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Abstract This paper presents a physically consistent approach to modify black-oil PVT tables for (1) eliminating, in some cases, so-called negative compressibilities, (2) extrapolating saturated and undersaturated properties to conditions beyond the limits of original PVT tables, and (3) guaranteeing physical consistency of gas and oil properties as a critical condition is approached. For a number of reasons a black-oil PVT table may contain inconsistencies that result in non-physical behavior in reservoir simulators, sometimes leading to slow run times and, sometimes, premature run termination. Physical inconsistencies can even arise when the black-oil PVT table is created by a physically-consistent EOS model. Black-oil behavior can also be inconsistent as a result of the method used to create the tables - e.g. correlations, conversion of laboratory data, or using EOS models where gas and oil phases are not in thermodynamic equilibrium. Three main methods are developed in the paper. First, an analysis of negative compressibilities is given and an approach to eliminate the problem is proposed. Negative compressibilities can arise because derivatives are held constant from one pressure table point to the next, inconsistent with the pressure-dependent evaluation of properties themselves. The second contribution of our paper is a method to extrapolate an existing black-oil table to higher saturation pressures than found in the original table. Extrapolation is possible to any higher pressure - including a critical ("convergence") pressure where phase properties become identical. The proposed method uses a piecewise-linear log-log relationship between black-oil (surface gas and surface oil) K-values and pressure. Our final contribution is a consistent method to calculate saturated and undersaturated black-oil PVT properties at interior and extrapolated pressures to those in the original table. A cubic EOS and the LBC viscosity correlation methods are used to provide physical consistency, even approaching a critical condition where gas and oil properties must become equal. Introduction Sometimes black-oil reservoir simulators take unexpectedly-large CPU time and experience numerical instability due to "problem" PVT data - e.g. physically-inconsistent or ill-behaved input, or "fill-in" data (in this paper, the black-oil PVT data are divided in two groups - input and fill-in data. All PVT data in the input table are termed as input data and all calculated (interpolated and extrapolated) PVT data are termed as fill-in data. Thus the fill-in data includes both interpolated and extrapolated data). The problem may be more pronounced for near critical fluid systems, but "bad" black-oil PVT data can be found for even the simplest fluid system. In this study, different types of consistency checks of the black-oil PVT data are described. An existing black-oil PVT table may need to be extrapolated to higher saturation pressures. A method to extrapolate an existing table is described. The extrapolation of the fluid (which is defined by RS or rs) is based on K-values of the surface oil and surface gas. In the paper, the fluids are divided in two groups - input fluids and extrapolated fluids. The fluid is termed "extrapolated" fluid if the solution Rs (or rs) is higher than the maximum solution Rs (or rs) in the input table. An EOS based method is used to calculate saturated and undersaturated fill-in data. The fill-in data are calculated both for input and extrapolated fluids. The LBC correlation is used to calculate oil and gas viscosities. Consistency Checks The conditions of physical and "numerical" consistency are defined for black-oil PVT tables. In general, physical consistency guarantees numerical consistency - i.e. reservoir simulation model stability with respect to phase and volumetric calculations. However, for near-critical conditions we have found that model stability is sometimes jeopardized by PVT properties with large pressure derivatives - e.g. dRs/dp and drs/dp. The reason for model instability may be the fill-in method, or it may be due to inadequate numerical methods.
If pore volume contraction contributes prominently to overall expansion while the reservoir is saturated, then the reservoir is classified as a compaction drive. Compaction drive oil reservoirs are supplemented bysolution gas drive if the reservoir falls below the bubblepoint; they may or may not be supplemented by awater or gas cap drive. Compaction drives characteristically exhibit elevated rock compressibilities, often 10 to 50 times greater than normal. Rock compressibility is called pore volume (PV), or pore, compressibility and is expressed in units of PV change per unit PV per unit pressure change. Rock compressibility is a function of pressure.
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Tor Formation (0.99)
- Europe > Norway > North Sea > Central North Sea > Central Graben > PL 018 > Block 2/4 > Greater Ekofisk Field > Ekofisk Field > Ekofisk Formation (0.99)
- Information Technology > Knowledge Management (0.41)
- Information Technology > Communications > Collaboration (0.41)
Consistent Black Oil PVT Table Modification using the Generalized Reduced Gradient Method and Constrained Cubic Spline for Variable Bubblepoint Simulation
Algdamsi, Hossein (Independent Consultant) | Agnia, Ammar (Schlumberger) | Alkouh, Ahmad (College of Technological Studies) | Alusta, Gamal (United Arab Emirates University) | Amtereg, Ahmed (Schlumberger) | Kcharem, Basem (Schlumberger)
This paper presents a physically consistent approach to modify black oil PVT tables to guarantees numerical consistency in reservoir simulation model stability with respect to phase and volumetric calculations. Three sets of checks are performed to detect the following data issues (1) monotonicity errors (2) inconsistent pressure ranges in oil and gas PVT tables (extrapolating saturated and undersaturated properties to conditions beyond the limits of original PVT tables (3) total compressibility checks for the oil and gas phases eliminating, in some cases, so called negative compressibility. Three main method are developed in this paper. First total compressibility was analysed and negative compressibility was eliminated using Generalized Reduced Gradient Method GRG with linear constraints to minimize in particular the changes to the formation volume factors Bo and Bg for oil and gas simultaneously with total compressibility to a positive value at evenly distributed pressure nodes throughout the pressure range by expressing the total compressibility of oil and gas as linear functions of Bo and Bg. Second monotonicity errors was readily corrected so that the changes to the original data are minimized where the original values at each data point satisfy the monotonicity constraints to ensures that all the data points remain positive and prevent negative properties from being obtained. Third PVT Fill in data by Interpolation is made wherever a new data point between defined pressure nodes is inserted into the saturated oil or gas curves, the undersaturated curve is calculated by interpolation of the neighbouring undersaturated curves using cubic spline with constrain to limit the convexity of interpolated value. Extrapolations are performed depending on the quantity and direction with linearly constrained cubic spline no attempt is made to fit more physically meaningful correlations to the properties. CPU time, inability to converge, hindered and oscillate simulation run were compared for the cases with\without physical consistence gas and oil properties in PVT black oil table for syntactic reservoir model of reservoir under depletion drive, water and gas injection. The quality checks of the Laboratory PVT data encompass abundant validity assurance procedures Nevertheless those routine checks may not identify all the pitfalls that may led to nonphysical behaviour in reservoir simulators. Inconsistent or limited PVT data, ill - behaved input or fill in data sometimes led to unexpectedly large CPU time, experience numerical instability and premature run termination. Although this does not necessarily indicate or invalidates PVT laboratory data it always highlights the lack of consistency of the generated black oil tables even though black oil PVT table is created by a physically consistent EOS model. Black oil behaviour can also be inconsistent as a result of the method used to create the tables correlations, conversion of laboratory.
