Skip Nav Destination
Filter
Filter
Filter
Filter
Filter

Update search

Filter

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

- Title
- Author
- Author Affiliations
- Full Text
- Abstract
- Keyword
- DOI
- ISBN
- EISBN
- ISSN
- EISSN
- Issue
- Volume
- References
- Paper Number

### NARROW

Format

Subjects

Date

Availability

1-13 of 13

R. Aguilera

Close
**Follow your search**

Access your saved searches in your account

Would you like to receive an alert when new items match your search?

*Close Modal*

Sort by

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-103

Abstract

Abstract 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 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. Introduction Methods for estimating the optimum number of wells in a given reservoir have been available for over 80 years (Haseman, 1 1929). More recently Nelson 2 (2001) analyzed cumulative production per well in individual naturally fractured reservoirs and found that there are distinctive variations in the production distributions depending on the amount of natural fracturing and heterogeneity present in the reservoir. From this observation Nelson concluded that these distributions are a function of fractured reservoir type, something that has been corroborated by this author in several instances as discussed in this study. Figure 1 shows the ABC classification of naturally fractured originally introduced by McNaughton and Garb 3 (1975). In naturally fractured reservoirs of Type A the storage capacity in the matrix porosity is large compared with storage capacity in the fractures ( Figure 1A ). This is generally equivalent to a reservoir of type 3 in Nelson's classification (2001). For this case, it can be seen in the lower part of Figure 1A that a small percentage of the total porosity is made out of fractures. In general, this situation would tend to occur in reservoirs where the matrix porosity is rather high (larger than 10 up to more than 35%). However, there are exceptions. For example reservoirs in tight gas formations can be generally classified as being of type A even if their porosity is usually smaller than 10%. If the matrix has some permeability so as to allow flow into the wellbore, Type A reservoirs can be considered equivalent to what Nelson (2001) has called "fracture permeability assist" reservoirs, i.e., reservoirs where the fractures contribute permeability to an already producible reservoir. Figure 1B shows a schematic of rocks with about the same storage capacity in fracture and matrix porosity (Type B reservoirs).

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-105

Abstract

Abstract In Alberta and British Columbia, a huge amount of tight gas is trapped in relatively impermeable rock formations. Physical fracturing of these formations could enhance the overall formation permeability and, thus improve tight gas extraction. One of the outstanding issues in rock fracturing is to determine the magnitude of applied effective stress. The general effective stress law is defined as: σ eff = σ c – α σ p , where σ c and σ p are total confining and fluid pore pressures, respectively. The Biot's constant α is not only a particular material property, but also markedly sensitive to the magnitude of applied confining and pore pressure. The main objective of this study is to experimentally determine stress dependency on the Biot's constant which controls fracturing mechanics in the tight gas formation and gas production rate from the formation at low and high effective stresses, respectively. A series of permeability measurements were conducted on Nikanassin Sandstone core samples from the Lick Creek region in British Columbia under various combinations of confining and pore pressures. In addition, permeability values were measured both along and across bedding planes to investigate any anisotropy in Biot's constant. Introduction Effective stress is the real item which actually controls the mechanical and hydraulic properties of porous rock and soil materials. Terzarghi (1,2) first brought the effective stress principle, which is defined as σ eff = σ c – σ p , into soil mechanics, where σ c and σ p are the total confining and fluid pore pressures, respectively. The effective stress principle, though basically very simple, is of fundamental significance in rock and soil mechanics. However, in rocks, especially, the fluid-related or petroleum-related rocks, Terzarghi's effective stress principle may not be always valid. Therefore, the Biot's constant a other than 1.0 was suggested to modify the effective stress principle, and the effective stress principle finally is given by σ eff = σ c – σ p (3) . The value of Biot's constant a for permeability has been found to be 0.9 for joints with polished surfaces and 0.56 for joints made from tension fracture (4) , and 0.6-0.7 for intact Chelmsford granite (5) . Keaney et al. (6) estimated that the average value of Biot's constant α for permeability of Tennessee sandstones is 0.75. Berryman (7) found that for a rock whose mineral phase consists of a single mineral, the value of Biot's constant α should not exceed unity. However, Zoback and Byerlee (8,9) found that Biot's constant α of some clay-rich sandstones can be as high as 3–4. Walls and Nur (10) found that α varies from 1.2 for clean sandstone to 7.1 for sandstone containing 20% clay. It turns out that the Biot's constant α is not only a mechanical property depending on many factors such as rock type, porosity, pore geometry, rock constituents and their geometrical arrangement, but also markedly sensitive to the magnitude of applied confining and pore pressure. In Alberta and British Columbia, a huge amount of tight gas is trapped in relatively impermeable rock formations.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-153

