Integration of Geological, Geophysical, and Historical Production Data in Geostatistical Reservoir Modelling

Transcription

1 Integration of Geological, Geophysical, and Historical Production Data in Geostatistical Reservoir Modelling Clayton V. Deutsch (The University of Alberta) Department of Civil & Environmental Engineering 220 Civil / Electrical Engineering Building University of Alberta, Edmonton, Alberta, Canada T6G 2G7 A longstanding vision of geostatistics is that teams of geoscientists and engineers would routinely build predictive reservoir models that, by construction, honour all available data. These models will provide reliable predictions of future reservoir performance at all stages of the reservoir life cycle. The unavoidable uncertainty in reservoir performance forecasting will be measured and minimized by such reliable numerical reservoir models. The available data includes conceptual geological models, seismic data, core data, well log data, DST/RFT data, well test data, and historical production data. Each source of data carries information, at different scales and with varying levels of precision, related to the true distribution of petrophysical and fluid properties in the reservoir. Our vision holds that powerful diagnostic and numerical techniques will overcome the challenge of integrating these disparate data. The aim of reservoir modelling is to create high-resolution 3-D models of reservoir properties (lithofacies, porosity, permeability, residual water saturation, and so on). Multiple stochastic realizations are created to quantify uncertainty, which is due to inexact and incomplete information at a large scale. Aggressive industrial and academic research over the last fifteen years has led to significant progress toward this vision, that is, development of tools for reservoir modelling. Techniques have advanced to the point where a wide range of relevant geological, geophysical, and engineering data can be accounted for. This short abstract and presentation reviews these techniques and describes outstanding research directions. Hierarchical Approach A hierarchical workflow whereby large-scale structures are modelled first is routinely used in reservoir modelling. Stochastic techniques are applied to all stages when there is significant uncertainty associated with modelling. The large-scale bounding stratigraphic surfaces and faults are modelled first. Lithofacies are modelled within each major stratigraphic unit. Then, continuous petrophysical properties such as porosity and permeability are assigned on a by-layer and by-facies basis. Multiple stochastic realizations are constructed by repeating the entire workflow resulting in different structure, lithofacies, and petrophysical properties. Good software is essential. Known data must be honoured at all times, that is, each resulting model must be consistent with all available data. This is the challenge. Where do Different Data Intervene in Reservoir Modelling? Each source of data carries different information. The available data must be interpreted to remove artifacts and calibrated to reservoir geometry and continuity. Conceptual geological models do not provide local constraints on reservoir properties, but rather global spatial data in the form of trends and spatial statistics. Such trends and spatial statistics may be inferred from reservoir-specific data, if a sufficient quantity is available. In presence of few wells, however, this general reservoir knowledge is used at virtually all stages in reservoir modeling. Such data intervene in (1) the choice of property modeling techniques (object-based, surface-based, indicator, Gaussian), (2) the spatial statistical parameters needed by the chosen modeling technique, and (3) large-scale soft data for trend constraints. Conceptual geologic

