Estimation of Permeability and Permeability Anisotropy From Straddle-Packer Formation-Tester Measurements Based on the Physics of Two-Phase Immiscible Flow and Invasion

Abstract

We describe the successful application of a new method to estimate permeability and permeability anisotropy from transient measurements of pressure acquired with a wireline straddle-packer formation tester. Unlike standard algorithms used for the interpretation of formation-tester measurements, the method developed in this paper incorporates the physics of two-phase immiscible flow as well as the processes of mudcake buildup and invasion.An efficient 2D (cylindrical coordinates) implicit-pressure explicit-saturation finite-difference algorithm is used to simulate both the process of invasion and the pressure measurements acquired with the straddle-packer formation tester. Initial conditions for the simulation of formation-tester measurements are determined by the spatial distributions of pressure and fluid saturation resulting from mud-filtrate invasion. Inversion is performed with a Levenberg-Marquardt nonlinear minimization algorithm. Sensitivity analyses are conducted to assess nonuniqueness and the impact of explicit assumptions made about fluid viscosity, capillary pressure, relative permeability, mudcake growth, and time of invasion on the estimated values of permeability and permeability anisotropy.Applications of the inversion method to noisy synthetic measurements include homogeneous, anisotropic, single-and multilayer formations for cases of low-and high-permeability rocks. We also study the effect of unaccounted impermeable bed boundaries on inverted formation properties. For cases where a priori information can be sufficiently constrained, our inversion methodology provides reliable and accurate estimates of permeability and permeability anisotropy. In addition, we show that estimation errors of permeability inversion procedures that neglect the physics of two-phase immiscible fluid flow and mud-filtrate invasion can be as high as 100%. MethodThere are three main components in the workflow developed in this paper:1. Mud-filtrate invasion algorithm 2. Two-phase axisymmetric simulator 3. Nonlinear minimization algorithm Transient measurements of pressure and flow rate are compared to the outputs of a two-phase axisymmetric simulator to yield new model parameters through nonlinear minimization. The invasion algorithm makes use of these parameters (permeability and permeability anisotropy), in addition to pressure overbalance, invasion geometry, mudcake properties, and other rock-formation properties, to simulate the process of mud-filtrate invasion. Subsequently, the calculated spatial distributions of pressure and fluid saturation resulting from mud-filtrate invasion are used as initial conditions for pressure-transient tests. To reduce the time required by the inversion, this last step could be approximated with an invariant mud-filtrate invasion profile calculated only once during the minimization. However, such a strategy is not recommended for supercharged formations where updates of initial conditions during minimization can drastically impact inversion results. For the synthetic case examples cons...

Efficient and Accurate Estimation of Permeability and Permeability Anisotropy from Straddle-Packer Formation Tester Measurements Using the Physics of Two-Phase Immiscible Flow and Invasion

“…An alternative approach is to define the measurements as differential pressure, i.e., ∆p j = p hydrostatic -p j , where p hydrostatic is the hydrostatic pressure prior to the time of measurement, or to use the logarithmic value of pressure, log(p j ). These alternative methods to define the measurements are discussed by Angeles 13 . The vector of model parameters, x, is given by the difference between the vector of the actual model parameters, y, and a reference model (or background model), y R , i.e.,…”

“…On the other hand, when inverting for permeability anisotropy ratios, raw values are used instead. This transformation increases the convergence rate of the inversion algorithm 13 . If values of mobility are required, the viscosities of the fluids involved are assumed constant by the inversion.…”

“…Different inversion techniques were implemented to obtain the results described above 13 . Using a-priori knowledge, the initial guess parameters were given values close to their actual values.…”