Abstract

Abstract This study examines the results of laboratory work to establish rock strength data, acid solubility, fracture fluid selection and mineral identification of a fractured tight gas carbonate reservoir. Basic to a successful acid fracture design are acid etching and rotating disc tests which show for a given acid system, conductivity at a given stress (etched width or how much rock is eaten away) and parameters necessary to determine acid reaction rate, reaction order, rate constant and energy of activation at a given temperature. These tests address the measurement of mass transfer and diffusion with or without leak off in carbonates, and also enable the prediction of reactivity versus temperature for various acid strengths. Dynamic fluid losses are measured experimentally and laboratory data are converted to an estimate of in-situ leak off. The leak off profile and wall building coefficients enable a consideration of fluid loss additives for fracturing fluids to build up pressure for fracture opening. In the fracture conductivity tests, closure stress is applied across a test unit for sufficient time to allow the proppant bed to reach a semi-steady state condition while test fluid is forced through the bed. At each stress level, pack width, differential pressure, and average flow rates are measured as fluid is forced through the proppant bed. The proppant pack permeability and conductivity are then evaluated and compared. Introduction A discussion of dominant considerations for effective hydraulic fracturing in naturally fractured tight gas carbonates is presented along with the results of laboratory work to establish rock mechanical properties data, acid solubility, fracture fluid selection and mineral identification for a selected naturally fractured tight gas carbonate reservoir. 1 The carbonates under consideration are located in the Western Canadian Sedimentary Basin (WCSB) in what is usually known as the "Deep Basin" of Alberta ( Figure 1 ). The core samples studied come from the Savannah Creek field ( Figures 2 ) and correspond to the Rundle group Mississippian Mount Head and Livingston carbonates ( Figure 3 ). These carbonates were deposited in a shallow marine ramp setting. These are upward-shallowing cycles ranging from crinoid / bryozoan shoals to lagoonal mud facies. The reservoirs comprise dolomudstones and wackstones with an average pay of approximately 35 m. Reservoir zones can be discontinuous due to lateral facies changes and minor faulting. The presence of natural fractures in the tight formations considered in this research is corroborated by cores and thin sections. Notice the presence of calcite cemented fractures in the whole core and plugs displayed in Figure 4 . The thin section shown on Figure 5 presents calcite-filled fractures (pink strip running from upper left to lower right) that have been re-fractured (thin blue streak). The thin section work corroborates that it possible to re-fracture existing healed fractures. General Considerations There are many mechanisms that contribute to the final created geometry (fracture height, fracture width, hydraulic or created fracture length or effective fracture length)2–8 and its evolution in naturally fractured tight gas carbonates. Pump rate, volume injected, fluid viscosity, fluid loss and proppant scheduling combine with static and dynamic rock properties.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-104

