SPE 39714
`
`Probabilistic Reserves Assessment Using A Filtered Monte Carlo Method In A
`Fractured Limestone Reservoir
`L.R. Stoltz SPE, Fletcher Challenge Energy Taranaki, M.S. Jones SPE, Fletcher Challenge Energy Canada,
`A.W. Wadsley, Optimiser Consulting
`
`Copyright 1998, Society of Petroleum Engineers, Inc.
`
`This paper was prepared for presentation at the 1998 SPE Asia Pacific Conference on Integrated
`Modelling for Asset Management held in Kuala Lumpur, Malaysia, 23–24 March 1998.
`
`This paper was selected for presentation by an SPE Program Committee following review of
`information contained in an abstract submitted by the author(s). Contents of the paper, as
`presented, have not been reviewed by the Society of Petroleum Engineers and are subject to
`correction by the author(s). The material, as presented, does not necessarily reflect any position
`of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE
`meetings are subject to publication review by Editorial Committees of the Society of Petroleum
`Engineers. Electronic reproduction, distribution, or storage of any part of this paper for
`commercial purposes without the written consent of the Society of Petroleum Engineers is
`prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300
`words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment
`of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836,
`Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
`
`Abstract
`A new approach to the estimation of reserves in a fractured
`limestone reservoir is presented and verified with a lookback
`analysis over the past five years of production from the field.
`This approach uses a filtered Monte Carlo method to integrate
`independent reserves calculations based upon volumetric,
`material balance, well pressure survey analysis, and well decline
`estimates of oil in place and recovery. For the Waihapa-Ngaere
`field, two estimates of oil in place are available: a volumetric
`estimate obtained from mapped gross reservoir volume and
`formation parameters; and a material balance estimate obtained
`from pressure decline and production data. Independent
`estimates of oil recovery can be obtained from estimation of
`recovery factors based upon areal and vertical sweep in the
`fractured reservoir, and recovery obtained from extrapolation of
`well decline. The approach taken, that is to integrate all of the
`available information and only accept parameter sets which are
`consistent, led to an estimate of reserves and production
`potential from the field which has proved remarkably accurate as
`a predictor of field performance and recovery over the past five
`years.
`
`Background
`The Waihapa Field lies at the southern end of the Tarata Thrust
`zone, within the eastern edge of the Taranaki Basin, New
`
`Zealand (Figure 1). The field was discovered in February 1988
`with flows of up to 3124 bopd and gas up to 3.2 MMscf/d from
`the fractured Tikorangi Limestone during drillstem testing of the
`Waihapa-1B well. The Toko-1 well, to the north of the Ngaere
`area of the field, was the first well to be drilled in the area in
`November 1978 but a test of the top section of the Tikorangi
`formation was inconclusive. Following the success of the
`Waihapa-1B well, Waihapa-2, 4, 5, 6, 6A were drilled in the
`structure from the period 1988-1989 with all but Waihapa-6
`(which was tight) being successful. Northern extension wells
`Ngaere-1, -2 and –3 were successfully drilled from March 1993
`through February 1994.
`
`Geological Setting. The Waihapa structure is the southern
`termination of a west-directed thrust sheet which formed as a
`result of movement along the NS-trending Taranaki Fault. At top
`Tikorangi level the structure develops from a simple low-
`amplitude, symmetrical fold in the south to an overthrust
`structure in the north. A major tear fault, with a westerly
`displacement of approximately 2 km, lies between the Ngaere-2
`and Ngaere-3 wells. A schematic top depth map showing well
`locations and the major faults, as seen on seismic, is shown in
`Figure 2.
`The Tikorangi Formation is an interbedded foraminiferal
`limestone, siltstone and mudstone sequence averaging 230m
`thickness in the Waihapa area. Diagenetic features in the
`limestone matrix
`include extensive pressure solution and
`concomitant calcite cementation reducing the original primary
`porosity to the typically observed 5 to 7%. The matrix, although
`of reasonable measured porosity, is of low permeability (< 0.01
`mD), is water saturated and is currently postulated to make no
`contribution either to oil production or to pressure support to the
`field. The significant secondary porosity development for the oil
`accumulation is from post-burial fracturing of the formation.
