Page 291 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

458 Reservoir Engineering

elements, each having the properties and spatial orientation of the associated
blocks of a physical reservoir [273]. The simulator treats each block as a small
reservoir, and keeps track of fluid entering or leaving the block. When a change
in pressure due to injection or withdrawal of fluid occurs, the simulator solves
the material balance equation for a number of time steps for each block until
equilibrium is reached, Blocks are usually configured so that each well is in an
individual block. Time steps are .picked so that the required information is
resolved without using excessive computer time. Since the simulator keeps track
of fluid movement through the reservoir, the output can include a wide variety
of parameters. Fluid fronts, saturation changes, pressure distribution, and oil-
water contact movement are a few of the things that can be plotted. The three
general classifications of simulators are gas, black oil, and compositional. Gas
simulators model one or two phases (gas or gas and water). Black oil simulators
are designed to model any proportion of gas, oil, and water, and they account
for gas going into or out of solution. Compositional simulators are used when
PVT data does not adequately describe reservoir behavior such as in condensate
reservoirs. These simulators calculate the mass fraction of individual components
in each phase and mass transfer between phases as each phase flows at different
rates. Most models are run with limited information and must be tuned to
properly predict actual reservoir performance. This is done by changing para-
meters such as relative permeability, porosity, and permeability data until the
simulator matches the field history.
Production Decline Curves

The most widely used method of estimating reserves is the production rate
decline-curve. This method involves extrapolation of the trend in performance.
If a continuously changing continuous function is plotted as the dependent
variable against an independent variable, a mathematical or graphical trend can
be established. Extrapolation of that trend can then permit a prediction of future
performance. For an oil reservoir, the plot of the logarithm of production rate
against time is most useful. Although decline-curve analysis is empirical, if care
is taken to ensure that production rates are not being affected by such things
as the mechanical degradation of equipment or the plugging of the formation
by fines or paraffin, the method is reasonably accurate. As discussed, there are
three major types of decline curves: constant percentage or exponential, hyper-
bolic, and harmonic. Although analysis of a large number of actual production
decline curves indicates that most wells exhibit a hyperbolic decline with an n
value falling between 0 and 0.4, the constant-percentage exponential decline-
curve is most widely used. The exponential decline curve is most popular
because, when plotted on semilog paper the points make a straight line which
is easiest to extrapolate to the economic limit. Now that programmable cal-
culators and personal computers reside at most every engineer's desk, it is easy
to punch in the production data and decide which decline curve is best.

Quality of Reserve Estimates
If reserve estimates contained no risk, no dry holes would be drilled. Unfor-
tunately, risk is inversely proportional to knowledge and the least is known
before a well is drilled. Hudson and Neuse E2741 presented a graphical repre-
sentation (reproduced in Figure 5-147) of reserve estimate quality throughout
the life of a property. Section 1 shows the production history of the property.
Section 2 indicates the probable risk factor associated with each stage of