I WORKSHOP ON MULTISCALE COMPUTATIONAL MODELS OF UNCONVENTIONAL OIL AND GAS RESOURCES
CENPES/ PETROBRAS August 27-28 2014 Organization:
Ramon Domingues (Cenpes/Petrobras) Abelardo Barreto (Cenpes/Petrobras) Márcio Murad (LNCC/MCTI)
WORKSHOP OBJECTIVES Unconventional sources of energy, which occur, for instance, in shale gas, shale oil, coalbed methane and hydrate formations, are becoming more popular since the oil/gas production by conventional reservoirs has already been widely explored worldwide and budget became more economics to reach such resources. On the other hand, the exploitation of unconventional reservoirs gives rise to new technological challenges for the industry, such as: characterization of multi-fracture systems, description of multi-scale flow and reactive transport mechanisms along with the anomalous constitutive behavior of fluids in nano-pores and the development of accessible computational apparatus. Indeed, such achievements shall be capable of capturing the complex interplay between several coupled phenomena that take place simultaneously at different spatial and temporal scales. The aim of this workshop is to bring together researchers working on different aspects of reservoir engineering offering a fruitful multidisciplinary forum among the attendees to enhance common knowledge on the subject by bringing new networking opportunities. Owing to the widespread applications of unconventional modeling, the workshop will be focusing on aspects that emphasizes flow and transport of natural gas, condensate gas, light oil, methane hydrate, water and fracking fluids in multiple porosity systems; as well as, the characterization of natural and induced fracture networks, the thermodynamics aspects of inhomogeneous systems in confined media and the application of microseismic to monitor and map hydrocarbon reservoirs.
INVITED SPEAKERS • • • • • • • •
Micheal Kendall Dept of Earth Sciences Univ of Bristol (UK) Erdal Ozkan Colorado School of Mines (USA) Frederico Tavares PEQ/COPPE Brazil Dung Lee (LNCC/MCTI) Brazil Malgorzata Peszynska Oregon State Univ (USA) Ben Clennel CSIRO (Australia) Quentin Fischer (Univ of Leeds (UK) Nicolas Espinoza (Univ of Texas at Austin (USA)
CONTACT Jeane Ramos
[email protected]
PRELIMINARY PROGRAM Wednesday (27/08) •
08:00 – 09:00 – Registration
Opening Ceremony 09:00 – 09:25 – José Roberto fagundes Neto (Cenpes), Flavia Pacheco (Cenpes); Abelardo Barreto (Cenpes); Ramon Domingues (Cenpes); Marcio Murad (LNCC).
Shale Gas Modeling Chairman: Adolfo Puime (LENEP/UENF)
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09:30 – 10:30 – Quentin Fischer (University of Leeds UK). “Modelling gas flow in shales: from the laboratory to the field”
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10:30 – 11:00 – Coffee Break
Petrophysics Chairman: Flavia Falcão (Cenpes/Petrobras)
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11:00 – 12:00 – Ben Clennel (CSIRO, Australia). “Shale Petrophysics”
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12:00 – 13:30 – Lunch
Characterization Chairman: Abelardo Barreto (Cenpes/Petrobras)
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13:30 – 14:30 – Erdal Ozkan (Colorado School of Mines, USA). “Modeling and Characterization Challenges for Tight, Unconventional Reservoirs”
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14:30 – 15:00 – Coffee Break
Microseismicity Chairman: Ramon Domingues (Cenpes/Petrobras)
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15:00 – 16:00 – Michael Kendall (University of Bristol, UK). network stimulation and passive seismic monitoring”.
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20:00 – Barbecue Party at Churrascaria Lago Sul (Petrópolis)
“Fracture
Thursday (28/08)
Coal Bed Methane Chairman: Marcio Murad (LNCC/MCTI)
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09:00 – 10:00 – Nicolas Espinoza (University of Texas at Austin, USA). “Coal bed methane: adsorptive, poromechanical and transport properties of fractured coal seams”
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10:00 – 10:30 – Coffee Break
Methane Hydrates Chairman: Marcio Murad (LNCC/MCTI)
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10:30 – 11:30 – Malgorzata Peszynska (Oregon State University, USA). “Computational Modeling of Methane Hydrates at Multiple Scales”
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11:30 – 13:00 – Lunch
Fluids in Nanopores Chairman: Ramon Domingues (Cenpes/Petrobras)
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13:00 – 14:00 – Frederico W. Tavares (COPPE/UFRJ, Brazil). “Phase Equilibrium of Fluids Confined in Porous Media from an Extension of the Generalized van der Waals Theory”
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14:00 – 14:30 – Coffee Break
Multiscale Modeling Chairman: Ramon Domingues (Cenpes/Petrobras)
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14:30 – 15:30 – Marcio Murad and Dung Le (LNCC/MCTI, Brazil). “A New Multiscale Computational Model for Flow and Transport in Shale-gas Reservoirs”
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15:30 – 16:15 – Discussion and Networking Opportunities
Closing Session •
16:15 – 16:20 – Closing Remarks
Modelling gas flow in shales: from the laboratory to the field Fishera, Q.J., Lorinczia, P., Angusa, D., Burnsa, A.D., Lesnica D., Crooka, A.J., Grattonia, C., Rybalcenkoa, K., Kendallb, J-M., Rancec, J. and Dutkoc, M. a - Centre for Integrated Petroleum Engineering and Geoscience, University of Leeds, Leeds, LS2 9JT, UK
[email protected]
b - Department of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, Bristol, BS8 1RJ
[email protected]
c -Rockfield Software Ltd, Ethos, Kings Road, Swansea Waterfront, SA1 8AS, UK
[email protected] Abstract Even at the core plug scale, gas flow in shale remains a poorly understood and potentially complex phenomenon. It is currently being investigated using a variety of experimental techniques including the analysis of transient experiments conducted on core plugs and crushed shale using a range of gases. A range of gas flow mechanisms may operate including continuum flow (i.e. Darcy flow), slippage, transitional flow and Knudsen diffusion [1,2]. It has been argued that these processes, as well as gas sorption, need to be taken into account when interpreting experimental data and using the results to predict flow in the subsurface [3,4]. To this end we have developed two numerical models based on the formulation of Civan et al. [4] and linked them to inversion algorithms to extract the key parameters that control gas flow from laboratory experiments. In the first model, a 2D finite volume method is used to model gas flow; experimental results are matched by minimisation of a nonlinear least-squares objective function using the NAG routine E04FCF. This routine is a comprehensive algorithm for finding an unconstrained minimum of a sum of squares of M nonlinear functions in N variables [5]. In the second model, using 3D finite element method, both thermal and mechanical coupling are linked to a nearest neighbourhood algorithm to invert for the experimental data. The gas flow model is applicable to non-linear diffusion problems in which the permeability and fluid density both depend on the scalar variable, pressure. The governing equation incorporates the Knudsen number, allowing different flow mechanisms to be addressed, as well as the gas adsorption isotherm. The two models have been validated for unsteady-state problems for which analytical or numerical solutions are available. Both numerically simulated noisy and experimental data are input into the formulation of the inverse problem. Error analysis is undertaken to investigate the accuracy of results. A good agreement between inverted and exact parameter values is obtained for many parameters. However, it was found that the strong correlation between absolute permeability and tortuosity meant that it was not possible to accurately invert for both parameters. We therefore adopted an alternative approach, in which we inverted experimental data using an industry-standard package, ENABLE, which links the ECLIPSE production simulator to model gas flow. A nearest neighbourhood algorithm is used to history match the results. A large number of pulse-decay permeametry measurements have now been conducted and inverted using the latter method. In virtually all cases it was only possible to gain a robust history match of experimental data using a dual permeability model. It is likely that this reflects the presence of microfractures
within the sample formed as the sample was brought to the surface. As the early time behaviour of the experiments is dominated by fractures, it is necessary to conduct long-term experiments to invert results for matrix properties. To model field scale problems, we have developed a coupled fluid flowgeomechanical model that outputs the key parameters needed to model a range of seismic parameters/attributes including: P and S wave velocities and anisotropy, AVOA, microseismic event locations etc. For modelling dry gas flow, we use the ELFEN finite element code. A user-friendly GUI has been built to allow modelling of hydraulic fractures, proppant transport, clean-up and production. The software incorporates a range of gas flow models including Darcy and slip flow as well as transitional flow and Knudsen diffusion. The SR3 (Soft Rock 3) constitutive relationship is used by the geomechanical simulator and is derived from laboratory experiments that incorporate linear elastic and plastic behaviour [6], as well as lithology specific behaviour [7]. We have generated a discrete fracture network generator (DFN) to allow interaction of hydraulic and naturally occurring fractures to be modelled. ELFEN does not model multiphase flows, so for liquid-rich plays we have coupled the code to industry standard production simulation modelling software such as ECLIPSE, TEMPEST and VIP. To model the seismic response due to geomechanical deformation, rock physics models are required to link changes in fluid saturation, pore pressure and triaxial stresses to changes in the dynamic elastic stiffness. These models should incorporate phenomena observed in both laboratory core experiments and in the field, such as the non-linear stress-velocity response and the development of stress-induced anisotropy in initially isotropic rocks. The nonlinear rock physics model is generally incorporated within an aggregate elastic model. The approach has the benefit of allowing us to incorporate phenomena that act on multiple length-scales. Intrinsic anisotropy, caused by alignment of anisotropic minerals (such as clays and micas), can be included using an anisotropic background elasticity. Stress-induced anisotropy is incorporated implicitly within the non-linear rock physics model. Finally the influence of larger-scale fracture sets can also be modelled using the Schoenberg and Sayers (1995) effective medium approach [8], adding the additional compliance of the larger fracture sets to the stress-sensitive compliance. Fluid substitution can also be included using either the Brown and Korringa (1975) anisotropic extension to Gassmann's equation [9], which is appropriate as a low-frequency end member, or incorporating the dispersive effects of squirt-flow between pores [10]. References 1.