Abstract

Abstract Subsurface fluid injections such as waste water disposal, waterflooding, and CO 2 sequestration cause reservoir dilation. The reservoir dilation propagates to the surrounding formations and extends up to the ground surface resulting in surface heave. Previous studies have illustrated that it is possible to delineate the extent of the reservoir dilation from the surface heave measurement using inverse technique. This paper suggests that the inverse technique could be extended to estimate the growth and propagation of the reservoir dilation during the fluid injection if the surface heave is monitored continually. Then, the reservoir pressure distribution and hydraulic properties are also possibly determined from the fluid flow equations. The results obtained from the proposed technique were compared with these obtained from a fully-coupled finite element simulation of a fluid injection problem. It was found that the numerical tool could be successfully adopted to estimate an approximate value of the reservoir permeability. Introduction Subsurface fluid injections such as waste water disposal, waterflooding, and CO 2 sequestration cause reservoir dilation. The reservoir dilation propagates to the surrounding formations and extends up to the ground surface resulting in surface heave. Meanwhile, the reservoir dilation changes the reservoir formation porosity which directly affects the reservoir pressure distribution and hydraulic properties. In reservoir engineering, it is critical to estimate the reservoir pressure distribution and hydraulic properties subject to subsurface fluid injections. The inverse problem of using displacements observed at the surface of reservoir formation to infer in-situ processes and volume changes within the reservoir has been taken as a noninvasive method(1–3). This paper suggests that the inverse technique could be extended to estimate the growth and propagation of the reservoir dilation during the fluid injection if the surface heave is monitored continually. Then, the reservoir pressure distribution and hydraulic properties are also possibly determined from the fluid flow equations. Inversion of Volume Strain in Reservoir from Surface Heave in 2-D Case Segall(4) proposed an equation for the vertical displacements in terms of change in pore fluid mass content in a 2-D plane strain case. Further, Nanayakkara and Wong (5) modified the equation by expressing the vertical displacements in terms of the volumetric strains. "Observation point" and "source point" are proposed and used in this method (see Figure 1). The approach is to divide the region, in which the subsurface volumetric strains occur, into a number of infinitesimal elements. Then, each element is represented by a center of dilatation (or compression) corresponding to an infinitesimal volume change (dV), which is known as a "source point". The total vertical displacement at a given surface "observation point" is obtained by summing the contribution from each source point. Accordingly, the vertical displacement at a given surface observation point, induced due to the reservoir volumetric strains, is given by: Equation (1) (Available in full paper) where a, b are the source point coordinates and the minus sign infers that the displacement direction of the surface observation point is upward in the coordinate system shown in Figure 1.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 16–18, 2009

Paper Number: PETSOC-2009-163

Abstract

Abstract Outcrops of the Milk River Formation (sandstone, Cretaceous age) at the Writing on Stone Provincial Park in Alberta, Canada have been scanned using ground LiDAR (light detection and ranging) technology. Milk River outcrops represent a real 3D challenge for this technology because of the complexity of hoodoos emanating from pronounced erosion in the area as a result of wind, water and ice following the melting of ice at the end of the last ice age. In addition to the 3D complexity of the hoodoos, the Milk River Formation at Writing on Stone was selected for this project because the geology, studied in detail previously, is characterized by intervals that include a range of sand-rich lithofacies, and is distinguished primarily by subtle differences in grain size and current structures of the sandstones. Also present in the area are relatively flat 2D cliff faces and subvertical fractures. The outcrop exemplifies a challenge for realistic fluid flow modeling. This is of practical importance because these types of rocks develop significant hydrocarbon reservoirs in the Western Canadian sedimentary basin and throughout the world. When buried significant volumes of gas can be trapped in tight formations of similar age. This paper describes an evaluation sequence that includes the planning for LiDAR data collection, actual work and rock sample collection in outcrops, the interpretation and integration with geoscience in a 3D visualization room, and the potential for improved drilling and completion techniques, and reservoir simulation by using the concept ‘from rocks to realistic fluid flow models’. It is concluded that LiDAR provides a powerful technique for sound interpretation of reservoirs rocks and their integration with other sources of information. Introduction The present study was undertaken to test and evaluate the capabilities and limitations of ground-based laser scanning technology (LiDAR) for the construction of reservoir models based on surface outcrops. A multidisciplinary team of the University of Calgary has embarked on a project to investigate and better characterize tight gas/fractured reservoirs, in which the study of outcrop analogues is an integral part. The multidisciplinary research project is called GFREE, an acronym that stands for the integration of geoscience (G), formation evaluation (F), reservoir drilling, completion and stimulation (R), reservoir engineering (RE), and economics and externalities (EE). Before investing heavily in expensive, up-todate LiDAR hardware and software, and in the time and effort of researchers, a pilot study was deemed to be necessary to evaluate the feasibility and usefulness of LiDAR-based mapping/imaging methods. The University of Calgary and the University of Texas at Dallas joined forces to achieve this objective. Herein we report on this pilot study of the various phases in the use of LiDAR, that is, data acquisition, data and image processing, and possible qualitative and quantitative applications of the resulting model. The rocks chosen for the pilot study are the Virgelle Member sandstones at Writing-on-Stone Provincial Park (WOS) in southern Alberta, an area with relatively continuous, superbly exposed outcrops along the Milk River valley.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 17–19, 2008

