Numerical Model

Key Takeaways

• Reservoir numerical models (reservoir simulation models) discretize the reservoir volume into a 3D grid of cells (corner-point geometry or Cartesian, typically 10 to 100 meters in the horizontal plane and 0.5 to 5 meters vertically for fine-scale sector models, or 50 to 500 meters horizontal and 2 to 20 meters vertical for full-field models), assign petrophysical properties (porosity, permeability in three directions, water saturation, net-to-gross ratio) to each cell from geological modeling and geostatistical methods, specify fluid properties (PVT tables from laboratory analysis of reservoir fluid samples, relative permeability and capillary pressure tables from core analysis), define well locations and completion intervals (from well logs and completion schematics), and specify operating constraints (maximum production rates, minimum wellhead pressures, injection rates); the simulator then solves the partial differential equations of multiphase flow (Darcy's law for each phase combined with material balance equations) at each time step, predicting pressure, saturation, and composition distributions throughout the model and computing phase production rates and cumulative recovery at each well; commercial reservoir simulators (Schlumberger Eclipse, CMG IMEX/GEM/STARS, Roxar More, Halliburton Nexus) run on Windows or Linux workstations or cluster computing environments, with model sizes ranging from thousands of cells (simple tank models or sector models) to hundreds of millions of cells (full-field compositional models with detailed geological heterogeneity).
• Model construction workflow for a full-field reservoir numerical model typically requires 6 to 18 months of integrated geoscience and engineering effort and involves a multi-disciplinary team: the geologist builds the structural framework (a 3D grid following the major faults and stratigraphic horizons from seismic interpretation, using software such as Petrel, Kingdom, or Paradigm SKUA) and populates the stratigraphic layers with facies, lithology, and petrophysical properties (using geostatistical methods such as sequential Gaussian simulation or sequential indicator simulation, conditioned to well log data and constrained by the seismic-derived property maps); the reservoir engineer translates the geological model into a simulation model (upscaling the fine-scale geological grid to a coarser simulation grid, preserving the effective flow properties through pseudo-relative permeability or flow-based upscaling, calibrating the PVT model from fluid samples, and specifying the well models and production constraints); the model is then history-matched by comparing simulated production to actual field production and adjusting uncertain parameters (permeability multipliers, fault transmissibility, aquifer strength) to minimize the discrepancy; once history-matched, the model is used to forecast production under different development scenarios (infill drilling, enhanced recovery, pressure maintenance) to support investment decisions; the total cost of building a full-field numerical model from scratch, including data integration, geostatistical modeling, simulation, and history matching, typically ranges from $500,000 to $5,000,000 in consultant and internal engineer time and software licensing costs.
• Uncertainty in numerical models arises from multiple sources at every stage of model construction, and quantifying that uncertainty is essential for making risk-informed investment decisions: geological uncertainty (the uncertainty in the subsurface structure, stratigraphy, and petrophysics from limited well control and seismic resolution) is typically the largest source of uncertainty in undeveloped or partially developed fields, manifested as multiple plausible geological realizations that all honor the available data; fluid property uncertainty (PVT model parameters from limited fluid sampling) affects recovery factor and GOR predictions particularly in gas condensate and volatile oil systems; relative permeability uncertainty (from the limited number of core plugs and their representativeness of the full reservoir facies distribution) affects water breakthrough timing and ultimate oil recovery in waterflood and water injection projects; model uncertainty (the appropriateness of the governing equations and discretization for the specific reservoir type) is a fundamental limitation in fractured reservoirs, in highly compressible chalk reservoirs, and in reservoirs with strong compositional effects that cannot be represented by the black-oil simplification; modern uncertainty quantification workflows use ensemble-based methods (EnKF, ensemble smoother, multi-realization history matching) that run hundreds to thousands of model realizations with different parameter combinations to generate probabilistic production forecasts that explicitly represent the geological and engineering uncertainty rather than providing a single deterministic prediction.
• Seismic numerical models (velocity models and elastic property models) are the subsurface representations used in seismic imaging and inversion workflows: the velocity model (a 3D array of P-wave and S-wave velocities at each grid node) serves as input to seismic migration (which uses the velocity model to collapse diffractions and focus reflections into their correct subsurface positions) and to full-waveform inversion (FWI, which iteratively updates the velocity model to minimize the misfit between observed and synthetic seismograms); the velocity model is constructed from a combination of well log velocities at well locations, surface seismic velocity analysis (semblance or MVA in the offset-midpoint domain), checkshot surveys (calibrating the seismic velocity to the formation velocity measured by timing seismic pulses between surface and downhole geophones), and FWI for high-resolution updates; the elastic property model (including density, P-wave impedance, S-wave impedance, and anisotropy parameters) is derived from the velocity model and well data by seismic inversion (model-based, sparse-spike, or simultaneous inversion) for use in direct hydrocarbon indicator analysis and reservoir characterization; the resolution of seismic numerical models is fundamentally limited by the seismic wavelength (typically 10 to 50 meters for exploration seismic), preventing the imaging of features below this scale without integration with well data and geostatistical interpolation methods.
• Digital twins of oil and gas facilities (a specific category of numerical model that integrates real-time sensor data with a dynamic simulation model of the facility) are an emerging application of numerical modeling for production optimization and integrity management: a digital twin of an offshore platform integrates process simulation (multiphase flow in pipelines, separator performance, compressor curves) with real-time production data (well flowrates, separator pressures and temperatures, compressor operating points) to continuously update the model state and predict near-term production behavior, equipment failures, and process optimization opportunities; machine learning models trained on historical process data are increasingly combined with physics-based numerical models in hybrid digital twins that capture both the fundamental physics (which the physics model handles well) and the complex empirical relationships between variables (which machine learning handles better when sufficient training data is available); the economic value of digital twins is realized through improved production optimization (identifying constraint-relaxation opportunities by running real-time "what-if" scenarios), predictive maintenance (flagging equipment behavior that deviates from the digital twin prediction as an early warning of degradation or impending failure), and training (allowing operators to train on realistic simulator scenarios without risk to the actual facility).