The authors used historical field data from a deepwater turbidite reservoir to investigate several history-matching strategies. This project involved an integrated seismic-to-simulation study. The trade-offs between exploring many models vs. calibrating a single model were explored. The scale at which the geologic model was constructed and how the simulation scale could be determined were examined. The large discrete steps in the process and the smaller local assisted parameter calibration were studied. The results provided general guidance on workflow sequence, model selection, and the scales of static and dynamic modeling.
Introduction
History matching is a process wherein changes are made to one or more parameters of the initial geologic models so that the predicted reservoir performance matches production history. The history match calibrates reservoir descriptions that then may be used for performance prediction and reservoir-management decisions. The initial geologic model represents the reservoir structure, its stratigraphy, layering, sedimentology, and facies distribution. The static model consists of a 3D spatial distribution of porosity and permeability derived from the geologic model. An initial distribution of water, oil, and gas is added to the static model to enable flow simulation. Historical data from the well, injection, and a subset of production provide boundary conditions for reservoir-simulation performance prediction, and the remaining production and pressure data are used to test those predictions.
The intent of this study was to emphasize the importance of multiple initial geologic models and to demonstrate an uncertainty-assessment strategy on the basis of multiple geologic interpretations. The uncertainty assessment is a precursor to a full-history-match study. It may be thought of as a means of generating multiple starting points for history-match-model calibration, or, perhaps more importantly, may be used to obtain an improved reservoir description even without full implementation of a history match.
An SPE reprint collection (Datta-Gupta, Akhil, ed. 2009. History Matching and Conditioning Geologic Models to Production Data. Richardson, Texas: Reprint Series, SPE.) provides an excellent starting point to understand current, developing, and historical practice. This paper describes the history match within an integrated seismic-to-simulation research study, including the interpretation of seismic data, assembly of geologic information, petrophysical log evaluation, and well-test pressure-transient interpretation. The results of this integrated geoscience study were used as the starting point for the history match. Field data for the study were provided by a major producer for research and educational purposes. However, this study was performed without their direct intervention.
Methodology
The interpreted seismic data were used to build horizons and faults for the structural model of the field, which then was used to construct a 3D gridded geologic model. The uncertainty study began with a diagrammatic approach in which the major subsurface uncertainties were displayed visually. This approach assisted in creating a sufficiently broad range of starting models. It also provided rapid documentation in post-project reviews in that uncertainties that did not appear in the visual display were not considered within the study. The second stage of the uncertainty study was based on the calculation of an objective function that measures the mismatch between historical and predicted values for each model. It was found that this combination of qualitative and quantitative analysis provided excellent insight into the reservoir description, even before starting a full history match.
The first stage of the history match was performed by subdividing the field into regions, which could correspond to geologic units, facies types, or other areal divisions. Regional properties, typically porosity and permeability, could be modified independently. Initially, a screening study was performed, from which the authors obtained an importance ranking for each parameter. The highest-ranking subset of parameters then was used to minimize the objective-function mismatch with an evolutionary strategy.
These techniques can provide one or more sets of parameters, which are optimal in the sense that they minimize a misfit function. However, in terms of providing reservoir characterization, the spatial resolution of the parameter changes is limited by the initial region definitions. At best, these parameters, or their changes, must be thought of as averages over each region. Attempting to redefine regions or including additional degrees of freedom for increased spatial resolution of regions is an active area of research. In later stages of the history match, the authors increased the number of regions, guided by the performance of the history match.
In contrast, streamline-based analysis techniques do not rely on predefined region definitions, instead they use bundles of streamlines for dynamic-region definitions. This concept may be extended further by using streamlines to calculate spatial-sensitivity information, which describes how a change in the permeability of any cell in the model contributes to a change of water cut at each well. This sensitivity information may be combined with the mismatch in water-cut progression at each well to determine changes in permeability within the reservoir model. To ensure uniqueness in these cell-by-cell changes, the inversion is regularized by constraining it to have minimum changes from the previous geologic model together with a smoothness constraint. These techniques are related to the formal inversion techniques used in geophysical travel-time inversion. As a reservoir-characterization tool, changes are made to the previous model, driven by spatial-data support of the well. No previously defined regions are required. However, these techniques are based on convective processes and work best to modify transport properties (i.e., permeability) once a water cut matures. In contrast, variation of region properties may be used to modify porosity and permeability (e.g., volumes and transport).
The overall methodology is summarized in Fig. 1 and is detailed in the complete paper. Each element of this workflow is available commercially or has been demonstrated in other research papers.
