Breaking of a Paradigm: Geology Can Provide 3D Complex Probability Fields for Stochastic Facies Modelling

Stationarity of the random function is the key property of stochastic models to the extent that wrong hypotheses could lead to very unrealistic reservoir modeling for flow simulations. When non stationarity is suspected at the scale of the domain to be modeled, geologists usually propose either geological drift or seismic attributes to constrain stochastic models. However, in both cases, confidence in the soft data is limited by the rough aspect of the trends from geological input, the scale problem, and the quality of correlations between the random function and the variables from seismic data. This paper presents an original approach for building complex 3D prior probability fields of geological facies. It constitutes a very challenging way of integrating two major advances in geosciences in recent years: geostatistics and sequence stratigraphy. From facies descriptions on cores and logs, palaeobathymetry curves of deposits are constructed for each well. Logs of the accommodation potential (increment of space available for sediment accumulation) are then produced from those curves and deposit thicknesses in the wells. A Principal Components Analysis of data in all wells makes it possible to separate the signal into two components: a common factor which represents the tectono-eustatic activity at field scale (easily extrapolated), and residuals which correspond to local variations in subsidence. 3D grids of accommodation potential and palaeobathymetry can then be modeled, with respect to the time intervals within each layer. Geological inversion is therefore possible and leads to the proposal of a complex 3D prior probability field for facies modeling, with different organizations in both the transgressive and the prograding parts of the sequence. When constrained by such trends, stochastic modeling (object based or SIS) can render very realistic images of reservoir heterogeneity. This method was applied successfully in carbonate and mixed (silici-clastic and carbonate) platform reservoirs, in which properties are highly variable and non stationary. Introduction The recent development of stochastic simulation of reservoir heterogeneity was conducted in a balanced way between the two persistent and yet opposing concerns: • the quest for objectivity, that has led to abuses in principles such as parsimony, indifference and moreover maximum entropy –any model should introduce minimum artifacts of its own– ; • the quest for reality, motivated by the needs of getting geologically realistic 3D distribution of sedimentological, and therefore petrophysical, features. The quest for objectivity leads to favoring hard data – usually well data in reservoir modeling– whereas the quest for reality leads to integrating additional information available on the spatial distribution, through concepts or soft data. The realistic or non realistic aspect of geological images generated by stochastic simulations is a consequence of two stochastic model input parameters, stationarity (explicit parameter) and the constancy of the sedimentation rate (implicit parameter): • Stationarity: it has been demonstrated as a key parameter on both the evaluation of Original Hydrocarbons In Place and flow simulation results . For a given random function (RF), stationarity can be an acceptable hypothesis at a given scale, but unacceptable at other scales. Equally, this hypothesis can be valid for some types of reservoirs, but could be impossible to apply for other types. Usually, due to the low density of hard data in the oil industry, stationarity is a hypothesis which is not tested. It is therefore a choice, a decision, which has a major effect on the results. When modeling geological facies –a categorical RF– using sequential simulation, the local conditional SPE 56652 Breaking of a Paradigm: Geology Can Provide 3D Complex Probability Fields for Stochastic Facies Modelling Gerard J. Massonnat, SPE, Elf Exploration Production 2 GERARD J. MASSONNAT SPE 56652 probability is calculated using the conditioning data (original and previously simulated), the prior probability and variograms. When the RF is stationary, the prior probability is constant: in that case it corresponds to the average of the facies proportions encountered in the wells. If the stationarity hypothesis is refuted, additional information, generally of geological or seismic origin, must be input. Geological knowledge at basin scale or even at reservoir scale –if the well information is considered good–can be added through external drift. Due to the uncertainty which generally exists around the sedimentary model, this external drift is usually highly smoothed, as is consequently the evolution of the prior probability. Other methods can be used to input non stationarity in the stochastic simulation. However, all such methods are based on prior knowledge usually obtained from an interpretation, and therefore of level n+1 with respect to the information contained in the hard data. Another, now conventional, method of building non stationary reservoir models is to use seismic information. Seismic information has the incomparable advantage of being present over the entire 3D field. Co-simulation techniques exist, making it possible to respect the hard data, the global statistics, and the covariance between the seismic variable and the RF being modeled. However, use of seismic attributes during co–simulation of facies can generate a certain number of problems related to: the resolution difference between the variable being simulated and the seismic information, the type of variable (a seismic attribute is a continuous RF, a geological facies is a categorical RF) and the level of correlation between the RF being simulated and the seismic attribute. In all cases, non stationary simulation of geological facies for a reservoir model building appears to be a delicate process: external drifts are over–smoothed and little documented, seismic variables must be used with caution, .... The ideal solution would be to create a prior probability field in which geological information would be used more advantageously than it is now, so that the