Paper Number: PETSOC-2008-161

Abstract

Abstract A tight gas reservoir is commonly defined as a reservoir having less than 0.1 millidarcies permeability. There are several basic concepts and field cases of different well tests in tight gas reservoirs in the literature, but not presented as a general guide. In this paper, we gather valuable information and provide a useful guide to the most important well tests in tight gas reservoirs. Generally due to low permeability of these reservoirs, a well will not flow initially at measurable rates and conventional well testing cannot be applied. Therefore, fracture stimulation must be considered. Many authors present procedures for design of pre and post-frac tests. The pre-frac test permits calculating preliminary estimates of reservoir permeability and initial pressure. Because of economic and environmental reasons, short duration procedures are of interest. Hence, prime candidates are pre-frac, short time, small volume, closed chamber tests. These tests have to be analyzed by special methods to provide improved values of reservoir parameters. In this study, we also present a review of some aspects in tight gas well testing like pressure-dependent permeability, estimation of pseudo-time at the average pressure of the region of influence, supercharge effect, the problem of treating the pressure-dependent product µc t during pre-frac test analysis and the concept of instantaneous source response Introduction Large decreases in production and increases in demand for fossil-fuels cause the economic gas production from unconventional resources (tight gas, coal bed methane (CBM), and gas hydrate) to be a great challenge. Huge reserves, longterm potential, low gas prices and some other factors account for the great influence of these resources on the future of energy. There is no formal definition for "Tight gas". Commonly used definition, describes tight gas reservoirs as those having permeabilities less than 0.1 millidarcies. Recently, the German Society for Petroleum and Coal Science and Technology (DGMK) defined tight gas reservoirs as those with average effective gas permeability of less than 0.6 mD. "Ultra tight" gas reservoirs may exhibit permeabilities down to 0.001 mD. To improve the recovery of this resource, GFREE [1] research program has been created at the University of Calgary. GFREE [1] stands for: Geoscience aspects (G) Formation evaluation by petrophysics and well test (F) Reservoir drilling, completion and stimulation (R) Reservoir Engineering (RE) Economics and long run supply curves (E) As a part of the activities of this research program, we have concentrated on Formation evaluation (F) by well testing, and conducted a literature survey which is presented in this paper. Well testing is generally done to estimate hydrocarbon (here gas) in-place and recoverable resources. Initial pressure is a critical parameter not only for estimating gas in-place, but also for determining how much field development is required and whether or not the field is overdeveloped. In addition to p i , well testing provides an estimate of permeability. A problem associated with well testing in tight gas sands is that usually long times are required to reach redial flow, due to their extremely low permeabilities.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 17–19, 2008

Paper Number: PETSOC-2008-110

Abstract

Abstract A model is developed for petrophysical evaluation of naturally fractured reservoirs where dip of fractures ranges between zero and 90 degrees, and where fracture tortuosity is greater than 1.0. This results in an intrinsic porosity exponent of the 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 an example. Introduction The petrophysical analysis of fractured and vuggy reservoirs has been an area of interest in the oil and gas industry. In 1962, Towle 1 considered some assumed pore geometries as well as tortuosity, and noticed a variation in the porosity exponent m in Archie's 2 equation ranging from 2.67 to 7.3+ for vuggy reservoirs and values much smaller than 2 for fractured reservoirs. Matrix porosity in Towle's models was equal to zero. Aguilera 3 (1976) introduced a dual porosity model capable of handling matrix and fracture porosity. That research considered 3 different values of Archie's2 porosity exponent: One for the matrix ( m b ), one for the fractures ( m f =1), and one for the composite system of matrix and fractures ( m ). It was found that as the amount of fracturing increased, the value of m became smaller. Rasmus 4 (1983) and Draxler and Edwards 5 (1984) presented dual porosity models that included potential changes in fracture tortuosity and the porosity exponent of the fractures ( m f ). The models are useful but must be used carefully as they result incorrectly in values of m > m b as the total porosity increases. Serra et al. 6 developed a graph of the porosity exponent m vs. total porosity for both fractured reservoirs and reservoirs with non-connected vugs. The graph is useful but must be employed carefully as it can lead to significant errors for certain combinations of matrix and non-connected vug porosities (Aguilera and Aguilera 7 ). The main problem with the graph is that Serra's matrix porosity is attached to the bulk volume of the "composite system". More appropriate equations should include matrix porosity (Ø b ) that is attached to the bulk volume of the "matrix system" (Aguilera, 1995). Aguilera and Aguilera 7 published rigorous equations for dual porosity systems that were shown to be valid for all combinations of matrix and fractures or matrix and nonconnected vugs. The non-connected vugs and matrix equations were validated using core data published by Lucia. 8

