Streamline-Based History Matching of Arrival Times and Bottomhole Pressure Data for Multicomponent Compositional Systems

Abstract

Streamline-based history matching techniques have provided significant capabilities in integrating field-scale water-cut and tracer data into high resolution geologic models. The effectiveness of the streamline approach lies in the fact that parameter sensitivities can be computed analytically as one-dimensional integrals along streamlines and requires little additional computational overhead beyond the forward simulation. However, application of the streamline-based approach for simultaneous integration of water-cut and bottomhole pressure has been rather limited. This is partly because the convective streamlines appear to offer no particular advantage while computing parameter sensitivities for the bottomhole pressure data. This limits the utility of streamline-based history matching particularly for three-phase black-oil and compositional systems where the integration of pressure data is a requirement to accurately model reservoir depletion mechanisms. In this paper we first introduce a novel semi-analytic approach to compute the sensitivity of the bottomhole pressure data with respect to grid block properties. The approach takes advantage of the streamline trajectories and yields results that are comparable to sensitivities computed from adjoint methods, at a fraction of the computational cost. The bottomhole pressure sensitivities can be easily integrated with the water-cut, gas oil ratio or composition sensitivities for a joint inversion of pressure data using high resolution geologic models. An iterative least squared method (LSQR) is used to minimize a penalized objective function that includes the data misfit and appropriate ‘norm’ and ‘roughness’ penalty terms to preserve the prior model characteristics during the inversion. The proposed approach is well suited for both streamline and finite difference methods with access to streamlines, and has been generalized for application to three-phase and compositional systems by integrating water-cut, gas oil ratio, and bottomhole pressure data. We demonstrate the power and utility of our proposed method using synthetic and field examples. The synthetic examples include black-oil and compositional cases involving gas injection. The streamline-based sensitivities are compared with adjoint methods for verification purposes. We then apply the method to the Brugge benchmark case and the Norne field to demonstrate the practical feasibility of the proposed method.

Modeling Flow and Pressure Fields in Porous Media with High Conductivity Flow Channels and Smart Placement of Branch Cuts for Variant and Invariant Complex Potentials

“…The real part of the complex potential yields the potential function, which can be used to calculate the pressure field in a reservoir (as detailed in Section 4.1). Several of our prior studies [12,13] include pressure field solutions for several analytical elements (such as point sources and sinks representing vertical injectors and producers, as well as line sinks, representing hydraulic fractures) and obtained excellent matches with independent pressure field solutions generated using a numerical reservoir simulator.…”

“…The real and imaginary parts of certain single-valued complex potentials provide physical descriptions for respectively the potential field contours or isobars (see later Equation (10a)) and the flux across specific regions in the flow between specific streamlines. Although complex potentials for 3D flows are possible [10][11][12], the most convenient formulations are for 2D flows.…”

Development of Decline Curve Analysis Parameters for Tight Oil Wells Using a Machine Learning Algorithm

“…The challenges become even more discouraging with a lack of rock and fluid data and insufficient production history. Researchers have tried to accelerate simulations through techniques such as upscaling [5,6], multiscaling [7][8][9], and streamline methods [10,11]. However, all of these speed-ups require a full physics-based model as a starting point for simplification.…”