This paper presents a simplified method of production forecasting for tight/shale-gas reservoirs exhibiting extended periods of linear flow, without the use of complex tools (e.g., analytical models or numerical models). The method, which is applicable to hydraulically fractured vertical wells and multifractured horizontal wells, is simple because it relies principally on a plot of inverse rate vs. square root of time, and it is rigorous in that it is based on the theory of linear flow and combines the transient linear-flow period with hyperbolic decline during boundary-dominated flow.
The dominant flow regime observed in most tight/shale-gas wells is linear flow, which may continue for several years. This linear flow will be followed by boundary-dominated flow at later times. Therefore, the method proposed in this study is applicable for forecasting production data for these wells because it considers these two important flow regimes. The derivation is presented for a hydraulically fractured well, and this simplified method can be applied both to hydraulically fractured vertical wells and to horizontal wells with multiple fractures. The application of this method to multifractured horizontal wells in the Marcellus and Barnett shale gas is also presented.
The method is validated by comparing its results with test cases, which are built using numerical simulation for hydraulically fractured vertical wells. For each case, only the first year of the synthetic production data is then used for the analysis. It is found that there is reasonable agreement between the forecast rates obtained using this method and the numerically simulated rates.
Currently, analysis techniques using material-balance time are being used in industry to analyze tight/shale-gas reservoirs. Because material-balance time is actually boundary-dominated flow superposition time, these analyses may show symptoms of boundary-dominated flow even though the reservoir is still in transient flow. The advantages of the forecasting method proposed in this study are that: (1) it is not biased toward any flow regimes because no superposition time functions are used; (2) reliable forecasts can be obtained without using pseudotime--this is an advantage because using pseudotime introduces complexities and an iterative procedure; and (3) the only major unknown is the drainage area.
Shale gas reservoirs have become a significant source of gas supply in North America owing to the advancement of drilling and stimulation techniques. Long horizontal wells completed with multiple-fracturing stages (MFHW) are the most popular method for exploiting shale gas reservoirs today and therefore, development of analysis methods for analyzing production data from these wells has gained tremendous attention in the last decade. The analysis methods developed so far are aimed to obtain understanding of fracture length, fracture conductivity, stimulated reservoir volume (SRV), contacted gas-in-place and other information for a MFHW being analyzed. Although single well analysis methods are of tremendous value, the industry also needs analysis methods for analyzing a group of MFHWs. In this paper, analysis methods developed for single well analysis of MFHWs are extended to analyze a group of MFHWs. These analysis methods are proved to be very useful for cases that adjacent wells are in communication (ex. fracturing one well affected the production of the adjacent wells). It is shown how these methods help engineers to diagnose and characterize the communication between MFHWs and use the results to optimize the size of frac job and spacing between horizontal wells in tight/shale gas plays.
It is well-known that many unconventional reservoirs experience porosity and permeability changes with pressure change during production. In recent work, authors have incorporated geomechanical modeling into production analysis procedures to account for stress-sensitivity of permeability of unconventional gas reservoirs, such as shale gas. Such corrections are necessary for deriving both accurate estimates of reservoir and hydraulic fracture properties from rate-transient analysis and for developing accurate long-term forecasts.
Some shale gas reservoirs are unique in that dynamic changes may occur in both the induced hydraulic fracture AND matrix permeability, which could have a substantial impact on shale gas productivity. Stress-dependence of shale gas permeability has been quantified in the lab by several researchers, but measurements of this kind for propped or unpropped fractures under in-situ conditions are less routinely measured. For the latter, a variety of mechanisms, caused in part or wholly by stress changes in the induced hydraulic fracture, could lead to conductivity changes.
In the current work, we investigate the impact of both stress-dependent matrix permeability and fracture conductivity changes on 1) rate-transient signatures and 2) derived reservoir and hydraulic fracture properties. Stress-dependent matrix permeability is incorporated into rate-transient analysis using modified pseudopressure and pseudotime formulations, and fracture conductivity changes are approximated by applying a time-dependent (dynamic) skin effect.
We demonstrate that when rate-transient analysis incorporates both matrix permeability changes and dynamic skin, the resulting rate-transient signature looks very similar to other shale plays (long-term transient linear flow). Uncorrected data appear to have a very short transient linear flow period, followed by apparent boundary-dominated flow. The impact of the applied corrections on estimates of system permeability and fracture half-length is demonstrated as is the impact on production forecasts.
Various forms of shale gas (SG) material balance equations (MBE) have been developed in the past several decades, dating back to the first round of coalbed methane (CBM)/SG development in North America. These equations attempt to incorporate various aspects of SG storage mechanisms and reservoir characteristics; simple to complex forms exist, depending on the number of assumptions made in their derivation. All of the equations account for adsorbed gas storage, but may or may not include corrections for pore volume (PV) and fluid compressibility, water influx etc. In higher-permeability fractured SG and CBM plays, application of material balance using static (shut-in) pressures to derive original gas-in-place (OGIP) and drainage area estimates has proven useful. With the current development of ultra-low permeability SG (and shale liquids) plays, shut-in times for wells is impractically long so as to preclude the use of static material balance (SMB) methods. Use of rate-transient analysis (RTA) techniques, such as the flowing material balance (FMB), is much more common for original gas-in-place (OGIP) derivations in ultra-low permeability reservoirs, yet some form of MBE is often required for application of these methods. For example, pseudo-time and material balance pseudo-time is commonly used in advanced RTA methods, and hence the form of MBE could impact reservoir and/or hydraulic fracture properties derived from the analysis.
