New Method for Reservoir Mapping
Authors: Journel Andre G. , Alabert Francois G. 
Published: December 2007

Summary
The sequential indicator simulation (SIS) algorithm allows buildingalternative, equiprobable, numerical models of reservoir heterogeneities thatreflect spatial connectivity patterns of extreme values (e.g., permeability)and honor data values at their locations. This paper presents a case study of asampled presents a case study of a sampled slab of Berea sandstone.

Introduction
A map or, more generally, a numerical model of an attribute's distributionin space is rarely an end goal. Maps are used as input to some transferfunction designed to simulate a response of interest (Fig. 1). The"quality" of a map or numerical model should be appreciated in relationto the particular transfer function through which it will particular transferfunction through which it will be processed. A map is a poor model of realityif it does not reflect those characteristics of the real spatial distributionthat most affect the response function.
The goal of reservoir characterization is to provide a numerical model ofreservoir attributes (porosity, permeability, saturations, etc.) for input intocomplex transfer functions represented by the various flow simulators. Thereservoir model is "good" if it provides response functions similar tothose that would be provided by a perfect model based on an exhaustive samplingof the reservoir (see Fig. 1). Aspects of the reservoir that have littleinfluence on the response of the flow-simulation exercise considered need notbe modeled; however, reproduction of critical reservoir aspects isessential.
In most flow simulations, the single most influential input is thepermeability (or transmissivity) spatial distribution that conditions flowpaths. In a heterogeneous reservoir involving layers (e.g., shales/sands/fractures) with permeability values differing by several orders of magnitude, flow is conditioned primarily by connected paths of high or low permeabilityvalues (flow paths and barriers, respectively). The histogram shape, whetherlog normal or not, and the proportions of extreme permeability valuesproportions of extreme permeability values do not matter as much as the spatialconnectivity of these extreme values. Randomly disconnected small fractures maynot generate flow paths, whereas a minute volume proportion of connected highpermeability proportion of connected high permeability values may control flowand thus sweep efficiency and recovery. In such situations, reservoircharacterization should detect patterns of connected extreme values andpatterns of connected extreme values and represent them in the numericalmodel(s) to be used for flow simulations. In the following we argue thattraditional mapping criteria, such as smoothness of the resulting surface orminimum-error variance, may not be relevant because they are not related toreservoir connectivity.
Focusing on spatial connectivity of extreme-valued attributes involves ahigh degree of uncertainty that must be assessed. For example, if a given mapor numerical model features a string of high permeability values, is thatstring an artifact of the geological interpretation or the interpolationalgorithm used? Assessing spatial uncertainty is much more demanding thanassessing the local accuracy of all estimated values along the stringconsidered. Our solution does not provide a single estimated map, as in Fig.provide a single estimated map, as in Fig. 1b, but several alternative, yetequiprobable, maps, as in Fig. 1c. All such maps honor the data values at theirlocations and reproduce a certain number of connectivity functions that modelthe dependence in space of the attribute considered; map differences image theprevailing spatial uncertainty. Features that appear on all maps are deemedreliable, and those that appear only on some maps unreliable, although theirpossible occurrence elsewhere cannot be ruled out. The reservoir engineer thencan make a management decision with some awareness of the risk imparted byspatial uncertainty.
Finally, "hard" data on extreme values are scarce or nonexistent andmust be supplemented by "soft" information. For example, because plugsare not taken in shaly or fractured parts of the core, core plugs fail tosample extreme values, thereby biasing the permeability distribution. Loginterpretation, however, can indicate the presence of such extreme values. Information comes from various sources at various scales with various degreesof reliability, yet all information sources must be accounted for when dealingwith the spatial distribution of extreme values.
Indicator formalism allows numerical or interpretive information to becommonly coded into elementary bits (valued at zero or one). These bits arethen processed independently of their origins to generate the requirednumerical models of the reservoir.