Roy, S., Raju, R., Chuang, H.F., Cruden, B.A., Meyyappan, M. 2003. Modeling Gas Flow Through Microchannels and Nanopores. J. Appl. Phys. 93 (8), pp. 4870–4879.
2.
Cui, X., Bustin, A.M., Bustin, R. 2009. Measurements of Gas Permeability and Diffusivity of Tight Reservoir Rocks: Different Approaches and Their Applications. Geofluids 9, pp. 208–223.
3.
Freeman, C.M., Moridis, G.J., Blasingame, T.A. 2011. A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas Reservoir Systems. Transport in Porous Media 90, pp. 253-268.
4.
5.
Civan, F., Rai, C.S., Sondergeld, C.H. 2011. Shale-Gas Permeability and Diffusivity Inferred by Improved Formulation of Relevant Retention and Transport Mechanisms. Transport in Porous Media 86 (3), pp. 925-944.
Gill, P.E. and Murray, W. 1978. Algorithms for the Solution of the Nonlinear Least-Squares Problems. SIAM J. Numer. Anal. 15, pp. 977–992. 6. Crook, A.J.L., Yu, J.-G., Willson, S.M. 2002 Development of an orthotropic 3D elasticplastic material model for shale. Society of Petroleum Engineers, 78238. 7. Crook, A.J.L., Willson, S. M., Yu, J-G., Owen D.R.J. 2006. Predictive modelling of structure evolution in sandbox experiments. Journal of Structural Geology, 28, pp. 729-744. 8. Schoenberg, M. and Sayers, C.M.. 1995. Seismic anisotropy of fractured rock. Geophysics, 60, pp. 204-211. 9. Brown, R.J.S. and Korringa, J. 1975. On the dependence of the elastic properties of a porous rock on the compressibility of the pore fluid. Geophysics, 40, pp. 608-616. 10. Chapman, M. 2003. Frequency-dependent anisotropy due to meso-scale fractures in the presence of equant porosity. Geophysical Prospecting, 51, pp. 369-379.
Shale Petrophysics M. Ben Clennell*, Matthew Josh*, Lionel Esteban* Iko Burgar**, David Dewhurst*, Neil Sherwood***, Mark Raven****, Claudo Delle Piane*, Marina Pervukhina* * CSIRO Energy ARRC, 26 Dick Perry Avenue, Kensington WA 6151 Australia **RMIT University 124 Little La Trobe St, Melbourne VIC 3000 *CSIRO Energy Riverside Corporate Park, Julius Avenue North Ryde NSW 2113 ****CSIRO Land and Water Waite Road - Gate 4 Glen Osmond SA 5064 Australia
[email protected]
ABSTRACT Shale is a complex geomaterial that has aspects of a rock, a soil and a colloidal system. Shales contain a range of different minerals, and in the case of gas shales or source rocks, may also contain organic matter of various types and levels of maturity, and may contain hydrocarbons in addition to water. The physical properties of a particular shale depend on mineral composition, especially the fraction of clays, on the nature and strength of bonding or cementation between particles, on the presence and state of organic solids and fluids, and on the state of water saturation, which in a gas shale may be low. Economically important gas “shales” from North America are in fact often geologically classified as siltstones, limestones, or cherts rather than true shales as shown by the scatter of points on a clay-silica-carbonates ternary plot (Passey et al. 2010, Aplin and Macquaker 2011, Gamero Diaz et al. 2013). Petrophysical workflows There are no well established rules as to how to characterize a shale petrophysically, though in recent years, there have been some attempts to establish and standardize methods for core and log, (Josh et al. 2012, Eslinger and Everett 2012, Bust et al. 2013). In fact, given the paucity of core material in a good state of preservation, there is often relatively little sound quantitative information available from samples, and therefore log analysis may be conducted with very little ground truth. Clennell et al. (2006) introduced a workflow for shale sample analysis that is designed to make the most of available preserved core material, commencing with non-destructive analyses, and progressing to analyses that require exposing the rock to fluids, stress and eventually permanent deformation in rock mechanics/rock physics tests. In our
view, access to ground truth samples, preferably cores in their preserved state, but at least cuttings material, is vital to obtain any reasonable assessment of shale physical characteristics and to perform resource evaluation in the case of a gas shale. Mineralogy. In parallel with analysis on preserved core samples, detailed mineralogical and organic petrographic analysis is needed. The mineralogical investigations may include quantitative XRD, FTIR (Charsky and Herron 2012), and determination of Cation Exchange Capacity. Among the most critical mineralogical parameters are clay mineral percentages and types, with high surface area and high CEC minerals dominating some of the properties such as electrical conductivity/permittivity and swelling tendency. Among downhole logs, the density log and photoelectric factor give some mineralogical indications while gamma ray and especially spectral gamma ray is often a good clay indicator and can help to identify changes in clay type. The uranium from SGR can of course indicate indirectly the presence of organic matter owing to the variable redox state of that element in the subsurface and its affinity to stabilize in reducing conditions. In any shale though, an elemental spectroscopy log (neutron activation tools such as Schlumberger’s ECS, Baker’s FLEX and newer technologies that combine elastic and inelastic scattering responses) is invaluable for determining the matrix mineralogy and helping to build an accurate petrophysical model with grain density, porosity, clay content, brittle mineral content and accessory mineral contents being the useful outputs. Some samples (typically cuttings) are needed to provide some ground truth points so that the mineralogical model is calibrated as opposed to being a shot in the dark. Shale Sensitivity and Chemoporomechanics. Among the important properties that control shale behaviour during drilling/completions and hydraulic fracturing as the chemoporoelastic and osmotic characteristics (Sarout and Detourney 2011); in the case of unsaturated shales (which would include any gas shales), there is additionally a capillary pressure characteristic, which interacts with the chemical-osmotic characteristics to control the responses of the shale when exposed to fluids of varying composition. Therefore chemoporomechanical properties are important to consider when chosing fracture fluids and drilling fluids. Even if samples are available, tests to determine whether the shale is sensitive to fluids or not are complex (Dewhurst et al. 2013), and therefore finding simple correlations between petrophysical properties, mineralogy and the chemoporomechanical properties can be very useful for planning wells, fo targeting intervals to be completed and for designing optimal well stimulation. Mineralogical logs (leading to Vclay, clay type) and cuttingsbased analyses are the main source of information on shale sensitivity, together with estimates of water saturation. As permittivity is largely controlled by fluid content and clay mineral activity, dielectric measurements downhole or in the lab may be useful in this regard to compliment general characteristics (is the shale electrically active or not?) gained from resistivity log responses. There is a close relationship between surface area, cation exchange capacity, the controlling clay type, and the sensitivity of clays, and this can be picked up by dielectric analysis of intact and remoulded shale samples (Josh et al. 2014). Mechanical Properties and Brittleness. Some shales can behave as strong rocks despite not having a permanent cementation of quartz or carbonate bonding the particles together; these highly compacted muds (a well studied example is the Opalinus Clay from Switzerland) are the type of shale most susceptible to fluid-rock interactions, and can become weak and ductile, making them poor candidates for fracture stimulation. On the other hand, some shales have a matrix that is strongly bonded by silica and carbonate, and exhibit little