`Fracturing is common over the entire thickness of the Tikorangi
`Formation and extensive over a wide area.
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`Based on a field wide correlation, four units have been
`defined within the Tikorangi Formation. Unit A, the uppermost,
`appears as a relatively uniform interval with a blocky GR and
`sonic response, both indicating massive moderately clean
`carbonate. Unit B has a more irregular log response, indicative
`of an interbedded lithology, most likely limestone and shale.
`Unit C, directly beneath this, has a blocky appearance indicating
`relatively clean carbonate. This generally grades to a more shaly
`lithology towards the top of unit D. The lowermost unit, unit D,
`has a more uniform character and appears as a more silty/shaly
`lithology.
`
`Introduction
`No reservoir parameter in the Waihapa field is known with any
`confidence: fracture porosity and areal distribution is not known;
`fracture compressibility can not be measured directly; the
`reservoir closure has not been mapped or the nature of the
`closure
`identified;
`the
`initial oil-water contact was not
`penetrated; and the reservoir top structure is uncertain outside of
`well control because of large uncertainty in seismic velocity
`trends in the field. Thus it is extremely difficult to obtain reliable
`estimates of oil initially in place (OIIP) and reserves for the
`field. However, a large body of data has been gathered over
`time, including well and average reservoir pressures, oil and
`water production trends, interference and transient pressure
`analyses, core analyses, interpretation of 3-D seismic, and results
`of specialist studies. Much of this data appeared only marginally
`consistent. For example, the CO2 concentration for the produced
`gas was 7% in the Waihapa-1B well and 12% in the Waihapa-2
`well implying different oil compositions and possible reservoir
`compartmentalisation. Notwithstanding this, these are the closest
`wells
`in
`the
`field
`(600m apart) and are
`in pressure
`communication (as unequivocally shown by interference test
`analysis).
`The approach taken was to integrate all of the quantitative
`data observations
`into a single Monte Carlo estimation
`procedure for oil in place and reserves. For the field, two
`independent estimates of oil in place are available: a volumetric
`estimate obtained from mapped gross reservoir volume and
`formation parameters; and a material balance estimate obtained
`from pressure decline and production data. Independent
`estimates of oil recovery can be obtained from recovery factors
`based upon areal and vertical sweep in the fractured reservoir
`and, and recovery obtained from extrapolation of well decline.
`Each reservoir parameter is estimated independently and only
`those sets of parameters which lead to consistent estimates of
`OIIP and recovery are accepted. This methodology filters out the
`inconsistent sets of reservoir parameters and is referred to in this
`paper as the filtered Monte Carlo method.
`In 1989, just after the start of field production, it was
`uncertain as to the nature of the fractured reservoir and whether
`
`or not the matrix was contributing to flow. At this time the
`filtered Monte Carlo method was used to differentiate between
`alternative reservoir models. Following further drilling and
`production a revised analysis was undertaken in 1993 which has
`proven to be a robust estimator of reserves to the present time.
`
`Fractured Reservoir Models
`After Nelson1 we can distinguish four types of fractured
`reservoir model: Type 1, fractures provide
`the essential
`(hydrocarbon) reservoir porosity and permeability; Type 2,
`fractures provide the essential reservoir permeability; Type 3,
`fractures assist permeability in an already producible reservoir;
`Type 4, fractures provide no additional porosity or permeability
`but create significant reservoir anisotropy.
`
`Classification of the Waihapa Tikorangi Formation. The
`Tikorangi formation
`is a Type 1 reservoir under
`this
`classification. That is, the fracture network provides the whole of
`the hydrocarbon storage. This interpretation is based upon core
`observations and wire-line log interpretation: very low matrix
`permeabilities were measured in core plugs (<0.01mD); oil was
`not observed in solvent extracted core plugs; and hydrocarbon
`saturations were not interpreted in logs.
