Zsay-Shing Lin

A committee machine with empirical formulas for permeability prediction

This study integrates log-derived empirical formulas and the concept of the committee machine to develop an improved model for predicting permeability. A set of three empirical formulas, such as the Wyllie-Rose, Coates-Dumanoir, and porosity models to correlate reservoir well-logging information with measured core permeability, are used as expert members in a committee machine. A committee machine, a new type of neural network, has a parallel architecture that fuses knowledge by combining the individual outputs of its experts to arrive at an overall output. In this study, an ensemble-based committee machine with empirical formulas (CMEF) is used. This machine combines three individual formulas, each of which performs the same evaluation task. The overall output of each ensemble member is then computed according to the coefficients (weights) of the ensemble averaging method that reflects the contribution of each formula. The optimal combination of weights for prediction is also investigated using a genetic algorithm. We illustrate the method using a case study. Eighty-two data sets composed of well log data and core data were clustered into 41 training sets to construct the model and 41 testing sets to validate the models predictive ability. A comparison of prediction results from the CMEF model and from three individual empirical formulas showed that the proposed CMEF model for permeability prediction provided the best generalization and performance for validation. This indicated that the CMEF model was more accurate than any one of the individual empirical formulas performing alone.

Lithology identification of aquifers from geophysical well logs and fuzzy logic analysis: Shui-Lin Area, Taiwan

The purpose of this study is to construct a fuzzy lithology system from well logs to identify formation lithology of a groundwater aquifer system in order to better apply conventional well logging interpretation in hydro-geologic studies because well log responses of aquifers are sometimes different from those of conventional oil and gas reservoirs. The input variables for this system are the gamma-ray log reading, the separation between the spherically focused resistivity and the deep very-enhanced resistivity curves, and the borehole compensated sonic log reading. The output variable is groundwater formation lithology. All linguistic variables are based on five linguistic terms with a trapezoidal membership function. In this study, 50 data sets are clustered into 40 training sets and 10 testing sets for constructing the fuzzy lithology system and validating the ability of system prediction, respectively. The rule-based database containing 12 fuzzy lithology rules is developed from the training data sets, and the rule strength is weighted. A Madani inference system and the bisector of area defuzzification method are used for fuzzy inference and defuzzification. The success of training performance and the prediction ability were both 90%, with the calculated correlation of training and testing equal to 0.925 and 0.928, respectively. Well logs and core data from a clastic aquifer (depths 100-198m) in the Shui-Lin area of west-central Taiwan are used for testing the systems construction. Comparison of results from core analysis, well logging and the fuzzy lithology system indicates that even though the well logging method can easily define a permeable sand formation, distinguishing between silts and sands and determining grain size variation in sands is more subjective. These shortcomings can be improved by a fuzzy lithology system that is able to yield more objective decisions than some conventional methods of log interpretation.

Identification of stratigraphic formation interfaces using wavelet and Fourier transforms

The purpose of this study was to identify the formation interfaces from geophysical well log data using the wavelet transform, and a combination of the wavelet transform and the Fourier transform methods. In the wavelet transform method, the identification of formation interfaces is based on the wavelet coefficients from the wavelet transform of spontaneous potential (SP) log and gamma ray (GR) log data. In the combination of the wavelet transform and the Fourier transform methods, the wavelet transform, spectrum analysis, and logarithmic transform of well logs were applied to the SP and GR log data successively to obtain clear signals for identifying the stratigraphic formation interface. In this study, a set of ideal log data was first created and analyzed to test the validity of the developed procedures. In analyzing the SP and GR logs from a field, both the wavelet transform method and conventional well log analysis showed similar results. The results from a combination of the wavelet transform and the Fourier transform methods, however, were better than those from the wavelet transform method and the conventional well log analysis.

Stochastic analysis of production decline data for production prediction and reserves estimation

Abstract The purpose of this study is to develop a stochastic method which analyzes production data to predict future performance and to estimate reserves probabilistically. A methodology for the stochastic analysis, using the statistical properties of production data and the rate–time equation, is presented. Data from an oil field was analyzed by the stochastic method. For comparison, both deterministic decline curve analysis and conventional probabilistic analysis are conducted. In deterministic decline curve analysis, only a single value for the reserves is estimated and a smooth curve for the production rates is predicted. The analysis does not take into consideration the uncertainty of the data. In probabilistic analysis and stochastic analysis, the ranges of reserves which include the uncertainty of the production history data are estimated. The results from conventional probabilistic analysis depend on the distribution of input parameters which are assumed or subjectively determined by an evaluator. In analysis by stochastic method, the result, however, is fully dependent on the production history data instead of subjective judgment.

Propagation of Radius of Investigation from Producing Well

Abstract The purpose of this study is to estimate the pressure disturbance area, or the propagation of the radius of investigation, from a producing well in an infinite reservoir by using both analytical and numerical methods. A linear (or radius) coefficient in the relationship between the square of the dimensionless radius of investigation and the dimensionless time is studied and derived. The radius coefficient in the equation is a constant, and varies with different criteria of radius of investigation defined, i.e., the amount of pressure change from the initial formation pressure at the pressure front of the pressure disturbance area. As the dimensionless pressure defined at the pressure front changed from 0.1095 to 10−9, the radius coefficient varied from 4 to 71.15. The radius coefficient is independent of the level of the flow rate for a well producing at a constant flow rate. For a well producing with variable flow rates, the radius coefficient is not a constant for the case of larger pressure drops defined at the pressure front. The skin factor does not affect the result of the calculated radius of investigation. The wellbore storage volume will affect the propagation of the radius of investigation only at an early time, depending on the wellbore storage volume.