tendency for swelling or strength degradation, maintaining a brittle rheology under a range of loading scenarios. These shale types are the most likely to form good fracture networks. Petrophysical discrimination of these mechanical rock types typically relies heavily on sonic log characteristics, as Vp, Vs and derived properties such as Poisson’s ratio often show good correlations with strength and brittleness. Again the prediction of mechanical properties is further aided by knowledge of the rock mineralogy and electrical properties, which are controlled by clay content, water saturation and connectivity of brine in the pore space. High silica and high calcium and magnesium are indicators of the presence of cementing minerals, but most petrophysical workflows are based on clay fraction not cementation degree and assume that fracturing will target low clay zones in order to avoid more ductile clay shales in the section. Organic matter. Many works on gas shales/source rocks/oil shales treat all the solid organic matter as a single material called kerogen. Kerogen isn’t a real material with predictable physical properties, it is just a convenient name for all of that insoluble black stuff that makes the rock have high TOC. Most shales will contain a number of different organic matter types or macerals, and individual particles of organic matter may themselves be composed of subdomains with different composition and microstructures. Therefore proper characterization of a shale with appreciable (>1%) TOC should include a proper organic petrographic analysis, as well as proper quantification of TOC and H/O/C ratios by some combination of pyrolosis, Rock-Eval, FTIR, Raman spectroscopy and so on. The important characteristics such as gas content, level or organic maturity, can then be related back to the macerals present- this may be a simple process if the organic matter is mainly of one type, or more complex if several types are present (Bernard and Horsfield 2014). In mature and overmature source rocks- i.e. in gas shales- the organic matter will have generated hydrocarbons, which can then change the predominant organic matter types, and these can include bitumen (migrated and resolidified liquid hydrocarbons) and pyrobitumen (residual organic matter that has generated hydrocarbons). The textures of these secondary OM types can be quite different from the original OM in the rock, and this is important for how they affect the petrophysical properties of the rock and the way that gas is stored in the shale and can move through it. The petrophysical characteristics of organic matter are mostly subtle, and often relationships between TOC and log response are non-linear. OM has lower mass density than silicate or carbonate minerals, typically from 1.2-1.6, and so the solids density can be used to estimate TOC when the mineralogy and grain density is known. Generally this is not accurate enough, and so the most popular method to determine TOC from logs is the socalled Delta-LogR technique (see Passey et al. 2010 for an update of the original method), which relies on the high resistivity of organic matter compared with either clay minerals or brine in the pore space of a shale. This method often does seem to work reasonably when several calibration points are available, even though the physics is not very rigorous, and especially the adjustment for level of organic maturity (LOM) seems arbitrary. Pitfalls of DlogR include poor baseline, instances where the resistivity is suppressed by pyrite, clay rich laminations, or else is too high and out of the range that the logging tool can measure accurately (2000 ohmm for induction logs) in very dehydrated shale systems. The latest generation of nuclear tools now offers the possibility of direct TOC determination based on multiply activated neutron response (e.g. Schlumberger Lithoscanner); one of course still needs to understand well the amounts of any inorganic carbon in the rock for any elementally-based method- and this does need some cores or cuttings for ground truth and calibration of logs.
Porosity and Pore Types. The pores in gas shales are very small (a few nm to tens of nm), and often are not well connected, so that permeability is typically extremely low (nanodarcy range for dry gas). The poor connectivity also means that helium porosity determination is often very slow to equilibrate, which has led to the widespread use of crushed sample analysis (so called API methods). The pores in shales can only be seen with extremely high resolution electron microscopy; the tool of choice being focused ion beam or broad ion beam (FIB or BIB) (e.g. Loucks et al. 2012, Bernard and Horsfield 2014), which reveals that inter-mineral and intra-organic pore types are often present in gas shales. There is a question as to whether core retrieval from depth, sampling and preparation procedures, and even the ion or electron beam itself creates artefacts that are mistaken for pores in the organics. Inter-grain porosity is usually insufficient to store economic quantities of gas in shale; negligible amounts are adsorbed onto silicates, and therefore the main gas storage is usually pore space within the organic matter and adsoption of gas onto internal surfaces of the nanoporous framework of organic matter- the nature and quantity of gas storage is revealed by isotherm experiments. So the Original Gas in Place must then be related back to the sum of the different available pore types. Petrophysically speaking, these pore types are very difficult to quantify. The mass and volume balance for a gas shale includes the mineral solids, the organic solids and then the clay bound water, intermineral pores and finally the intraorganic pores. As the mineral solids are usually a combination of minerals with very different grain densities, and the organic matter also has unknown grain density and internal porosity, one has many more unknowns to solve than in conventional petrophysics. Therefore an interative processes is needed to estimate and update matrix density, organic matter, pore volumes, and saturations to close the loop on what constitutes each volume fraction of the rock, and what is then filling each type of pore space. Fluid Saturations. The saturation state of a gas or oil shale is extremely difficult to determine from logs; simple methods based on resistivity can work in shales that are “shaly sand” like in their texture and mineralogy, but will generally fail otherwise. One must work with a range of information sources in order to determine the composition of the rock to account for all of the solids and all of the fluids using the correct total porosity model. Only when all of those components are determined can one then estimate volume saturation of water in the pore space. The presence of solid organic matter whose properties are very different from matrix minerals confounds the estimation of gas and brine content. If oil as well as gas is present, the mass/volume balance process is doubly difficult. Therefore, in situ gas saturation of most shales is never actually known: there is an estimate of Original Gas in Place that comes from well production data with some constraints from lab measurements of desorption isotherms, but the amount of free, dissolved and adsorbed gas are rarely determined to a high degree of accuracy. Conceptually speaking nuclear magnetic resonance, which is sensitive to the physical state of hydrogen nuclei, has the potential to determine water, oil and gas saturations in a gas shale in situ. CSIRO has been conducting research to this end for some years. However the practical difficulties of implementing complex laboratory NMR protocols downhole, with a volume of investigation that is sufficiently undisturbed, are very far from being overcome. At the moment downhole NMR can at best give indications of the mobile fluid contents and clay bound water, and little useful information about adsorbed gas content. Dielectric logs can help to determine water contents: both free water and its salinity, and the water that hydrates the mobile ions in clays and activates the surface double layers of minerals to become electrically polarized. There is not any published dielectric log data to
