Reservoir-simulation models play an essential role in generating optimal field-development strategies, but they need to be history-matched before they can be used for reliable forecasting. Traditional history matching of a reservoir involves matching observed production and pressure data at well locations by changing the uncertain parameters in the reservoir model within the acceptable range. The parameters can be classified broadly as static and dynamic. Static parameters include permeability, porosity, and net to gross, among many others. Dynamic parameters may include oil/water contacts, fault transmissibilities, relative permeability curves, and flow pathways.
Deterministic modeling focuses on a single scenario of the reservoir model, ignoring the effect of uncertainty in the parameters considered. Probabilistic history matching is the process of selecting nonunique and multiple history-matched reservoir models by altering the uncertain static and dynamic parameters to obtain a range of possible forecasts. Typically, in probabilistic work flows, objective functions composed of a combination of differences in measured and simulated bottomhole pressure data and individual fluid-phase flow rates are used to identify significant factors or uncertainties. The functions are typically based on surveillance data obtained at well locations and therefore may not be sensitive to key reservoir uncertainty away from wells. A good match with production data for a given reservoir model does not ensure robustness in making performance forecasts.
Reservoir heterogeneities—high-permeability pathways, barriers and baffles, or vertical connections forged from geologic erosion—can significantly affect drainage and swept patterns and well-production forecasts. Especially during early stages of field production, history matching to pressure and fluid-rate production data often lacks information necessary to resolve these critical heterogeneities fully, which may significantly affect production. Even a well-posed probabilistic history-matching approach cannot incorporate the variety and complexities of heterogeneities that are yet to have a strong imprint on future production because of insufficient data away from wells and the sheer number of static and dynamic uncertainties that can affect production.
Surveillance seismic data, or 4D seismic, provides a spatial interpretation of the dynamic fluid and pressure distributions between wells and facilitates choosing models that mimic the interwell areal fluid distributions accurately. Integration of 4D seismic data into reservoir-simulation models has been used typically to improve the reliability of simulation by aiming to capture relative locations of water and gas fronts accurately. Traditionally, 4D seismic data in the form of interpreted saturation and pressure changes have been used to aid in qualitative and deterministic updating of reservoir-simulation models. Porosity and permeability typically are the main variables updated to match the evolution of flood fronts between well locations.
Stochastic modeling techniques, including ensemble- and streamline-based methods, have gained popularity by using 4D seismic data to update the reservoir models. These methods require a large set of simulations to work efficiently and avoid collapsing, which increases the computational resources and time needed. A correlation-based adaptive localization scheme that uses the spatial distributions of correlations to update the reservoir models has been proposed. More recently, a streamline-based data-integration method was used to assimilate 4D data into reservoir-simulation models by calibrating the permeability field at the simulation-grid-cell level.
Quantitative Method Reduces Uncertainty
The methodology presented in this paper uses history-matched reservoir-simulation models and a filtering work flow (called 4DHAM by the authors) to use spatial constraints generated from 4D seismic data to reduce uncertainty and improve production performance. The method endeavors to incorporate spatial locations of flood fronts, address uncertainty in the full range of static and dynamic parameters, and analyze the history matching quantitatively and probabilistically. In comparison with other methods, one of the main advantages of this method is the ability to reduce uncertainty with a relatively small amount of work or time
If the uncertainty in the seismic prediction of flow properties is understood, incorporating seismic data in a probabilistic history-matching work flow is relatively straightforward. Seismic data can be integrated into reservoir models in three different approaches:
- Matching the seismic response through forward seismic modeling
- Matching the changes in elastic properties with seismic inversion
- Matching interpreted pressure and saturation changes
The first approach is computationally extensive, requiring seismic forward modeling, which usually adds uncertainties associated with the seismic data. The second approach also is computationally intensive because it requires the simulation model to be coupled with a given petroelastic model, as well as an inversion of the seismic data to estimate changes in elastic properties. In both approaches, the reservoir models must be transformed into a space to be compared with the seismic data, which inhibits speed and efficiency in history matching. A variety of cases have used forward modeling techniques to calculate impedance changes, or seismic attribute changes, as a function of reservoir properties such as porosity, pore pressure, and saturations. These techniques produce nonunique solutions, which makes constraining reservoir-simulation models an iterative procedure with computational overheads. Resolution differences that arise from seismic and synthetically modeled data from simulation models increase the challenges of achieving a history match.
The third approach—proposed in this paper—assumes the seismic data can be interpreted or inverted for pressure and saturation changes, avoiding additional steps whereby the reservoir-simulation model must be modified to determine a match to seismic. Mismatches can be analyzed quickly and used to drive changes or selections to improve the history match. The proposed work flow uses pressure and saturation changes interpreted from 4D surveillance data and compares them with simulation outcomes, eliminating the need to have a fully coupled model for history matching.
Design of experiments is used initially to generate the probabilistic history-match simulations by varying the range of uncertain parameters. Saturation maps are extracted from the production history-matched simulations and then compared with 4D-predicted swept anomalies. An automated extraction method was created and is used to reconcile spatial sampling differences between 4D data and simulation output. Interpreted 4D data are compared with simulation output, and the mismatch generated is used as a 4D filter to refine the suite of reservoir-simulation models. The selected models are used to identify reservoir-simulation parameters that are sensitive for generating a good match. The methodology and the steps involved in the work flow are discussed in detail in the complete paper.
Deepwater Africa Case Study
A detailed case study and results from adopting the 4DAHM filtering work flow in two different deepwater reservoirs offshore Africa are presented in the complete paper. Using the proposed methodology not only reduced uncertainty but also provided information on key performance indicators critical in obtaining a robust history match to informing decisions on infill drilling opportunities.
History matching was achieved by changing both dynamic and static properties. Erosional contacts and sand-on-sand connections were established through 4DAHM efforts. Pore volume, transmissibility, and multiplier ranges were tested. Latin hypercube sampling was used to generate 500 probabilistic simulations and, subsequent to changes in water saturation, changes in pressure were extracted. Production rate and pressure matching reduced the 500 simulations to a subset of 77, which were further reduced to 20 simulation models after applying a 4D filter. Original oil in place (OOIP), estimated ultimate recovery (EUR), and initial parameter distributions were analyzed for the simulations before and after 4D filtering to quantify the effect (Fig. 1). The analysis indicated that 4D filtering resulted in an increase of 24% P50 OOIP, an increase in P10 EUR, and assistance in reliably estimating the sweep patterns at the target locations. In addition to a reduction of OOIP uncertainty, the work flow helped quantify the optimal infill well target location by providing updated S-curves of saturation change. It also produced significant cycle-time savings.
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