Enhancing Model Consistency in Ensemble-Based History Matching
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The aim of this work is to present the effectiveness of a fully integrated approach for ensemble-based history matching on a complex real-field application. The predictive ability of the ensemble of models is greatly enhanced through an integrated work flow promoting collaboration between all subsurface disciplines. One key feature of the ensemble-based method that is especially important for complex reservoirs is that it overcomes the typical limitation of the traditional approaches where the number of uncertainty parameters resulting from practical or algorithm constraints often has to be reduced.
The distinguishing feature of ensemble-based methodologies is their capability of integrating multiple sources of data while quantifying and propagating the uncertainty in reservoir-model parameters. In order to achieve a proper uncertainty assessment, one must couple the ensemble-based data-assimilation technique with an integrated work flow covering the entire reservoir-modeling process. The core of this methodology is an iterative data-assimilation process, which incorporates the reservoir-modeling steps in order to condition the ensemble of model realizations to the available data.
The integrated reservoir-modeling process is used to generate an initial guess for the reservoir models, representing prior knowledge of the reservoir uncertainties. Throughout this process, the relevant model uncertainties must be properly identified and quantified. It is worth noting that significant differences among models may arise from different geological hypotheses or scenarios and from the random component typically introduced by geostatistical methods.
In the complete paper, the authors use the ensemble-smoother-with-multiple-data-assimilation (ES-MDA) algorithm to condition the ensemble of reservoir models to the historical observations. According to this methodology, the ensemble predictions are used to compute a statistical approximation of the sensitivity to the input (uncertain) variables, which are modified in a predefined number of iterations to reduce the mismatch between the simulated and measured dynamic data. The methodology requires the definition of an error associated with each observed source (e.g., field, wells) and data type (e.g., rates, pressures). The ensemble approach allows for a grid-based parameterization, which, driven by the ensemble correlations, provides the ability to modify the value of a variable at some specific location without inappropriately forcing a change to other variables or locations. Consequently, all uncertain model parameters are retained because they may still have a relevant effect on the production forecasts.
Because of the limited ensemble size, localization can be adopted as a form of regularization. For the grid-based properties, this is achieved through the definition of model regions that could reasonably influence the performance of given wells, similar to the use of covariance functions in geostatistical methods. Once an acceptable level of data matching is achieved, the updated models can be used for robust forecasting and reservoir-management optimization.
Integrated Reservoir Modeling. The authors applied the proposed methodology on a clastic reservoir characterized by a large turbiditic channel complex. The reservoir trap is a salt-induced anticline with some radial faulting. The channel complex is subdivided into zones and two hydraulically independent segments. The upper zones culminate above the oil/water contact, where two subhorizontal production wells were drilled, while the basal zones are reached by two injection wells.
The reservoir model integrates all the information coming from the available static data. A full seismic revision and fault interpretation led to the definition of a predrill structural model, confirmed by the development wells, resulting in a simulation grid of almost two million cells. Through the revision of seismic attributes and channel mapping, a series of environment-of-deposition (EOD) objects were defined to capture the main sedimentological features of the reservoir. For practical reasons, the channelized complex was characterized by merging the EODs into six different objects, two of which were used to describe the main pay bodies. Next, a cluster analysis was performed to characterize five different facies with petrophysical distribution parameters.
The work flow for the generation of the reservoir-model realizations can be described as a sequence of three main processes: the generation of the EOD grid, the facies modeling, and the petrophysical modeling. While the shape and position of the channels are clearly identified from seismic, the main uncertainties are related to their lateral and vertical extent. Hence, the channel bodies are fully parameterized through zone-independent variable channel and channel-margin widths.
To populate the facies and petrophysical properties in the reservoir model, a hierarchical simulation method was introduced. The different facies combinations are first simulated over the entire 3D grid and then recombined according to the actual EOD structure. In the same way, the different facies-driven petrophysical properties are first distributed over the entire grid and then recombined according to the actual facies configuration. The method has significant advantages from a practical standpoint, because it enables updating of the underlying (Gaussian) 3D properties, while preserving the multimodal nature of the effective petrophysics and the geological consistency with the updated channel dimensions.