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 12–14, 2007

Paper Number: PETSOC-2007-208

Abstract

Abstract As part of the activities of the Conoco Phillips Chair in Tight Gas Engineering in the Chemical and Petroleum Engineering Department at the University of Calgary, a comprehensive literature review has been conducted that has led to our understanding of the current status on the study of tight gas sand formations. This paper presents the results of that work concentrating initially on Canadian and U.S. tight gas sands. Next, we will examine these types of formations throughout the world. The resource base of tight gas sands is estimated to be between 90 and 1500 trillion cubic feet in Canada. The resource base around the world has been estimated at some 7500 trillion cubic feet. The literature survey discussed in this paper is the basis for the mission-oriented research on tight gas reservoirs conducted at the University of Calgary. This research looks at refining the resource base and recoveries from tight gas in Canada and finding economic means of extracting as much of this gas as possible. The planned research program will be presented. It is expected that the research program will result in the delivery of highly qualified professionals, with significant knowledge of tight gas formations, needed by industry and research organizations. In addition, it is likely that the research results will prove to be of value in other parts of the world, and will be exportable, creating business opportunities for Canadian companies. 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 economic means of producing as much of this gas as possible. Introduction Tight gas production is not reported in Canada. However, the interest in this resource is growing significantly. For example, a quick search in the SPE website using the words "tight sands" resulted in 5842 publications as of March 14, 2007. Obviously our goal in this survey paper is not to list everything that has been published in the literature but to highlight what we consider key issues in the evaluation and commercialization of tight gas sand production. Tight gas sands are part of what is usually known as unconventional gas which also includes coal bed methane, shale gas and natural gas hydrates. Tight gas sands have been defined in different ways by different organizations but a unique definition has proven elusive. 1 The original definition dates back to the U.S. Gas Policy Act of 1978 that required in-situ gas permeability to be equal to or less than 0.1 md for the reservoir to qualify as a tight gas formation. 2 At present this is probably the most commonly accepted definition. A second U.S. legal definition indicates that in a tight reservoir an average sustained un-stimulated initial gas rate is less than the maximum specified for a given depth class. However, it is important to understand that, although convenient, not only permeability and/or depth play a role in gas production from tight gas reservoirs.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 7–9, 2005

