A Two-Stage Stochastic Model Applied to a North Sea Reservoir

Abstract

Summary We present a two-stage stochastic model that caters to the large-scalegeological heterogeneities resulting from different rock types and the inherentspatial variability of rock properties. The suggested approach combines severalelements from a variety of models, methods, and algorithms that have emergedduring the last few years. This twostage procedure can be used to generateseveral geologically sound realizations of a reservoir in an efficient manner. Stage 1 preserves the important geological architecture, while Stage 2 providessmall-scale variability in the rock properties. At both stages, the stochasticmodels are conditional on the actual values observed in wells. Hence, everyrealization honors the observations. An example from a highly heterogeneous North Sea reservoir, deposited in an upper shore-face environment illustratesapplication of the model. Introduction As a result of high costs in offshore areas like the North Sea, only aminimum of exploration and appraisal wells can be justified before importantfield development decisions are made. The use of oversimplified geologicalmodels based on data from a limited number of widely spaced wells is probablyone of the most important reasons probably one of the most important reasonsfor the failures in predicting field performance. Oversimplification and theuse of performance. Oversimplification and the use of unrealistic geologicalmodels partly results from the paucity of well data but also results from theinappropriate use of available data. Experience shows, for example, that linearinterpolation of petrophysical characteristics between wells some kilometersapart usually will not give a realistic image of the heterogeneity required topredict fluid flow. To give a realistic description of the point-to-pointvariation, we resort to point-to-point variation, we resort to stochasticmodels and simulation. A reservoir is intrinsically deterministic. It exists, and its propertiesand features are potentially measurable at all scales. A potentially measurableat all scales. A reservoir is the product of many complex processes(sedimentation, erosion, burial, processes (sedimentation, erosion, burial, compaction, diagenesis, etc.) that operate over millions of years. Why, then, do we have to apply stochastic modeling? Haldorsen and Damsleth list thefollowing reasons:the incomplete information about a reservoir'sdimensions, internal architecture, and its rock-property variability at allscales;the complex spatial disposition of reservoir building blocks orfacies;the difficult-to-capture rock-property variability and variabilitystructure with spatial position and direction;the unknown position anddirection;the unknown relationships between the property value and thevolume of rock used for averaging (the scale problem);the relativeabundance of static (point values along the well for kH, Sw, and seismicdata) over dynamic (time-dependent effects, how the rock architecture affects arecovery process, etc.) reservoir data; andconvenience and speed--handdrawing reservoir architectur and point-value realizations in three-dimensionsis a very difficult and time-consuming process. The phenomena or variables that we normally describe with stochastic modelsare those that influence the amount, position, accessibility, and flow offluids through reservoirs. Thus, stochastic modeling or simulation in thiscontext usually refers to the generation of synthetic geological architectureand/or property fields in one, two, or three dimensions. The differentrealizations are conditioned to observations and possess a number of otherdesirable reservoir/geological features that should provide an improved basisfor recovery predictions. In addition, the uncertainty and risk associated withdifferent development options can be quantified better Dubrule gives a very good review of stochastic models for reservoirdescription, while Weber and van Geuns discuss the problem from a geologist'spoint of view, problem from a geologist's point of view, including some of thepossible pitfalls. Several authors present valuable contributions to the theoryand applications of stochastic modeling within the petroleum industry. Two-Stage Model To mimic reality, heterogeneity must be accounted for because it is one ofthe most important factors governing fluid flow. A number of differentapproaches exist for the stochastic modeling of heterogeneities. The choice oftechnique depends on (1) the objective and scale of the study, (2) theavailable input data, (3) the theoretical skills of the people involved, and(4) the software available. The goal is to improve the evaluation of theproduction capacity of the field by introducing small- and/or large-scaleheterogeneities into the reservoir description. Discrete vs. Continuous Models. The distinction between two main classes ofstochastic models (discrete and continuous) is convenient. A finerclassification of the discrete models has been proposed. Discrete models weredeveloped to describe geological features of a discrete nature (e.g., locationsof sand in fluvial depositional environments or locations of shales suspendedin sands). JPT P. 402

Geostatistical modeling for fine reservoir description of Wei2 block of Weicheng oilfield, Dongpu depression, China

“…In this study, all the information needed for modeling has been verified and thus the accuracy is eligible. Damsleth pointed out that linear interpolation of petrophysical characteristics between wells some kilometers apart usually will not give a realistic image of the heterogeneity required to predict fluid flow (Damsleth and Charlottle 1992). That means the greater the distances between wells are, the less convincing the outcomes from guessing will be.…”

“…Physical property values and variance of different sedimentary microfacies types vary largely (Qiu 1991). It assumed that geo-bodies which formed in the same region and were affected by similar diagenetic environment would most possibly have similar characteristics (Damsleth and Charlottle 1992;Zhou et al 2006). It is based on such an assumption that the facies-controlled modeling method is put forward.…”

“…In fact, geo-bodies forming in different microfacies are diversified in terms of geometrical patterns as well as their communication connectivity (Damsleth and Charlottle 1992;Zhang et al 2008). Thereby, microfacies should be used for and are capable of serving as one of the criteria for optimizing well patterns.…”

“…Reservoir heterogeneity is one of the main factors that affect fluid flow (Damsleth and Charlottle 1992;Qi et al 2007;Hatampour et al 2014).Reservoir physical properties, mainly referring to porosity and permeability, are studied in different methods such as empirical approach, formation testing, and experimental measuring (Zhou et al 2006;Kaydani et al 2014;Brigaud et al 2014). Through those ways, a preliminary understanding of underground flow and the reservoir storing them could be captured.…”

An Amplitude-Based Modeling Method and its Application on the Impedance Inversion in Heterogeneous Paleokarst Carbonate Reservoirs

“…On the contrary, anomalously strong seismic amplitudes that frequently occur in the Middle and Lower Ordovician succession beneath the top Ordovician unconformity are characteristic of the Tarim Basin. These anomalous amplitudes (i.e., the 'bead-like reflections' (BRs, often called lamb kebabs) in the post-stack section ( Figure. For the modeling of this very heterogeneous reservoir, the traditional lateral interpolation and extrapolation of impedance logs between well locations are obviously unqualified, while the current geological rules such as sedimentary facies of clastic rocks (Damsleth et al, 1992) and weathering karst facies of carbonate rocks (Huo et al, 2007) (Liu et al, 2010) are contaminated by AVO effects and also not acceptable.…”