Source functions in early time pressure transient analysis

Abstract The pressure responses of a reservoir can be obtained by convolving source functions and flow rates. Although the literature reports on deriving source functions analytically from the diffusivity equation, there is no study on deriving source functions using flow rates and pressure responses obtained from pressure transient tests. We therefore wanted to develop a methodology for obtaining the formation source functions using pressure data when pressure and flow-rate data are known. In addition, we wanted to study the characteristics of some source functions both from simulated data and from analytical methods in the literature. We demonstrate that the pressure functions (solutions of the diffusivity equation) of a test well can be calculated by convolving flow rates with source functions, and that the source functions can be derived by deconvoluting the pressure drop and flow rates available from the pressure-test data. Pressure function, flow rate, or source function can be obtained when two of these three functions are known. A source function (in time domain) with the wellbore storage effect is a horizontal line in a very early time and coincides with the infinite line source function or the infinite surface cylinder source function after the end of the wellbore storage effect. The source functions are almost the same for different positive skin factors. For a negative skin factor, a source function is initially a horizontal line and subsequently coincides with the infinite line source or infinite surface cylinder source functions.

Uncertainty Analysis of Production Decline Data

Abstract Decline rate-time equations, including uncertainty characteristics of production data, were developed to estimate the probabilistic reserves and production life of hydrocarbon reservoirs. The uncertainty characteristic, or residual function, is a statistical distribution of the difference between field data and the deterministic production decline curve. The reserves may be estimated directly by summing the production rates, including the residual function, which is referred to as the summation method. Alternatively, other equations for estimating the probabilistic reserves and production life are also derived, based on the integration of the decline time-rate equations that include uncertainty. This is referred to as the integration method. In both methods, Monte-Carlo simulation is used. The uncertainty analysis is applied to the production data from two gas fields located in Taiwan: the Chinshui and the Tiechenshan gas fields. In the case studies, production data for the Chinshui gas field shows an exponential decline, whereas the Tiechenshan gas field exhibits hyperbolic decline. The residual function for the Chinshui gas field is a normal distribution with a mean of zero. In the Tiechenshan gas field, the residual function approximates a normal distribution. Thus, the determined probabilistic reserves for both fields also have a normal distribution. The range of reserves, which is defined as the difference between proven and mean reserves, is estimated using both summation and integration methods. The Chinshui gas field is 10.6% of mean reserve value, whereas for the Tiechenshan range of probabilisitc reserves of value is 8.9%. The methods derived in this study are more accurate than those determined by the conventional probability method where the range of reserves depends on the assumed ranges of the parameters used. A set of new decline curves equations in residual form, instead of conventional equations of decline curves, are derived. In addition, the equations of cumulative production in residual form are derived. A new method based on the equations of decline curves in residual form and those of cumulative production in residual form are developed (uncertainty analysis method). Case studies with conventional decline curve analysis, probabilistic decline curve analysis, and a new method of uncertainty analysis are presented. The results of the three methods are compared and discussed.

Estimation of groundwater aquifer formation-strength parameters from geophysical well logs: The southwestern coastal area of Yun-Lin, Taiwan

Abstract The purpose of this study is to estimate groundwater aquifer formation-strength parameters including shear modulus, bulk modulus, Poissons ratio, and Youngs modulus by using geophysical well logs. A new dispersed-shale index equation was developed by using the natural gamma-ray log and the compensated formation density log to solve a confusing problem of the compaction factor setting in the calculation of sonic porosity for an unconsolidated groundwater aquifer. A useful Poissons ratio estimation method was employed to estimate groundwater aquifer formation-strength parameters when shear-wave transit time data is lacking in groundwater wells. Hydrogeologic parameters are characterized in estimating formation-strength parameters. Five wells in the southwestern coastal area of Yun-Lin, Taiwan, were logged, and four shallow aquifers were identified from log-derived hydrogeologic characteristics less than 200 m in depth. The formation-strength parameters for aquifers between 310 and 500 m in depth were calculated in two wells because complete formation density and compressional-wave transit time data were available. The results of the aquifers formation-strength parameters demonstrate that both shear modulus, ranging from 0.15 to 0.42 * 106 psi, and Youngs modulus, ranging from 0.40 to 1.07 * 106 psi, increase with depth, whereas bulk compressibility, ranging from 1.2 to 2.6 * 10−6 psi−1, decreases with increasing depth.

Determination of the constant coefficient in pressure propagation equation

Abstract Many studies on the pressure propagation in porous media show that the relationship between the square of the radius of investigation and the producing time of a well is linear. The linear relationship is the pressure propagation equation (or pressure equation). However, these studies do not arrive at the same constant coefficient representing the linear relationship. The purpose of this study is to find the constant coefficient for the pressure propagation equation. The constant coefficient from this study is derived from analyzing pressure transient behavior and observing the boundary effect time (the starting time of wellbore pressure affected by the reservoir boundary). The results show that the constant coefficient in the pressure equation, i.e., the linear constant between the square of dimensionless radius of investigation and the dimensionless producing time is 17.82.

A prediction of pressure behavior with production data only

Abstract The purpose of this study is to derive and calculate a pressure response function in order to predict the pressure behavior of a producing or testing well without knowledge of reservoir parameters. The equation of pressure response function is theoretically derived from an analytical solution of the diffusivity flow equation. The pressure response function for a specific reservoir can be derived from the equation of the pressure response function with known production data, such as wellbore pressure and flow rate information. Once calculated, the pressure response function can be used to calculate future wellbore pressures for given flow rates. In these calculations or predictions, no reservoir and fluid parameters are necessary. The derived equations and the calculation methodology have been verified in this study by using reservoir simulation data. The ability to predict future wellbore pressure behavior from a pressure response function is also demonstrated.