Page History

...

To ensure the smooth transition from historical data

LaTeX Math Inline

body	[(t_1,q_1)... (t_N, q_N)]

to the production forecasts in future time moments one may wish to math production at the last historical moment

LaTeX Math Inline

body	(t_N, q_N)

which leads to the following form of Arp's model:

LaTeX Math Inline

body	b=0

LaTeX Math Inline

body	0<b<1

LaTeX Math Inline

body	b=1

LaTeX Math Block

anchor	1
alignment	left

q(t)=q_N \exp \left( -D_0 \, (t-t_N) \right)

LaTeX Math Block

anchor	003NF
alignment	left

q(t) = \frac{

q_0}

1+b \cdot D_0 \cdot t_N \right)^{1/b}}
{ \left( 1+b \cdot D_0 \cdot t \right)^{1/b} }

LaTeX Math Block

anchor	1
alignment	left

q(t) = \frac{

q

1+D_0 \cdot t_N \right)^{1/b}}
{ \left( 1+ D_0 \

,

cdot t \right)^{1/b} }

The Exponential and Hyperbolic decline are applicable for Boundary Dominated Flow with finite reserves

LaTeX Math Inline

body	--uriencoded--Q_%7B\rm max%7D \leq \infty

while Harmonic decline is associated with production from the reservoir with infinite reserves

LaTeX Math Inline

body	--uriencoded--Q_%7B\rm max%7D = \infty

.

...

Page tree