Paper Number: PETSOC-2005-250

Abstract

Abstract The radius of investigation (r i ) in a naturally fractured reservoir is dependent on flow time, the relative storativity of matrix and fractures, and the size and shape of the matrix blocks. Not taking this into account and using the conventional radius of investigation equation developed for single porosity, isotropic reservoirs, can lead to significant errors. This paper presents an equation that can be used for the case of pseudo steady state (restricted) or transient (unrestricted) interporosity flow when radial flow is dominant during the test. A straight forward approach using a function Y a permits calculating interconnected pore volume in the fractured reservoir. The method is illustrated with an example. In addition, an equation is presented for calculating the distance of investigation in those cases where linear flow (as opposed to radial) is dominant. This occurs for example in paleo channels of continental origin. The radius of investigation is strictly a flow equation (not a buildup equation). Introduction The radius of investigation (r i ) has been shown throughout the years to be a very useful concept for designing tests, estimating the influenced pore volume and evaluating the hydrocarbons investigated during the test. The concept assumes radial flow into a common source or sink, in a homogeneous, isotropic reservoir where permeability, porosity, thickness, and saturation are constant. The fluid is only slightly compressible. The compressibility is constant and small. The effects of gravity and inertial forces in fluid flow are ignored. Radius of investigation, as used in this paper, is the distance that a pressure disturbance (transient) moves into a reservoir at a certain time as a result of changing the flow rate in a well. On the other hand the drainage of radius of a well is the distance reached at a stabilization time (t s ), i.e., the time at which pseudo steady state begins. Different authors have used different concepts for estimating the radius of investigation (and radius of drainage) and for defining the stabilization time. For example, Muskat1 assumed a constant flow rate and a succession of disturbances (transients) going from unsteady to steady state. Miller et al. 2 and Brownscombe and Kern 3 estimated a stabilization time (ts) that occurs when the reservoir is within 2% of equilibrium. Chatas 4 used the same basic assumptions as Muskat 1 to develop equations for stabilization time, radius of drainage and linear distance of investigation. Tek et al. 5 defined the drainage radius at that point where the fluid flowing is 1 percent of the fluid flowing into the wellbore. Jones 6 assumed that the drainage radius is that distance at which the pressure changes only 1 percent. These assumptions with respect to 1 or 2 percent of the pressure (or sometimes the flow rate) are arbitrary and because of that, the equations have to be used with care. van Poollen 7 used a different approach that allows calculating radius of investigation, radius of drainage or stabilization time depending on the type of data available. He used Jones6 Y functions for finite and infinite reservoirs.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 8–10, 2004

Paper Number: PETSOC-2004-111

Abstract

Abstract The material balance (MB) equation for stresssensitive ndersaturated and saturated naturally ractured reservoirs (nfr's) has been written taking into ccount the presence of an unsteady state naturally ractured aquifer (nfa). The nfa can be of limited or nfinite size. The solution is presented in finite difference orm to achieve a quick convergence of the iteration rocess. Historically, non-fractured aquifers have been ttached to material balance calculations of naturally ractured reservoirs. This is not realistic from a geologic oint of view as it implies that fractures are present in the il portion of the reservoir but disappear the moment the ater oil contact is reached. It is shown that the use of an nfractured aquifer in a naturally fractured reservoir can ead to erroneous oil recovery estimates. The effect of ater influx on the material balance equation is llustrated with an example. Introduction Forecasting the performance of a nfr subject to water entrance from a nfa is a major challenge. The problem is compounded when the nfr and nfa are stress-sensitive. In this paper the nfr is stress-sensitive, but the nfa is not. The work presented in this paper is not meant to replace a detailed reservoir simulation, which is, in my opinion, the best way to solve the problem, provided that the original oil in place, size of the aquifer, reservoir characterization and quality of the pressure and production data is good. The idea is to have a tool that can provide a quick idea with respect to potential oil recoveries from stresssensitive nfr's affected by water influx from nfa's. Various analytical aquifers have been considered in the literature, most notably those developed by Schilthius 1 Hurst 2 and van Everdingen and Hurst 3 for edge water and Allard and Chen, 4 for bottom water. All of these aquifers considered matrix porosity but ignored the presence of natural fractures. Aguilera, 5, developed equations to account for the presence of natural fractures in unsteady state edge aquifers. The equations were validated by successfully comparing results against those published by van Everdingen and Hurst. 3 This paper presents MB equations for predicting oil recovery of undersaturated and saturated nfr's affected by water influx from nfa's. The nfa can be of limited or infinite size. The infinite case applies, in practice, to those aquifers that are connected with the external world (for example connected with lakes and rives). The equations are written taking into account the effective compressibility of matrix and fractures. Stress-sensitive properties such as fracture porosity, fracture permeability, partitioning coefficient and exponent for shape of relative permeabilities are taken into account. Unsteady State Naturally Fractured Aquifer Aguilera 5 presented a solution to the problem of nonstressed nfa's following the work of van Everdingen and Hurst. 3 For the case of constant pressure at the inner boundary (constant terminal pressure case) and constant pressure at the outer boundary, the dimensionless water influx is given in Laplace space by: Equation (1) (Available in full paper)

