A Practical Approach to the Numerical Simulation of Vertical Wells with Negative Skin Factors on Fine-Scaled Grids
Abstract
In a numerical simulator, the inflow from the reservoir grid into a producer well is governed by well connections. The transmissibility of each well connection is calculated using a connection transmissibility equation. On Cartesian grids, the pressure equivalent radius ro is calculated using Paceman’s formula. To ensure the denominator of the transmissibility equation remains positive, it is necessary for the term ln(ro/rw), where rw is the well radius, to be greater than the dimensionless skin factor S.
However, when using fine-scale local grid refinements (LGRs) and reducing the grid block size, the term ln(ro/rw) approaches zero, limiting the effective magnitude of the negative skin value. Increasing the grid size can overcome this issue, but for certain cases smaller grid sizes are necessary to accurately model the flow from the reservoir into the well. This paper aims to present an alternative practical approach to address this problem by applying a permeability multiplier to a “skin zone” across the near-wellbore grid cells, while still accurately equating it to an equivalent dimensionless skin factor.
To demonstrate the proof of concept, a simple 2-dimensional, homogeneous, water-bearing, single-well, numerical model was created. Various cases were simulated with different grid sizes, skin zone multipliers, and skin zone radii. An equivalent analytical model using the infinite-acting radial flow equation was then used to develop a relationship between the analytical skin factor and the numerical skin zone (multiplier and radius) for different grid sizes. A clear correlation was found between the analytical model and the numerical model of the simple 2-dimensional model. Using this correlation, the work was successfully extended to real field tests.
Based on the results of this work, the following conclusions can be made. As the grid size is reduced in the numerical model, the minimum effective skin factor ‘S’ increases. The minimum effective skin factor for a given grid size can be calculated analytically using the well radius and the grid dimensions. An equivalent “skin zone” (i.e., permeability multiplier in a defined area around the wellbore) can be used on any grid size to replicate the analytical model skin factor. A correlation has been developed to identify the necessary skin zone permeability multiplier and skin zone radius to replicate negative dimensionless skin factors for vertical wells on fine-scale grids.
This work demonstrates a practical and reliable alternative for reservoir simulation engineers to numerically simulate vertical wells with high negative skin factors on fine-scale grids. A mathematical correlation is presented to inform the engineer of the required skin zone radius and permeability multiplier necessary to model the equivalent negative dimensionless skin for various fine-scale grid sizes.