When tight gas sand reserves are assessed using the Arps rate-time equations, the decline behavior is typically defined in terms of the Arps decline exponent, b. The original Arps paper indicated that the b-exponent should lie between 0 and 1.0 on a semilog plot. However, in practice we often observe values much greater than 1.0, especially prior to the onset of true boundary-dominated flow. Unfortunately, the correct b-exponent is difficult (if not impossible) to identify during the early decline period — and (obviously) the selection of the wrong b-exponent will have a tremendous impact on reserve estimates, particularly when the b-exponent estimate is too high. As an exercise to evaluate the b-exponent as a continuous function of time, we have used synthetic and field production profiles. We then compare the computed b-exponent trend graphically to assess the "hyperbolic" nature of each case (recall that the b-exponent should be constant for a given hyperbolic rate decline). The field data cases used in this study were selected from a tight gas reservoir that has been previously evaluated on a per well basis using the production model based on the elliptical flow concept. These cases indicate that only portions of the production history are matched by the hyperbolic rate decline relation — suggesting that using the hyperbolic relation by itself may not be appropriate for reserves extrapolations in tight gas reservoirs, or at least that great care must be used in creating production forecasts based on the hyperbolic rate decline relation. In addition to the hyperbolic rate decline relation we have also developed and employed a new "power law loss-ratio" rate relation that has more generality than the hyperbolic rate decline relation. This new model tends to match production rate functions much better than the hyperbolic rate decline relation for tight gas and shale gas applications, but we must stress that at this time, the "power law exponential decline" rate relation is empirically derived from only tight gas/shale gas performance cases. We have applied the new model as well as the hyperbolic rate model to two synthetic (simulated) and field (tight gas well) cases for production forecast. Furthermore, the results of our synthetic performance cases do suggest that layered reservoir behavior can be accurately represented by the hyperbolic rate decline relation. Unfortunately, as other studies have shown, multilayer reservoir performance can be extremely difficult to generalize — particularly when layers in transient and boundary-dominated flow are in communication. Hyperbolic rate decline relation might be considered as an acceptable mechanism for estimating reserves in tight gas/shale gas systems, however we urge extreme caution as the hyperbolic relation must be constrained to a relative small duration production forecast. The major impact of this work is that it enables the analyst to have a diagnostic understanding of the hyperbolic rate decline relation (in terms of the D and b-parameters). Further, we also provide an alternative to the hyperbolic rate decline relation that appears to be substantially more robust, and the new "power law loss-ratio" rate relation can be validated and calibrated directly using rate functions.

This work addresses the problem of estimating Klinkenbergcorrected permeability from single-point, steady-state measurements on samples from low permeability sands. The "original" problem of predicting the corrected or "liquid equivalent" permeability (i.e., referred to as the Klinkenbergcorrected permeability) has been under investigation since the early 1940sin particular, using the application of "gas slippage" theory to petrophysics by Klinkenberg. 1 In the first part of our work, the applicability of the Jones-Owens 4 and Sampath-Keighin 5 correlations for estimating the Klinkenberg-corrected (absolute) permeability from singlepoint, steady-state measurements is investigated. We also provide an update to these correlations using modern petrophysical data. In the second part of our work, we propose and validate a new "microflow" model for the evaluation of an equivalent liquid permeability from gas flow measurements. This work is based on a more detailed application of similar concepts employed by Klinkenberg. In fact, we can obtain the Klinkenberg result as an approximate form of our result. Our theoretical "microflow" result is given as a rational polynomial in terms of the Knudsen number (the ratio of the mean free path of the gas molecules to the characteristic flow length (typically the radius of the capillary)). The following contributions are derived from this work: •Validation and extension of the correlations proposed by Jones-Owens and Sampath-Keighin for low permeability samples. •Development and validation of a new "microflow" model which correctly represents gas flow in low permeability core samples. This model is also applied as a correlation for prediction of the equivalent liquid permeability in much the same fashion as the Klinkenberg model, although our new model is substantially more theoretical (and robust) as compared to the Klinkenberg correction model.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis work addresses the problem of estimating Klinkenbergcorrected permeability from single-point, steady-state measurements on samples from low permeability sands. The "original" problem of predicting the corrected or "liquid equivalent" permeability (i.e., referred to as the Klinkenbergcorrected permeability) has been under investigation since the early 1940s -in particular, using the application of "gas slippage" theory to petrophysics by Klinkenberg. 1 In the first part of our work, the applicability of the Jones-Owens 4 and Sampath-Keighin 5 correlations for estimating the Klinkenberg-corrected (absolute) permeability from singlepoint, steady-state measurements is investigated. We also provide an update to these correlations using modern petrophysical data.In the second part of our work, we propose and validate a new "microflow" model for the evaluation of an equivalent liquid permeability from gas flow measurements. This work is based on a more detailed application of similar concepts employed by Klinkenberg. In fact, we can obtain the Klinkenberg result as an approximate form of our result. Our theoretical "microflow" result is given as a rational polynomial in terms of the Knudsen number (the ratio of the mean free path of the gas molecules to the characteristic flow length (typically the radius of the capillary)).The following contributions are derived from this work:• Validation and extension of the correlations proposed by Jones-Owens and Sampath-Keighin for low permeability samples. • Development and validation of a new "microflow" model which correctly represents gas flow in low permeability core samples. This model is also applied as a correlation for prediction of the equivalent liquid permeability in much the same fashion as the Klinkenberg model, although our new model is substantially more theoretical (and robust) as compared to the Klinkenberg correction model.

