number of unknowns. We propose to freeze the ratio of facies proportions as additional constraints. For example consider the four facies in a fluvial reservoir. By freezing the channel to levee ratio and the channel to crevasse ratio, we can eliminate two unknowns, i.e. the proportion of levee and crevasse, and solve for channel and floodbasin proportions using Equation 6. Once the proportion of channel is known, we can easily retrieve the proportions of levee and crevasse. The ratios to be frozen are uncertain parameters; they can be read from a training image, an outcrop or analog reservoirs or from geological expertise. This approach works best when the facies proportions are related as in the fluvial case. In case of the WCA, we froze the facies 2 to facies 4 proportions ratio and that between facies 3 and facies 4. These ratios were read from the Ti, see Table 4. 7

8 Facies # Ti Ti Table 4: Facies proportion found in Ti1 (Figure 5(a)) and Ti2 (Figure 5(b)). 4 Results and Discussion 4.1 Impact of geological scenario The goal of this section is to understand how the uncertainty on the geological scenario affects the posterior NTG distribution. In case of the WCA reservoir the main source of geological uncertainty is related to the type of depositional facies. As discussed in section 2.1 we retain the two scenarios shown in Figure 5 as representatives from the two families of scenarios. The NTG uncertainty workflow is carried out twice, first using the Ti1 (Figure 5(a)), then using Ti2 (Figure 5(b)). All other parameters of the workflow were frozen; see Table 5 for details. The NTG values within each facies (Table 1) are held constant throughout the study and the same values are used for both scenarios. Parameter Parameter Wells 4 Well NTG 0.48 Seismic data Acoustic Impedance Nb secondary classes 15 Prior NTG distribution from database Nb of NTG classes 10 Nb of realizations 1 Nb of resamplings 500 per classes per class Minimum interdistance 200 m Preferential No between wells resampling Table 5: Key parameters of the NTG uncertainty workflow used to study the impact of geological scenario uncertainty on posterior NTG distribution. The posteriors obtained using Ti1 and Ti2 given a NTG estimate of (see Table 3) are shown in Figure 10. Selected statistics of these two posteriors are summarized in Table 6. Geol Scenario Mean [p 10, p 90 ] Ti [0.312, 0.451] Ti [0.308, 0.454] Table 6: Statistics of the posterior NTG distribution obtained using the two geological scenarios, Ti1 (Figure 5(a)), and Ti2 (Figure 5(b)). The first thing to notice is that the two posteriors are very similar; their posterior statistics differ only in the third decimal. This is also observed for posteriors obtained using 8

9 different number and location of wells. This leads to the conclusion that the two geological scenarios retained, though different in some of their depositional facies, are not very different from the perpective of NTG uncertainty. The main reservoir facies is similar in both scenarios and the relative proportion of facies is also similar. Moreover, the same prior NTG distribution was used for both scenarios, which further reduces the difference between the two posteriors. Figures 11 and 12 show some realizations generated using the two training images for selected classes of global NTG. Notice how in both cases the channel continuity is better reproduced as the global NTG ratio becomes higher. This is a limitation of the multiple-point simulation algorithm snesim; in low NTG cases it is difficult to reproduce thin, connected facies such as channels. Using a Ti that is several times larger than the simulation domain would help improve this continuity. Moreover, in this case a strong servo-system control is used to exactly reproduce the desired global facies proportions. When the Ti facies proportions are drastically different from the target simulation proportions a strong servo-system correction is needed to enforce the reproduction of these target proportions, at the cost of deviating from the Ti structures thus leading to poor structure reproduction. A better alternative is to build, for each global NTG class, a Ti whose facies proportions are reasonably close to the desired target proportions. In terms of spatial distribution of the reservoir rock the two scenarios are also very similar because the channel sands are distributed fairly uniformly in the reservoir, i.e. the sands are not localized. Consequently, the impact of geological scenario uncertainty as assessed through spatial boostrap is low. Consider for example the two end-member scenarios shown in Figure 13; both scenarios have the same global NTG of In Figure 13(a), the sand and shale layers are horizontally stacked hence any vertical well would sample exactly the global NTG value. On the other hand, in Figure 13(b) the sand and shale layers are vertically stacked, hence the NTG of any vertical well would be either 0 or 1 and the NTG estimate on an average would be In this latter case the uncertainty about the NTG estimate is much higher and is dependent on the number of wells. Figure 14 shows the spatial bootstrap histograms corresponding to these two scenarios using 1, 2 and 4 wells respectively. Both scenarios are stationary, but in the vertically stacked case uncertainty about the NTG estimate is much higher. If horizontal wells were used the results would be reversed. 4.2 Impact of prior NTG distribution As mentioned in section 2.2, only one prior NTG distribution is available for the two geological scenarios because, in the analog database system used for this study, the reservoirs are classified at the system scale and not based on the depositional facies. Ideally, each geological scenario should have a different prior distribution associated with it. Since, we do not have an alternate prior NTG distribution for the WCA reservoir, we retain a uniform prior distribution over [0.06, 0.61] and run the workflow with Ti1 to study the impact of prior distribution on posterior NTG distribution. Note that the bounds of this uniform distribution are the same as that of the prior distribution obtained from the analog database, 9