`
`Matrix Fracture Communication. Identification of the degree
`of matrix fracture communication in the reservoir is important
`notwithstanding that the potential for oil storage in the matrix is
`small. Even at the low permeabilities measured in the Tikorangi
`core plugs, there is potential for water movement from the matrix
`into the fractures because of the large surface area available to
`flow. At permeabilities of <0.001mD water influx from the
`matrix can still make a substantial contribution to material
`balance and pressure support.
`Both cemented and slickenside fractures have been observed
`in Waihapa cores. Calcite cementation provides an impermeable
`barrier between the fracture channels and matrix porosity, whilst
`slickensiding gives rise to a zone of compacted and crushed
`grains along the fracture planes which can significantly reduce
`permeability and hence matrix-fracture communication. It is
`consistent with these observations to propose that the Waihapa
`Tikorangi formation is a non-porous fractured reservoir with no
`fracture-matrix interaction.
`In 1989, when the first filtered estimates of OIIP were made
`for the Waihapa Field, pressure surveys were interpreted as
`classic dual porosity systems. Thus, at that time, the porous
`fractured reservoir model was considered more likely in which
`the matrix can provide pressure support (albeit water only) to the
`fractures. Subsequently, in November 1990, reanalysis of the
`transient pressure test trends showed that a conventional, single
`porosity model (fluid storage and permeability assigned solely to
`the fracture system) with boundary gave better agreement
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`between observed and calculated pressure trends than did the
`dual porosity model. Notwithstanding this the analysis presented
`below also includes a term for fracture-matrix interaction.
`
`Dual Fracture Model. The dual fracture model consists of a
`primary
`fracture network of
`large open
`fractures
`in
`communication with a secondary fracture system of smaller, less
`extensive micro-fractures or fissures. Large extensional fractures
`have been observed with fracture widths up to 16mm that could
`constitute the primary fracture system. There are numerous
`conjugate shear fractures on a smaller scale. Shear fractures (and
`their conjugates) may exist on all scales, from fractured grains in
`the matrix to reservoir wide fractures across
`the whole
`formation. These fractures may be fold related2, and can be
`associated with faulting. The relationship of fractures to faults
`exists on all scales: Friedman3 used
`the orientation of
`microscopic fractures from oriented cores in the Saticoy Field to
`determine the orientation and dip of a nearby fault. In a Triassic
`limestone, a frequency analysis4 of widths of open fractures was
`interpreted to arise from several sets of fracture distributions
`superimposed upon each other: the first was due to initial
`tectonic stresses; the second to weathering and exfoliation, and
`other sets to karstic and strongly faulted zones.
`In the Waihapa Tikorangi no evidence exists for sub-aerial
`exposure (that is, weathering) and detailed core analysis failed to
`find evidence of micro-fractures or fissures. However, there is
`evidence of different fracture regimes in the field which could
`possibly lead to a dual fracture flow regime. There is a dominant
`NE to ENE striking trend with an apparent but less dominant N
`to NW striking trend. The NE-ENE striking sets are generally
`near vertical and the N-NW sets have shallow to moderate dips
`(20 to 50o). Many fractures seen in Waihapa-2 and Ngaere-2 are
`highly shattered with pieces of host rock being incorporated in
`the mineralising calcite. In the Ngaere-2 well these are northerly
`striking which is consistent with the trend of reverse faulting
`observed in the seismic interpretation.
`
`Complex Porosity Model. The complex reservoir model is
`similar to the dual fracture model with the additional assumption
`that both fracture sets are in communication with a porous and
`permeable matrix.
`
`Dual Porosity Model. The dual porosity reservoir model
`assumes that there is a single dominant fracture system in
`communication with a porous and permeable matrix.
`
`Non-Porous Fracture Model. The non-porous fracture model,
`or single porosity fracture model, is equivalent to a conventional
`single porosity model in which the fracture system provides all
`of the reservoir storage and permeability.
