Ensemble-Based Assisted History Matching With 4D-Seismic Fluid-Front Parameterization
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An ensemble-based 4D-seismic history-matching case is presented in the complete paper. Seismic data are reparameterized as distance to a 4D anomaly front and assimilated with production data. This study shows that adding the 4D reparameterized seismic data in addition to the production data keeps a reasonable match with production data while constraining the overall gas distribution in the reservoir to the observed seismic data.
The complex construction of a petroelastic model renders the use of quantitative seismic data in history-matching work flows quite challenging. Several authors have investigated quantitative approaches for incorporating a large number of seismic data into history-matching work flows for production data. The work flows adopted in most of these studies require significant reduction of the uncertainty space or produce on a single history-matched model.
In recent years, an algorithm that has gained increased popularity is the ensemble Kalman filter (EnKF). The EnKF and its derived algorithms are called ensemble methods, and their most notable characteristic is being computationally feasible for large systems and being relatively easy to implement. Several authors have investigated the effect of assimilating 3D- or 4D-seismic data with EnKF and have had to face the problem of building an accurate petroelastic model. To circumvent this problem, some authors have reparameterized 4D-seismic anomaly-front data into arrival times. Despite the advantage of eliminating seismic inversion, this method presents the disadvantage of at least doubling the simulation time for accurate ensemble arrival-time predictions.
In the complete paper, the assisted history matching is performed on a large turbiditic field with the ensemble method to assimilate production and 4D-seismic data by use of the distance-to-front parameterization. The field is a large turbiditic body, with initial fluid pressure close to the bubblepoint. Oil production causes the pressure to fall below the bubblepoint in the very early life of the reservoir, leading to a widespread gas exsolution. The time-lapse change in gas saturation is considered the only factor responsible for the observed negative relative changes in seismic velocity seen over the entire reservoir. There is water injection occurring, but with a local effect, and it is therefore neglected.
The innovation of this study is that the distance-to-front parameterization is applied to the gas phase, which can appear everywhere in the field, rather than coming from an injection source. Another innovation of this study is that the binarization of the simulated time-lapse anomaly is performed without use of a petroelastic model, which would be necessary to relate the measurements to fluid-property changes and to decide a threshold for binarizing observations and pressure. However, the effect of gas is so widespread and evident that the petroelastic model can be replaced by a clustering approach based on the gas-saturation change of the reservoir cells.
The Distance-to-Front Parameterization
This parameterization has been introduced in order to assimilate 4D-seismic data while avoiding the uncertainty coming from seismic inversion and forward rock-physics modeling. There are three steps in this parameterization:
- Binarizing the seismic image according to a selected threshold value
- Applying the fast-marching algorithm calculating distance away from the anomaly boundaries
- Selection of the points at which the data mismatch between the observed and the simulated distance is calculated
In this study, seismic data are selected along the front with no subsampling and, at the same time, distance-based localization is used. The localization length factor is set equal to 25 cells.
Complex production and injection mechanisms occur at the same time in this field, and it is nontrivial to identify a unique cause of the observed 4D effect. In order to match 4D, the inclusion of the petroelastic model into the ensemble-smoother-with-multiple-data-assimilation (ES-MDA) loop would allow forward modeling of all of the fluid-property changes that cause 4D anomalies at the same time. The operator has dedicated considerable effort to building a petroelastic model for this field; however, large uncertainty is associated with many parameters and the prediction of the 4D effect is deemed to be not perfectly accurate. For this reason, the distance parameterization came to be preferred.
The distance parameterization has so far always been applied to cases where the observed 4D-seismic anomaly could be easily linked to a single reservoir-simulation dynamic property change. Thresholding the time-lapse change of that property would provide the binarized image to be entered into the fast-marching algorithm.
In order to identify the predominant reason for the overall 4D anomaly, a qualitative analysis was performed. In this analysis, each of the changes in fluid properties potentially responsible for 4D anomalies (pressure, water saturation, and gas saturation) has been compared with the observations.