10 however, this is an extreme distribution because it implies that each class of NTG between its bounds is equally likely. The summary statistics of the two prior distributions and their resulting posterior distributions are give in Table 7. Distribution Mean [p 10, p 90 ] Uniform prior [0.115, 0.555] Analog prior [0.180, 0.520] Posterior from [0.317, 0.461] Uniform prior Posterior from [0.312, 0.451] Analog prior Table 7: Summary statistics of two prior NTG distributions and their corresponding posterior distributions for scenario Ti1 (Figure 5(a)). Figure 15 compares the posteriors resulting from using the two different prior distributions. Note that the initial NTG estimate, 0.436, is identical in both cases because the same set of four initial wells and acoustic impedance data are retained. We notice that the [p 10, p 90 ] interval corresponding to the posterior distribution resulting from the uniform prior is slightly wider than that of the posterior resulting from the prior distribution shown in Figure 7. Also, the posterior distribution corresponding to the uniform prior distribution is more symmetric than the latter posterior distribution. Both these observations also apply to the prior distributions, which suggests that the shape and range of the prior distribution does impact the resulting posterior distribution. Indeed, recall that the prior probability of the global value being in a certain class given a geological scenario, P(A = a m S = s k ), impacts the posterior probability P(A = a m A = a, S = s k ) through Equation Impact of additional data The impact of additional data on the posterior NTG distribution is studied using only the Ti1 scenario, since both Ti1 and Ti2 give similar posterior distributions. The goal is to see how the posterior NTG distribution changes as we add new well data. We perform the entire workflow four times, first using only well 1, then adding well 2, then well 3 and finally with all four initial wells. The only parameters that change from one run to another are the initial NTG estimates and the number of wells used for spatial bootstrap. Table 8 summarizes the well NTG and the updated NTG estimates after integration of acoustic impedance data. The resulting posterior NTG distributions are shown in Figure 16; summary statistics are given in Table 8. First thing we notice is that the [p 10, p 90 ] interval of the posterior distribution with the first well (Figure 16(a)) is much narrower than that of the prior NTG distribution (Figure 7. The posterior distribution mean and the [p 10, p 90 ] interval shifts to the right when well 2 is introduced (Figure 16(b)) because the combined NTG estimate of wells 1 and 2 is much higher than that of well 1. Also, the [p 10, p 90 ] interval of the posterior with two wells is narrower than that with well 1 only. This trend is also observed when wells 3 and 4 are introduced. In all four cases the [p 10, p 90 ] interval is roughly centered over 10

11 Nb wells Well NTG Updated NTG Posterior mean Posterior [p 10, p 90 ] [0.218, 0.441] 1, [0.329, 0.514] 1,2, [0.311, 0.459] 1,2,3, [0.312, 0.451] Table 8: Well NTG and the corresponding updated NTG estimates for wells 1 to 4. The updated estimates are retained for the study. the corresponding mean as expected. The initial NTG estimates (Table 8) are included in all posterior [p 10, p 90 ] intervals. The mean and the [p 10, p 90 ] intervals of the posterior distributions are strongly impacted by the initial NTG estimate as demonstrated by this study. Hence, when estimating NTG it is paramount to carefully choose the estimation function and consider all available data while accounting for errors in data, data uncertainty and the redundancy between different data. 4.4 Impact of seismic data The four initial wells are used to study the impact of seismic data on the posterior NTG distribution. The workflow is run twice, once using acoustic impedance and once without using it. Ti1 (Figure 5(a)) and the prior distribution shown in Figure 7 are used for both runs. Table 9 gives the initial NTG estimate and the posterior statistics resulting from the two runs. The resulting posterior distributions are shown in Figure 17. with seismic (AI) without seismic Well NTG Initial estimate Posterior mean Posterior [p 10, p 90 ] [0.324, 0.457] [0.404, 0.539] Table 9: Posterior NTG distribution statistics with Ti1 using four initial wells, with and without using acoustic impedance data. When seismic data is not used the initial estimate is the same as the well estimate. Integrating seismic data lowers the estimate which indicates that the initial four wells were preferentially located. Comparing the posterior distribution in Figure 17(a) with that in Figure 17(b) we observe that the posterior [p 10, p 90 ] interval widths are comparable in the two cases, however, the [p 10, p 90 ] without seismic is shifted to the right as the initial NTG estimate without seismic data is higher. Note that in both cases the initial estimate is included in the posterior [p 10, p 90 ] and this interval is roughly centered around the posterior mean. 11