Determination of Rock Compressibility in Unconsolidated Sand in Heavy and Extra-Heavy Oil Fields in Mexico
Fragoso, A. (Schulic School of Engineering, University of Calgary, Calgary, Alberta, Canada) | Aguilera, R. (Schulic School of Engineering, University of Calgary, Calgary, Alberta, Canada) | Cinco-Ley, H. (Universidad Nacional Autonoma de Mexico and Consultant, Mexico)
Abstract Unconsolidated sands in heavy and extra-heavy oil fields in Mexico have significant potential that has not been fully evaluated yet. Thus, this paper examines petrophysics and geomechanical aspects with a view to estimating rock compressibility. This is important since determining this parameter from cores has proved to be difficult many times as the samples tend to collapse easily during laboratory experiments. The proposed method uses an empirical correlation for estimating Biot coefficient (Li et al., 2020) and more established geomechanical equations written in such a way as to allow the estimation of several types of compressibilities including: bulk compressibility, uniaxial bulk compressibility, pore compressibility, uniaxial pore compressibility, and pore compressibility under hydrostatic load. The data are loaded on a Pickett plot (1966, 1973) to demonstrate the value of pattern recognition. There are several intermediate results from calculations leading to the compressibilities mentioned above. These include process speed (ratio of permeability and porosity), pore throat aperture in microns at 35 percent cumulative pore volume (rp35), water saturation (Sw), mercury-air capillary pressure (pc), pore throat apertures (rp) at different water saturations, Biot coefficient (ฮฑ), Poisson's ratio (PR), shear modulus (G), Young's modulus (YM), and fluid compressibility (cf). An important observation is that although use of the equations presented in the paper are straight forward and lead to quick calculation of all parameters mentioned above, it is likely that calculations from well logs without using pattern recognition may lead to uncertain results. The novelty of the paper is developing a methodology for calculating diverse types of rock compressibilities in unconsolidated sandstone reservoirs. Application of the methodology can lead to improved calculated recovery factors of unconsolidated sandstone reservoirs in heavy and extra-heavy oil fields in Mexico by at least 10%.
- North America > Mexico (1.00)
- North America > Canada > Alberta (0.68)
- North America > United States > Texas (0.46)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Sandstone (1.00)
- Geology > Petroleum Play Type > Unconventional Play > Heavy Oil Play (1.00)
- Geology > Geological Subdiscipline > Geomechanics (1.00)
- Geophysics > Seismic Surveying (1.00)
- Geophysics > Borehole Geophysics (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Oil sand, oil shale, bitumen (1.00)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics > Flow in porous media (1.00)
- Reservoir Description and Dynamics > Reservoir Characterization > Reservoir geomechanics (1.00)
- (2 more...)
Abstract Effective procedures for the integrated reservoir and surface facility compositional simulations have been developed. Multiphase compositional fluid flow equations in reservoir, well tubing strings, and surface pipeline network system are solved simultaneously. The procedures have been implemented in the commercial compositional reservoir and surface facility simulator VIP. The equation of state is applied for the phase-equilibrium calculations. New equation of state (EOS) interpolation procedure has been developed (as an option) for simplified phase-equilibrium calculations in integrated compositional simulations. The EOS interpolation procedure can be effectively applied for phase-equilibrium calculations in reservoir, well tubing strings, pipelines, and/or separators. Saturation pressure, recovery factors of hydrocarbon components, and compressibility factors are determined as tabular functions of pressure, temperature, and fluid compositions. The equation of state is applied for the automatic generation of these functions in an initialization step of a reservoir simulation. The effectiveness and accuracy of the new simplified phase-equilibrium procedure have been confirmed in many full field compositional models and pattern models. The new option significantly reduces the CPU time required for the simulations and it matches results of hilly compositional simulations in tested models. The developed procedures for the integrated reservoir and facility compositional simulations have been applied in many reservoir studies. Their applications in the integrated reservoir and surface facility model of the giant Prudhoe Bay oil field have been demonstrated. P. 297
- North America > United States > Alaska > North Slope Basin > Prudhoe Bay Field (0.99)
- Oceania > Australia > Queensland > Surat Basin > Eos Block (0.89)
- Information Technology > Modeling & Simulation (0.50)
- Information Technology > Communications > Networks (0.36)