use to develop proper petrophysical models for shales or gas shales unfortunately, so the approach at CSIRO has been to combine laboratory broadband dielectric measurements with effective medium modelling. Confounding factors. Several factors may make the resource evaluation of a shale play more complex from a petrophysical point of view. Not all clay mineral assemblages are associated with higher contents of potassium thorium and uranium, and therefore the gamma ray API value may not be a good indicator of clay content; heavy minerals and uranium enrichment associated with organics may also be variable in a section depending on changes in source provenance and diagenetic evolution. So therefore methods based on gamma ray should be cross-checked with another method. Pyrite is a common mineral in shales; it is often closely associated with organic matter because of the redox conditions of early microbially-mediated diagenesis. So it can be useful to identify high TOC zones, but on the other hand it can affect electrical logs very significantly, disrupting the delta-log R type of methods often used for TOC estimation. Moreover, pyrite has a very strong effect on dielectric properties, so laboratory or log correlations may also be thrown off. Another issue that can be a curse, or a benefit if properly employed is shale anisotropy. Shales always have a degree of material property anisotropy (Clavaud 2008), and this can be extremely variable on a small scale or within a broader depositional sequence owing to the conditions of original deposition and burial, the presence of compositional laminations and the presence or absence of bioturbating organisms (Aplin and Macquaker 2011). In general, organic rich shales deposited into anoxic conditions leads to a higher level of anisotropy because of the lack of bioturbation, the presence of organic rich layers multiplies up the electrical effects of the anisotropy (Revil et al. 2013) in addition to the anisotropy in elastic properties seen also in lean shales (Nadri et al. 2012). These characteristics are clearly useful to identify potential zones that are more organic rich, and which may be more clay rich compared with a more isotropically textured silty background (Pervukinha et al., 2008). However, if the anisotropy is not accounted for then the interpretation of horizontal and vertical well logs, and also sample analysis results may be misinterpreted. The biggest confounding effect in shale property investigation is undoubtedly poor preservation of material. One is typically faced with either no preserved core, or core of dubious quality. Dewhurst et al. (2014) have shown the pitfalls of using non-preserved core to estimate shale mechanical and rock physics properties, strength and brittleness can be over or under-estimated. Partial saturation has a significant impact on shale properties. Strength and stiffness significantly increase as saturation decreases, dynamic rock properties can change by 1520% and electrical properties are also impacted. This has implications for both field assessments of gas saturation in shale reservoirs and for laboratory testing of clay-bearing gas shales which are not well preserved. Summary. The petrophysical world is catching up with shale characterization, though long after the gas shale revolution in N.America has morphed into a shale liquids rush. The major service companies are now providing new tools including advanced nuclear logs, that are designed for shale environments, and have also developed workflows that take into account a much wider range of possibilities, and look not only at organic matter and gas in place, but also at the context of the gas bearing intervals and their relationship to mechanically brittle zones and/or naturally fractured zones that may produce effectively after fracture stimulation. If anything the petrophysicist may actually be confused by the number of “solutions” being offered by vendors, who claim to have a complete package accessible through a few simple steps. For countries, Australia and South American nations where economically very
interesting shales are found in abundance but are yet to be unlocked, the range of petrophysical tools now available, if properly employed and developed for local circumstances could make the development of unconventional resources much less hit and miss than it was in the N. American case. The enemy of good petrophysics still remains the high cost of obtaining quality data versus drilling cost and cost to “keep on fracking”. The cost of not knowing important first order information about matrix properties, organic matter richness and maturity, gas in place, overpressure condition and rock ductility should therefore be considered carefully in the balance. A good petrophysical model underpins resource estimatation and must be developed in concert with, and used to enable a valid Mechanical Earth Model. In just the same way the petrophysical model informs and is informed by a predictive rock physics model for the gas shale (anisotropic, stress sensitive, capable of handling variable saturation and incorporating orghanic matter) that is needed to take core and log information away from well control and into the wider rock volume (Pervukhina et al. 2011). REFERENCES Alpin, A.C. and Macquaker, J.C.S. 2011. Mudstone diversity; origin and implications for source, seal, and reservoir properties in petroleum systems AAPG Bulletin 95(12):2031-2059 Bernard, S., & Horsfield, B. 2014. Thermal maturation of gas shale systems. Annu. Rev. Earth Planet. Sci. 2014. 42:635–51 Bust, V., A. Majid, J. Oletu, and P. Worthington 2013. The petrophysics of shale gas reservoirs: technical challenges and pragmatic solutions, Petroleum Geoscience v. 19 no. 2 p. 91-103 doi: 10.1144/petgeo2012-031 Charsky, A. and Herron, M.N. 2012. Quantitative analysis of kerogen content and mineralogy in shale cuttings by Diffuse Reflectance Infrared Fourier Transform Spectroscopy. International Symposium of the Society of Core Analysts held in Aberdeen, Scotland, UK, 27-30, 2012. Paper SCA2012-27 Clavaud, J.B. 2008. Intrinsic electrical anisotropy of shale: the effect of compaction. Petrophysics 49, 143-153. Clennell, M.B. Dewhurst, D.N. & Raven M. 2006. Shale Petrophysics: electrical, dielectric and NMR characterization of shales and clays Paper KK, presented at the 47th Annual Symposium of the SPWLA, Veracruz, Mexico, June 2006. Dewhurst, D., Bunger, A., Josh, M., Sarout, J., Delle Piane, C., Esteban, L., Clennell, M.B., 2013, Mechanics, physics, chemistry and shale rock properties. Paper 13-0151, Proceedings of the 47th American Rock Mechanics Association Annual Conference, San Francisco, 11pp. Dewhurst, D.N., Minaeian, V., Delle Piane., C., Josh, M., Esteban, L.,, Sarout, J. & Clennell, M.B. 2014. Geomechanical and Petrophysical Impact of Partial Saturation in Clay-Bearing Shales .Australian Clay Minerals Society Conference – Perth 3-5 February 2014 55 Eslinger, E., & Everett, R.V. 2012 , Petrophysics in gas shales, in J. A. Breyer , ed., Shale reservoirs—Giant resources for the 21st century : AAPG Memoir 97 Gamero-Diaz, H., Miller, C., Lewis, R., 2013 sCore: A Mineralogy Based Classification Scheme for Organic Mudstones. SPE 166284 SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 30 September–2 October 2013
Josh M, Esteban L, Delle Piane C, Sarout J, Dewhurst DN, Clennell MB. 2012. Laboratory characterisation of shale properties. J. Pet. Sci. Eng. 88–89:107– 24 Josh, M., Bunger, A., Kear, J., Sarout, J. Dewhurst, D.N. Raven, M.D. Delle Piane, C., Esteban, L. and Clennell, M.B. 2014. The Role of Specific Surface Area and Cation Exchange Capacity in Determining Shale Rock Properties Fourth EAGE Shale Workshop, Porto Portugal 06-09 April 2014. Josh, M., Clennell, M.B. and Siggins, A.J. 2009. Practical broadband dielectric measurement of geological samples, Transactions Society of Petrophysicists and Well Log Analysts Annual Logging Symposium, Woodlands, Tx, June 21-24. Laloui, L., Slager, S. & Rizzi, M. 2013. Retention behaviour of natural clayey materials at different temperatures. Acta Geotechnica 8:537–546 Loucks RG, Reed RM, Ruppel SC, Hammes U. 2012. Spectrum of pore types and networks in mudrocks and a descriptive classification for matrix-related mudrock pores. AAPG Bull. 96:1071–98 Nadri, D., Sarout, J., Bona, A. & Dewhurst, D., 2012. Estimation of the anisotropy parameters of transversely isotropic shales with a tilted symmetry axis, Geophys. J. Int., 190, 1197–1203. Passey, Q. R., Bohacs, K. M., Esch, W. L., Klimentidis, R., and Sinha, S. 2010, From oil-prone source rock to gas-producing shale reservoir: Geologic and petrophysical characterization of unconventional shale-gas reservoirs: International Oil and Gas Conference and Exhibition in China, Beijing, China, June 8–10, 2010, SPE Paper 131350, 29 p. Pervukhina, M., Dewhurst, D.N., Gurevich, B., Kuila, U., Siggins, A., Raven, M.D. & Norgad Bolas, H.M. 2008. Stress dependent elastic properties of shales: measurement and modelling. v. 27 p. 772-779 doi: 10.1190/1.2944162 Pervukhina, M., Gurevich, B., Golodoniuc, P. & Dewhurst, D.N., 2011. Parameterization of elastic stress sensitivity in shales, Geophysics, 76,WA147–WA155. Revil, A., Woodruff, W.F., Torres-Verdín, C., Prasad, M. 2013. Complex conductivity tensor of anisotropic hydrocarbon-bearing shales and mudrocks Geophysics 78 (6), pp. D403-D418 Sarout, J. & Detournay, E., 2011, Pore pressure transmission test for reactive shales: Chemoporoelastic analysis and experimental validation. Int. J. Rock Mech. Min. Sci. 48:759-772.