2 data includes interpretations from available reservoir-specific data, interpretations from a regional geological setting, and analogue data from ancient and modern settings. Although seismic stratigraphic interpretation provides some general knowledge similar to conceptual geologic data, the main use of seismic is local data that constraints primarily large-scale reservoir geometric features. Good quality seismic data provides almost deterministic constraints on major stratigraphic surfaces and faults. Geostatistical techniques are sometimes used to add correlated errors to the deterministic interpretations of seismic. It would be more correct to say that Geostatistical techniques intervene in the structural model of seismic. Interpreted and depth corrected seismic data also provide information on vertically averaged facies proportions and petrophysical properties. This large-scale soft data is considered as local data to be honored with some measure of precision in subsequent facies and property modeling steps. It is important to note that seismic cannot visualize the reservoir properties at the required scale; there remains uncertainty due to the physical constraint on the frequency content of the seismic and the relation between acoustic properties and the reservoir properties we are modelling. Moreover, sparse well data permit the calculation of vertical spatial statistics, but not needed horizontal statistics. Such horizontal spatial statistics may be borrowed from laterally continuous seismic data. Core and well log data provide local hard measurements, albeit at a small scale, of the facies and reservoir properties to be modeled. Although these data constitute an extremely small fraction of the reservoir, they are the main source of data for local spatial constraints and the source of data for spatial statistics, such as the variogram. Geostatistical models are built at some intermediate resolution between the core and well log data and the ultimate flow simulation scale. This intermediate scale is vastly larger than the core data. Some call this scale difference the missing scale because it is almost always ignored in reservoir modeling. Scale-up refers to the calculation of effective properties at the flow simulation scale from the geostatistical model. Core and log data intervene (1) as local hard data in facies and property modelling, (2) as the source of spatial statistical parameters for the chosen modelling method, and (3) as the ground truth or hard data to which soft data are calibrated. DST, RFT, and single well test data are interpreted to provide local data. Much information can be squeezed from such data including identification of fluids, facies, effective flow properties, and distances to faults or stratigraphic barriers. Only rarely can such well test data be used to infer general reservoir data such as spatial statistics. Interpreted well test data intervene as local soft data to be reproduced by subsequent property modeling. The challenges associated with well test data are (1) the interpretation and calibration of the raw data to the reservoir properties being modeled, and (2) the large scale of the data relative to the hard core and log data. Notwithstanding these challenges, DST, RFT, and single well test data are among the most critical data because they directly measure the reservoir response of interest. Historical production data are also directly related to the reservoir response that we are trying to forecast. Nevertheless, relating historical production data to local constraints on reservoir properties and integrating these constraints with the variety of data mentioned above remains one of the greatest outstanding challenges in geostatistical reservoir modeling. The multiple well pressure and rate measurements that make up historical production data must go through a mathematical inversion to provide constraints on reservoir properties. The forward problem relates reservoir properties to flow response; the inverse problem is to relate flow response to reservoir properties. Although this mathematical inversion is ill posed and non-unique, techniques are being developed and beginning to see some practical application.

3 Reservoir data, including our professional opinion regarding reservoir geometry and continuity, intervene in the choice of modeling procedure, parameters for the chosen technique, local hard data, and large-scale soft data. Let s turn our attention more specifically to geostatistical modeling techniques. Surface-Based Modelling As mentioned above, the hierarchical approach to reservoir modelling requires that the large-scale structural and stratigraphic architecture be modelled first. There are a number of issues related to surface-based modelling: (1) deterministic interpretation from the reservoir-specific data mentioned above, (2) attaching uncertainty to the deterministic interpretation, and (3) modelling surfaces that are at a toosmall scale for deterministic interpretation. The last two issues are in the domain of geostatistical reservoir modelling. Stratigraphic bounding surfaces and faults may be interpreted directly from seismic that is tied to local well data. This interpretation is uncertain due to the time-to-depth conversion of seismic and potential errors in picking the surface locations from seismic data. It is becoming increasingly common to create multiple realizations of the surface locations by adding a simulated residual to the deterministic interpretation. Most often the simulated residuals are generated with a Gaussian simulation technique constrained to be zero at the well locations. Cross validation (leave-one-out re-estimation) and evaluation of the uncertainty in the velocity model sometimes provide input to the histogram and spatial correlation of the residuals; however, they are often arbitrary. Conventional Cartesian topology and regular grids may be used for nearly horizontal surfaces; however, more flexible triangulated grids are needed for faults and overturned beds. This surface flapping, as it is sometimes called, provides uncertainty in estimated volumes and a set of alternative structural models that can be carried forward to facies and property modelling. There may be additional stratigraphic surfaces of importance within the (alternative) large-scale structural models provided by seismic interpretation and geological correlation. Although these surfaces cannot be correlated between wells, they could have a dominant affect on fluid flow and recovery. Such surfaces can be modelled with geostatistical techniques to reproduce well intersections and general knowledge about the stratigraphy. These sub-seismic surfaces are transferred to subsequent facies and property models as additional constraints. As an aside, one can envision the explosion in uncertainty, e.g., N models of large-scale structure, N models of sub-seismic structure, N models of facies, N models of porosity, and so on. It is neither practical nor necessary to consider N K models, where K is the number of variables. In practice, N models are constructed where each is a set of K variables. The first variable is the structural model, then, the facies model must be built for each structural model. Cell- and Object-Based Facies Modelling The facies must be represented within the stratigraphic framework of each reservoir layer. There are two classes of methods used for facies modelling: cell- and object-based methods. Both methods are needed for different depositional environments. Cell-based techniques assign the categorical facies one cell at a time subject to statistical model. Object-based models position geological facies objects within a background, e.g., sand-filled channels within a background of floodplain shale. Sequential indicator simulation (SIS) and truncated (pluri) Gaussian simulation (TGS) are the two common cell-based techniques. SIS works with a conventional indicator or probability coding of the facies and considers the variogram or transition probabilities for spatial constraints. TGS approaches the simulation of the categorical facies through the truncation of one (or more) continuous Gaussian variables. Both

