Prior to investigating coalbed methane (CBM) decline performance, conventional gas well decline performance was studied. We reviewed the relevant literature, performed reservoir simulations and evaluated the applicability of traditional decline analysis presented by Arps.

Review of decline analysis
The Arps decline equation is an empirical relation, valid only when the well is flowing at a constant backpressure (i.e., flowing pressure) and is in boundary dominated flow. Decline

Figure 1. Effects of Drawdown, Turbulence and Multiple Layers on Conventional Gas Decline Performance. (Images courtesy of Fekete)
analysis is a procedure for curve-fitting historical production data and generating a forecast of future production. An initial decline rate, Di, and decline exponent, b, are determined based on the curve fit of historical data and are used to define the shape of the forecasted production profile. The decline exponent (b) describes the change in the decline rate (D) with time. The generally accepted limits on the decline exponent (b) are 0 and 1. There are three specialized forms of the decline equation: exponential, hyperbolic and harmonic.

Exponential decline is defined by a b value of 0, and a constant decline rate (D). It corresponds to the theoretical (Darcy’s law) rate-time solution for a single phase liquid undergoing volumetric depletion at constant flowing wellbore pressure.

Hyperbolic decline is defined by a b value between 0 and 1 and is often used to model gas decline, because unlike single phase liquids, gas properties (mainly compressibility) change during depletion, which results in b values greater than 0.

Harmonic decline is when b = 1. During both hyperbolic and harmonic behavior, the decline rate (D) decreases with time. Accordingly, the choice of b value not only influences the estimate of reserves, but it also affects how long and at what rates the well will produce, which directly affects the economic projections. In practice, it is often difficult to distinguish between exponential and hyperbolic decline without having a considerable amount of production data, so it is up to the judgment of the evaluator to use an appropriate b value. This article discusses b values for both conventional and CBM wells.

Decline performance of conventional gas wells
Numerous simulations of gas production from conventional gas reservoirs (single layer) were performed, and could be matched with b values between 0 and 0.5. Exponential decline
Figure 2. Langmuir Isotherms: same Langmuir Volume but Two Different Langmuir Pressures.
(i.e., b value of 0) implies that the fluid properties (compressibility and viscosity) are relatively constant during depletion, whereas a b value of 0.5 implies that there is a significant change in the fluid properties. Because the change in fluid properties becomes more significant at lower pressures, the value of b changes with reservoir depletion. Factors such as the flowing wellbore pressure and turbulence affect the drawdown in the reservoir, and have a strong effect on the b value. For example, a high backpressure does not reduce the reservoir pressure as significantly as a low backpressure, which results in less fluid property change and therefore a value of b closer to 0. Similarly, turbulence near the well bore reduces the drawdown within the reservoir and therefore reduces the value of b.

In practice, many gas wells (e.g., tight gas wells) are produced at the highest possible drawdown. For these cases, b values approaching 0.5 are anticipated. On the other hand, high deliverability wells may be produced at high backpressures in order to restrict gas production, thereby decreasing the reservoir drawdown and the b value.

According to Fetkovich, b values as high as 1 (i.e., harmonic decline) can be used to match the behavior of layered gas reservoirs. He observed that if one layer depletes quicker than another due to higher permeability or less skin damage, the b value increases.

The results of our simulations for conventional gas well decline are:
• Low drawdowns result in b values approaching zero, while high drawdowns result in b values approaching 0.5;
• Turbulence around the well bore (high rate wells) decreases the value of b; and
• Multilayer reservoirs can exhibit b values as high as 1 when there is a significant contrast between the layer properties.
The effects of these three factors on conventional gas decline are illustrated in Figure 1. The base case in this figure was simulated assuming that the well produced from a single layer at a high drawdown with no turbulent effects.

Decline performance of CBM wells
Production of gas from coal differs from that of conventional reservoirs because of the manner in which the gas is stored. In conventional reservoirs, the gas is compressed in the pore volume of the reservoir, while in CBM reservoirs the majority of the gas is adsorbed onto the surfaces of coal in a liquid-like state. Gas adsorption in coals is typically modeled using a Langmuir isotherm. The isotherm provides a non-linear relationship between the adsorbed gas content (Gc) and pressure (p), and is defined by two adsorption properties: the Langmuir volume (VL) and Langmuir pressure (PL). The Langmuir volume (VL) is the maximum amount of gas that can be adsorbed at infinite pressure. The Langmuir pressure (PL) affects the curvature of the isotherm and corresponds to the pressure at which half of the Langmuir volume is adsorbed. Two Langmuir isotherms are shown in Figure 2 for the same value of VL and two different values of PL. Adsorbed gas is produced from coals by reducing the reservoir pressure, which releases the gas from the adsorbed state, and allows it to flow to the well bore. This process is known as desorption.

Based on our simulations, the flowing pressure, Langmuir pressure, matrix shrinkage and layered reservoirs were found to have a significant effect on CBM decline performance. These simulations verified that the production decline performance of a single layer, CBM reservoir can be estimated using the traditional decline equations (Arps) and can be matched with b values between 0 and 0.5, similar to conventional gas wells. Due to the non-linear shape of the isotherm (Figure 2) a significant volume of gas will desorb as the reservoir pressure depletes (i.e., late-life production), which stabilizes the late time gas
rates and increases the b value. The isotherm becomes more non-linear as the Langmuir pressure decreases (Figure 2) and for this reason coals with lower Langmuir pressures desorb more gas at late time and therefore exhibit higher b values. The value of b was not dependent on the Langmuir volume because it does not affect the curvature of the isotherm.

As gas desorbs, the coal matrix may shrink, which increases the permeability of the coal cleat network. Our simulations show that as the effect of matrix shrinkage increases, the value of b decreases. This is consistent with the observation that any phenomenon that results in a lower reservoir drawdown tends to decrease the b value.

Like conventional gas decline, the value of b used to match the CBM production history is proportional to the wellbore drawdown and may approach 0 in low drawdown scenarios. The
Figure 3. Effect of Drawdown, Matrix Shrinkage, Langmuir Pressure and Multiple Layers on CBM Decline Performance.
effect of turbulence is relatively insignificant in CBM wells compared to conventional gas wells because of the relatively low production rates experienced in CBM operations. Given that CBM is typically produced at the highest possible drawdown, it is reasonable to expect b values of 0.4 to 0.5. The effect of multiple layers on CBM decline performance is similar to that observed in conventional gas systems. If the productivity of the layers is different, then the b value will increase.

The following observations were made in regards to CBM decline performance:
• Low drawdowns result in b values approaching zero. However, because most CBM wells are produced at the highest drawdown possible, b values approaching 0.5 are expected.
• As the Langmuir pressure decreases, the isotherm becomes more non-linear and the b value increases.
• Increasing permeability caused by matrix shrinkage tends to reduce the b value.
• Multilayer CBM reservoirs exhibit b values greater than 0.5 when there is a significant contrast between layer properties.
Figure 3 illustrates these four observations in reference to a base case. The base case was simulated assuming that the well produced from a single layer of coal at a relatively high drawdown with no matrix shrinkage effects.

Summary
Any factor that lowers the drawdown in the reservoir will cause the decline to approach exponential behavior.

Any factor that increases the drawdown will result in b values approaching 0.5.
The difference between exponential and hyperbolic decline may not become evident until late in the life of a well. Determining the appropriate value of b can be difficult as there are few CBM analogies available at the present time. Therefore, an evaluator may have to rely on theoretical principles in order to estimate a suitable value of b.

In spite of the more complex production mechanisms, CBM decline behavior is similar to that of conventional gas wells.