Modeling and Characterization Challenges for Tight, Unconventional Reservoirs E. Ozkan* *Colorado School of Mines Petroleum Engineering Department 1600 Arapahoe Street Golden, Colorado, 80401, USA
[email protected] ABSTRACT The performances of nano-porous unconventional reservoirs are dominated by the heterogeneity due to the existence of fractures, fissures, micro, macro, and inter-aggregate pores, and the conglomerations of organic matter. The heterogeneity of the microscopic structures causes preferential flow at the macroscopic level by creating a highly nonuniform velocity field and the sizes of the nanopores cause high capillary and surface forces creating poreproximity effects on phase-behavior. This presentation summarizes our efforts aiming at a fundamental overhaul of the perceptions of flow in nano-porous, unconventional reservoirs. We propose to model flow in naturally fractured, tight porous media by using anomalous diffusion, instead of the conventional dual-porosity idealization, and discuss the relations of the model parameters to the physical structure of the flow domain, which has bearings on unconventional rock characterization. In statistical physics, classical (normal) diffusion is a special case where the random Brownian motion of the diffusing particles is governed by a Gaussian probability density whose variance is proportional to the first power of time 2 ( σ r t ). A more comprehensive relationship between the mean square 2 α variance and time is given by σ r t and leads to anomalous (fractional) diffusion for α ≠ 1 . In the last two decades, non-local, hereditary descriptions of flow and transport have gained notable popularity in applications in nanoporous systems [1-12]. We also introduce an approach to define and account for the effect of poreproximity on phase behavior and coupled diffusive flows in nano-porous matrix. Firincioglu et al. [13], Honarpour [14], Sapmanee [15], and Devegowda et al. [16] have discussed pore-size dependent bubble-point suppression or dewpoint enhancement in nanoporous media. Firincioglu et al. [13] have also noted that the pore-size dependency of phase behavior may cause concentration gradients and diffusion in heterogeneous nanoporous media. However, because some pore-throat sizes are at the scale of membrane pores, they do not permit the passage of heavier hydrocarbons with large molecules. This sieving effect may cause an osmosis-like behavior, which may act countercurrently with the concentration-driven diffusion in heterogeneous, nanoporous systems. Consequently, the coupled flows can be described by a fluid dissipation function, which is the sum of the coupled fluxes where the flux of type i is related to the gradient of type j through some transport parameters. For
coupled flows, the interdependency of transport parameters complicates or prohibits their estimation. Therefore, this presentation will give a perspective of scale for the appropriate flow regimes and the modeling approaches. The flow mechanisms and phase behavior in conventional and unconventional reservoirs will be compared in connection with the data needs for unconventional flow models and performance prediction tools. REFERENCES [1] Gefen, Y., Aharony, A. and Alexander, S. 1983. Anomalous Diffusion on Percolating Clusters, Phys. Rev. Lett., 50 (1): 77-80. [2] Le Mehaute, A. and Crepy, G. 1983. Introduction to transfer and motion in fractal media: The geometry of kinetics, Solid State Ionics, 1 (9-10): 17-30 [3] Nigmatullin, R. R. 1984. To the Theoretical Explanation of the Universal Response, Physica Status Solidi B, Basic Research, 123 (2): 739-745 [4] O’Shaughnessy, B. and Procaccia, I. 1985. Analytical solutions for diffusion on fractal objects, Phys. Rev. Lett. 54 (5): 455-458 [5] Chang, J. and Yortsos, Y. 1990. Pressure Transient Analysis of Fractal Reservoirs. SPE Formation Evaluation 5 (1) [6] Dassas, Y. and Duby, Y. 1995. Diffusion toward Fractal Interfaces, Potentiostatic, Galvanostatic, and Linear Sweep Voltammetric Techniques, Journal of The Electrochemical Society, 142 (12): 4175-4180 [7] Caputo, M. 1998. 3-dimensional physically consistent diffusion in anisotropic media with memory, Matematica e Applicazioni Rendiconti Lincei, 9 (2): 131-143 [8] Molz III, F. J., Fix III, G. J. and Lu, S. S. 2002. A physical interpretation for the fractional derivative in Levy diffusion, Applied Mathematics Letters, 15 (7): 907-911 [9] Flamenco-Lopez. F. and Camacho-Velazquez, R. 2003. Determination of Fractal Parameters of Fracture Networks Using Pressure Transient Data. SPE Reservoir Evaluation & Engineering 6 (1). SPE 82607-PA. [10] Camacho-Velazquez, R., de Swaan-Oliva, A., Vasquez-Cruz, M., 2011. Interference Tests Analysis in Fractured Formations with a Time Fractional Equation. SPE 153615. [11] Raghavan, R. 2011. Fractional derivatives: Application to transient flow, Journal of Petroleum Science and Engineering, 80, 7-13 [12] Fomin, S., Chugunov, V. and Hashida, T. (2011), Mathematical modeling of Anomalous Diffusion in Porous Media, Fractional Differential Calculus, 1, 1-28 [13] Firincioglu, T., Ozkan, E., Ozgen, C. 2012. Thermodynamics of Multiphase
Flow in Unconventional Liquids-Rich Reservoirs, paper SPE 159869, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8-10, 2012. [14] Honarpour, M. M., Nagarajan, N. R., Orangi, A., Arasteh, F., and Yao, Z. 2012. Characterization of Critical Fluid, Rock, and Rock-Fluid PropertiesImpact on Reservoir Performance of Liquid-rich Shales, paper SPE 158042, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8-10, 2012. [15] Sapmanee, K. 2011. Effects of Pore Proximity on Behavior and Production Prediction of Gas/Condensate, MS Thesis, The University of Oklahoma, Norman, Oklahoma, 2011. [16] Devegowda, D., Sapmanee, K., Civan, F., and Sigal, R. 2012. Phase Behavior of Gas Condensates in Shales Due to Pore Proximity Effects: Implications for Transport, Reserves and Well Productivity, paper SPE 160099, presented at the SPE Annual Technical Conference and Exhibition, San Antonio, TX, Oct. 8-10, 2012.
Fracture network stimulation and passive seismic monitoring. J-M. Kendall, J. P. Verdon, A. F. Baird, A. Stork and P. Usher – Bristol University Microseismicity Projects (BUMPS) University of Bristol, School of Earth Sciences, Queen’s Road, Wills Memorial Building, Bristol, BS8 1RJ, UK.
