Distinguished Author Series articles are general, descriptive representations that summarize the state of the art in an area of technology by describing recent developments for readers who are not specialists in the topics discussed. Written by individuals recognized to be experts in the area, these articles provide key references to more definitive work and present specific details only to illustrate the technology. Purpose: to inform the general readership of recent advances in various areas of petroleum engineering.
The use of advanced wells to improve the economics of production is now common practice. The term "advanced" is used to cover horizontal, multilateral, and smart wells (those containing sensors, flow-control, and other devices such as downhole separators). A single advanced well can contact a larger region of the formation and may contact several isolated oil-bearing regions. Control devices enable progressive reduction of production from high water-cut or high gas/oil ratio (GOR) regions. However, advanced wells are considerably more expensive to drill and complete, and their use must be justified by a corresponding increase in economic recovery. Reservoir simulation plays an important role in this decision. But to provide meaningful results, the simulation model must be able to predict well performance accurately over the lifetime of the reservoir. For smart wells, the model also must be able to predict effects of the control devices. Therefore, it is important that the well model be able to calculate, with a reasonable degree of accuracy, the pressure and fluid-flow rates at all locations in the well (including any lateral branches) and the pressure drop across control devices. For this degree of functionality, a suitably advanced form of well model must be used.
In reservoir simulation, the basic purpose of a well model is to supply source and sink terms to the reservoir model. For a production well completed in a single cell of the reservoir simulation grid, the corresponding sink term is represented by an inflow-performance relationship.1,2 This relationship describes the inflow rate of each fluid as proportional to the drawdown (the difference between the pressure in the grid cell and the pressure in the wellbore), the fluid mobility (relative permeability divided by viscosity), and a term known as the "well index" or "connection transmissibility factor" that accounts for pressure losses within the grid cell resulting from radial inflow into the well.3
For a well completed in two or more reservoir grid cells, a similar inflow-performance relationship is applied in each completed cell. Typically, wellbore pressures at each grid-cell completion are related by a simple estimate of the hydrostatic-pressure difference in the wellbore. It can be calculated from the average density of the fluid mixture in the wellbore or, more accurately, from the local density of the fluid mixture in each section of the wellbore between adjacent grid-cell completions. Usually, the calculation neglects other contributions to the wellbore pressure gradient (such as friction), but in general it is adequate for vertical or deviated wells because the hydrostatic gradient is the dominant component of the overall wellbore pressure gradient. Some degree of approximation still exists in the hydrostatic gradient; slippage between the wellbore fluids is neglected and the hydrostatic gradient reflects the homogeneous density of the fluid mixture in the wellbore, which assumes that all the fluids flow with the same velocity. A different approach is required to model the pressure drop from formation level to the tubing head. For this length scale, slippage effects can be very important, and friction also may have a significant effect. A common approach is to perform the pressure-drop calculation for a combination of pressures, flow rates, and water/gas fractions, then store the results in a multidimensional wellbore hydraulics table. This table must be computed for each well before the simulation is performed. However, with this approach, the simulator can simply interpolate the table each time it needs to know the pressure difference between the tubing head and bottom hole, which is considerably faster than calculating the pressure each time.
Typically, for this simple well model, a single variable corresponding to the well's bottomhole pressure (BHP) represents the state of the well. At a given set of reservoir conditions, the BHP value is obtained from a relation that depends on the well's operating target. For a well controlled to operate at a given oil-rate target, the sum of the oil inflow rates from each completed grid cell must equal the target oil rate. It was recognized at an early stage that there were advantages in solving the well equation for the BHP simultaneously with the equations describing fluid flow in the reservoir grid. This strongly coupled approach was developed initially for a single-well simulator,4 in which it is necessary to solve all variables simultaneously (implicitly) to achieve a stable solution in the small radial grid cells near the well. However, the strongly coupled approach was soon adopted in full-field simulators that were able to handle many wells completed in multiple grid cells and operating under a comprehensive range of control modes.5,6