`
`Fracture Continuity and Permeability. Calculations5 of
`effective fracture permeability for a 10mm opening based upon
`(laminar) Poiseiulle flow between the fracture walls gave values
`ranging from 1000mD for 80m spacing between fractures to
`greater than 80000mD for a fracture spacing of 1m. These
`calculated permeabilities are significantly higher than the
`permeability interpreted from pressure test analyses of between
`27mD and 158mD. The most likely explanation for this
`discrepancy between observed permeability and theoretical
`calculation is that the large extensional fractures observed in
`core are not continuous or connected over large distances. They
`may be en echelon with fluid flow from fracture to fracture being
`through lower permeability matrix or, more likely, through a
`network of smaller fissures. Alternatively,
`the degree of
`cementation in these fractures may vary, with some sections
`being almost completed cemented with paths for flow being
`either extremely tortuous or disconnected.
`
`Components of Material Balance and Volumetrics
`The reservoir model used for the material balance calculations is
`based upon a Type 1, complex porosity, fractured reservoir with
`gas cap and aquifer, no hydrocarbon saturation in the matrix, and
`constant bubble-point pressure in the oil column,
`The reservoir is naturally zoned into gas, oil and water zones
`with boundaries at the initial gas-oil and water-oil contacts,
`respectively. Subzones also develop during production of the
`reservoir: in particular, a gassing zone6 develops below the
`original gas-oil contact (OGOC) as the reservoir pressure drops.
`Initially, the pressure at the original gas-oil contact equals the
`bubble-point pressure, with an increase in pressure with depth
`due to the oil density gradient down to the original oil-water
`contact (OOWC). As the average pressure in the reservoir
`declines, both the gas-cap and the water-leg will expand (the
`latter due also to aquifer influx) to new contact levels, being the
`current gas-oil contact (GOC) and the current oil-water contact
`(OWC). Because there are assumed to be no capillary forces
`present in the fracture networks, there will be no water-transition
`zone above the OWC and no residual oil saturation in the gas-
`invaded and water-invaded zones behind the new contacts.
`However, there could be oil saturations trapped in dead-end
`fractures.
`As the reservoir pressure declines, the pressure at the GOC
`will not equal the initial bubble-point pressure of the oil, but will
`be in equilibrium with oil at a lower bubble-point. Because the
`oil column was everywhere at the same initial bubble-point (see
`PVT discussion below), we can define a current bubble-point
`level (BPL) as that depth where the oil pressure equals the initial
`bubble-point pressure. The zone between the current bubble-
`point level and the current gas-oil contact is called the gassing
`zone. In this zone, the oil pressure is everywhere below the
`initial bubble-point pressure and gas is being liberated from
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`solution. This gas percolates vertically upwards to form either
`secondary gas caps or merge with the expanded original gas cap
`of the reservoir.
`The following zones can be identified: original gas-cap, gas
`invaded zone, gassing zone (saturated oil), under-saturated oil
`column, water-invaded zone, and original water-leg.