The change in pressure is very smooth and is diffused all over the reservoir model; furthermore, the change in pressure is negative and a change in fluid pressure reduces the effective pressure, causing an increase in seismic velocity, while the observed anomaly is negative. The change in water saturation takes place only at a few selected locations in the reservoir (water injectors); also, water replacing oil results in local hardening. Therefore, the change in water saturation can be considered responsible for the local hardening spots, but certainly not for the overall softening effect. The change in gas saturation noticeably resembles the observed seismic anomaly in extension of the covered area and is almost perfectly centered inside the 4D anomaly front; furthermore, gas re-placing oil results in softening. Hence, the change in gas saturation, caused by a general decrease in pressure, can be considered the cause of the overall negative seismic anomaly observed. For this reason, the change in gas saturation is chosen as the dynamic property causing the 4D effect in the prediction and the distance from the binarized change in gas saturation is used as predicted seismic output.
Although the distance parameterization avoids some of the risks related to forward modeling seismic attributes by use of an uncertain petroelastic model and the inversion process, the petroelastic model is often necessary to calibrate the threshold at which the predicted anomaly is binarized. In fact, the petroelastic model would translate simulated changes in gas saturation into the observed relative changes of seismic velocity. However, an incorrect model would bias the overall matching results. For this reason, in this study, an alternative approach is used, circumventing the use of the petroelastic model completely.
The field can be divided into a number of different reservoir systems that are characterized by deposition within both confined and unconfined turbidite systems. The reservoirs are situated within two main stratigraphic intervals of channel systems, each composed of stacked channelized turbidites deposited within confined fairways. These deepwater mass-transport facies are enclosed within hemipelagic shales. Located laterally to each of the main channels is a series of unconfined turbidite deposits (flanks). The reservoir-simulation model comprises different channel systems; however, in this study, the ES‑MDA update concerns only one channel (Channel A), the one with the highest well density and where the 4D‑seismic anomaly is strongest.
An ensemble of 100 realizations was built as Gaussian realizations, though not always respecting the constraints from 3D seismic. Production and injection take place for 6.5 years; the base seismic is available at time zero, while two monitors are acquired at the end of the two different cases and are compared: one where only production data are assimilated (bottomhole pressures, oil and water production, formation pressures, and gas production) and another where the same production data are assimilated with seismic data reparameterized as distance to the gas-front anomaly. The first case is called production only (PO), whereas the second case is called production and seismic (PS). In both cases, the parameters to update include porosity; permeability; net/gross ratio; Corey coefficients for relative permeabilities of oil, water and gas; critical gas saturation; aquifer strength; fault transmissibility multipliers; and flow-region multipliers. Fig. 7 of the complete paper shows the production plots for the two cases from four different randomly selected wells. The overall match is satisfying from both cases. Matching formation pressures is always quite difficult; however, the updated ensembles present improvements in matching these measurements with respect to the previous ensemble.
Another way to evaluate the overall performance of the history-matching process is to sum up the single cost functions, but instead of summing with respect to all ensemble members, summing with respect to all the wells and obtaining a value for each ensemble member. The distribution can be represented by a box plot.
In order to validate the quality of the history matching, it is necessary to look at the updated geology and make sure that it is consistent with the prior information and that the final model makes geological sense. Fig. 1 compares porosity (top row) and horizontal permeability (bottom row) from one layer of one realization extracted from the prior ensemble (first column), from the updated ensemble in case PO (second column), and from the update in case PS (third column). This layer has been chosen because it is the one most-densely perforated. The legend is in exponential values. In both cases, the updated realization shows features similar to those of the prior.
Cases PO and PS present similar results in terms of production mismatch; that is to be expected, because in the seismic cost function, only the distance to the front of the 4D gas anomaly is taken into account. In fact, the real added value of adding 4D seismic in the observations is improving the areal distribution of the time-lapse change in gas saturation. Improving the gas-saturation distribution by use of 4D seismic does not affect the quality of the production-data history matching.
Ensemble-Based Assisted History Matching With 4D-Seismic Fluid-Front Parameterization
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16 April 2018