Roberto Aguilera

Knudsen’s Permeability Correction for Tight Porous Media

Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy’s law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen’s flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg’s effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen’s permeability is studied. As opposed to Klinkenberg’s correlation, which is a first-order equation, Knudsen’s correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen’s permeability correlation is more accurate than Klinkenberg’s model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg’s model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.

A Physics-Based Method for Production Data Analysis of Tight and Shale Petroleum Reservoirs Using Succession of Pseudo-Steady States

Analysis of production data from tight and shale reservoirs requires the use of complex models for which the inputs are rarely known. The same objectives can also be achieved by knowing only the overall (bulk) characteristics of the reservoir, with no need for all the detailed rarely known inputs. In this work, we introduce the concept of continuous succession of pseudo-steady states (SPSS) as a method to perform the analysis of production data. It requires very little input data yet is based on rigorous engineering concepts which works during the transient as well as the boundary dominated flow periods. This method consists of a combination of three simple and well-known equations: material balance, distance of investigation and boundary dominated flow. It is a form of a capacitance-resistance methodology (CRM) in which the material balance equation over the investigated region represents the capacitance, and the boundary dominated flow equation represents the resistance. The flow regime in the region of investigation (whose areal extent varies with time during transient flow) is assumed to be pseudo-steady state. This region is depleted at a rate controlled by the material balance equation. The initial flow rate and flowing pressure are used to define the resistance, and the distance of investigation defines the capacitance. The capacitance and resistance are then used in a stepwise procedure to calculate the depletion and the new rates or flowing pressures. The method was tested, for linear flow geometry, against analytical solutions for liquids and numerical simulations for gas reservoirs, exhibiting both transient and boundary dominated flow. Excellent agreement was obtained, thus corroborating the validity of the method developed in this paper. The proposed method is easy to implement in a spreadsheet application. It indicates that complex systems with complicated mathematical (e.g. Laplace space) solutions can be represented adequately using simple concepts. The approach offers a new insight into production analysis of tight and shale reservoirs, using familiar and easy-to-understand reservoir engineering principles.

A Complete Petrophysical-Evaluation Method for Tight Formations From Drill Cuttings Only in the Absence of Well Logs

The amount of tight-formation petrophysical work conducted at present in horizontal wells and the examples available in the literature are limited to only those wells that have complete data sets. This is very important. But the reality is that in the vast majority of horizontal wells, the data required for detailed analyses are quite scarce. Petrophysical evaluation in the absence of well logs and cores can now be considered owing to the possibility of measuring both the permeability and porosity of drill cuttings. This is essential because the application of the successive correlations used throughout the paper is based on porosity and permeability data. To try to alleviate the data-scarcity problem, a new method is presented for complete petrophysical evaluation derived from information that can be extracted from drill cuttings in the absence of well logs. The cuttings data include porosity and permeability. The gamma ray and any other logs, if available, can help support the interpretation. However, the methodology is built strictly on data extracted from cuttings and can be used for horizontal, slanted, and vertical wells. The method is illustrated with the use of a tight gas formation in the Deep basin of the western Canada sedimentary basin (WCSB). However, it also has direct application in the case of liquids. The method is shown to be a powerful petrophysical tool because it allows quantitative evaluation of water saturation, porethroat aperture, capillary pressure, flow units, porosity (or cementation) exponent m, true-formation resistivity, and distance to a water table (if present). Also, the method allows one to distinguish the contributions from viscous and diffusion-like flow in tight gas formations. The method further allows the construction of Pickett plots without previous availability of well logs, and it assumes the existence of intervals at irreducible water saturation, which is the case of many tight formations currently under exploitation. It is concluded that drill cuttings are a powerful direct source of information that allows complete and practical evaluation of tight reservoirs in which well logs are scarce. The uniqueness and practicality of this quantitative procedure originate from the fact that it starts only from the laboratory analysis of drill cuttings— something that has not been performed in the past.

State-of-the-Art Tight Gas Sands Characterization and Production Technology

As part of the activities of the ConocodPhillips-NSERC- AERI Chair in Fight Gas Engineering established in the Chemical and Petroleum Engineering Department at the University of Calgary. a comprehensive literature review has been conducted that has led to an understanding of the current status of the study of tight gas and formation. This paper presents the results of that work, concentrating initially on Canadian and U.S. tight gas sands. The literature survey discussed in this paper is the first part of the mission oriented research on tight gas reservoirs conduct at the University of Calgary. The planned research looks at refining the resource based and recoveries from tight gas formations in Canada. Evaluating the current status of geologic models, reservoir characterization, recovery and production technologies currently available for these types of formations is the first step in the effort to reach the final goal: finding the economic means of producing as much of this gas as possible. It is expected that the research results will prove to be of value in other parts of the world and will be exportable, creating business opportinities for Canadian companies. The program will also result in a supply of highly qualified professionals having significant knowledge of tight gas formations.