Field Description
The studied reservoir is a deepwater channelized turbidite reservoir in the Gulf of Mexico, producing oil from Middle Miocene sands. The field has a combination of structural and stratigraphic traps. It is bounded on the northeast by a west/east fault that dips northward, it has a stratigraphic pinchout on the eastern and northeastern flanks, and it has a salt dome on the western edge. The oil/water contact is at 14,300 ft. The reservoir consists of sand, silt, and shale laminations. Well-log and core data indicate that reservoir facies can be divided into two main subcategories: clean channel-fill sands and low-quality overbank deposits. The low-quality overbank deposits can be subdivided further into proximal-levee and distal-levee facies, which have increasing shale content. Fig. 2 shows the seismic root-mean-squared (RMS) amplitude map. The bright regions correspond to hydrocarbon presence, which is linked to high net-/gross-pay ratio. Although the amplitude will dim, channel sands are expected to continue into the aquifer.
The field is in 5,000-ft water depth. It is developed with nine dry-tree wells, of which seven are M-Sand producers and two are M-Sand injectors. The M-Sand is subdivided into three intervals (M1, M2, and M3), with most of the production coming from the M2 sand. Field production began in November 2002, and water injection began in September 2003.
There is no evidence of compartmentalization, except for Well A9, the easternmost well in the field. A mass-balance drive-mechanism analysis was performed with pressure and production data. It showed that the single largest source of reservoir energy is aquifer influx, followed by water injection and a combination of rock and fluid compressibility.
Additional information on water influx was obtained from a 4D-seismic survey taken after several years of production, which showed regions with increased water saturation. This information was not used in the history-match procedures, although it did contribute to the geologic interpretation of multiple channels.
Uncertainty Study
Fig. 3 shows input for the uncertainty study. Each element was designed to be independent of the others, so that the four major elements combine their features to provide 4×2×2×2=32 models. Fig. 3 also indicates geologic uncertainties that were excluded from the study. For instance, variations in the overall reservoir structure were not considered. It was described as a simple structure on which any internal faulting acted only to provide potential baffles, not to compartmentalize the reservoir. Fig. 3 also summarizes the dynamic sensitivities included in the history match. When screening geologic models, each dynamic parameter was maintained at its base-case value.
The large-scale reservoir architecture is consistent with a channelized reservoir with north/south-trending channels. The channels control the quantity of sand and reservoir quality, with a potential order-of-magnitude reduction in net permeability in the off-channel portions of the reservoir. Within each channel, the more-heterogeneous trends in porosity and permeability consistently performed better, even with the fairly coarse five-layer models used in the screening study. The creation of multiple and distinct geologic models enabled inferring many geologic features directly from the production data.
History Match
The base-case dynamic sensitivities were used in the uncertainty study. Each history-match case consisted of four stages: identification of one of the three geologic scenarios, a sensitivity run to determine the most important parameters, a pressure history match providing calibrated values for average properties for spatial regions, and a water-cut history match based on streamline sensitivities.
Overall, the assisted-history-match (AHM) techniques provided a successful history match. The ability to create new cases, identify key parameters, and then adjust those parameters is a powerful capability that allows many more cases to be explored than would be possible without the assisted techniques. However, current technology appears to be limited by the requirement to specify spatial regions for the pressure history match. This limitation can be compensated for, to some extent, by the streamline-based water-cut matching techniques, but these are designed to make changes in reservoir permeability, not volumes. Limitations in the spatial resolution of the changes in pore volume continue to limit the water-cut matches, especially in the case of this channelized turbidite reservoir. Also, the sequential use of multiple AHM algorithms can be improved, which was clear for many of the cases studied when the aquifer strength needed to be recalibrated after the water-cut match to better honor the late-time pressure response in the field.
There was interesting interplay between the history-matching performance and vertical resolution. Very-low-resolution models could be used for numerical efficiency early in a history match, but they were not adequate to represent the interplay between heterogeneity, gravity, and sweep as a flood front progresses. Also, a match for later stages of a waterflood was required. There was an interesting interplay between the effective relative permeability curve and the degree of fluid segregation, which is not understood fully. Finally, the example of simulation-layer design indicated that it may be effective to retain log resolution within the geologic model and then scale up to both a reasonably coarse and a reasonably accurate simulation model, removing the approximations that were made with geologic models at intermediate vertical resolution.
Conclusions
- The use of multiple simple geologic models is extremely useful in screening possible geologic scenarios and especially for discarding unreasonable alternative models. This was especially true when developing an understanding of the large-scale architecture of the reservoir.
- The AHM methodology was effective in exploring a large number of parameters, running the simulation cases, and generating the calibrated reservoir models. The calibration step consistently worked better when the models had more spatial detail compared with the more-homogeneous models used for the initial screening.
- Implementation of the AHM methodology followed a sequence of pressure and water-cut history matching. An examination of specific models indicated that cases that minimized conflict between these two match criteria also provided a better geologic description.
This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 160171, “Combined Uncertainty and History-Matching Study of a Deepwater Turbidite Reservoir,” by Akshay Aggarwal*, SPE, Song Du, SPE, and Michael J. King, SPE, Texas A&M University, prepared for the 2012 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. The paper has not been peer reviewed.