A new method of formation evaluation computes permeability using standard well test and log data.

According to a recent US National Petroleum Council survey, development of a permeability logging technique is one of the oil and gas industry's top research and development priorities. Researchers have developed a method to compute values of permeability for medium- to low-permeability (0.001 to 20 md) gas reservoirs using logging data. The method incorporates knowledge from prior research at Texas A&M University and a mudcake model developed earlier. The program models mud filtrate invasion from the time the zone is penetrated by the bit until it is logged. An improvement over methods to compute permeability from time-lapse logging, it:
l includes an experimentally verified model for predicting the thickness and permeability of the mudcake during static and dynamic filtration conditions; and
l uses data from an array induction tool (AIT) log to reconstruct the invasion profile and does not require multiple "time-lapse" logging runs.
Previous versions of the program used a trial-and-error solution procedure. The new version operates in two modes: forward simulation for manual matching of the log data by the computer program, or parameter estimation for automatic matching. In the automatic mode, the nonlinear regression algorithm (NLRA) compares a simulated resistivity profile to one measured by the AIT log. Reservoir permeability (controls depth of the invasion), dispersivity (controls sharpness of the transition zone), equilibrium invasion rate (controls buildup and erosion of the mudcake) and pore size distribution index (controls the shape of relative permeability functions) are allowed to vary during the calculations. Variations of these parameters change the simulated resistivity profile. The NLRA perturbs the history-matching parameters and determines the set of parameters that produces the best match between simulated and observed resistivity profiles. The permeability that produces the best match between actual log measurements and simulated log measurements is an estimate of the formation's absolute permeability.
Methodology
To illustrate how this technique is applied, consider a typical tight gas well. Perform a single forward simulation run, which requires a simulated mud filtrate invasion accounting for mudcake growth and erosion. First, the equilibrium invasion rate must be calculated. This is the rate at which the amount of mudcake buildup due to filtrate invasion is exactly equal to the amount of mudcake erosion due to mud circulation in the wellbore, so the net effect is constant mudcake thickness. Then, the invasion rate, mudcake thickness and pressure drop across the mudcake vs. time is simulated. The pressure drop across the mudcake can be as large as several hundred pounds per square inch absolute. The difference between the pressure drop in the mudcake and the pressure drop in the formation due to mud filtrate invasion poses the principal limitation of the program. It does not work well in high-permeability formations (k>20 md), where mudcake builds up quickly and controls the invasion process. In high-permeability zones, virtually all of the pressure drop is across the mudcake. To accurately estimate formation permeability from the analyses of mud filtration effects upon the logs, the mud filtration process must be at least partially controlled by the flow of mud filtrate in the formation. Thus, this method works best in low- to medium-permeability gas wells.
Just like any reservoir simulator, the program calculates the water saturation in the formation near the wellbore. The salinity profile due to mud filtrate invasion also is computed. Once the saturation and salinity profiles developed during the time since the zone was penetrated are determined, the formation resistivity and multiarray induction model calculates the synthetic log response. This computation is the heart of this program, where all types of information concerning the petrophysical, hydrodynamic and electrodynamic parameters are combined to produce a model response. An NLRA compares this response to the resistivity data from the AIT log and finds the set of reservoir parameters that produce the best match of simulated and observed resistivity data.
The water resistivity for each grid block is calculated from the formation temperature and water salinity. The formation resistivity profile is determined using one of four formation resistivity models available in the program.
The formation resistivity profile is convoluted with log geometric factors to produce a synthetic AIT log response. Geometric factors for each simulation cell
are derived from response functions of the AIT tool to account for finite-difference representation and block-centered grid.
The program imports tables of geometric factors for AIT logs. It varies
the formation permeability and other reservoir parameters until
a satisfactory match of the synthetic and measured AIT profiles is obtained. Often, analysis requires iterations in log analysis to accurately evaluate true formation resistivity and water saturation.
Data requirements
The petrophysical engineer needs to meet with the operator prior to drilling to:
determine if the well is targeting gas-bearing zones likely to have permeabilities in the range of 0.001 to 20 md;
make sure the necessary drilling and mud data will be collected; and
ensure adequate log and core data will be provided for verification.
The data required are normally necessary to run a reservoir simulator and perform a log analysis. The only extra data required to use the program are drilling mud circulation data and special mudcake tests. Table 1 lists the required input data for the program and the primary and secondary sources for each data item.
Expected accuracy
One of the major challenges in the development of the program was to quantify the uncertainty associated with the analysis. The expected accuracy of the analysis procedures was studied thoroughly using statistical methods and realistic estimates of the quality of input data. Knowledge of water saturation and the parameters used to calculate water saturation is necessary for accurate permeability analysis.
A Monte Carlo error analysis proved that if errors in input data are random, the program produces an unbiased estimate of permeability.

Field example from a Wilcox gas zone
The data for this example are from the Hamel No. 1 well, operated by Prime Energy Co. The well was a wildcat, 9 miles southwest of Columbus in Colorado County, Texas.
Logs and core data for this example are from a Wilcox Sand oil reservoir with about 207ft of gas cap and 10ft of wet sand in the bottom. The gas cap was analyzed. Figure 1 shows the gamma ray, caliper and the AIT and processed logs, including effective porosity, water saturation, shale volume and bulk volume water. The AIT logs show some invasion in the upper half of the interval (9,010 to 9,050ft) and significant invasion in the bottom half of the interval (below 9,050ft). The core porosity is shown on the third track.
Figure 2 shows the permeability calculated by the program together with the moving geometric average permeability from a profile permeameter and conventional core plugs. The agreement of all three sets of measurements appears adequate. In general, the core plug permeability values are consistent with the trend profile permeability values. The program results and the permeameter data show similar increasing downward trends.
In the absence of actual test data, analysts constructed a 40-layer numerical model of the gas-saturated zone at 9,025 to 9,045ft using the profile permeameter measurements, corrected for net overburden pressure. They simulated a buildup test with this 40-layer reservoir model and analyzed synthetic data to find effective permeability.
The final step in this example was to predict reservoir performance for:
the four reservoir descriptions;
the core-based description, taken as a benchmark or true system;
the 40-layer model based on the program's permeability estimates; and
the single-layer model based on the permeability from the buildup test.
The 40-layer model based on the program's analysis was corrected to agree with the permeability estimated from the buildup test analysis.
The results of forecasts using these four reservoir descriptions are shown in Figure 3.

AIT log
This method of estimating formation permeability using data from an AIT log simulates mud filtrate invasion that occurs from the time the zone is drilled to the time it is logged. The simulated resistivity profile is compared with the observed resistivity profile measured by an AIT log. The NLRA finds the value of formation permeability that produces the best match of simulated and measured resistivity profiles.
In evaluating the accuracy of this method, analysts found values of water saturation and the other parameters used to calculate water saturation are most important for accurate estimates of absolute reservoir permeability. If errors in the input parameters are random, the method produces an unbiased permeability estimate. Analysis revealed it may be difficult to improve the accuracy of permeability estimates from this method beyond the factor 3 of the true value.
One example shows the method provided reasonably accurate permeability estimates in moderate permeability reservoir. The reservoir permeability distribution provided by the method, combined with the permeability estimate from well test analysis, allows a more accurate forecast of production performance than well test data alone.
More field tests are needed to fully validate this method. The ideal situation would be to conduct a multiwell study with one or two wells drilled, cored, logged with all necessary logs and then production-tested.