In this work, we first summarize the MBEs that have been derived specifically for SG and/or CBM, with an emphasis on the assumptions, limitations and applications of each equation. We then derive a new MBE that dynamically adjusts free-gas storage volume during depletion according to the amount of volume occupied by sorbed gas, as recently suggested by Ambrose et al. (2010) for volumetric gas-in-place determination. Finally, we examine the impact of MBE selection on quantitative rate-transient analysis (for estimation OGIP). Two simulated cases for SG reservoirs are used to demonstrate the impact of the selected MBE. Finally, a modified transient productivity index (PI) using average pressure in the region of influence was developed and is compared to conventional transient PI. The results of this study are of interest to those engineers performing unconventional reservoir characterization work using RTA and for reserves estimators.
SG is defined as a natural gas resource stored in an organic-rich, fine-grained reservoir in which gas is stored both as free gas within the matrix and fracture porosity and as adsorbed gas on the surface of the organic fraction (Faraj et al., 2004; Hamblin, 2006; Bustin et al., 2008; Rokosh et al., 2009; CSUG, 2010). The adsorbed gas portion ranges from about 20% (Barnett Shale) to 85% (Lewis and Antrim Shale) and is dependent on a variety of geologic and geochemical properties (Canadian Discovery, 2006; Drake, 2007). Shale plays dominated by adsorbed gas production are commonly organic, clay-rich shales, while those dominated by free gas production tend to be quartz-rich shales (Frantz and Jochen, 2005). SG resources are basin-centered, self-sourced and continuous accumulations that are often classified as "dysfunctional?? petroleum systems as they do not efficiently expel gas to other more traditional conventional gas reservoirs (Hamblin, 2006).
The permeability of unconventional gas/oil reservoirs is a critical control on economic viability of unconventional plays, yet its determination, particularly in ultra-low permeability shale reservoirs, remains a challenge. Some of the difficulties in obtaining accurate permeability measurements in the lab include: recreating in-situ stress and fluid saturation conditions; establishing the appropriate sample size for measurement; correcting for sorption of gases on kerogen and clays; accounting for non-Darcy flow (slippage and diffusion); among many others. Unsteady-state measurements are most popular for establishing permeability in ultra-tight rock; both pressure-decay and pulse-decay decay techniques have been used. Analysis methods for these techniques have been established, but there remain some questions about whether these analysis methods are optimal for establishing permeability.
In this work, we investigate the use of pressure- and rate-transient analysis (PTA/RTA) methods to analyze data obtained from a new core plug analysis procedure, designed specifically to extract information (permeability and pore volume) from ultra-low permeability reservoir samples (core plugs). The new analysis procedure calls for analyzing the rate and/or pressure data analogously to larger-scale well-test/production data. During a core plug production test for example, derivative analysis of rate-normalized pseudo-pressure change is first analyzed to determine flow-regimes. For homogenous samples, linear flow is followed by boundary-dominated flow; for this scenario, permeability can be established by noting the end of linear flow and using the distance of investigation calculation to calculate permeability (knowing core length). Permeability can also be established independently from a linear flow (square-root of time) plot. Pore volume can also be established. Analytical simulation is used to verify estimates of permeability and pore volume from RTA/PTA. Our solutions allow complex unconventional gas reservoir behavior to be incorporated, including corrections for adsorbed gas and non-Darcy flow. Our new methodology is tested using various simulated cases which differ due to: 1) reservoir type (single or dual porosity, homogenous or heterogeneous); 2) matrix permeability; 3) analysis type (post injection/falloff production test, or post-injection falloff); 4) adsorption (compressed gas storage only or compressed + adsorbed gas storage); Darcy or non-Darcy flow. In all cases, reasonable estimates of permeability and pore volume were obtained, provided the appropriate corrections are made.
We believe this new technique for analyzing core data, and the proposed core testing procedure, will considerably improve on current techniques for establishing permeability and pore volume of unconventional reservoir samples.
Multifractured horizontal wells are currently the most popular method for exploiting low-permeability tight and shale gas reservoirs. Production data analysis is the most widely used tool for analyzing these reservoirs for the purpose of reserves estimation, hydraulic fracture stimulation optimization, and development planning (Ambrose et al. 2011). However, as pointed out by Clarkson et al. (2011), a fundamental problem with the application of conventional production data analysis to ultralow permeability reservoirs is that current methods were derived with the assumption that flow can be described with Darcy's law. This assumption may not be valid for tight/shale gas reservoirs, as they contain a wide distribution of pore sizes, including in some cases nanopores (Loucks et al. 2009). Therefore, the mean-free path of gas molecules may be comparable to or larger than the average effective rock pore throat radius, causing the gas molecules to slip along pore surfaces. This results in slippage non-Darcy flow, which is not accounted for in conventional production data analysis.
