Graphs are presented which require only minutes to use that will forecast the waterflood performance of the five-spot and linear patterns with reasonable accuracy, using permeability curves and the viscosity of the water and oil in place. They contain the relationships between oil recovery as ordinate, and displaceable volumes of water infected as abscissa. The parameter is a dimensionless ratio which is a function of the viscosity of the oil and water in the reservoir and the shape of the relative permeability curves. The graphs give the performances of water floods starting with no gas present in the reservoir before the flood and with gas initially present increasing by increments. Graphs for predicting the performance of multilayered reservoirs also are presented.
Aids to reservoir performance predictions by use of graphs have been presented in the literature from time to time. Such graphs reduce the time and/or equipment to process a reservoir performance prediction. A need exists for a graphical method which will aid in predicting the performance of five-spot and linear water floods and which incorporates fewer assumptions than have been used, previously. The use of fewer and better substantiated assumptions is possible because of the increased knowledge of fluid mechanics in porous media - particularly of multiphase flow - and the advent of the electronic computer. The latter makes it possible to employ more variables without the problem becoming too formidable and to prepare graphs that incorporate more fluid mechanics than have been used in the past.
Graphical methods can be useful to petroleum engineers even though a high-speed computer may be available to them, as a computer program often has not been written or is not conveniently available. Another advantage of using graphs is the ease of obtaining the range of the effect of changes in basic data. For example, if the quality of the permeability curves given to the engineer is not satisfactory it is easy to obtain the performances that represent the upper and lower limits of the permeability other source data. Graphical methods also are useful to consultants, students and others when the details and connections required to process material through a computer would be too troublesome for the number of predictions to be calculated.
The authors have been working on the water-flood predictions over a period of time. This experience combined with a study of groups of dimensionless ratios resulted in a few graphs which handle many combinations of permeabilities and viscosities. The ordinates, abscissas and parameters presented on these graphs make it possible to make a waterflood prediction in a very short time.
The theory, principles, equations and techniques to calculate the performance of water floods for two-phase flow [oil and water] and three-phase flow [oil, water and gas] have been explained and demonstrated by the authors in two recent papers. These papers present the performance prediction methods using a curve for relative permeability to oil and one for water both functions of water saturation. Likewise, the resulting calculations pertain to just one porosity, viscosity ratio, and beginning and ending oil and water saturations.