Consistent Black Oil PVT Table Modification using the Generalized Reduced Gradient Method and Constrained Cubic Spline for Variable Bubblepoint Simulation

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.