`
`Volume Contributions to Reservoir Voidage. Oil production for
`a depleting reservoir is a result of volume changes for all of the
`communicating components of the reservoir system:
`
`Shrinkage of total reservoir volume
`
`(1+m+w)cfϕf
`primary fracture volume
`secondary fracture column (1+m+w)cdϕd
`(1+m+w)cmϕm
`matrix volume
`
`Expansion of water in matrix
`
`(1+m)ϕmSwcw
`
`Expansion of oil in undersaturated zone
`
`(1-s)( ϕm(1-Sw)+ϕf+ϕd)co
`
`Shrinkage of oil in gassing zone
`
`s (ϕm(1-Sw)+ϕf+ϕd) (Bob/Boi-1)
`
`Expansion of gas cap
`
`m(ϕm(1-Sw)+ϕf+ϕd)(Bg/Bgi-1)
`
`Liberation of gas from gassing zone
`
`s(ϕm(1-Sw)+ϕf+ϕd) Rsbp(Bg/Bgi)
`
`Expansion of water-leg
`
`w(ϕm+ϕf+ϕd)cw
`
`Expansion of aquifer
`
`BwWe
`
`Material Balance Estimate of Oil in Place. At the start of
`production the gassing zone has not formed, therefore s=0; and
`the aquifer has not been activated, therefore We=0. Thus the
`general material balance equation, at the start of production, is:
`
`Nmat = (dN/dP)/( { (1+m+w)(cfϕf+cdϕd+cmϕm)
`+(1+m)ϕmSwcw
`+(ϕm(1-Sw)+ϕf+ϕd)co
`+m(ϕm(1-Sw)+ϕf+ϕd)cg
`+w(ϕm+ϕf+ϕd)cw }/{ ϕm(1-Sw)+ϕf+ϕd } )
`
`The decline rate, dN/dP, is defined as the cumulative
`production per unit pressure decline at the start of production.
`Thus it is unaffected by pressure support arising from creation of
`the gassing zone or from aquifer influx.
`The components of material balance included in this complex
`porosity reservoir model are: shrinkage of total fracture volume,
`expansion of oil in primary fractures, expansion of oil in
`secondary fractures, expansion of water in matrix, expansion of
`water below oil-water contact, and expansion of gascap. The
`components of material balance excluded from the model are:
`shrinkage of oil in gassing zone (0 @ t=0), gas liberated in
`gassing zone (0 @ t=0), aquifer influx (0 @ t=0), expansion of
`oil in matrix (0 in this model, Sw=1), expansion of gas in matrix
`(0 in this model).
`
`Volumetric Estimate of Oil in Place. Initial oil in place can be
`related to gross rock volume of the oil column by the equation:
`
`Nvol = fopenfmap(ϕm(1-Sw)+ϕf+ϕd)(V(zowc)-V(zgoc))/Boi
`
`Calculation of Oil in Place and Reserves
`Two estimates of oil in place are calculated during the Monte
`Carlo simulation. These are the volumetric estimate, Nvol,
`obtained from the mapped gross reservoir volume and formation
`parameters, and the material balance estimate, Nmat. In order to
`obtain a consistent estimate of oil in place, both the volumetric
`and material balance estimates were rejected if they were not
`sufficiently close:
`
`Nvol and Nmat rejected if |1-Nmat/Nvol| > ε
`
`where ε is fractional tolerance, set to 0.1 in this analysis.
`
`Recovery. Recovery can be estimated from a volumetric sweep
`efficiency and oil remaining in the reservoir between the
`abandonment gas-oil contact, zagoc, and the abandonment oil-
`water contact, zaowc. Total remaining oil in the reservoir at
`abandonment is
`
`Na = fopenfmap{ (ϕm(1-Sw)+ϕf+ϕd)(V(zaowc)-V(zagoc))
` + (1-EaEv)( V(zagoc)-V(zogoc) + V(zoowc)-V(zaowc) ) }/Boa
`
`Volumetric recovery is defined by Rvol = 1-Na/Nvol.
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`RESERVES IDENTIFICATION IN THE FRACTURED LIMESTONE, WAIHAPA FIELD, NEW ZEALAND
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`
`A further constraint is applied to the recovery obtained from
`the oil in place estimate by application of the recovery
`efficiency. The volumetric recovery is rejected if it is not
`sufficiently close to the recovery estimate, Rwell, obtained from
`well decline curve analysis:
`
`Rvol and Rwell rejected if |1-Rwell/Rvol| > ε.
`
`This criterion also ensures that the volumetric estimate is
`realistic and can be tied to a proper well development sequence.
`In particular, extremely low or high estimates will be rejected if
`they cannot be realised by at least one well sequence.