Advances in the study of naturally fractured hydrocarbon reservoirs: a broad integrated interdisciplinary applied topic

Abstract Naturally fractured reservoirs, within which porosity, permeability pathways and/or impermeable barriers formed by the fracture network interact with those of the host rock matrix to influence fluid flow and storage, can occur in sedimentary, igneous and metamorphic rocks. These reservoirs constitute a substantial percentage of remaining hydrocarbon resources; they create exploration targets in otherwise impermeable rocks, including under-explored crystalline basement, and they can be used as geological stores for anthropogenic carbon dioxide. Their complex fluid flow behaviour during production has traditionally proved difficult to predict, causing a large degree of uncertainty in reservoir development. The applied study of naturally fractured reservoirs seeks to constrain this uncertainty and maximize production by developing new understanding, and is necessarily a broad, integrated, interdisciplinary topic. Some of the methods, challenges and advances in characterizing the interplay of rock matrix and fracture networks relevant to fluid flow and hydrocarbon recovery are reviewed and discussed via the contributions in this volume.

Is Depletion Likely to Create Significant Scarcities of Future Petroleum Resources

Some energy analysts are concerned that the world will soon face a global crisis due to dwindling petroleum resources and a peak in oil production. To shed light on the subject, we have assessed the threat that depletion poses to the availability of petroleum resources by estimating cumulative availability curves for conventional petroleum (oil, gas, and natural gas liquids) and for three unconventional sources of liquids (heavy oil, oil sands, and oil shale). Our analysis extends the important study conducted by the US Geological Survey (World petroleum assessment. CD-ROM. U.S. Geological Survey, Reston, 2000) on this topic by taking account of (1) conventional petroleum resources from provinces not assessed by the Survey or other organizations, (2) future reserve growth, (3) unconventional sources of liquids, and (4) production costs.

Effect of Fracture Dip and Fracture Tortuosity on Petrophysical Evaluation of Naturally Fractured Reservoirs

A model is developed for petrophysical evaluation of naturally fractured reservoirs where dip of fractures ranges between zero and 90°, and where fracture tortuosity is greater than 1.0. This results in an intrinsic porosity exponent of fractures (m f ) that is larger than 1.0. The finding has direct application in the evaluation of fractured reservoirs and tight gas sands, where fracture dip can be determined, for example, from image logs. In the past, a fracture-matrix system has been represented by a dual-porosity model which can be simulated as a series-resistance network or with the use of effective medium theory. For many cases both approaches provide similar results. The model developed in this study leads to the observation that including fracture dip and tortuosity in the petrophysical analysis can generate significant changes in the dual-porosity exponent (m) of the composite system of matrix and fractures. It is concluded that not taking fracture dip and tortuosity into consideration can lead to significant errors in the calculation of water saturation. The use of the model is illustrated with examples.

The Economics of Oil and Gas Supply in the Former Soviet Union

Supply costs curves for the Former Soviet Union (FSU) are constructed for conventional petroleum, which is defined as conventional oil, natural gas and natural gas liquids (NGL). The supply figures show how petroleum quantities vary with production costs over time. Five resource quality categories, distinguishable according to production costs, are used in the estimation. The quantities are allocated across the five categories in a fixed proportion in order to generate the supply cost curves. The role of annual productivity gains, i.e., technological progress, to the year 2030 is also included. Results indicate that petroleum in the FSU is abundant and can be produced economically. In addition, production costs are found to decrease further over time as technology advances. With appropriate energy policy, FSU petroleum resources should assist in meeting domestic and international energy demand.

A Method for Estimating Hydrocarbon Cumulative Production Distribution of Individual Wells in Naturally Fractured Carbonates, Sandstones, Shale Gas, Coalbed Methane and Tight Gas Formations

A method, based on factual observations of naturally fractured reservoirs in several countries, is presented for estimating distribution of hydrocarbon cumulative production in wells drilled in fractured reservoirs of Types A, B or C. These observations indicate that in reservoirs of Type C, most of the cumulative production is provided by just a few wells, while the majority of the wells contribute a small part of the reservoir cumulative production. In reservoirs of Type B, the number of wells contributing significantly to cumulative production becomes larger relative to the case of Type C reservoirs. Finally, in reservoirs of Type A, a large number of wells contribute to field production, as compared with Type B reservoirs. The method is shown to be useful for tackling problems of practical importance in naturally fractured reservoirs, including performing or not performing infill drilling, estimating the variation in cumulative hydrocarbon production per well in a given reservoir and estimating the number of wells that might be required for a given field hydrocarbon recovery. The method is illustrated using data from various fractured reservoirs, including the Barnett shale and sandstone reservoirs in the United States, carbonate reservoirs in Mexico and Venezuela and coalbed methane reservoirs and tight gas sands in Canada.

Geologic Controls of Gas Production from Tight-Gas Sandstones of the Late Jurassic Monteith Formation, Deep Basin, Alberta, Canada.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s).