2D conditional simulation of channels on wells using a random walk approach
Channel modeling is one of the popular topics in the application of geostatistics to fluvial reservoir modeling. This paper presents an approach to designing channels which have a general flow direction through sand well locations and which avoid shale well locations. This approach is named the random walk on graphs of well locations, and is applied to model channel reservoirs. This modeling process consists of two parts: one direction walk modeling and two direction walk modeling. The first model aims to determine each channel location by the use of a transition probability with a random walk essentially in the main flow direction, say the northsouth direction, while the second model simulates different channels that can be oriented in both directions, either from north to south or from south to north. In both parts of the model, the transition probability is estimated based on two coefficients: one is the correlation coefficient of channel observations; the other is the obstacle coefficient of non-channel observations. A case study with a dense array of 332 wells is presented using the proposed random walk model. For the purpose of model verification, channel maps created by the random walk are compared to the hand-drawn channel maps made by geologists. The results show a good agreement in both types of maps, but in contrast to the single map supplied by geologists, the random walk model is capable of generating many realizations of channel configuration, hence allowing for uncertainty evaluation. A limitation of this approach, related to the influence of the number of wells, is discussed.
random walk channel modeling one direction walk modeling two direction walk modeling transition probability correlation coefficient obstacle coefficient