Data-Driven Analytics Provide Novel Approach to Performance Diagnosis
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This work describes a heuristic approach combining mathematical modeling and associated data-driven work flows for estimating reservoir-pressure surfaces through space and time using measured data. This procedure has been implemented successfully in a giant offshore field with a complex history of active pressure management with water and gas. This practical work flow generates present-day pressure maps that can be used directly in reservoir management by locating poorly supported areas and planning for mitigation activities.
The giant oil field offshore Abu Dhabi covers an area of approximately 40×25 km. The structure is a low-relief anticline. The fault pattern is dominated by steep northwest/southeast strikes, with less-abundant northeast/southwest strikes. The fault throws are generally small, and most faults are unlikely to be sealing laterally. The oil accumulation is separated by dense argillaceous limestones into three distinct, stacked reservoirs (A, B, and C), each approximately 20 to 35 ft thick. Formation-pressure tests showed good intrareservoir vertical pressure communication. Occasionally, especially toward the north and east, a generally tight clay-prone lithology forms a localized barrier between the upper and basal layers of Reservoirs A and B. The complete paper examines the case of the upper layers of Reservoir A in particular, a laterally extensive porous carbonate deposited in a shallow-water environment, although the work flows developed are equally applicable to other reservoir zones. Commercial production of Reservoir A began in the late 1960s. After an initial period of natural depletion, various pressure-maintenance strategies were deployed, namely dumpflood (1972–1984), peripheral water injection (from 1979), and crestal gas injection (from 2005).
Spatiotemporal Analysis of Pressure Data
Prediction of spatial random fields is a common task in geostatistics and arises in geology, mining, hydrology, and atmospheric sciences. Kriging procedures are used routinely to make optimal predictions at unsampled locations. For quantities that vary in space and time, such as reservoir pressure, spatiotemporal interpolation can provide more-accurate predictions than purely spatial interpolation because observations at other times are considered. In producing oil and gas assets, reservoir-pressure measurements are made at a much higher frequency in the time domain compared with the spatial domain, which requires additional wells to be drilled. The conventional approach of using a spatial interpolation on the basis of a certain time period misses valuable information and could result in inconsistencies between maps from one time period to the next. In this case study, the authors present a heuristic approach to estimating reservoir pressure maps in Reservoir A on the basis of spatiotemporal interpolation. Reservoir pressure is modeled using smooth functions that capture global trends while preserving the spatial and temporal continuity of pressure and pressure gradient. The residuals can be described by a stationary and spatially isotropic process. Residuals then can be predicted at unsampled space and time locations by kriging.
Pressure Global Trend Using a Generalized Additive Model (GAM). More than 3,000 validated reservoir-pressure data points have been measured at 260 wells in Reservoir A throughout its 50 years of production. These pressures were determined by means of static gradient surveys, pressure transient analysis, and formation-pressure tests. To capture the field geometry and pressure characteristics, a quasicylindrical coordinate system combining true vertical depth and angle was adopted.
A correlation matrix, provided in the complete paper, was computed to explore the relationship between pressures and other variables. The variables analyzed include time (date, development phase), geometry (depth, angle), and well type. The Pearson correlation coefficient, which measures the linear correlation, indicated that pressure is highly correlated with the well type and depth. The bivariate scatterplot revealed nonlinear U-shaped behavior of pressure with depth. Other important relationships not captured by the Pearson correlation include combined time-and-depth and angle-and-depth correlation with pressure. Indeed, throughout the well history, the pressure around injectors tended to increase while pressures updip declined or remained stable. The pressure differential between injectors and producers is lower in the east (low angle) than in the west. This low differential in the east is indicative of good pressure communication between injectors and producers.
On the basis of this analysis, pressure can be modeled as a parametric function of time and depth and angle and depth. To capture the globally smooth spatial and temporal variations of pressure, GAMs were used. GAMs are flexible, smooth estimators that capture nonlinear relationships by using basis functions that can be splines, polynomials, or step functions.
Smooth surfaces of pressure as a function of time and depth can be generated for different areas of the field. Fig. 1 shows the computed pressure surface and reveals a complex structure. The pressure response in the west differs from the pressure response in the east with an apparent pressure baffle at mid-depth that began in the 1980s. This corresponds to the dumpflood effect. Pressure maps were generated yearly.
Pressure Local Trend Using Spatiotemporal Kriging. Although a global trend of pressure was obtained, detailed reservoir performance and baffle identification required capturing local trends. The spatial as well as temporal continuity of pressure (and residuals) steers one toward spatiotemporal kriging, whereby near and recent observations are more correlated than distant ones. More rigorously, for a Gaussian stationary and isotropic random field—in this case, pressure residuals—the covariance between two points only depends on their spatial separation and their temporal separation.
The empirical variogram surface for pressure residuals was computed over a distance of 10 km and a time lapse of 5 years using regular binning intervals of 1 km and 1 year. The process is discussed in detail in the complete paper.
A blind test showed that this work flow, combining smooth functions and spatiotemporal kriging, can predict pressures accurately at untested locations and can fill gaps in time series.
Applications to Reservoir Diagnostics
History-Matching Benchmarking. The history-matching work flow typically starts with dynamic pressure match under liquid-voidage control, followed by fractional flow match under oil-rate control, and requires most of the time iterations between these two steps. The pressure match quality control commonly is presented in the form of pressure time series at the well level and, sometimes, the region level. The drawback of this approach is the lack of spatial understanding of the mismatch area and clustering. Conversely, data-driven pressure maps conveniently can be compared with simulation-based pressure maps to identify areas of poor match. The added value, with regard to well-by-well quality-control plots, is the spatial dimension, which allows trends to be identified.
Optimization of Pressure-Data Acquisition. Understanding of the uncertainty associated with the data-driven pressure predictions is critical in planning the drilling of new infills and optimizing the data-acquisition plan. The square root of the kriging variance at the last timestep provides insight about the areas, mostly located away from pressure-control points, where standard deviation exceeds 300 psi. Combined with a pressure-time-derivative map that shows areas where pressures vary the most, this can be a powerful tool for optimizing the pressure-data acquisition plan. More observations would be required in areas where uncertainties are high or where pressure is changing fast.
Interreservoir Differential-Pressure Analysis. The pressure-mapping process was repeated for Reservoir B. Because of its more-favorable reservoir properties and smaller areal extent, Reservoir B is generally overpressured in comparison with Reservoir A. To reduce noise, the absolute differential pressure was averaged across the last 5 years. Differential pressure did not show any prospect of interreservoir communication.
Another area of application for the work flow is the understanding of fluid movement through the computation of streamlines. Data-driven streamlines were computed from the pressure maps and the productivity and injectivity index interpolation map.
Lagrangian Coherent Structures (LCSs)
Streamlines are sensitive to short-term perturbations and small-scale noise. In the case of a dynamic reservoir system with changes in flux, shifts in development strategy, and continuous drilling, the velocity vector field is time-dependent. Thus, streamlines, which would need to be applied to isolated timesteps, are not suited to analyze time-dependent dynamics. In recent years, many of the recently developed methods for the analysis and visualization of fluid-flow time-dependent vector field topology are related to LCSs, which separate regions of qualitatively different ﬂow behavior. Examples of LCSs in nature include eddies in oceanography and hurricanes in meteorology. The complete paper discusses the applicability of the LCS concept to the reservoir flow, in particular for the detection of barriers.
The paper introduces a novel work flow for generating pressure maps from measured data using GAMs for large-scale trends and spatiotemporal kriging of residuals for small-scale features. The developed method was implemented successfully in an offshore field with complex geological features as well as a long history of pressure-maintenance schemes. The method proved valuable in guiding the process of history matching in the giant field by offering a benchmark against which simulated pressures can be compared. The work flow improves the understanding of fluid-flow movements, helps to identify baffles, and assists in field sectorization, especially when combined with data-based streamlines computation. Such understanding is critical in deriving the best reservoir-management guidelines for reservoir-energy conservation and increased production.
Data-Driven Analytics Provide Novel Approach to Performance Diagnosis
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