12 4.5 Comparison with dense well data When studing the NTG uncertainty for real reservoirs like the WCA, we do not have the luxury of knowing the true NTG value unlike in synthetic examples. However, we do have at later times dense well data set that provides a good coverage of the WCA reservoir, see Figure 6(a) for the location of all 28 wells. The 28 well NTG estimate and the integrated NTG estimate are given in Table 10 along with the estimates from the four initial wells. We notice that after integrating seismic data the 28 well NTG estimate is only slightly lowered. This suggests that these wells sample the reservoir NTG reasonably well. Also, notice that the NTG estimate from the initial, clustered, four wells is not too far from the estimate from all 28 wells. This implies that the pay zones in the reservoir are reasonably well distributed such that even a few clustered wells are able to sample the global NTG value fairly closely; see Figure 13 and refer to the corresponding discussion in section initial wells All 28 wells Well NTG Initial estimate Posterior mean Posterior [p 10, p 90 ] [0.324, 0.457] [0.363, 0.428] Table 10: Comparison of posterior NTG distribution statistics resulting from using the initial four wells and all 28 wells from the reservoir. Ti1 and the prior distribution shown in Figure 7 are used in both cases. Figure 18 compares the posterior distributions resulting from using only the four initial wells and then using all 28 wells. The means of the two posterior are comparable. However, the posterior [p 10, p 90 ] interval corresponding to the 28 wells case is narrower compared to that with four initial wells. This confirms the conclusion in section 4.3 that additional data reduces the uncertainty about NTG distribution. 5 Conclusions The impact on NTG of the geological scenario is larger when the facies are distributed in space differently or if the facies shapes are very different. In case of the WCA reservoir the main reservoir facies (channels) had the same shape in both scenarios; consequently, the posteriors from these two scenarios are very similar. Moreover, the stratigraphic style was clearly determined from the common seismic data interpretation, which significantly reduced the geological uncertainty. Ideally, different prior NTG distributions should be used with different scenarios. With the WCA reservoir, however, the posteriors were similar in spite of using two different prior distributions because the geological scenario is overriding the impact of other parameters. In case of WCA, each additional well data contributed towards reducing the uncertainty about the posterior. The mean of the posterior distribution is heavily influenced 12

13 by the initial NTG estimate, hence if that initial estimate is biased then the posterior mean would also be biased. Particular attention should be paid to avoid any such bias. By integrating seismic data the NTG estimates from the different wells are reduced. This suggests that the original four wells were somewhat preferentially located. The global NTG of the WCA reservoir seems relatively stable; indeed the posterior means from using 4 wells versus that using 28 wells, which provide a good coverage of the reservoir, are very similar. Acknowledgements We thank Chevron Energy Technology Company (ETC) for providing this dataset. We also acknowledge the financial support of the Stanford Center for Reservoir Forecasting (SCRF). References Bitanov, A. and Journel, A.: 2004, Uncertainty in n/g ratio in early reservoir development, Journal of Pet. Sci.& Engr. 44. Caers, J. and Ma, X.: 2002, Modeling conditional distributions of facies from seismic using neural nets, Mathematical Geology 34(2), Caumon, G., Strebelle, S., Caers, J. and Journel, A.: 2004, Assessment of global uncertainty for early appraisal of hydrocarbon fields, In SPE Annual Technical Conference and Exhibition, SPE paper 89943, Houston, TX. Fournier, F. and Derain, J.: 1995, A statistical methodology for deriving reservoir properties from seismic data, Geophysics 60. Goovaerts, P.: 1997, Geostatistics for natural resources evaluation, Oxford University Press, New York. Journel, A. G.: 1993, Resampling from stochastic simulations, Environ. Ecol. Stat 1, Norris, R., Massonat, G. and Alabert, F.: 1993, Early quantification of uncertainty in the estimation of oil-in-place in a turbidite reservoir, In SPE Annual Technical Conference and Exhibition, SPE paper 26490, Houston, TX. Strebelle, S., Payrazyan, K. and Caers, J.: 2002, Modeling of a deepwater turbidite reservoir conditional to seismic data using multiple-point geostatistics, In SPE Annual Technical Conference and Exhibition, SPE paper 77425, San Antonio, Texas. 13