`
`Storativity. Consistency can also be realised with respect to well-
`test analysis in the case of dual porosity or dual fracture
`reservoir models. The ratio of primary fracture storativity to
`volumetric system storativity, ωvol, is defined by:
`
`ωvol = sf /stot
`
`where
`
`sf = ϕf(cf+co),
`stot = ϕf(cf+co)+ϕd(cd+co)+ϕm(cm+Swcw+(1-Sw)co).
`
`The Monte Carlo trial is rejected if the volumetric storativity
`ratio is not consistent with the storativity ratio, ωpre, calculated
`from pressure test analysis:
`
`ωvol and ωpre rejected if |1-ωvol/ωpre| > ε.
`
`Based on the analysis of interference tests, an independent
`constraint can be also imposed on primary fracture storativity
`calculated volumetrically, sf, and from interference test analysis,
`spre:
`
`sf and spre rejected if |1-sf /spre| > ε.
`
`Further, fracture storativity is the product of fracture
`compressibility and porosity. Thus a further constraint can be
`applied to the independently sampled storativity, compressibility
`and porosity values:
`
`ϕf, cf and sf rejected if |1-ϕfcf/sf| > ε.
`
`Reservoir Parameters
`No reservoir parameter is known with any confidence in the
`Waihapa Field. The following discussion highlights
`the
`difficulties encountered in defining or measuring these values
`and, by implication, explains the necessity of using the filtered
`Monte Carlo method for reserves estimation.
`
`Areal Closure. Neither the areal extent of fractures nor the
`nature of the reservoir closure to the north of the field is known
`with any confidence. A separate pressure regime is known to
`exist to the north and updip of the Toko-1 and Toko-2 wells. The
`Waihapa reservoir closure could be due to faulting or lack of
`fracturing but no feature has been observed which clearly defines
`the reservoir extent. In the analysis, separate depth volume tables
`were derived for both the Waihapa/Ngaere area to the Ngaere-3
`well, VWN ,and for the undeveloped Toko area to the north of the
`field, VTK. A combined depth volume table for the whole field
`was defined by
`
`V(z) = VWN(z)+θVVTK(z)
`
`where θV ⊂ U(0,1) was a parameter selected from a uniform
`distribution between 0 and 1.
`
`Mapping Uncertainty. Because of the significant velocity
`gradients in the field, depth conversion of seismic time maps
`outside of well control is uncertain but is likely to be
`systematically in error in the flanks of the field. This uncertainty
`was expressed by multiplying the total depth volume relation for
`the field by a parameter, fmap, where
`
`fmap ⊂ Cum(0.6,0.7,0.8,1.0,1.2,1.3,1.4).
`
`(Cum specifies a standard cumulative probability distribution
`defined in Appendix I.)
`
`Average Fracture Porosity. Effective fracture porosity in the
`area of open fractures is not known. The total of all analysed
`core from the Waihapa well has been calculated to average
`0.13% porosity. However, this value excludes the absence of
`open fractures in the Waihapa-6 well (porosity=0%) and the
`effective linear porosity of 1% observed during the drilling of
`Waihapa-6a and Toko-1. (During the drilling of both of these
`wells the bit was observed to fall by 2m ~ porosity=1% in 200m
`of Tikorangi limestone). Fracture aperture imaging (FMS) in the
`borehole is generally limited to calculating apertures of less than
`1mm in size. The fractures contributing the most porosity in the
`Waihapa wells are much larger than this with oil stained open
`fractures of greater than 16mm being observed in core.
`Generally, core derived fracture porosity is dominated by
`relatively few fractures. In Waihapa-2, four fractures have an
`individual porosity contribution greater than 0.01% porosity, but
`these four fractures account for around 68% of the total porosity.
`The largest frequency of occurrence is the size class 0.001–
`0.0001% porosity, but these fractures contribute less than 5% to
`the total porosity. Core porosity ranged from 0% to 0.198%;
`FMS porosity ranged from 0.12% to 0.56%; drilling porosity
`ranges from 0% to 1% based upon drilling breaks. Various
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`calculations based upon fracture density, orientation and well
`sampling ranged from 0.6% to 0.75%. There is extremely low
`confidence in any of these porosity estimates. Fracture porosity,
`ϕf, and secondary fracture porosity, ϕd, used in the Monte Carlo
`analysis were defined by
`
`ϕf ,ϕd⊂ Cum( 0,0.0005,0.0015,0.005,0.0085,0.0095,0.01).