Clarkson et al. (2011) modified the pseudovariables used for analyzing gas reservoirs in production data analysis to account for slippage. They demonstrated that if the effect of slippage is not considered, it leads to noticeable errors in reservoir characterization. Clarkson et al. (2011) also mentioned that even after using the modified pseudovariables, the values for permeability and fracture half-length do not exactly match the input data to simulation. In this paper, a methodology to properly analyze the production data from a fractured well in a tight/shale gas reservoir producing under a constant flowing pressure in the presence of desorption and slippage is presented. This method uses a new pseudotime definition instead of the conventional pseudotime currently being used in production data analysis. The method is validated using a number of numerically simulated cases. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length or contacted matrix surface area, if permeability is known.
Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using a square-root-of-time plot, a plot of rate-normalized pressure vs. the square root of time. Linear flow appears as a straight line on this plot, and the slope of this line can be used to calculate the product of fracture half-length and the square root of permeability.
In this paper, linear flow from a fractured well in a tight/shale gas reservoir under a constant-flowing-pressure constraint is studied. It is shown that the slope of the square-root-of-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure, and formation compressibility. An analytical method is presented to correct the slope of the square-root-of-time plot to eliminate the overestimation of fracture half-length. The method is validated using a number of numerically simulated cases. As expected, the square-root-of-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully analytical, results in an improvement in linear-flow analysis over previously presented methods. Finally, the application of this method to multifractured horizontal wells is discussed and the method is applied to three field examples.
Shales and some tight-gas reservoirs have complex, multimodal pore-size distributions, including pore sizes in the nanopore range, causing gas to be transported by multiple flow mechanisms through the pore structure. Ertekin et al. (1986) developed a method to account for dual-mechanism (pressure- and concentration-driven) flow for tight formations that incorporated an apparent Klinkenberg gas-slippage factor that is not a constant, which is commonly assumed for tight gas reservoirs. In this work, we extend the dynamic-slippage concept to shale-gas reservoirs, for which it is postulated that multimechanism flow can occur. Inspired by recent studies that have demonstrated the complex pore structure of shale-gas reservoirs, which may include nanoporosity in kerogen, we first develop a numerical model that accounts for multimechanism flow in the inorganic- and organic-matter framework using the dynamic-slippage concept. In this formulation, unsteady-state desorption of gas from the kerogen is accounted for. We then generate a series of production forecasts using the numerical model to demonstrate the consequences of not rigorously accounting for multimechanism flow in tight formations. Finally, we modify modern rate-transient methods by altering pseudovariables to include dynamic-slippage and desorption effects and demonstrate the utility of this approach with simulated and field cases. The primary contribution of this work is therefore the demonstration of the use of modern rate-transient methods for reservoirs exhibiting multimechanism (non-Darcy) flow. The approach is considered to be useful for analysis of production data from shale-gas and tight-gas formations because it captures the physics of flow in such formations realistically.
Hydraulically fractured vertical and horizontal wells completed in shale gas and some tight gas plays are known to exhibit long periods of linear flow. Recently, techniques for analyzing this flow period using (normalized) production data have been put forth, but there are known errors associated with the analysis. In this paper, linear flow from fractured wells completed in tight/shale gas reservoirs--subject to a constant-production-rate constraint--is studied. We show analytically that the square-root-of-time plot (a plot of rate-normalized pressure vs. square root of time that is commonly used to interpret linear flow) depends on the production rate. We also show that depending on production rate, the square-root/time plot may not be a straight line during linear flow; the higher the production rate, the earlier in time the plot deviates from the expected straight line. This deviation creates error in the analysis. To address this issue, a new analytical method is developed for analyzing linear-flow data for the constant-gas-rate production constraint. The method is then validated using a number of numerically simulated cases. As expected, on the basis of the analytical derivation, the square-root/time plots for these cases depend on gas-production rate and, for some cases, the plot does not appear as a straight line during linear flow. Finally, we found that there is excellent agreement between the fracture half-lengths obtained using this method and the input fracture half-lengths entered in to numerical simulation.
In this paper, the sensitivity of expected ultimate recovery (EUR) for horizontal wells with multiple fractures to decline exponent is studied using the simplified forecasting method introduced by Nobakht et al. (2010). This is very important from the reserves evaluation perspective due to uncertainty in decline exponent, b. This uncertainty is caused by many factors like adsorption and reservoir/completion heterogeneity. It is found that in case of time-based forecast (duration of forecast is specified), the ratio of EURs for two different specified values of decline exponent depends on the ratio of economic life time of a well to the duration of linear flow. On the other hand, this EUR ratio depends on the ratio of rate at the end of linear flow to economic rate limit for economic limit-based forecast (economic rate limit rate is specified).