A method for incorporating well drawdown effect into reservoir calculations ispresented in detail, together with examples of its use for widely divergentconditions that could be normally encountered in oil reservoir sands. Tentativeconclusions as to the effect such factors as permeability, producing interval, well spacing, or well damage caused by completion or repair practice could haveupon economic ultimate recovery are reached. It is carefully pointed out thatthe conclusions reached are subject to limitations indicated in the text, andplaced upon all calculations made in the paper.
Papers have been presented I-a in which theoretical depletion histories forreservoirs under equilibrium conditions and no appreciable well-bore drawdownpressure are determined. However, except for a limited number of cases, appreciable drawdown pressures in a well bore exist, and pressure andsaturation gradients consequently vary throughout a reservoir.
This paper is an attempt to incorporate well-pressure drawdown into reservoirhistory, and to analyze certain factors, such as those involving recovery, wellspacing, and productivity index, from the standpoint of permeability anddrainage radius. By incorporation? of drawdown into reservoir history, it isbelieved that theoretical considerations will more closely approximate actualreservoir behavior experienced in an oil field. For purposes of simplification, a solution gas-drive typefield, without primary gas cap, has been selected.
Details of equilibrium saturation conditions for no drawdown production forvarious pressures in a reservoir are determinable by methods described byseveral authors permitting the construction of a curve of oil saturation vs.pressure for any selected combination of initial interstitial water andhydrocarbon saturation (Fig I). This curve is then a description of equilibriumsaturation conditions at any given pressure in a reservoir.
Developing the above, details of saturation and flow permeability may thus bedetermined for any increment or portion of a well drainage area or reservoir, In this manner the effect of pressure differential (draw down) may beincorporated into reservoir and well drainage considerations.
It is pointed out that this method thus makes use of no-drawdown equilibriumproduction data, superimposing a drawdown effect upon them. It also assumesthat net flow conditions in any considered increment of reservoir are notmaterially altered by the entrance of fluids from other increments into them, but approach equilibrium for the existing pressure and saturation (i.e., eachincrement behaves in more or less independent fashion, dependent largely uponthe equilibrium considerations mentioned above).