[email protected] Summary The successful exploitation of many reservoirs requires fracture networks, sometimes naturally occurring, often hydraulically stimulated. Microseismic data acquired in such environments hold great promise for characterising such fractures or sweet spots. The loci of seismic events delineate active faults and reveal fracture development in response to stimulation. However, a great deal more can be extracted from these microseismic data. Source mechanisms and magnitudes provide insights into faults and fractures and their stress regimes. Inversions of shear-wave splitting data provide a means of mapping fracture densities and preferred orientations, useful information for drilling programs. They can also be used to track temporal variations in fracture compliances, which are indicative of fluid flow and enhanced permeability in response to stimulation. Furthermore, the frequency-dependent nature of shear-wave splitting is very sensitive to size of fractures and their fluid-fill composition. Here we discuss a range of methods for extracting spatial and temporal variations in sub-seismic scale fractures. Introduction Small microseismic events, or acoustic emissions, occur both naturally and a result of anthropogenic influences in reservoirs. Sudden stress release leads to elastic rock failure, which serves as an effective seismic source. These microearthquakes may be the result of production or hydraulic stimulation, but they may also be a consequence of natural tectonic activity. They are usually only detectable using sensitive sensors and after careful data processing. Such passive seismic monitoring has been used in mining settings for over 100 years, but its application in petroleum setting is relatively new. As such, it is a rapidly advancing field of technology, where the challenges are manifold and involve issues associated with data acquisition, processing, and interpretation. Much can be learned from methods and case studies developed for microseismic monitoring in volcanological, geothermal and mining settings, but one of the key advantages in oilfield monitoring is that a great deal is ordinarily already known about the reservoir. Comparatively good velocity models exist and production or injection information is available – the same is obviously not true for a volcano. Clusters of microseismic events delineate faults and fracturing, highlighting reactivation or the generation of new zones of failure. Such monitoring can be done with sensor arrays deployed in boreholes or using dense arrays of sensors deployed on the surface or in shallow boreholes. Surface arrays provide better spatial coverage, whilst borehole sensors provide better sensitivity – ideally one would employ both types of monitoring arrays. Such monitoring has been very
effective in helping assess the efficacy of hydraulic stimulation (i.e., frac monitoring). Longer term monitoring will no doubt provide an early warning system for detecting top seal leakage and fault reactivation in CO2 sequestration projects, for example. Beyond event locations Until recently, most microseismic monitoring studies in petroleum settings have concentrated on detecting and locating events. However, considerably more information can be extracted from such data. For example, source characteristics and mechanisms provide helpful information about the stress field, especially as multi-well monitoring and surface arrays become more common. Magnitudes (e.g., Stork et al., 2014) help quantify stress drop and focal mechanisms provide insights into the magnitude and orientation of the stress tensor. The amplitude-frequency relation, or so-called b-value, is sensitive to fluid properties and fracture network development. Furthermore, microseismic events can be used to image the surrounding media. They can help refine velocity models, study attenuation, and are ideally suited to estimating anisotropy parameters. Insights into the nature of faults, estimates of the stress tensor and velocity model refinement are all valuable inputs for reservoir simulators. Figure 1 shows a suggested processing flow for microseismic data.
Figure 1 A proposed processing flow for microseismic data. Event locations will help delineate faults and locations of fractures; source characteristics reveal the style of failure and provide insights into the stress field; hydraulic stimulation will lead to fracture development, fluid injection and hence changes in attributes such as velocities, fracture-induced anisotropy and attenuation. All results are useful information for interpreting the efficacy of fracture stimulation and serve to inform geomechanical models.
Fracture-induced anisotropy Measurements of shear-wave splitting in microseismic events provide unambiguous evidence of seismic anisotropy, which may be caused by the rock fabric and/or aligned fractures, which in turn offers insights into the state of stress in the rock. We have developed a strategy to automatically process shear-wave splitting in large microseismic datasets (Wuestefeld et al., 2011). This includes an objective quality control of the shear-wave splitting results, based
on characteristic differences between two independent splitting techniques. Reliable measurements can be then used in inversion schemes for anisotropy parameters, including those controlled by rock fracturing. Recent work has focused on fracture compliance inversion, including both spatial and temporal variations in rock fracture networks, which can be used to track fracture development during stimulation (Baird et al., 2013). Furthermore, the frequency dependent nature of shear-wave splitting provides insights into fracture dimensions and fracture fluid content (Al-Harrasi et al., 2011). Our work has shown that shear wave splitting analysis can provide a useful tool for monitoring spatial and temporal variations in fracture networks in a range of environments. Conclusions Cumulatively, our proposed processing flow for microseismic data acquired during hydraulic facture stimulation may provide a useful toolbox for assessing the efficacy of fracture stimulation in a range of settings, including tight-gas reservoirs. Acknowledgement We gratefully acknowledge the support of the sponsors of the Bristol University Microseismicity Projects: BP, Schlumberger, Wintershall, Tesla, CGG/Magnitude, Total, ExxonMobil, Microseismic Inc., Chevron, Cuadrilla and the Natural Environment Research Council (NERC), UK. References Al-Harrasi, O. H., J-M. Kendall and M. Chapman, Fracture characterisation using frequency-dependent shear-wave anisotropy analysis of microseismic data, Geophys. J. Int., 85, 1059–1070, doi: 10.1111/j.1365246X.2011.04997.x, 2011. Baird, A. F., J-M. Kendall, A. Wuestefeld, T. Noble, Y. Li, M. Dutko and Q. Fisher, Monitoring increases in fracture connectivity during hydraulic stimulations from temporal variations in shear-wave splitting polarization, Geophys. J. Int., 195, 1120-1131, 2013. Stork, A. L., J. P. Verdon and J-M. Kendall, The robustness of seismic moment and magnitudes estimated using spectral analysis, Geophys. Prosp., 62, 862-878, 2014. Wuestefeld, A., O. Al-Harrasi, J. P. Verdon, J. Wookey and J-M. Kendall, A strategy for automated analysis of passive microseismic data to image seismic anisotropy and fracture characteristics, Geophys. Prosp, 58, 755773, 2010. doi: 10.1111/j.1365-2478.2010.00891.x, 2011.
