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Wells represent the internal boundaries of the reservoir systems. At the well location, like any other boundary, a boundary condition must be specified. An equation representing the relationship between the pressure of the block hosting the well, the sandface pressure, and the flow rate at the sandface is known as the well reservoir coupling. In this chapter, we will review how a well equation is incorporated into reservoir simulation models.

At the wellpoint (the sandface), there are two options to constrain the well: either the pressure or the flow rate at the sandface is specified. While pressure specification at the sandface is a Dirichlet-type boundary condition, flow-rate specification at the sandface is a Neumann-type boundary condition. Fig. 6.1 shows the three important dependent variables—pressure of the block hosting the well (pi,j,k), sandface pressure of the well (psfi,j,k), and the flow rate of the well (qsci,j,k) —that coexist in a wellblock.

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