14 Appendix: Notation The following nomenclature is adopted from Caumon et al. (2004). a, A true global value and corresponding random variable a, A global estimate and corresponding random variable d 0 observed quantitative data (wells + seismic) d,d alternative quantitative data and corresponding random variable vector n i net-to-gross ratio within facies i p w i proportion of facies i observed in the wells p i proportion of facies i after integrating well and seismic data s k, S a geological scenario and the corresponding random variable 14

15 Figures Figure 1: Workflow of Caumon et al. (2004) shown in greater detail. 15

16 (a) Conceptual model (b) Stratigraphic model Figure 2: The early stratigraphic interpretation is retained for this study. (a) (b) (c) (d) Figure 3: Training images from the first family of interpretations. Notice the different channel widths and sinuosity. 16

17 (a) (b) (c) (d) Figure 4: Training images from the second family of interpretations. Notice the different channel widths and sinuosity. (a) Ti1 (b) Ti7 Figure 5: Two representative geological interpretations retained to study the impact of geological scenario. 17

18 (a) All available wells (b) First four wells Figure 6: Figure showing the location of all available wells and the four wells available at appraisal stage in the Slope Valley region. mean: std. dev.: P10: median: P90: Figure 7: Prior distribution for the WCA reservoir obtained from a database of analog reservoirs. 18

19 mean: std. dev.: minimum: P10: median: P90: maximum: mean: std. dev.: minimum: P10: median: P90: maximum: mean: std. dev.: minimum: P10: median: P90: maximum: (a) facies (b) facies 2 mean: std. dev.: minimum: P10: median: P90: maximum: (c) facies (d) facies 4 Figure 8: Likelihood of observing impedance value (x axis) given a particular facies obtained using Bayes inversion in the Slope Valley region. Impedance values have been normalized between 0 and 1. Y axis is the frequency. 19

20 mean: std. dev.: minimum: P10: median: P90: maximum: mean: std. dev.: minimum: P10: median: P90: maximum: (a) facies 1 mean: std. dev.: minimum: P10: median: P90: maximum: (b) facies 2 mean: std. dev.: minimum: P10: median: P90: maximum: (c) facies (d) facies 4 Figure 9: Likelihood of observing VShale value (x axis) given a particular facies obtained using Bayes inversion in the Slope Valley region. X axis represents the Vshale values. Y axis is the frequency. mean: std. dev.: P10: median: P90: mean: std. dev.: P10: median: P90: (a) with Ti (b) with Ti2 Figure 10: Posterior NTG distributions obtained using Ti1 and Ti2 given a NTG estimate of obtained using first 4 wells and acoustic impedance. 20

21 (a) NTG: 0.14 (b) NTG: 0.25 (c) NTG: 0.36 (d) NTG: 0.47 Figure 11: Facies realization using Ti1 for selected values of global NTG values. There are a total of 10 NTG classes ranging from 0.08 to 0.58 discretizing the prior NTG distribution shown in Figure 7. 21

22 (a) NTG: 0.14 (b) NTG: 0.25 (c) NTG: 0.36 (d) NTG: 0.47 Figure 12: Facies realization using Ti2 for selected values of global NTG values. There are a total of 10 NTG classes ranging from 0.08 to 0.58 discretizing the prior NTG distribution shown in Figure 7. (a) Horizontal Layers (b) Vertical Layers Figure 13: Two end-member geological scenarios with NTG of

23 (a) 1 well (b) 1 well (c) 2 wells (d) 2 wells (e) 4 wells (f) 4 wells Figure 14: Spatial bootstrap histogram of NTG estimates obtained by doing 1000 resamplings in the two scenarios shown in Figure 13. Left column corresponds to the horizontal layers case and right column corresponds to the vertical layers case. 23

24 mean: std. dev.: P10: median: P90: mean: std. dev.: P10: median: P90: (a) with uniform prior distribution (b) with prior distribution from database Figure 15: Posteriors with Ti1 resulting from two different prior distributions. mean: std. dev.: P10: median: P90: mean: std. dev.: P10: median: P90: mean: std. dev.: P10: median: P90: (a) With 1 well mean: std. dev.: P10: median: P90: (b) With wells 1 and (c) With wells 1,2 and (d) With wells 1 to 4 Figure 16: Posterior NTG distributions obtained using Ti1 to study the impact of additional data on the posterior. 24

25 mean: std. dev.: P10: median: P90: mean: std. dev.: P10: median: P90: (a) with seismic (AI) (b) without seismic Figure 17: Posteriors with Ti1 with and without using seismic data (AI). mean: std. dev.: P10: median: P90: mean: std. dev.: P10: median: P90: (a) with four initial wells (b) with 28 wells Figure 18: Posteriors resulting from using only four initial wells and all 28 wells from the WCA reservoir. 25