multivariate production systems optimization - Stanford University

q is the mass production rate from the reservoir, the source-sink term, and
∇.
k ρ ∇P
μ
VB
is the mass flux term across the reservoir boundaries.
A material balance considers the reservoir to be a single cell with no-flow boundaries.
Therefore the mass flux term is zero and the equation simplifies to
∂m
∂t
Discretizing and multiplying by a time interval Δt yields
+ q = 0 (2.6)
Δm + q Δt = 0 (2.7)
which simply states that the change of fluid mass in the reservoir must be equivalent to the
mass of fluid that was produced or injected.
Equation 2.7 consists of a mass accumulation term and mass source-sink term. The
accumulation term consists of the change in the mass of the reservoir fluids over time. The
fluid mass in the reservoir at any given time (implied standard conditions) may be given as
where
m O = m OO + m OG
m G = m GG + m GO
mOO = φ SO
S
ρOO BO
mOG = φ SG
S
ρOG BG
mGG = φ SG
S
ρGG BG
mGO = φ SO
S
ρGO BO
10
VB
VB
VB
VB
(2.8)
(2.9)
(2.10)
(2.11)
(2.12)