Gas-Well Decline Curve — Type, Reserves and Economic Limit: 24-Pet-A6 Well Logging and Formation Evaluation, May 2015, Q3

Problem 3: Gas-Well Decline Curve — Type, Reserves and Economic Limit (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. Thirteen monthly rate readings from 1/1/02 ($q=1000$ MMscf/month) to 1/1/03 ($q=631$ MMscf/month); economic limit $q_a=25$ MMscf/month.

Find. (a) the decline type; (b) reserves from 1/1/03 to abandonment; (c) the calendar time abandonment is reached.

Approach. Fit $\ln q$ vs. $t$ (months) by least squares; a straight line (constant percentage decline) identifies exponential decline and gives $D$ directly, after which the exponential decline-curve formulas $N_p=(q_i-q_a)/D$ and $t_a=\ln(q_i/q_a)/D$ apply, restarting the clock at 1/1/03.

(a) Decline type. Regressing $\ln q=\ln q_i-Dt$ on the 13 points gives $\ln q_i=6.9078$ ($q_i=1000.0$ MMscf/month, matching the first point exactly) and $\boxed{D=0.0383\text{/month}}$, with $R^2=0.9999$ — essentially a perfect straight line on the semilog plot (Fig. 1), so this is a constant-percentage exponential decline ($b=0$), not harmonic or hyperbolic.
(b) Reserves to economic limit. Restarting the exponential formula at 1/1/03 with $q_i'=631$ MMscf/month and $q_a=25$ MMscf/month: $N_p=\dfrac{q_i'-q_a}{D}=\dfrac{631-25}{0.0383}$, so $\boxed{N_p\approx15{,}800\text{ MMscf}\ (15.8\text{ Bcf})}$.
(c) Time to economic limit. $t_a=\dfrac{\ln(q_i'/q_a)}{D}=\dfrac{\ln(631/25)}{0.0383}=\dfrac{3.229}{0.0383}$, so $\boxed{t_a\approx84.2\text{ months}\approx7.0\text{ years after }1/1/03}$ — i.e. the well reaches the 25 MMscf/month limit around early 2010.

Fig. 2: log(rate) vs. time is a straight line ⇒ exponential decline. Fitted D = 0.0383/month.

Quantity	Value
Decline type	Exponential, $D=0.0383$/month ($R^2=0.9999$)
Reserves, 1/1/03 to economic limit	$\approx15{,}800$ MMscf
Time to economic limit	$\approx84.2$ months ($\approx7.0$ yr) after 1/1/03

Topic: Arps exponential decline-curve analysis.

Key relations: $q=q_ie^{-Dt}$; $N_p=(q_i-q_a)/D$; $t_a=\ln(q_i/q_a)/D$.

Why this works: exponential decline is the constant-percentage-decline solution of the material-balance/decline differential equation $dq/dt=-Dq$; taking logs turns the exponential into a straight line, so a clean semilog fit is itself evidence for the decline type before any reserves number is trusted.

Common pitfall: fitting $D$ from just the two endpoints instead of a full regression (amplifies the effect of any one noisy reading); forgetting to re-anchor $q_i$ at the NEW starting point (1/1/03) rather than the original 1/1/02 rate when projecting forward.

Source: Ahmed, Reservoir Engineering Handbook, 5th ed., Ch. 9 (decline-curve analysis); Craft & Hawkins, Applied Petroleum Reservoir Engineering, 3rd ed., Ch. 10.

Question 3 of 8: Gas-Well Decline Curve — Type, Reserves and Economic Limit

Problem 3: Gas-Well Decline Curve — Type, Reserves and Economic Limit (20 marks)