4 methods have the flexibility to account for trends and secondary data arising from seismic and production data. The spatial variability of each facies may be specified more independently with SIS; however, the facies transitions implicit to TGS may be realistic in certain depositional settings. Object-based techniques are applicable when the facies appear as clear geometrically defined objects, e.g., fluvial channels, crevasse splays, dunes, algal mounds and so on. There are a number of approaches to object positioning. Some iteratively adjust the positions until all data sources are honoured. Others build in data conditioning explicitly. Inevitably, there is some degree of arbitrariness in the distributions of object sizes and in the ultimate positioning. Nevertheless, such techniques have proven themselves in practice; particularly in low to intermediate net-to-gross fluvial reservoirs. Petrophysical properties such as porosity and permeability must be assigned within each facies. Petrophysical Property Modelling A variety of techniques exist for constructing modelling petrophysical properties. The most common by far are Gaussian-based techniques including sequential Gaussian simulation. Simulation from the multivariate Gaussian distribution is remarkably straightforward. There are variants of Gaussian simulation to account for large-scale secondary data arising from seismic and production data. The limitations of these methods include (1) the maximum entropy character of the Gaussian distribution, (2) the necessity for linear averaging, and (3) in presence of multiple variables, their joint distribution must follow the linear equal variance constraints of the multivariate Gaussian distribution. These limitations of Gaussian techniques are often overlooked because of their simplicity. Indicator methods such as sequential indicator simulation and the Markov-Bayes extension to indicator simulation relax some of these limitations at the expense of more variogram inference and more CPU requirements. Iterative techniques including simulated annealing relax some of the limitations inherent in Gaussian techniques, but also cost in terms of increased CPU time and the delicate adjustment of many tuning parameters. These alternative methods have never gained wide application in geostatistics because of the additional effort required. Future Work Notwithstanding the relatively complete set of procedures for reservoir modeling and data integration, there are outstanding issues in geostatistical numerical modeling. The rigorous integration of production data has yet to see routine application because of the difficult inverse problem confounded by incomplete data. Another important future work is to handle the missing scale from core and well log data to the scale of our numerical models. Conceptual geologic data remains poorly handled; in other words, geostatistical models are often not visually correct. Future work will also be directed toward integration of data from permanent pressure gauges and decision making in presence of uncertainty. Given the review nature of this abstract and associated presentation, the reader is left to seek out the relevant literature, which has exploded in the last 15 years. Biographical Note: Dr. Deutsch is presently an Associate Professor in the Department of Civil & Environmental Engineering at the University of Alberta. He teaches and conducts research into better ways to predict the spatial

5 distribution of natural phenomena. He has a B.Sc. in Engineering from the University of Alberta and M.Sc. and Ph.D. degrees in Applied Earth Sciences from Stanford University.