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 8–10, 2004

Paper Number: PETSOC-2004-110

Abstract

Abstract This paper presents a simplified method for drawdown and buildup analysis of naturally fractured reservoirs. This method permits handling of wellbore storage and matrix blocks of different shapes. Although there are excellent techniques in the literature for handling these problems, all of them require the use of specialized software. The technique developed in this paper allows approximate, yet sound solutions to these problems, using a few columns in a spread sheet. The method allows calculation of parameters such as fracture permeability, wellbore storage, skin, storativity ratio ?, interporosity flow coefficient λ, fracture spacing, number of fractures intercepted by the wellbore and amount of secondary mineralization within fractures. The method is illustrated with actual data from fractured reservoirs. Introduction There are excellent commercial software packages in the oil industry for evaluating well testing data from dual porosity models. The idea behind the methods presented in this paper is not to replace sophisticated software packages but to provide step by step simplified methods that still give reasonable results. Some of the basic principles behind well test analysis of naturally fractured reservoirs have been published by Barenblatt and Zheltov, 1 Warren and Root 2 Kazemi, 3 de Swann, 4 Najurieta, 5 and Streltsova. 6 Aguilera 7,8 published functions for handling various matrix block shapes. Several type curves have appeared in the literature (literally hundreds of type curves) including works by Bourdet and Gringarten 9 and Jalali and Ershagui. 10 Still the problem of non-uniqueness will be with us anytime that we analyze transient pressure data, due to the inverse nature of the problem we are dealing with. Drawdown Test Flow pressure (pwf) as a function of time (t), capable of matching recorded pressures that include skin and wellbore storage in a dual porosity system, can be calculated from the equation: Equation (1) (Available in full paper) where (ηgc) is a general hydraulic diffusivity that includes wellbore storage; c 1 , c 2 and c 3 are constants that apply to either customary or SI units. Other nomenclature are defined at the end of the paper. The general hydraulic diffusivity can operate under conditions of restricted or unrestricted interporosity flow. Restricted Interporosity Flow This section presents the equations for generating a synthetic drawdown. The procedure starts with an estimate of the ratio α' between the shape factor of matrix blocks and the shape factor of a stratum model. This is given by: Equation (2) (Available in full paper) A function, f (t, λ) for the case of restricted interporosity flow is determined from: Equation (3) (Available in full paper) Next a hydraulic diffusivity (ηg) for the dual porosity system, without wellbore storage, is calculated from: Equation (4) (Available in full paper) A pressure change (Δp)c that includes wellbore storage, C, is given by: Equation (5) (Available in full paper) A function of Equation that includes wellbore storage is determined from: Equation (6) (Available in full paper) The storativity ratio (ω) is calculated from: Equation (7) (Available in full paper) Eqs. 2 to 7 permit calculating the general hydraulic diffusivity (ηgc) from: Equation (8) (Available in full paper)