local conditioning probability could integrate most of the potentially available geological information. Since the development of sequence stratigraphy , sedimentary concepts have largely evolved and have acquired a greater predictive nature. This paper discusses how sedimentological advances can be used in non-stationary stochastic facies modeling while defining a new method constrained by sequence stratigraphy. This will finally break the paradigm saying that "Geology cannot provide quantitative trends". • The constancy of the sedimentation rate: when a reservoir is layered in order to build a stochastic model, there are 2 possible main cases: either the reservoir is considered as a "sugar box" (i.e. thickness is divided by the same number of layers everywhere in the model), or as a stratigraphic grid (with onlap or downlap). In both cases, and for a given location, the sedimentation rate is implicitly considered as homogenous as far as the layers are of the same thickness all along the vertical axis. When a prior facies proportion is computed from well data, proportions are computed for each layer as if it corresponded to a homogenous time interval. If this prior proportion exhibits vertical drift, then non stationarity will be considered as a very significant input parameter for the stochastic model. However, once again sequence stratigraphy has shown that this principle is erroneous, a time interval can in fact be represented either by a deposit or by a surface. Through pertinent use of sequence stratigraphy during well analysis, this paper also proposes a method of layering based on time, which would make it possible to calculate a much more realistic prior probability. What can we learn from sequence stratigraphy? Since its advent in the late 70's, this stratigraphic theory adapted to the seismic scale –seismic stratigraphy– has evolved in major ways, and is now widely a applied concept at any scale –sequence stratigraphy–in hydrocarbon exploration and reservoir studies. Its application at reservoir scale makes it possible to discern the following items: Accommodation and accommodation potential Accommodation is the total available space that can accommodate a sedimentary deposit. In marine domains, this includes a volume defined between sea level and the substratum at the beginning of the period of sedimentation (Fig. 1). Accommodation must not be confused with palaeobathymetry, which is the free space for sedimentation between sea level and the top of previously deposited sediments. The accommodation potential is a result of regional eustatic and local tectonic (subsidence or uplift) components. The space available for sedimentary accumulations, termed accommodation potential, varies with time. This parameter represents the sum of eustatic sea level variation and subsidence for given time In the stratigraphic record, the accommodation potential (per time interval) is best approximated by the sum of the ∆ palaeobathymetry between the bottom and top of interval, and the thickness of the deposits. SPE BREAKING OF A PARADIGM: GEOLOGY CAN PROVIDE 3D COMPLEX PROBABILITY FIELDS FOR STOCHASTIC FACIES MODELLING 3 Fig.1 — Accomodation as a result of eustatic, and regional / local tectonic subsidence components Fig.2 — Genetic stratigraphy as a tool for prediction of lateral evolution of facies (from Homewood) 4 GERARD J. MASSONNAT SPE 56652 Stratigraphic surfaces and system tracts Using seismic observations, an Exxon team has proposed a geometric organization –type of deposits on passive continental margins. By integrating the sedimentation rate and the accommodation potential, a complex evolution of the bathymetric deposits can therefore be produced for a given point. Remarkable surfaces are defined with respect to the bathymetric evolution: • the sequence boundary (SB) corresponds to the most regressive configuration in the stratigraphic architecture. It can be an unconformable surface in a continental or proximal position; • the transgressive surface (TS) is an erosional surface produced by wave action during transgression; it can coincide with the sequence boundary on continental platforms. • the maximum flooding surface (MFS) corresponds to the most transgressional configuration of the stratigraphic architecture, i.e. it corresponds to the maximum bathymetry of the deposits. Between these different surfaces, different system tracts (stratigraphic units determined by the evolution of the sea level with respect to the bathymetric profile) can also be defined: • the low stand system tract (LST) between the sequence boundary and the transgressive surface, downstream of the continental slope; • the transgressive system tract (TST) between the transgressive surface and the maximum flooding surface; • the high stand system tract (HST) between the maximum flooding surface and sequence boundary. All of these system tracts constitute a depositional sequence, which is the basic stratigraphic unit at seismic scale, delimited by two sequence boundaries. Based on analyses performed in seismic stratigraphy, curves have been produced of global sea level variations as a function of geological time. Genetic units Moving up from reservoir scale to high resolution sequence stratigraphy has required looking at things from a new angle and defining a new vocabulary. A genetic unit is therefore the smallest basic unit of the stratigraphic architecture which can be identified on an outcrop, core or log. It is a set of genetically related facies delimited by two maximum flooding surfaces. A genetic unit is the response to a variation in the accommodation rate (or sedimentary supply rate) and, through its regional continuity, has a chronostratigraphic value. Genetic stratigraphy and stratigraphic architecture Reasoning in terms of genetic stratigraphy makes it possible to predict lateral equivalents (Fig. 2) by producing an interpretation in terms of accommodation variations and integrating the effects of volumetric partitioning. The contributions of sequence stratigraphy essentially involve predicting the spatial distribution of deposits (by locating the available space => system tracts) and the volumetric partitioning (facies distribution in time and space). Depending on whether the