Coal bed methane: adsorptive, poromechanical and transport properties of fractured coal seams D. Nicolas Espinoza*†, Matthieu Vandamme*, Jean-Michel Pereira*, Patrick Dangla*, and Sandrine Vidal-Gilbert‡ *
Université Paris-Est, Laboratoire Navier (UMR 8205), ENPC, CNRS, IFSTTAR 6-8 Av. Blaise Pascal, 77420 Champs-sur-Marne, France
[email protected],
[email protected],
[email protected] The University of Texas at Austin Department of Petroleum and Geosystems Engineering 200 E. Dean Keeton, 78712 Austin, USA
[email protected] †
TOTAL S.A. Unconventional Gas Resources 168 Av. Larribau, 64018 Pau, France
[email protected] ‡
ABSTRACT Unmineable coal beds constitute important domestic sources of natural gas in several countries, Australia, USA, Canada, and China [1]. Coal seams differ from conventional reservoirs in the sense that they constitute the source and reservoir rock at the same time. Although limited in size, coal seams have the advantage of being naturally fractured, which facilitates drainage upon depletion. The reservoir response of unmineable coal seams to primary and CO2-enhanced natural gas recovery is strongly affected by the gas sorption and swelling properties of the coal reservoir rock. For example, order-ofmagnitude increases of permeability and significant production of fines have been observed during reservoir depletion [2-4]. Conversely, CO2 injection has led to significant reductions of injectivity [5,6]. In-depth understanding of the process of gas sorption/desorption in the coal matrix, induced deformation and measurement of relevant physical parameters are critical for predicting the evolution of seam permeability and managing the reservoir. Natural fractures in coal seams, called coal cleats, and micro/mesopores sized from 10−9 to 10−8 m constitute the double porosity of coal seams [7-9]. At the smallest scale, coal seams are constituted by a microporous disordered organic continuum, called the coal matrix. The coal matrix is capable of adsorbing various gases including CO2, CH4, and N2, which can lead to coal matrix volumetric swelling in the order of a few percents upon adsorption [8-13]. The variety of pore sizes in coal seams yields various types of
fluid pore habit. Models used in industry practice are based on sorption and swelling strain isotherms in which a coal sample is submerged into the adsorbate. Geomechanical models take those swelling strains as an input to calculate permeability changes based on changes of porosity or stress – this latter calculated assuming an analogy with thermoelasticity [2,14-16]. We have developed a fully coupled poromechanical model in which coal matrix microporosity and adsorption-induced phenomena are embedded into a transverse isotropic fractured reservoir rock. The model is based on energy conservation and follows from a thermodynamical formulation [17,18]. The adsorptive-mechanical coupling in the coal matrix is integrated through an adsorption stress function and seam permeability is estimated as a function of Terzaghi’s effective stresses (parallel and perpendicular to the bedding plane). The amount of fluid in the coal matrix and in fractures is directly coupled to adsorptive and poroelastic stresses. The discrimination of two porosity levels permits isolating poromechanical responses and calculating fluid amounts from either fractures or the coal matrix. The model is validated with triaxial testing measurements on 38 mm diameter fractured bituminous coal cores exposed to CO2. Testing includes the measurement of fluid uptake, adsorption-induced strains and stresses, and their impact on simultaneously measured permeability. The experimental results and model predictions help identify the characteristic response of coal microporosity and cleat macroporosity on the poromechanical response of coal cores, and suggest that the order of magnitude change of reservoir permeability observed in the field are linked to sorption-induced change on Terzaghi’s effective horizontal stress under laterally constrained displacement condition. The measured and predicted adsorptioninduced stresses are in the order of tens of MPa at typical reservoir pressure and temperature conditions. Together, the modeling and experimental characterization let us understand better the coupled pressure-stress response of adsorptive organic rocks. REFERENCES [1] EIA (2013). International Energy Outlook 2013 - Report number: DOE/EIA0484(2013). Technical report. [2] Palmer, I. and Mansoori, J. (1998). How permeability depends on stress and pore pressure in coalbeds: A new model. Evaluation, (December):539–544. [3] Pan, Z. and Connell, L. D. (2012). Modelling permeability for coal reservoirs: A review of analytical models and testing data. International Journal of Coal Geology, 92:1–44. [4] Scott, M., Mazumder, S., and Jiang, J. (2012). Permeability increase in Bowen Basin coal as a result of matrix shrinkage during primary depletion. SPE International, SPE 158152.
[5] Pekot, J. L. and Reeves, S. R. (2002). Modeling coal matrix shrinkage and differential swelling with CO2 injection for enhanced coalbed methane recovery and carbon sequestration applications. Technical report, Advanced Resources International, Houston, Texas. [6] Oudinot, A., Koperna, G., Philip, Z., Liu, N., Heath, J., Wells, A., Young, G., and Wilson, T. (2011). CO2 injection performance in the Fruitland Coal Fairway, San Juan Basin: Results of a field pilot. SPE Journal, 16(4):864–879.
[7] Laubach, S. E., Marrett, R. A., Olson, J. E., and Scott, A. R. (1998). Characteristics and origins of coal cleat: A review. International Journal of Coal Geology, 35:175–207. [8] Mazumder, S., Karnik, A., and Wolf, K. H. (2006). Swelling of coal in response to CO2 sequestration for ECBM and its effect on fracture permeability. SPE Journal, 11(3):390–398. [9] Pan, Z. J. and Connell, L. D. (2007). A theoretical model for gas adsorptioninduced coal swelling. International Journal of Coal Geology, 69:243–252. [10] Reucroft, P. J. and Sethuraman, A. R. (1987). Effect of pressure on carbon dioxide induced coal swelling. Energy Fuels, 1:72–75. [11] Ceglarska-Stefanska, G. and Czaplinski, A. (1993). Correlation between sorption and dilatometric processes in hard coals. Fuel, 72:413–417. [12] Levine, J. R. (1996). Model study of the influence of matrix shrinkage on absolute permeability of coal bed reservoirs. Geological Society, London, Special Publications, 109:197–212. [13] Pini, R. (2009). Enhanced coal bed methane recovery finalized to carbon dioxide storage. PhD thesis, ETH Zurich. [14] Shi, J. Q. and Durucan, S. (2004). Drawdown induced changes in permeability of coalbeds: A new interpretation of the reservoir response to primary recovery. Transport in Porous Media, 56(1):1–16. [15] Cui, X., Bustin, R. M., and Chikatamarla, L. (2007). Adsorption-induced coal swelling and stress: Implications for methane production and acid gas sequestration into coal seams. Journal of Geophysical Research, 112(B10202). [16] Wu, Y., Liu, J., Elsworth, D., Chen, Z., Connell, L., and Pan, Z. (2010). Dual poroelastic response of a coal seam to CO2 injection. International Journal of Greenhouse Gas Control, 4(4):668–678. [17] Brochard, L., Vandamme, M., and Pellenq, R. J. -M. (2012). Poromechanics of microporous media. Journal of the Mechanics and Physics of Solids, 60(4):606–622. [18] Nikoosokhan, S., Vandamme, M., and Dangla, P. (2012). A poromechanical model for coal seams injected with carbon dioxide: from an isotherm of adsorption to a swelling of the reservoir. Oil & Gas Science and Technology Rev. IFP, Energies Nouvelles, 67(5):777–786.
Computational Modeling of Methane Hydrates at Multiple Scales Malgorzata Peszynska*, and Ralph Showalter† * Department of Mathematics Oregon State University, Corvallis, OR 97331 e-mail:
[email protected], web page: www.math.oregonstate.edu/~mpesz †email:
[email protected], web page: www.math.oregonstate.edu/~show ABSTRACT
In this talk we present our recent and ongoing results from our group on modelling methane hydrates (MH). MH are an ice-like substance containing molecules of methane CH4 trapped in a lattice of water molecules; they are present in large amounts along continental slopes and in permafrost regions, and they have been studied as potential environmental hazards, and as an emerging energy source. An exciting technological opportunity is that of an exchange of CO2 and CH4 molecules in hydrates, which can supply CH4 and sequester CO2. There are recent initiatives by DOE's National Energy Technology Laboratory (NETL), in collaboration with USGS and industry consortia, in gas hydrate drilling, research expeditions, and observatories, to evaluate methane hydrate as an energy resource. Pilot projects on production of methane from MH, most recently in April'13 in Japan, and at Ignik/Sikumi in Alaska, are emerging. Challenges in computational methods for methane hydrates involve handling multiple solid and fluid phases and components in nonisothermal conditions, and lack of general mathematical framework which helps to define and tune the most appropriate computational model. Various community [1,2] and industry (STOMP-MH, Tough Hydrate, HydrateResSim) simulators were constructed, but until recently there has been no mathematical or numerical analysis of the underlying problem and/or computational methods. In [3] we have framed the (simplified) methane hydrate system as an abstract evolution problem of structure similar to that of Stefan free boundary problem. We proved well-posedness by extending the existing theory to cover the case in which the problem involves a measurable family of graphs which we represent as subgradients; this leads to optimal regularity and numerical convergence. Our recent results in [4] improve those in [3] and we extend the analysis to a problem with significant advection, We also have worked out an analytical solution which is compared to the numerical solution. For a more general realistic model involving variable salinity and free gas the analysis is not yet feasible, but we use the general framework of nonlinear complementarity constraints (NCC) and semi-smooth Newton framework to implement a fully implicit scheme. Various scenarios on modelling short and long time scales are considered; these are relevant, respectively, to the observatories and energy production, and to basin modelling.
