During a field development process, one of the parameters used to decide the in fill well locations is permeability-thickness (kh) map. This map can provide us with overall trends in the conductivity of the formation as well as information about optimizing water flood patterns. Rosneft routinely uses kh maps as a reservoir management tool. In addition to developing the well locations, it also uses the kh values to optimize the artificial lift design so that the wells are produced efficiently.
One difficulty typically observed in generating kh maps is a prominent display of "bull's eyes." The values of kh can change dramatically from well to well, which causes problems in interpolation of these values. Some times, because of large discrepancies, the overall patterns are hard to discern and well planning is more difficult.
In the proposed work, we developed a procedure for capturing the trends in kh maps by removing the bull's eyes. The kh values are determined by two methods: use the production data and using simplified procedure, determine the value of kh, or evaluate well test data and determine the kh values. In the first step, we developed a process of reconciling the well test data with the production data by adjusting the kh values and skin factors so that the productivity index can be maintained. In the second step, we assumed that uncertainty exists in determining the true kh value at each well location due to interpretation and resolution of data. Instead of strictly honoring the kh values at each location, using error kriging approach, we recalibrated the kh values so that the new kh maps are smoother and without bull's eyes, and are able to define the overall trends much better. We also ensured that the productivity index matches correctly. Further, by examining the productivity index as a function of time (based on production data), we are able to determine how the skin factor changes as a function of time, which provides valuable information about potential damage at the well location. The procedure was validated by applying it to a large oil field located in Siberia with successful application of in-fill well program.
Well capacity is the term used to describe the capacity of formation bed around a wellbore to flow the fluid. Mathematically, it is defined as the product between permeability and thickness, kh. Using diffusivity equation, this parameter is directly related to the well productivity index, PI, that can be evaluated based on the flow rate, q, and pressure difference between reservoir and well bore flowing pressure, pe - pwf. Therefore, knowing the distribution of kh for the overall field will help us in determining the quality of the reservoir, which in turn may be used for planning of a reservoir management program. For this reason, Rosneft has routinely used the kh map in helping the selection of well during the in-fill drilling program.
One of the issues of using the current method of generating kh map is that the map exhibits sudden discontinuity at well location, i.e., the bull's eye. This discontinuity does not match with the overall geological interpretation. Thus, it is an artifact due to the process used to obtain such a map. Figure 1 shows an example of typical kh map that exhibits the presence of bull's eye. Note that the scale of kh is given in the natural-logarithmic scale in order to have a linear scale for the conturing. The objective of the study presented in this paper is to obtain a procedure that will reduce the presence of bull's eyes on the kh map, i.e., to smooth the map, while preserving the original productivity index measured at each well locations.
In general, there are 2 sources of information for kh. The first one is from the well test, which is referred as khwt, and the other one is derived from the production index data, referred as khpr in this paper. Well capacity from well test, khwt, is calculated from a well test interpretation and represents the actual measured value of the formation. On the other hand, well capacity from production data, khpr, is calculated using an assumed value of skin factor, S. Therefore, this value contains some uncertainties due to the assumption on the skin factor. Meanwhile, for well test, the skin factor is also a result of the measured quantity. Therefore, the value from the well test is commonly used as the reference to represent the actual data.