depositional architecture is regressive (= seaward stepping) or transgressive (landward stepping) different facies tracts will be preserved during sedimentation (Fig 3). Fig.3 — Example of volumetric partitioning : facies tracts are different regarding the type of system tract (from Eischenseer) SPE BREAKING OF A PARADIGM: GEOLOGY CAN PROVIDE 3D COMPLEX PROBABILITY FIELDS FOR STOCHASTIC FACIES MODELLING 5 A methodology for constraining stochastic facies modeling using sequence stratigraphy Background: stratigraphic modeling The predictive aspect of sequence stratigraphy, especially through genetic stratigraphy, led sedimentologists, at a very early stage, to attempt to model a series of sedimentary deposits using stratigraphic methods. Stratigraphic modeling typically uses the sedimentary input parameters to reconstruct and predict the stratigraphic architecture. The accommodation potential is one of the most important input parameters, besides the rates of sedimentation and erosion. The accommodation potential, i.e. the increment of space available for sediment accumulation, is the sum of eustatic variations and rate of subsidence. Although most algorithms provide only 1D or 2D stratigraphic solutions, the most advanced stratigraphic models propose 3D solutions for sedimentary architecture. These deterministic simulations are based on the reconstruction of depositional processes in a sequence of time steps from past to present. This reconstruction is performed using the following main parameters: the accommodation potential (usually kridged throughout the domain), the sediment supply (both the sediment volume deposited in the basin and the total sediment supply provided by erosion are estimated by the user), and the sediment transport (the sediment transport function is a diffusive equation). The transport functions used in the model merely average several transport processes and therefore can only reproduce macro-scale average geometry and facies trends in the basin (typical grid size is 1 to 10 km). These large-scale modeling results can be input as an external drift in a stochastic simulation of geological facies at reservoir scale. This non-stationary stochastic simulation is widely influenced by large scale stratigraphic modeling, a process which is unfortunately essentially deterministic. However, the idea of constraining in this way facies simulation using a stratigraphic concepts is excellent. For this reason, the method proposed in this paper is based on the use of accommodation potential curves, but with a purely stochastic approach. Outline of the methodology The method is based on the principle that a close relationship exists between the facies and depositional bathymetry. This hypothesis is conventionally accepted to calculate the accommodation potential. It consists in describing a predetermined water depth value for given facies. The hypothesis is valid especially for platform deposits, and can be applied with good results to mixed and carbonate platforms. Although for the latter, facies distribution is more complex as it involves an additional parameter, climate. The principles of sequence stratigraphy usually work well and its use can thus be justified when calculating the accommodation potential. Furthermore, this type of environment can constitute a perfect case study for a non stationary simulation methodology. Due to the low bathymetry of the deposits, minor variations in the accommodation potential at a constant sedimentation rate lead to significant variations in the type of facies deposited. The facies proportions RF of these deposits is therefore generally non stationary at all scales and in 3D. The proposed methodology makes use of the correspondence between facies and bathymetry in order to both calculate the accommodation potential at the well and, at the end of the process, to generate an inversion and provide a prior facies probability which is a function of palaeobathymetry and system tract to the stochastic model. The key step in the method resides in building a 3D grid of the palaeobathymetry which is used in the inversion. Three main steps are therefore distinguished in the proposed methodology: • Constructing curves of accommodation potential at wells; • Processing of these curves in order to obtain a 3D palaeobathymetry grid; • Stochastic modeling based on a prior probability deduced from the inversion. Constructing curves of accommodation potential at wells Constructing palaeobathymetry curves at wells A series of sedimentary facies is described at the well using logs and cores, and is then interpreted and divided into genetic units. The facies are grouped into associations by sedimentologists who propose palaeobathymetry ranges for these associations (= environments), potentially supported by faunal indications. Assigning a palaeobathymetry value to each depth takes into account the sedimentary environment encountered at that depth and the direction of evolution of the curve with respect to successive environments pre-established for that sequencepalaeogeography (Fig. 4). A palaeobathymetry curve is thus automatically produced for each well. Depending on the position of the well in the palaeobathymetry profile, the palaeobathymetry curve will more or less exhibit high-frequency variations. Probability of facies = f (palaeobathymetry, system tract) Using the bathymetry ranges provided by sedimentologists for each environment (= facies association), the probability of the occurrence of an environment for a given palaeobathymetry can be calculated (Fig. 4). Furthermore, palaeobathymetry curves were calculated at the wells either directly from the faunal data, or using the bathymetry ranges of the environments. Statistics can therefore be calculated to test the relation between facies and palaeobathymetry. These statistics must be produced independently for each type of environment and system tract. • Probability (Environment) = f(palaeobathymetry) • Probability (facies) = f (palaeobathymetry, environment, system tract) ⇒ can then be used to calculate Probability (facies) = f (palaeobathymetry, system tract). 6 GERARD J. MASSONNAT SPE 56652 Fig.4a — Bathymetry range per environment (for given system tract) ENVIRONMENT FACIES