In the talk we focus on the computational modelling aspects of hydrates. We discuss the NCC solver framework and variants of time stepping. We also discuss how phase behaviour may depend on rock type [6], which creates a separate slew of challenges, especially if one allows the type to change following, e.g., preferential path/ fracture formation. While full flowgeomechanics model is not yet complete [5], we are considering time-lagged versions of coupling geomechanics with the pressure equation. Separate issue is the hydrate modelling at porescale, and we mention the underlying challenges [7-8] and our current modelling efforts on phase transitions at porescale [9].
REFERENCES [1] Liu, X. & and Flemings, P.: Dynamic multiphase model of hydrate formation in marine sediments. Journal of Geophysical Research, 112:B03101, 2008 [2] Peszynska, M., Torres, M., & Trehu, A.: Adaptive modeling of methane hydrates, International Conference on Computational Science, ICCS 2010 Procedia Computer Science Vol. 1 (2010), pp 709-717 [3] Gibson, N., Medina, P., Peszynska, M., & Showalter, R, Evolution of phase transitions in methane hydrate, J. Math. Anal. Appl., Volume 409, Issue 2 (2014), pp 816-833 [4] Peszynska, M., Showalter, R., Webster J., Advection of methane in the hydrate zone, manuscript to be submitted. [5] Peszynska, M., Showalter, R., Webster J., Biot system for methane hydrates, in preparation. [6] Daigle, H., Dugan, B., Capillary controls on methane hydrate distribution and fracturing in advective systems, Geochemistry Geophysics Geosystems (12) 2011, 1-18 [7] Peszynska, M. & Trykozko, A, Pore-Scale Simulations of Pore Clogging and Upscaling With Large Velocities, GAKUTO International Series, Mathematical Sciences and Applications, Vol. 36 (2013), 277-300 [8] M. Peszynska, A. Trykozko, Pore-to-Core Simulations of Flow with Large Velocities Using Continuum Models and Imaging Data, Computational Geosciences, Volume 17, Issue 4 (2013), Page 623-645, DOI: 10.1007/s10596-013-9344-4. [9] Peszynska, M. & Trykozko, A., Flow and phase change at porescale, in preparation
Phase Equilibrium of Fluids Confined in Porous Media from an Extension of the Generalized van der Waals Theory Leonardo Travalloni a, Marcelo Castier b, Frederico W. Tavares a,c
a Escola
de Química, Universidade Federal do Rio de Janeiro, CEP: 21949-900, RJ, Brazil
bChemical
Engineering Program, Texas A&M University at Qatar, Doha, P.O. Box 23874, Qatar
cPrograma
de Engenharia Química, COPPE, Universidade Federal do Rio de Janeiro, C.P.: 68502, CEP: 21941-972, RJ, Brazil ABSTRACT
Based on the generalized van der Waals theory [1, 2], a cubic equation of state (the van der Waals type equation) was extended to describe the behavior of pure fluids and mixtures confined in porous solids [3]. Each pore was assumed to be a cylinder with a continuous and homogeneous surface. Fluid molecules were assumed spherical, interacting with each other and with the wall of the pore through square-well potentials. Pairwise additivity was assumed for the attractive parts of all interaction potentials. The repulsive part of the equation of state for confined fluids was modeled based on literature data for the packing of hard spheres in cylinders. The effect of pore size on fluid properties was explicitly represented in the model, allowing its application to both confined and bulk fluids thus providing a consistent description of adsorption systems for all pore sizes. The resulting equation of state has two fitting parameters for each component of the fluid, which are related to the interaction between the fluid molecules and the pore walls. Calculations of pure fluid adsorption were carried out in order to analyze the sensitivity of the model to its fitting parameters and to pore size. It was found that the model is able to describe different types of adsorption isotherm [3] and critical point behavior for confined fluids [4]. The model correlated experimental data of pure fluid adsorption quite well and was then used to predict the adsorption of several binary mixtures and one ternary mixture with no additional fitting, with good results. The methodological framework presented here was extended to other widely used equations of state (Peng-Robinson EOS, Soave-Redlich-Kwong,
etc…) for modeling confined fluids [5]. The global phase stability test is executed to assess the need for phase additions. Results illustrate the potential of the model and of the multiphase equilibrium algorithm, by predicting different phase configurations under confinement. Each kind of pore may confine phases with very similar or very different densities. Furthermore, it is shown that the methodology of this work can predict the formation of transition regions like those of oil reservoirs.
Keywords: Adsorption, Porous media, Mathematical modeling, Statistical thermodynamics, State equation. REFERENCES [1] S.I. Sandler, Fluid Phase Equilibria 19 (1985) 233-257. [2] K.-H. Lee, M. Lombardo, S.I. Sandler, Fluid Phase Equilibria 21 (1985) 177-196. [3] L. Travalloni, M. Castier, F.W. Tavares, S.I. Sandler, Chemical Engineering Science (2010), doi: 10.1016/j.ces.2010.01.032. [4] L. Travalloni, M. Castier, F.W. Tavares, S.I. Sandler; J. Supercrit. Fluids 55, 455, (2010). [5] L. Travalloni, M. Castier, F.W. Tavares; Fluid Phase Equil. 362, 335, (2014).
A New Multiscale Computational Model for Flow and Transport in Shale Gas Reservoirs Tien Dung Le*, Marcio A. Murad*, Patricia A. Pereira* and Claude Boutin**, SIdarta Lima*, Eduardo Garcia*, Fernando Rochinha* *Laboratório Nacional de Computação Científica LNCC/MCT Av Getúlio Vargas 333, 25651–070 Petrópolis, RJ, Brazil Email
[email protected] [email protected] [email protected] **Ecole Nationale des Travaux Publics de l’Etat - ENTPE Rue Maurice Audin, 69518 Vaulx-en-Velin Cedex Email
[email protected] ABSTRACT The macroscopic behavior of gas flow and transport in multi-porosity shale gas reservoirs is rigorously derived within the framework of the reiterated homogenization procedure applied to the Thermodynamics of inhomogeneous gases in nanopores. At the finest nanoscale the Density Functional Theory is applied to construct general adsorption isotherms and local density profiles of pure methane which reflect both repulsive hard sphere effects and LennardJones attractive intermolecular interactions between fluid-fluid supplemented by a fluid-solid exterior potential. Such local description reproduces the monolayer surface adsorption ruled by the Langmuir isotherm in the asymptotic regime of large pore size distributions. The nanoscopic model is upscaled to the microscale where kerogen particles and nanopores are viewed as overlaying continua forming the organic aggregates at thermodynamic equilibrium with the free gas in the micropores. The resultant reaction/diffusion equation for pure gas movement in the aggregates is coupled with both Fickian diffusion of dissolved gas in water and free gas flow in the micropores along with the inorganic solid phase (clay, quartz, calcite) assumed impermeable. By postulating continuity of fugacity at the interface between free and dissolved gas in micropores and neglecting the water movement, we upscale the microscopic problem to the mesoscale, where both organic, inorganic solids and micropores are homogenized. The upscaling entails a new characteristic function which arises from the jumps in concentrations across the kerogen/micropore interface and leads to a new nonlinear pressure equation for gas hydrodynamics in the micropores including a new storage parameter strongly dependent on the total carbon content (TOC). When coupled with the nonlinear single phase gas flow in the hydraulic fractures the mesoscopic model leads to a new macroscopic triple porosity model with mass transfer functions between the different levels of porosity. Computational simulations illustrate the potential of the multiscale approach in numerically constructing accurate gas production curves in different regimes of gas flow.