A series of experiments to measure the water solubility in supercritical nitrogen and carbon dioxide have been conducted at experimental conditions up to 483 K and 134 MPa. The accuracy of the experimental procedure is verified by comparing the water content data of methane in the literature and our experimental data for the methane−water system. In addition, a fugacity−fugacity approach including the cubic-plus-association equation of state (CPA EoS) and a fugacity−activity approach based on the Peng−Robinson EoS and the Henry’s law model are incorporated to predict the water content data of methane, nitrogen, and carbon dioxide. A comparison between our experimental data, literature data, and the results of the fugacity−activity approach shows the reliability of the PR-Henry’s law model for the phase behavior studies of the nitrogen−water system over a wide range of pressure and temperature conditions. However, the CPA equation is not capable of reproducing the high pressure vapor and liquid phase compositions of the water−nitrogen system. The concept of cross-association satisfactorily improves the performance of the CPA equation of state in predicting the water content data of supercritical methane. On the basis of the literature and new measured data in this study, it has been found that the CPA equation better represents the phase behavior of the water−carbon dioxide system if carbon dioxide is considered as a self- and cross-associating molecule.

This paper presents a work-flow process to describe and characterize tight gas sands. The ultimate objective of this work-flow is to provide a consistent methodology to systematically integrate both large-scale geologic elements and small-scale rock petrology with the physical rock properties for low-permeability sandstone reservoirs. To that end, our work-flow integrates multiple data evaluation techniques and multiple data scales using a core-based rock typing approach that is designed to capture rock properties characteristic of tight gas sands. Fundamental to this process model are identification and comparison of three different rock types — depositional, petrographic, and hydraulic. These rock types are defined as:Depositional — These are rock types that are derived from core-based descriptions of genetic units which are defined as collections of rocks grouped according to similarities in composition, texture, sedimentary structure, and stratigraphic sequence as influenced by the depositional environment. These rock types represent original large-scale rock properties present at deposition.Petrographic — These are rock types which are also described within the context of the geological framework, but the rock type criteria are based on pore-scale, microscopic imaging of the current pore structure — as well as the rock texture and composition, clay mineralogy, and diagenesis.Hydraulic — These are rock types that are also defined at the pore scale, but in this case we define "hydraulic" rock types as those that quantify the physical flow and storage properties of the rock relative to the native fluid(s) — as controlled by the dimensions, geometry, and distribution of the current pore and pore throat structure. Each rock type represents different physical and chemical processes affecting rock properties during the depositional and paragenetic cycles. Since most tight gas sands have been subjected to post-depositional diagenesis, a comparison of all three rock types will allow us to assess the impact of diagenesis on rock properties. If diagenesis is minor, the depositional environment (and depositional rock types) as well as the expected rock properties derived from those depositional conditions will be good predictors of rock quality. However, if the reservoir rock has been subjected to significant diagenesis, the original rock properties present at deposition will be quite different than the current properties. More specifically, use of the depositional environment and the associated rock types (in isolation) to guide field development activities may result in ineffective exploitation. Introduction Unconventional natural gas resources — tight gas sands, naturally-fractured gas shales, and coalbed methane reservoirs — comprise a significant percentage of the North American natural gas resource base and these systems represent an important source for future reserve growth and production. Similar to conventional hydrocarbon systems, unconventional gas reservoirs are characterized by complex geological and petrophysical systems as well as heterogeneities — at all scales. However, unlike conventional reservoirs, unconventional gas reservoirs typically exhibit gas storage and flow characteristics which are uniquely tied to geology — deposition and diagenetic processes. As a result, effective resource exploitation requires a comprehensive reservoir description and characterization program to quantify gas-in-place and to identify those reservoir properties which control production. Although many unconventional natural gas resources are characterized by low permeabilities, this paper addresses only low-permeability sandstone reservoirs, i.e., tight gas sands.