Improving Peaceman Well Flow Modelling With 1D Radial Simulation

In reservoir simulation, Peaceman’s method is the most popular solution for simulating the flow from the reservoir to the well by knowing the gridblock and wellbore pressures, and the fluid phase properties in the well block. The Peaceman method is easy to implement and works well if there are no phase changes in the wellblock. A gas-condensate field is an example of a phase-change situation. When the pressure falls below the dewpoint, condensate drops out in the reservoir and accumulates near the wellbore. The gas relative permeability falls and the well productivity is affected. Evaluating the reservoir fluid phase behaviour using the gridblock pressure will give an incorrect value for well flow productivity. Rigorous well flow simulation requires a very fine grid level that demands a large computational effort. There are various methods for obtaining a detailed pressure profile around wells, for example, the pseudo-pressure method, local grid refinement and hybrid gridding. However, these methods either require many assumptions to estimate the phase properties (as in the pseudo pressure method) or a dedicated gridding technique (as in the local grid refinement method and hybrid gridding), or perform poorly.

In the present work, the Peaceman well flow modelling method has been improved with 1D radial simulation to mimics the local physics around a well accurately with little computational effort. For that goal, a local 1D cylindrical radial flow from the equivalent radius to the well bore was considered. Within the wellblock, cylindrical co-ordinates are used, with the well’s axis being the z-axis. Each radial node represents an annulus around the z-axis extending from the entry point to the exit point of the well in the wellblock in 3D space. Because the grid and internode properties of the radial nodes can be calculated analytically, there is no need to generate these nodes in the real grid space. In our present work, we have mapped the blocks generated by the local grid refinement to the 1D radial nodes. As these radial nodes are real model blocks, relative permeability and pressure–volume–temperature modelling are simulated in these blocks without extra effort. The new method is easily adapted by most reservoir simulators that implement the Peaceman method. Numerical experiments show that, with a few extra 1D radial nodes, the method can accurately and efficiently simulate the rapid pressure profile and phase changing within a wellblock.