Page 269 - Introduction to Petroleum Engineering

256 PRODUCTION PERFORMANCE
The workflow in Figure 13.2 is a Monte Carlo method because it incorporates the
following procedure:
1. Define a set of input parameter distributions.
2. Generate a set of input parameter values by randomly sampling from the
associated probability distributions.
3. Use the input parameter values in a deterministic model to calculate a trial
result.
4. Gather the results for a set of trials.

Example 13.4 LNDM Model of Shale Gas Decline
The LNDM model was used to model gas production rate for a set of shale gas
wells (Fanchi et al., 2013). The LNDM parameters for a high flow rate gas well
4
5
are a 10 10 and b 15 10 . Estimate the gas rate after 3 years of pro-
.
.
duction. Express time in months since the LNDM model parameters were cal-
culated using monthly gas production.
Answer
The gas rate at t = 3 years = 36 months is
5
q aln t b . 10 10 4 ln 36 . 15 10 5 . 11410 MSCF/mo

13.4 OIL RESERVOIR MATERIAL BALANCE

Material balance calculations are based on the law of conservation of mass. They
account for material in a system, entering a system, and exiting a system. The
reservoir is treated as a large, flexible tank of material. Material can be injected
into the tank and produced from the tank. It can also expand and shrink within
the tank. The balance can be written in simplified form as

Original mass in tank mass entering tank mass exitingtankmassin ttank (13.7)
Material balance calculations use measurable quantities to determine the amount
of a material in the tank. The measurable quantities include cumulative fluid pro-
duction volumes and cumulative fluid injection volumes for oil, water, and gas
phases; reservoir pressure; and fluid property data from samples of produced fluids.
Since reservoir pressure and cumulative volumes are needed in the material balance
calculation, it is necessary to have data measurements over a period of time long
enough to establish a trend. Consequently, the material balance calculation can yield
more accurate results as more data are acquired over time.
Material balance calculations provide an independent method of estimating
the original volume of oil, water, and gas in a reservoir. These volume estimates