Coupled Well Card Description (EOR)

Overview

Wells are the primary engineered component of geologic sequestration systems with deep subsurface reservoirs. Wells provide a conduit for injecting greenhouse gases and producing reservoirs fluids, such as brines, natural gas, and crude oil, depending on the target reservoir. Well trajectories, well pressures, and fluid flow rates are parameters over which well engineers and operators have control during the geologic sequestration process. Current drilling practices provided well engineers flexibility in designing well trajectories and controlling screened intervals. Injection pressures and fluids can be used to purposely fracture the reservoir formation or to purposely prevent fracturing. Numerical simulation of geologic sequestration processes involves the solution of multifluid transport equations within heterogeneous geologic media. These equations that mathematically describe the flow of fluid through the reservoir formation are nonlinear in form, requiring linearization techniques to resolve. In actual geologic settings fluid exchange between a well and reservoir is a function of local pressure gradients, fluid saturations, and formation characteristics. In numerical simulators fluid exchange between a well and reservoir can be specified using a spectrum of approaches that vary from totally ignoring the reservoir conditions to fully considering reservoir conditions and well processes. Well models are a numerical simulation approach that account for local conditions and gradients in the exchange of fluids between the well and reservoir. As with the mathematical equations that describe fluid flow in the reservoir, variation in fluid properties with temperature and pressure yield nonlinearities in the mathematical equations that describe fluid flow within the well. To numerically simulate the fluid exchange between a well and reservoir the two systems of nonlinear multifluid flow equations must be resolved. The spectrum of numerical approaches for resolving these equations varies from zero coupling to full coupling. In this paper we describe a fully coupled solution approach for well model that allows for a flexible well trajectory and screened interval within a structured hexahedral computational grid. In this scheme the nonlinear well equations have been fully integrated into the Jacobian matrix for the reservoir conservation equations, minimizing the matrix bandwidth.

Well Trajectory and Discretization

Figure 1. Well trajectories are declared by specifying linear sections of screened intervals (i.e., well intervals). Linear sections are defined by specifying the three-dimensional coordinate locations (i.e., x, y, z) of the two end points. Well trajectories are discretized into well nodes according to the computational grid and well intervals.

Figure 2. 

Well interval end points are located within a hexahedron grid cell by checking the sign of the dot product of the vector between the end point and surface centroid with the cross product of the vector between the end point and two vertices. Each hexahedron surface comprises four triangular planar surfaces. If the sign of the dot product is the same for all 24 grid cell surfaces, then the end point is within the grid cell, otherwise the end point is outside the grid cell.

Well Model

Mass flow between the well node and field node depends on the pressure differential, fluid viscosity, and the well index.

 

Mass flow for the well is the integrated mass flow over the well nodes.

 

The classical approach to the well problem is the Peaceman model for the well index, which is based on single-phase steady-state radial flow from a vertical well section into a grid cell. The radius of the grid cell is defined as the radial position at which the grid-cell pressure is equal to the pressure obtained from the analytical radial solution.

Figure 3. 

A projection well index replaces the classical Peaceman well index to account for non-vertically oriented well intervals.  Images from Shu, J. 2005. Comparisons of Various Techniques for Computing Well Index, Master of Science Thesis, Stanford University, Stanford, California.

 

Multiple well nodes within a single grid cell are combined into a single effective well interval by summing the well-node projections onto the local grid-cell coordinates

 

Well-node projections are combined into a single well index, using the projection model developed by Shu, 2005; where, the directional equivalent radii are defined in terms of directional intrinsic permeability and grid cell dimensions.

 

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