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 10–12, 2003

Paper Number: PETSOC-2003-113

Abstract

Abstract The tank material balance (MB) equation for undersaturated and saturated reservoirs has been written taking into account the effective compressibility of matrix and fractures. The solution is presented in finite difference form to achieve a quick convergence of the iteration process. Historically, compressibility has been neglected when carrying out MB calculations of conventional reservoirs producing below the bubble point. This assumes that the reservoir strata are static. It is shown however, that under some conditions, fracture compressibility can have a significant impact on oil rates and recoveries of naturally fractured reservoirs (nfr's) performing below the bubble point, as the fracture permeability and fracture porosity are stress-dependant. Other stress-sensitive properties discussed in this paper include the partitioning coefficient and the exponent for shape of relative permeability curves. The use of the MB finite difference equations is illustrated with an example. Introduction Forecasting the performance of nfr's is a major challenge. Various authors have tackled the problem throughout the years using MB calculations. To the best of my knowledge, the effect of fracture compressibility below the bubble point has been usually ignored in MB equations for saturated reservoirs. The work presented in this paper is not meant to replace a detailed reservoir simulation, which in my opinion is the best way to try to solve the problem, provided that reservoir characterization and quality of the pressure and production data is good. The idea is to have a tool that can provide a quick idea with respect to potential oil recoveries from stress-sensitive nfr's. Pirson 1 pioneered efforts to try to explain the high GOR associated with many nfr's once the bubble point is reached. He considered the reservoir to be made of two porosity and permeability systems in parallel and visualized production as a succession of equilibrium stages. Jones-Parra and Seijas-Reytor 2 studied the effect of gas oil ratio on the behavior of fractured limestone reservoirs using a two-porosity model. They assumed that gravity segregation took place freely and resistance to fluid flow was very small in the fracture network. In the matrix or fine porosity system, there was high resistance to flow and no segregation. Aguilera 3,4 used combined log analyses and MB to try to explain the high gas oil ratios observed in many nfr's. More recently, Penuela et al. 5 presented a MB for calculating oil in place in matrix and fractures taking into account the compressibility difference between matrix and fractures. This paper presents MB equations for predicting oil recovery and rates of undersaturated and saturated reservoirs. The equations are written taking into account the effective compressibility of matrix and fractures. Stress-sensitive properties such as fracture porosity, fracture permeability, partitioning coefficient and exponent for shape of relative permeabilities are taken into account. The solution is presented in finite difference form to achieve a quick convergence of the iteration process. General Observations Regarding Oil Recovery In general, if we make a comparison of 2 identical undersaturated reservoirs in every respect, except that one is fractured and the other one is unfractured, we find that the fractional recovery is larger in the undersaturated nfr.

Proceedings Papers

Publisher: Petroleum Society of Canada

Paper presented at the Canadian International Petroleum Conference, June 11–13, 2002

Paper Number: PETSOC-2002-157

Abstract

Abstract The integration of capillary pressures and Pickett plots has been shown recently to be a useful approach for determining flow units. The present study extends the method to the case of naturally fractured reservoirs by preparing Pickett plots for only the matrix. This requires calculation of matrix porosities and true resistivities for the matrix. By placing pore throat apertures, capillary pressures and heights above the free water table on Pickett plots, it is possible to generate matrix flow units and to estimate if the matrix will contribute to production. Pattern recognition is the key to success with this approach. Two examples are presented. Introduction Pickett plots 1,2 have long been recognized as very useful in log interpretation. In Pickett's method, a resistivity index, I, and water saturation, S w , are calculated from log-log crossplots of porosity vs. true resistivity (in some cases apparent resistivity, or resistivity as affected by a shale group, A sh ), as shown on Figures 1a, 1b, 1c, 1d, 1e and 1f. The Pickett plot has been extended throughout the years to include many situations of practical importance. For example, Aguilera 3,4 demonstrated that Pickett plots could be used for evaluating naturally fractured reservoirs. In these formations the value of the porosity exponent was shown to be smaller than usual (Figure 1b). Sanyal and Ellithorpe 5 and Greengold 6 have shown that a Pickett plot should result in a straight line with a slope equal to (n - m) for intervals at irreducible water saturation. Aguilera 7 extended the Pickett plot to the analysis of laminar, dispersed and total shale models (Figure 1c) . In this approach, the resistivity included in the plot is affected by a shale group, A sh , whose value depends on the type of shaly model being used. Aguilera showed that all equations for evaluation of shaly formations published in the literature, no matter how long they are, become S w = I sh −1/n . He further showed that a Pickett plot for shaly formations should result in a straight line with a slope equal to (n - m) for intervals at irreducible water saturation. Aguilera 8 demonstrated that a log-log crossplot of Rt vs. effective porosity, as determined from neutron and density logs, minus free fluid porosity, as determined from a nuclear magnetic log, should result in a straight line with a negative slope equal to the water saturation exponent, n, for intervals that are at irreducible water saturation (Figure 1d) . Extrapolation of the straight line to 100% porosity yields the product aR w . Gas intervals plot above the straight line. Intervals with movable water plot below the straight line. In the same paper, Aguilera 8 showed that a Pickett plot should result in a straight line for intervals of constant permeability at irreducible water saturation (Figure 1e) . The same concept has been used successfully by Doveton et al. 9 More recently Aguilera 10 presented techniques for incorporating capillary pressures, pore aperture radii, height above free water table, and Winland r 35 values on Pickett plots (Figure 1f) . He developed an equation, which compares favorably with Winland r 35 .