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Long-term transient linear flow of hydraulically fractured vertical and horizontal wells completed in tight/shale gas wells has historically been analyzed by use of the square-root-of-time plot. Pseudovariables are typically used for compressible fluids to account for pressure-dependence of fluid properties. Recently, a corrected pseudotime has been introduced for this purpose, in which the average pressure in the distance of investigation (DOI) is calculated with an appropriate material-balance equation. The DOI calculation is therefore a key component in the determination of the linear-flow parameter (product of fracture half-length and square root of permeability, x f ffiffi ffi k p) and the calculation of contacted fluid in place. Until now, the DOI for transient linear flow has been determined empirically, and may not be accurate for all combinations of fluid properties and operating conditions.In this work, we have derived the DOI equations analytically for transient linear flow under constant-flowing-pressure and -rate conditions. For the first time, rigorous methodologies have been used for this purpose. Two different approaches were used: the maximum rate of pressure response (impulse concept) and the transient/boundary-dominated flow intersection method. The two approaches resulted in constants in the DOI equation that are much different from previously derived versions for the constantflowing-pressure case. The accuracy of the new equations was tested by analyzing synthetic production data from a series of fine-grid numerical simulations. Single-phase oil and gas cases were analyzed; pseudovariable alteration for pressure-dependent porosity and permeability was required in the analysis.The calculated linear-flow parameters, determined from our new DOI formulations for the constant-flowing-bottomhole-pressure (FBHP) case, and the input values to numerical simulation, are in good agreement. Of the two new DOI-calculation methods provided, the maximum rate of pressure response (unit impulse method) provides more accurate results. Finally, a field case was analyzed to determine the impact of DOI formulations on derivations of the linear-flow parameter from field data.Linear-flow analysis on the basis of the DOI calculations presented in this work is significantly improved over previous formulations for constant FBHP.

In a previous study (Clarkson 2009), advanced production-analysis techniques, including production type curves and flowing material balance (FMB), were applied to Horseshoe Canyon (HSC) coal wells to establish the applicability of these techniques and to resolve the importance of multilayer behaviour for production analysis. The field examples chosen for analysis included single wells that exhibited production declines analogous to shallow gas wells, with decline in production occurring from day 1, and in one case exhibiting transient-flow characteristics. There are many more HSC wells that exhibit less-straightforward production characteristics, including flat or even inclining production. These wells have production profiles qualitatively similar to two-phase coalbed-methane (CBM) wells, yet lack water production. There are several possible explanations for the flat or inclining production behaviour, including changing skin associated with near-wellbore cleanup of drilling fluids over time, and increase in absolute permeability associated with matrix shrinkage. Regardless of the cause, these effects need to be accounted for in quantitative production analysis.In this follow-up paper, we continue to perform comparisons between multilayer and single-layer-equivalent production analysis of HSC wells, but focus on wells that exhibit inclining gas production. We develop a methodology to correct for changing skin in both type-curve and FMB analyses that allows this more-complex well behaviour to be analyzed. We validate the new methodology using a simulated example, and then apply it to actual field cases. Changing skin and absolute permeability by layer/coal zone was quantified through periodic shut-in/buildup testing of isolated coals throughout the life of the wells, and these dynamic properties were used in production-data analysis and analytical simulation. Comparing single-layer-equivalent and multilayer analysis, we have found differences in estimated-ultimate-recovery (EUR) values of less than 15% because the existence of one or two dominant (high-kh) coal zones. Additionally, we investigated the impact of free-gas storage on the results of productiondata analysis of HSC wells.The production-analysis methodology introduced in this work, while useful for analyzing HSC coal wells with dynamic skin/permeability, is expected to be applicable to a broader range of reservoir types that exhibit this complex behaviour. Production-Data-Analysis Techniques Incorporating Changing SkinThe adaptation of type-curve and FMB techniques for singlephase CBM reservoirs was previously discussed in Clarkson et al. (2007) and Clarkson (2009). The dimensionless rate and time

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With the current focus on liquid-rich plays in North America, and the importance of gas condensate reservoirs globally, there is an increased importance placed on reservoir engineering methods to analyze such reservoirs. This paper provides a new semi-analytic boundary-dominated flow equation (BDFE) and also adapts the existing BDFE of dry gas reservoirs for production analysis of constant flowing pressure wells producing from gas condensate reservoirs. To analyze long-term production data, these equations are coupled with a modified material balance equation to give gas-in-place and average reservoir pressure obtained from plotting techniques which use iterative procedures. The required input data for analysis are gas flow rate, bottomhole pressure, CVD test data, and a portion of the immiscible gas relative permeability curve. We also introduce a new material balance time function for gas condensate reservoirs. To verify our analysis methods, compositional numerical simulation is used. We also test the practicality of our approach through analysis of field data.