Reservoir Engineering - General - Predicting Gravity-Drainage Performance Using a Three-Dimensional Model

Reservoir and producing characteristics can govern the decision to use either a one-, two- or three-dimensional model for making predictions for gravity-drainage reservoirs. Examples of conditions requiring one-, two- and three-dimensional calculations are given. In 1961 the author presented a method for predicting one-dimensional gravity-drainage performance. This work has been exrendcd to obtain a three-dimensional model, which is described and for which a sample problem is presented. Introduction Many papers on gravity drainage or gas-cap drive'-3 have been presented for conditions where the reservoir is treated as a single areal segment so that, in effect, only one-dimen-sional flow is considered. Other authors'-Q ave given evidence showing that the one-dimensional concept would be unsatisfactory to predict reservoir performance for certain types of reservoirs. Experience has indicated that specific reservoir and producing conditions govern whether one-, two- or three-dimensional concepts must be used as a basis for reliable reservoir performance predictioils. Previously the author presented a paper outlining a method for predicting the performance of gravity-drainage reservoirs.' That paper treated the reservoir as a single areal segment so that it was applicable for only one-dimensional flow. The work has been extended to obtain a three-dimensional model that can be used to predict performance of gravity-drainage reservoirs. Although capable of being three-dimensional, it can be used equally well for one- and two-dimensional predictions. This paper discusses those reservoir and producing conditions governing the choice of model, and also describes a three-dimensional model suitable for predicting reservoir performance in the more complex situations. Discussion The Choice of Model To predict reservoir performance, it is necessary to represent the reservoir by a physical model. A mathematical model, based on the assumed physical model, then is used to predict the movement of oil and gas within the reservoir. The word "model" is used here to connote the combination of both a physical model and a mathematical model based on the physical model. Certain types of reservoir situations may be predicted suitably with a one-dimensional model, whereas two- and three-dimensional models may be required for other situations. This section illustrates reservoir conditions associated with the use of a specific type of model. Many types of reservoir structures are such that gravity drainage possibly could be an important factor in oil production. Production practices, as well as the nature of the structure. can influence the type of model that should be used. obviously, it is impossible to discuss all combinations of reservoir structure and production practices that might be encountered in gravity-drainage reservoirs. The following are typical examples of conditions where a choice must be made among a one-, two- or three-dimensional model to predict reservoir performance satisfactorily. Conditions Requiring a One-Dimensional Model Fig. la shows contours for an asymmetrical anticline in which gravity drainage might be expected to be important. Fig. Ib depicts a cross-section along Line A-A in Fig. la. Existence of a gas cap is a good clue that gravity drainage will be an important factor in producing oil from this type of reservoir. However, it is not essential since a gas cap will form as oil is produced from the reservoir. If the proper combination of reservoir permeability and withdrawal rates is present, the reservoir will behave like a