Stochastic Modeling of Reservoir Architecture for Field Management
- Mojtaba Taheri (Intevep S.A.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- November 1992
- Document Type
- Journal Paper
- 433 - 438
- 1992. Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 5.1.1 Exploration, Development, Structural Geology, 5.5.2 Core Analysis, 5.2.1 Phase Behavior and PVT Measurements, 5.6.1 Open hole/cased hole log analysis, 5.7 Reserves Evaluation, 1.6 Drilling Operations, 5.1.5 Geologic Modeling, 4.3.4 Scale, 5.5 Reservoir Simulation, 5.1 Reservoir Characterisation, 1.2.3 Rock properties, 5.1.3 Sedimentology, 5.6.2 Core Analysis
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This paper outlines a probabilistic geologic modeling system developed todescribe and characterize heterogeneous fluvio-deltaic sandstone reservoirs inthe San Diego area, Orinoco belt, eastern Venezuela. The model uses field,well, and laboratory data to simulate synthetic stratigraphic sections indifferent directions and to delineate the geometry, continuity, and anisotropyof sand bodies and the regional distribution of internal reservoir properties(porosity, permeability, and hydrocarbon saturation). From a stochasticviewpoint, the model introduces the following improvements: (1) a Poissonprocess to predict the occurrence of sedimentary sand bodies in thestratigraphic sections, (2) facies proportion curves to condition theoccurrence of sand bodies on the depositional environments, (3) Latin hypercubesampling (LHS) as a more precise sampling method in simulation, and (4) ageometric computer modeling technique (QUADTREES) to calculate the reservoirproperties and to delineate complex geometries and effective drainage areas.These techniques are illustrated by use of field data from a pilot developmentin the San Diego area.
Thorough knowledge of reservoir-rock heterogeneities and fluid distributionsis essential to obtain more reliable estimates of in-situ hydrocarbonaccumulations and to optimize their recovery. A common problem encountered inachieving these goals is the lack of sufficient information (well, seismic,etc.) necessary to predict the geometry of the reservoirs and their internalcharacteristics. In this respect, a probabilistic approach can help geologistsand engineers to obtain better reservoir models by establishing rules andprocedures that permit the interpolation/examination of the available data in avalid geologic manner. In this study, I present a methodology developed toconstruct a stochastic/geologic present a methodology developed to construct astochastic/geologic modeling system and its application to a series of sparselydrilled heterogeneous clastic reservoirs of the Orinoco belt.
The San Diego pilot area covers about 250 km2 in the southern flank of theEastern Venezuelan basin (Fig. 1), which, at the time this study began,included 12 widely distributed (1 to 5 km apart) exploratory wells. Later, anadditional 12 cluster wells were drilled at 300-m spacing in the northern partof the area. Stratigraphically, the area is made up of rocks ranging fromPaleozoic to Cenozoic Age that overlay the Precambrian igneous/metamorphiccomplex of the Guayana shield (Fig. 2). The principal hydrocarbon accumulationsare in the Tertiary Lower Oficina formation, which was deposited during atransgressive event that occurred in the Miocene time (Fig. 3). Well logs,correlations, and core analysis indicate that the productive section evolvesfrom fluvial (upper and lower) to coastal plain depositional environments withdeltaic developments. It is characterized by braided channels grading upwardthrough a sequence of point bars, crevasse splays, and distributary channels(Fig. 4). point bars, crevasse splays, and distributary channels (Fig. 4). Thefluvio-deltaic sands are fine to very coarse grained and mostly lenticular,with thicknesses ranging from 1.5 to 15 m, an average porosity of 30%, andpermeabilities of up to 2.5 darcies. They porosity of 30%, and permeabilitiesof up to 2.5 darcies. They have not suffered important diagenetic changes thataffect their reservoir quality.
The steps involved in the model development were (1) stochastic simulationfor generating sand bodies in stratigraphic sections, (2) detection ofsand-body continuity and interconnection and description of the distribution ofrock physical properties in the connected zones, and (3) definition ofdifferent drilling strategies for field development.
Generating Sand Bodies in Stratigraphic Sections. In previous work,sand/shale sequences in cross section were simulated stochastically, assuming auniform distribution for both lateral and vertical coordinates of the shalecenters. However, the size and behavior of these occurrences can be modeledwith information from the wells in the field or from outcrops with similardepositional and sedimentological characteristics. This problem and others,such as morphology, dimension, and internal properties of sand bodies indifferent sedimentary environments, are considered essential elements in anysand generation scheme.
Sand-Body Vertical Succession. The vertical succession of sand bodies indifferent wells was modeled under the assumption that their occurrence followsa stochastic process. As a first hypothesis, a Poisson process was used toexplore the distribution of the number of sands occurring in each well. This isequivalent to the hypothesis that the distances between the successions ofsands (tops or centers) follow an exponential distribution. This hypothesis wasexplored simply by plotting the distances between the sands ordered (ascending)against the order statistics of the exponential distribution. The latest isdirectly proportional to the quantity of (n + 1 - i)-1, where i = 1,2 ... n andn is the number of distances between sand successions. The result closelyfollowed a straight line, as expected for an exponential distribution,indicating that these distances follow the exponential probability law. Hence,we accepted the hypothesis that the probability law. Hence, we accepted thehypothesis that the vertical succession of sands follows the exponentialdistribution, or equivalently, that the number of sands occurring in the wellsfollows a Poisson process.
If the distances between sand successions (d1,d2 ... d.) follow anexponential distribution, with parameter (rate of occurrence), then theirprobability function can be defined as , where the estimator of is the inverseof the average distances between sand sequences in each well and in a givenstratigraphic unit. This method was used to estimate the sand occurrence ratefor the 24 wells in the study area. To describe the spatial distribution of ,two options were considered: (1) a normal distribution model was fitted to theX values for each well and (2) a random-walk model was defined such that the Xvalue at any point in space is a function of initial and final wells boundingthe simulation area. The function defined was where, and values of in theinitial and final wells, respectively; d = the lateral distance from theinitial well, and = expected correlation between values. The value of could beprovided by the geologists or be estimated by other means, such as variogrammodels.
Geometry and Properties of Sand Bodies. Of particular importance to oursimulation model were the morphologies of @ bodies, dimensions, and internalproperties. These characteristics were described as functions of theirdepositional environments and facies on the basis of published data. Thus,channel fills were given elliptical shapes (Fig. 5) as opposed to therectangular shapes used in other simulation models. Rectangular shapes wereused to represent crevasse splays because the sediments are distributeduniformly in space.
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