Simulation of reservoir permeability using porosity and acoustic impedance data

Permeability is a key parameter in reservoir characterization. In fact, without accurate information about reservoir permeability, there is no good solution for reservoir engineering problems. Up to now, permeability values of a reservoir have been calculated through laboratory measurements or well testing methods. These methods are useful but they cannot describe a reservoir reliably and precisely. Also, well logs and core analysis have been used for permeability estimation, but correlation methods also show that, estimation through these methods is not reliable.
Direct prediction of reservoir permeability from seismic data is often supposed impossible due to resolution limitations of seismic data and hydraulic nature of permeability. In many cases reservoir permeability estimation is restricted to core scale and wellbore proximity. Regarding the existing limitations, recent studies have shown that there are some experimental relationships between some petrophysical parameters and permeability.
In recent years, geostatistics and stochastic modeling have made a tremendous impact on scientific investigations. Geostatistics has been an increasingly important factor in the development of petroleum resources. So, a stochastic modeling of geostatistics is a reliable tool for estimating reservoir parameters including porosity and permeability. In geostatistics we suppose that variables have an effect on each other. So, the first concept of geostatistics is related to the variogram of values we want to estimate. It tells about the spatial correlation that exists between values. Distance that variables have an effect on each other and is called range of a variogram and is an important concept because after that distance, variables have no effect on each other. Geostatistical methods are meaningful in the range of variables and outside the range geostatistics is not applicable.
The investigated field is located in the Persian Gulf between Iran and Qatar, 80 km south west of Lavan Island and 40 km south east of south Pars gas field. The study area consists of two reservoir structure including Sarvak and Surmeh. In order to estimate permeability values of the reservoir, first, all data required for this approach should be collected. Needed data are: porosity logs and 3D seismic data of the study area. 3D seismic acquisition of this field has been done by TOTAL FINA ELF in 2000. Total area of investigation is about 96 km2. Interpretation of data has been done by TOTAL in 2003 and interpretations of this article have been validated by that. There are twelve wells in the study area of which seven of them have porosity logs.
First, a reliable structural model of study area (which is one of hydrocarbon fields in south of Iran) has been built from seismic data and wells information. Seismic data have been used in interpretation of horizons and characterization of faults in the reservoir. After determination of horizon surfaces in the reservoir, some horizons that have not been seen in seismic data have been determined using wells information by use of well tops. Using all horizons and fault plates we construct a structural model. Distances between horizons are divided into zones. In the model, with attention to importance of each zone, some layers have been defined. It's obvious that zones imbedding in reservoir parts, have more layers in order to increasing the validation of estimation.
After collecting required data and making the model, estimation of reservoir porosity values has been done with the aid of seismic impedance values through Geostatistics. Collocated co-Kriging method has been selected for this geostatistical estimation. In this method there is a secondary variable in addition to main data that improve accuracy of estimation. For starting geostatistical estimation, firstly analysis of data has been carried out. The analysis is based on calculating variograms. Then with the use of variogram values and considering acoustic impedance values as the second parameter in collocated co-Kriging method, porosity of the reservoir has been calculated. There are some anhydrite layers in the reservoir that we put zero value of porosity for them in order to have more control on our results and having more reliable porosity estimation for the reservoir. So the value of reservoir porosities becomes known in all parts of the model. In all parts of the reservoir, porosity values change between 0 to 30 percent.
In the next step, permeability values have been estimated using porosity values. There is a good correlation between porosity and permeability values. First, variography between permeability values have been done. Then using Sequential Gaussian Simulation (SGS) method as a reliable tool for the estimation, reservoir permeability values from porosity, have been calculated. Estimation has been done in all zones of the reservoir separately.
Again, as we have some anhydrite layers in the reservoir structure, for a better control on estimating permeability values of the reservoir, zero value of permeability has been devoted to anhydrite layers. So we have a better estimation of permeability in total volume of the reservoir. Values of permeability of the reservoir change between 0 to 100md.
Finally, validity of permeability estimation of the reservoir should be investigated. This has been done by cross validation method. Information of one well has been eliminated from the model, and using other wells, permeability estimation has been done. Then a comparison between permeability of the model at well location and well permeability was done and the correlation coefficient has been calculated. This process has been done for well 3W-01 and well 3W-03. Correlation coefficient for well 3W-01 is 0.86 and this coefficient for well 3W-03 is 0.81. Correlation coefficients show that results of permeability estimation are acceptable and Sequential Gaussian Simulation combined with collocated co-Kriging is a capable method in reservoir characterization. Using Sequential Gaussian Simulation alone is not reliable enough in porosity and permeability estimation especially when there is a complicated geological structure, because it uses mathematical calculations only, and its results may have no good compatibility with the truth of the geology. This problem has been solved by combination of acoustic impedance data with permeability values. Importing acoustic impedance values conduct the SGS algorithm and make it more compatible with the reality of the earth model.