`
`Extent of Open Fractures. Various fracture models have been
`proposed to define the extent of the open fractures both areally
`and with respect to the layering of the limestone. None of these
`models lead to quantitative predictions. Problems arise using
`curvature models because of the significant changes in curvature
`at all points in the formation during thrust development, and lack
`of well-defined time-depth conversion on the flanks of the
`structure. Although there is some evidence that fracturing in the
`limestone has a stratigraphic control, recent determination of
`formation storativity based upon interference test analysis (which
`calculates cϕh) and Earth-Tide analysis7 (which calculates cϕ)
`shows that all of the Tikorangi is contributing to formation
`storativity and hence any stratigraphic control on effective
`fracture porosity is weak. Of the twelve wells drilled and tested
`in the Waihapa Tikorangi, nine have been productive (>2000
`bpd), one has been of
`low productivity although
`in
`communication with the rest of the field, one has been tight, and
`one gave an inconclusive production test although losses were
`noted during drilling. The areal extent of open fractures, fopen,
`used in the analysis was defined by
`
`fopen ⊂ Cum(0.5,0.55,0.7,0.85,0.9,0.95.1).
`
`Fracture Storativity. A major uncertainty in the material balance
`estimate of oil in place is fracture storativity. Numerous
`interference tests have been completed with storativities, based
`upon the full Tikorangi interval contributing to flow from
`0.23x10-6 to 0.75x10-6 psi-1. These calculated storativities are
`assumed to apply to the fracture system only (that is, the primary
`fracture system for the single porosity and dual porosity model,
`and the primary and secondary fracture systems for the complex
`porosity and dual fracture systems). A difficulty in applying the
`interference test data, which was obtained assuming a single
`porosity system in the analysis, is that it may not apply to the
`fracture storativity concept applied in the material balance. It is
`not universally agreed as to whether the interpreted storativity
`applies to just the fracture system, or to both the fracture and
`matrix systems combined. This difficulty in interpretation is not
`a problem for the 1993 analysis which assumed that the reservoir
`consists of a single porosity system with only the primary
`fracture system contributing to flow.
`Direct rock stress measurements were obtained from core
`data for two plugs which gave storativities of 0.277x10-6 and
`
`0.081x10-6 psi-1 for plugs with measured porosities of 0.77% and
`0.25%. However, it is uncertain as to the relevance of these
`measurements as the plugs will have undergone stress relief
`during
`coring
`and mechanical
`estimates of
`fracture
`compressibility are difficult to interpret unambiguously. The
`storativities used in the Monte Carlo analysis were defined by
`
`sf ⊂ Cum( 0.02,0.05,0.10,0.27,0.35, 0.40,0.75)x10-6.
`
`Fracture Compressibility. Fracture compressibility can be
`calculated from published correlations, notably that of Jones8
`and Reiss5. Jones’s correlation gave a value of 100x10-6 psi-1 for
`an initial Waihapa reservoir pressure of 4257 psia and gross
`overburden pressure of 8857 psia. The method of Reiss gave
`values in the range 7x10-6 to 70x10-6 psi-1. The difference in
`compressibility estimates arises from different assumptions as to
`the compressibility of the matrix-matrix interaction at the
`fracture planes. If these are mainly grain supported as in the case
`of
`slickensided
`fractures,
`then
`the
`effective
`surface
`compressibility can be very large (due to the elastic compression
`of the surface asperities which are bearing a large load over a
`small area). In the case of vuggy or calcite cement supported
`fractures, the compressibility will tend to that of the country rock
`or cement, leading to low values. Fracture compressibility was
`measured in two core plug samples (the same samples for which
`storativity was calculated) with values of 32.4x10-6 and 35.9x10-
`6 psi-1. Both these samples were 50% cemented open fractures.
`The compressibilities used in the Monte Carlo analysis were
`defined by
`
`ϕf, ϕd ⊂ Cum(0,0.05,0.15,0.50,0.85,0.95,1.0)x10-6.
`
`Oil-Water Contract. None of the Waihapa wells penetrated an
`oil-water contact (OWC). The lowest known oil in the field was
`produced from fractures at 2838m TVSS in the Waihapa-2 well.
`However, in October 1989, water production (at a water-cut of
`40%) was observed from an interval 2751m to 2773m TVSS in
`the nearby Waihapa-5 well at the south of the field. A spinner
`survey showed that the water was being produced from the lower
`part of this interval. Coning analysis of multi-rate production
`tests, using both the method of Aguilera and Acevedo9 (which
`assumed flow in a single fracture plane) and an analysis based
`upon equations of Dake10 (which assumes segregated flow only)
`gave an OWC at 2848m. Recently, an analysis of pressure
`changes in the Ahuroa Gas Field, which is completed in the
`Tariki sandstone, indicated that a breach of the reservoir has
`occurred and that it is in communication with the Tikorangi
`limestone. The Ahuroa field is to the north of the Waihapa Field
`in
`the overthrust, with
`the Tariki
`sandstone being
`stratigraphically some 400m below the Tikorangi limestone.
`Tikorangi-Tariki juxtaposition occurs at the main tear fault
`
`6 of 13
`
`Ex. 2041
`IPR2016-00597
`
`

`
`SPE 39714
`
`RESERVES IDENTIFICATION IN THE FRACTURED LIMESTONE, WAIHAPA FIELD, NEW ZEALAND
`
`7
`
`between the Ngaere-2 and Ngaere-3 wells. If these fields are in
`communication or in the same pressure regime, then a contact at
`2835m TVSS can be established from the intersection of the
`water gradient in the Ahuroa field with the oil gradient in the
`Waihapa Field. This contact is consistent with that obtained from
`the coning analysis for the Waihapa-5 well. However, the nearby
`Hu Road well in the Tikorangi formation drilled to the south of
`the Waihapa field, which encountered water, gives an OWC at
`3090m TVSS via extrapolation of gradients. In the Toko-1 well
`to the north of the field, a kick occurred at 2891m TVSS and oil
`was reported in the pits. Provided the oil came from the bottom
`of the hole, this supports an oil down to of 2891m TVSS with an
`OWC greater than this. In the Monte Carlo analysis, the oil-
`water contact for the field was sampled as
`
`zowc ⊂ Cum(2780,2800,2840,2880,2890,2920,3090).
`
`Gas-Oil Contact. No gas-oil contact (GOC) was intersected by
`any well. Highest known oil was observed in Waihapa-4 at
`2579m TVSS. A sub-surface oil sample taken in Waihapa-1B
`from a producing interval 2679m to 2736m TVSS and sampled
`at 2677m TVSS had a bubble point pressure, when measured in
`the laboratory, of 3971 psia. This is some 285 psi below the
`initial reservoir pressure at 2700m TVSS. Based on an oil
`gradient of 0.9 psi/m this gives an equilibrium gas-oil contact at
`2443m TVSS, but an error of just 50 scf/bbl in recombination
`GOR leads to an error of 125m in GOC depth. Initial GOR was
`1100 scf/bbl which remained constant until the average field
`pressure went through the bubble point during 1994. In the
`Monte Carlo analysis the gas-oil contact was defined by
`
`zgoc ⊂ Cum(2280,2300,2380,2450,2500,2580,2600)
`
`Initial Pressure Decline. The initial pressure decline as a
`function of cumulative production gives the rate of oil in place
`change with pressure, dN/dP. This can be derived by
`extrapolating
`the slope of
`the
`initial pressure-cumulative
`production decline to time, t=0.
`a
`provides
`a