For the permeability field, a variable vertical trend was also introduced to account for a possible degradation of properties below the oil/water contact, as indicated by the available injectivity tests. The generation of the reservoir dynamic models was completed by defining the fluid properties and the other dynamic parameters, including fault transmissibilities, relative permeability curves, and numerical aquifers.
The described work flow was used in combination with Monte Carlo simulations to generate an initial ensemble of 100 model realizations honoring the static data and the initial conceptual assumptions.
Data Assimilation and Validation. The matching parameters for the dynamic data assimilation reflect the uncertainties that emerged in the integrated reservoir study, related to hydrocarbon-in-place volumes and to the sources of production pressure support. The chosen parameterization includes both scalar variables and 3D grid properties, for a total of almost 10 million parameters. The greater contribution to this very large parameterization is related to the hierarchical geomodeling process, because the individual petrophysical properties are updated at the full grid scale before being cut down to the final configuration.
The field production history consists of approximately 1 year of daily phase rates and flowing-pressure recordings for two production wells (P1 and P2) and two injection wells (I1 and I2). The history-matching objective function was defined in terms of flowing-pressure and water-cut mismatches by use of 5% tolerance values and a preliminary filtering out of data points that were clearly outside the main observed trends. When an initial ensemble of model predictions is compared with the updated ensemble after four ES-MDA iterations, a reasonable overall data match is achieved, although the updated predictions show a different degree of remaining variability and the ensemble seems to collapse around the injection pressures. However, the reliability of the updated models was assessed through a validation process, using approximately 4 months of additional observations.
In order to integrate the incoming production data and condition the model to a new perforated well, a second data-assimilation phase was carried out. The geological model was slightly revised on the basis of the previous results, without substantial modifications to the work-flow implementation. To better reproduce the water-cut behavior of Well P1, which was not correctly captured in the initial ensemble, a new channel-erosional scheme was proposed by increasing the heterogeneity in the main-channel EOD template. The increased heterogeneity affects the water-front propagation, favoring some water fingering toward the producers. Additionally, the parameterization was extended to include the connate water saturation in each grid cell.
The amount of available data for the new production well (P3) is not sufficient to reproduce the observed depletion satisfactorily with the current model parameterization. This is not surprising because the initial ensemble tends to overpredict the pressure in Well P3 while underpredicting the pressure in Well P1. However, it is also worth considering that the well drains the same area as Well P1 and, therefore, the ensemble predictions might be affected by the occurrence of conflicting objectives. Hence, improvements could be achieved potentially by adjusting the localization setup for the Well P1 and P3 objectives to avoid this conflict.
Uncertainty Quantification. Fig. 1 shows the results of the second update of the porosity and permeability fields on a representative layer of the reservoir model in terms of percentage variations of the ensemble mean and the ensemble standard deviation. It is worth noting that, according to the hierarchical modeling process adopted, these porosity and permeability fields are just two of the underlying components used to build the final facies-driven petrophysics. The properties variations are mainly concentrated in the regions of the perforated wells, with maximum absolute values of approximately 40% for the ensemble mean and 80% for the ensemble standard deviation. The main achievement is an overall reduction of the uncertainty, especially for the permeability in the reservoir region around injection Wells I1 and I2. In particular, the average permeability is increased around Well I2 and decreased around Well I1, suggesting the possible presence of a flow barrier between the two injectors, which could be included in further model revision. The interpretation is less straightforward in the production regions, where grid-cell modifications are much more heterogeneous and less spatially consistent. The increase in standard deviation for permeability in the region around Wells P1 and P3 is also noteworthy; this is a typical indication of inconsistencies in the prior model assumptions for this region, further supported by the apparent conflicting behavior in the simulated pressure for these two wells.
Enhancing Model Consistency in Ensemble-Based History Matching
01 April 2018
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16 April 2018