Accounting for Interpreted Well Test Pore Volumes in Reservoir Modeling

Optimal reservoir management requires reliable reservoir performance forecasts with as little uncertainty as possible. There is a need for improved techniques for dynamic data intergration to construct realistic reservoir models by using geostatistical techniques. This paper gives a method to create porosity models that honor interpreted pore volumes from well test data. Well porosity data, seismic data and well test results are integrated in sequential simulation. Seismic data is modified iteratively until the co-simulated porosity matches the interpreted well test pore volume. A number of examples are shown. Introduction There are many data that can be used to constrain reservoir models including core data, well logs, seismic and production data. There are few wells during reservoir exploration. Seismic data is areally extensive. The large-scale information provided by seismic data is accounted for in the structural framework and facies model. Seismic may also provide additional information on large-scale porosity variations within the facies. Production data are extraordinarily important because they are direct observations of reservoir performance. Any reliable reservoir characterization study should account for these dynamic data . Well test data is one kind of production data that can provide average porosity and permeability in some volume near the well. In fact, average porosity is an input to well test analysis, but it must be adjusted during well test interpretation in order to make the actual pressure curves and theoretical type curves match better. Because effective pore volume in the area around a well is a basic concept used in well test model and can be calculated by multiplying average effective porosity by formation thickness and relevant area, the basic idea of this paper is to account for the pore volume from well test data by slight modifications to seismic data when cosimulating porosity. This makes the model more predictive since it matches interpreted flow data and decreases uncertainty in the porosity model. Methodology Hard data include the facies assignments, porosity, and permeability observations taken from core and well logs that provide reliable measurements at the scale we are modeling. All other data including seismic data and production history are called soft data and must be calibrated to the hard data. Seismic data are frequently used as secondary data for cosimulation of porosity based on the relationship between porosity and seismic . The seismic data are often impedance values from seismic inversion or some other attribute if an inversion has not been undertaken. The sole calibration parameter is the correlation coefficient between the Gaussian transform of porosity and the Gaussian transform of seismic. Seismic data constrains the spatial distribution of porosity. Well test data can be seen as additional soft data that the porosity model must reproduce . The two soft data (seismic data and well test) must be considered simultaneously. Two significant complexities make this difficult. First, the volume scale difference between the hard data, the modeling scale, the seismic scale, and the well test make it very difficult to quantify the relationship between the data types. Second, the cross correlation or redundancy between the different soft data must be modeled at the same time as their correlation to the hard data. Finally, porosity does not average linearly after Gaussian transformation. For these reasons, a full cokriging approach is not practical. It is conceptually straightforward and practically efficient to slightly modify or update the seismic data to carry the information of the well test data. Using the updated seismic data as secondary data for Gaussian simulation will decrease the uncertainty of the results. Consider the estimation of an unknown Gaussian transform of porosity z*(u) at an unsampled location u by: