Permeability Prediction of Well Log Responses Using a Local Linear Model Tree Based on a TSK-fuzzy System

Abstract

A learned model obtained from a data set can be used for prediction, simulation, optimization, and analysis of the system. The local linear model tree used for the TSK-fuzzy system has been successful in predicting the permeability of a typical Iranian oilfield rock. The methodology involves the heuristic search to choose the space of the input partitions by axis-orthogonal splits and also automatic permeability estimation from digitized data (well logs) obtained from oil wells. The results show that the local linear model tree is incurred to the smallest error on the unseen data when compared to similar algorithms. On the other hand, the limited flexibility of the local estimation reduces the variance error due to the bias/variance dilemma. Consequently, the local estimation approach has a regularization effect on the estimation.     

The Estimation of Formation Permeability in a Carbonate Reservoir Using an Artificial Neural Network

Abstract

Reservoir permeability is an important parameter that its reliable prediction is necessary for reservoir performance assessment and management. Although many empirical formulas are derived regarding permeability and porosity in sandstone reservoirs, these correlations cannot be accurately depicted in carbonate reservoir for the wells that are not cored and for which there are no welltest data. Therefore, having a framework for estimation of these parameters in reservoirs with neither coring samples nor welltest data is crucial. Rock properties are characterized by using different well logs. However, there is no specific petrophysical log for estimating rock permeability; thus, new methods need to be developed to predict permeability from well logs. One of the most powerful tools that we applied by the authors is artificial neural network (ANN), whose advantages and disadvantages have been discussed by several authors. In particular, 767 data sets were used from five wells of Bangestan reservoir in a southwestern field of Iran. Depth, Neutron (NPHI), Density (RHOB), Sonic (DT) logs, and evaluated total porosity (PHIT) from log data were used as the input data and horizontal permeability obtained by coring was as target data. Sixty percent of these data points were used for training and the remaining for predicting the permeability (i.e., validation and testing). An appropriate ANN was developed and a correlation coefficient (R) of 0.965 was obtained by comparing permeability predictions and the actual measurements. As a result, the neural science can be used effectively to estimate formation permeability from well log data.     

Threshold Pressure Gradient in Ultra-low Permeability Reservoirs

Abstract

In a core displacement experiment, simulated oil, formation water, injected water, and distillated water were used as fluids to measure and analyze the threshold pressure gradient (TPG) for both a single- and two-phase fluid flow. A certain Chinese oil field core sample was used, which represents a typical ultra-low permeability reservoir: “block 119.” The study indicates that different types of fluids give a different TPG versus permeability power function, with index equal to approximately ?1. The study also indicates that, due to the capillary pressure and the Jamin effect, the TPG for the two-phase oil and water is greater than that for the single-phase flow. By combining laboratory and field data, the effect of the TPG in the development of the ultra-low permeability reservoirs can be explained.     

Prediction of Key Points of Water-oil Relative Permeability Curves Using the Linear Regression Technique

Abstract

Relative permeability is among the most critical parameters in reservoir performance evaluation and EOR projects. It reflects the ease of movement and trapping of different phases and affects the production rate and ultimate recovery from reservoirs. Experimental measurement of relative permeability curves is complicated, costly, time consuming, and the results can easily be influenced by test conditions and interpretation methods. Empirical correlations are alternative approaches that are based on existing experimentally measured relative permeability curves and rock and fluid properties. The authors used 260 relative permeability curves from Iranian carbonate and sandstone reservoirs. Six key points for each set of water-oil relative permeability were determined, which fully characterize these curves. Using linear regression technique, new correlations were proposed to predict these key points. Having this done, it is then easy and straightforward to construct unnormalized/real water-oil relative permeability curves.     

The Validation of Methods to Calculate Gas-Oil Relative Permeability Using Capillary Pressure Data from South Pars Reservoir

Abstract

Gas-oil relative permeability is the most important parameter in the simulation of fluid flow in the gas condensate reservoirs. Experimental measurements of relative permeability need core samples with regular shape, which is costly and time consuming. On the other hand, experimental data of relative permeability may also have significant error and uncertainty in many cases. One source of uncertainty is that the input to numerical simulator is uncertain and inaccurate; it may be reduced if the number of input parameters is decreased, especially if the parameters with the greatest uncertainty are avoided. It is possible to impose only capillary pressure data, because relative permeability can be predicted consistently using specific models. The present methods, which are based on capillary pressure, considered the porous media as a bundle of capillary tubes; they indeed are mercury flow paths that are filled during the mercury injection capillary pressure test at the certain value of capillary pressure. The authors applied the existing capillary models for relative permeability calculations to a gas condensate reservoir. The tested samples have a wide range of liquid permeability from less than 1 to 18 md. The results of this study show that the Purcell model has the best fit with experimental data for wetting phase (oil), and the differences between measured and model data were almost negligible. The predictions of nonwetting phase (gas) relative permeability were a good agreement with experimental data except for Purcell model. Results reveal that the relative permeability could be computed by using accurate capillary pressure data.     

Experimental Study of the Effect of Permeability on Foam Diversion

Abstract

Through single-core and dual-core experiments, relations of pressure, liquid flow rate of outlet, and gas-phase saturation to injection fluid volume were researched. Effect of permeability on foam diversion was analyzed. Experiments indicate that gas saturation increases and then decreases with core permeability at the same PV during subsequent liquid injection for single-core experiment. When the permeability ratio is less than 11, liquid flow rate ratio is less than 1. When permeability ratio lies in the range of 11 to 14.9, liquid flow rate ratio is greater than 1, and foam diversion is declining. The best diversion is observed at a permeability ratio of 4.0. The effect of permeability on foam diversion is that capillary pressure is greater in the low-permeability core, and bubbles in foam break easily, which causes cross flow of gas phase.     

An Experimental Investigation of the Effect of Pressure Gradient on Gas-oil Relative Permeability in Iranian Carbonate Rocks

Abstract

The authors examine the effect of pressure gradient on gas-oil relative permeability in horizontal and vertical immiscible displacement. The experiments are conducted on a core from lower Dalan formation in the South Pars oilfield of Iran, in constant pressure, unsteady-state condition, and different pressure gradients. The Toth method is used for calculating the relative permeability and plotting proper curves. Data analysis and the effect of pressure gradient on gas-oil relative permeability are investigated. Results show that relative permeability curves are affected by pressure gradient and this effect is much prominent at low pressures due to end-effect phenomena. The dependence of relative permeability curves on pressure gradient is correlated as a function of dimensionless capillary number. The accuracy of this correlation for relative permeability prediction is examined and a new method is introduced to minimize the end-effect phenomena on relative permeability curves.     

Estimation of the Reservoir Permeability by Petrophysical Information Using Intelligent Systems

Abstract

Permeability is one of the most important parameters in order to evaluate a hydrocarbon reservoir. The permeability of a formation is usually determined from the cores and/or well tests. It should be noted that cores and well test data are often only available from few wells in a reservoir while the logs are available from the majority of the wells. Therefore, the evaluation of permeability from well log data represents a significant technical as well as economic advantage. Many fundamental problems remain unsolved by most predictive models. This article introduces the use of an improved neural network trained by a back propagation learning algorithm to provide solution for the permeability prediction from well log data. An Iranian offshore gas field which is located in the Persian Gulf, has been selected as the study area in this article. Well log data are available on a substantial number of wells. Core samples are also available from a few wells. It was shown that the neural network system is the most effective method in predicting permeability from well logs.     

Research and Application of Deconvolution in Well Test Analysis of Extra-low Permeability Sandstone Reservoirs

Abstract

For extra-low permeability sandstone reservoirs, traditional well test analysis techniques are always limited by wellbore storage coefficient and the low flow velocity in the porous media. Results derived using traditional well test analysis techniques are meaningless or useless. A deconvolution method based on the newly robust solution algorithms is applied for extra-low permeability sandstone reservoirs. Deconvolution codes were developed based on von Schroeter deconvolution algorithm and Levitan deconvolution algorithm. Though the study is based on synthetic cases and a field case, it is proved that the deconvolution algorithm works well in well test analysis of extra-low permeability sandstone reservoirs.     

Hydraulic versus pneumatic measurements of fractured sandstone permeability

This paper investigates the issue of ascertaining whether gas can replace water for determining the flow parameters in fractured porous media. This is accomplished by the determination of the hydraulic parameters using brine, the pneumatic parameters using air, and the study of the correlation between these two parameters. The measurements are obtained for fractured sandstone cores from the middle Stubensandstein unit in the Southwest German Trias. In most cases, the intrinsic liquid permeability is lower than the intrinsic gas permeability. Intrinsic gas permeability (k_g) ranged from 32 to 159 md, while intrinsic liquid permeability (k_l) ranged from 12 to 47 md. The ratio of intrinsic gas permeability to intrinsic liquid permeability (k_g/k_l) shows two subgroups: (1) ratios ranging from 1 to 2 (62.5% of samples) and (2) ratios ranging from 4 to 5 (37.5% of samples). The reduction in the intrinsic liquid permeability is governed by three phenomena: physicochemically, by the migration of the clay particles which clog the pores, mechanically, by the breakdown of original fabrics caused by the passage of wetting fronts across relatively delicate clay mineral complexes, and experimentally, by the undersaturation of samples during liquid permeability measurements. This study concludes that gas permeability is more accurate than liquid permeability because it measures more closely intrinsic permeability especially for clay-rich rocks. In addition, because gas experiments can be conducted much faster than liquid flow experiments, gas is a desirable replacement fluid.     

Effective Permeability Calculation Using Boundary Element Method in Naturally Fractured Reservoirs

Abstract

A model is presented to calculate the effective permeability tensor in naturally fractured reservoirs using Boundary Element Methods (BEM). Arbitrary fractures of different scales based on their length are considered. Interface boundary condition is used to model the short fractures as an enhancement of matrix permeability. Long fractures, on the other hand are treated as source/sink in the corresponding blocks. Periodic boundary condition is applied to the grid-block boundaries to calculate the elements of effective permeability tensor. Darcy's law and Navier-stoke's equation are applied to fluid flow in rock matrix and fractures, respectively. An important feature of this approach is that the fluid flow in matrix-fracture interface is coupled by Poisson's equation and fluid flow in the rest of the matrix is formulated by Laplace's equation. This paper also presents an innovative approach to optimization and parallelization of the model by High Performance Computing (HPC) techniques. The model has been validated against analytical results and applied to a typical case where arbitrary fractures of different sizes are assumed within the grid blocks. The effective block permeability tensors can be implemented into a reservoir simulator to calculate fluid flow through the naturally fractured reservoirs.     

Improved Permeability Prediction of a Heterogeneous Carbonate Reservoir Using Artificial Neural Networks Based on the Flow Zone Index Approach

Abstract

Permeability is one of the most important parameters required for reservoir characterization. Although core analysis provides more exact information, core data do not exist for all wells in the reservoir because coring is expensive and time consuming. Therefore, another approach should be sought for permeability determination. The objective of this study was to create an artificial neural network (ANN) model in order to use well log data to predict permeability in uncored wells/intervals. The well log, core, and other data were gathered from an Iranian heterogeneous carbonate reservoir. A flow zone indicator was then predicted using an ANN approach with well logs as input variables. The reservoir was thus classified into different zones based on hydraulic flow units to overcome the extreme heterogeneity. Then, a separate ANN training procedure was followed for each flow zone with log data as input variables and permeability as output. This improved method is capable of permeability prediction in heterogeneous carbonate reservoirs in uncored wells/intervals with an average error of less than 10.9%.     

非均质油藏的岩石渗透率合成方法研究

渗透率合成方法经常应用在石油储量计算、油田开发方案编制和油藏数值模拟等油藏工程研究中,主要包括垂向上不同层段渗透率的合成以及沿渗流方向不同渗透率带渗透率的合成。根据达西定律及建立的渗流模型,经过数学推导,得到垂向和水平方向两类渗流模型的渗透率合成公式。其中,垂向上不同层段渗透率的合成按流量叠加原理进行推导,而沿渗流方向不同渗透率带的合成则按不同渗透率带的压差叠加原理进行合成。结合石油地质、开发研究工作的具体情况,用室内实验实测数据进行了验证,计算结果的误差为0.28%-5.35%,基本上在允许的范围之内。     

Pseudo Relative Permeability Compensation for Numerical Dispersion

Abstract

Reservoir simulation is an approach of recreating the occurring phenomena of the reservoir by solving the general governing equations that describe the reservoir processes. Finite difference technique is an effective method to get the solution out of the reservoir models for different scenarios. In light of many benefits of using course grid models rather than fine grid and simplification, using the same relative permeability curves from laboratory cannot be applied in the fields having large grid dimensions because of numerical dispersion (smearing) of finite difference modeling. Thus, the relative permeability curves must be modified based on the grid size and then applied into the simulator. The authors introduce a methodology to demonstrate how the lab relative permeability curves can be modified based on coarse grid sizes to honor the same anticipated rock behavior. Thus, an objective function is developed to minimize the numerical dispersion in a synthetic tilted reservoir by automatically changing the relative permeability and comparing the results with the equivalent fine model. By this method, modified relative permeability curves can be obtained and introduced to the coarse model. This modification workflow is almost inevitable for reservoir simulation models with very coarse grids and it eases the history-matching process by approaching more realistic solution.     

基于岩石物理相的储层渗透率解释模型研究

陆相储集层非均质性严重 ,不同层位的物性变化规律不同 ,如果在一个区块采用同一渗透率解释模型 ,势必造成较大的误差。为此 ,提出了一种基于岩石物理相的储层渗透率解释方法。储层岩石物理相是沉积作用、成岩作用、后期构造作用和流体改造作用的综合反映 ,同一岩性相可对应于不同的岩石物理相 ,而同一种岩石物理相则具有相似的水力学特征和相似的物性特征。根据流动层带指标 ,将辽河油田沈 84块砂岩储层定量划分为 4类岩石物理相 ,每一类岩石物理相代表着不同的岩性和物性 ,在表征各类岩石物理相的基础上 ,建立了各类岩石物理相的渗透率解释模型。该模型改善了储层渗透率的预测精度 ,且反映了储层沉积特征和非均质性 ,为油田高含水期精细油藏描述提供了可靠的渗透率参数。     

Estimating the Reservoir Permeability and Fracture Density Using Petrophysical Logs in Marun Oil Field (SW Iran)

Surveying the pores, permeability, and fractures in an oil field using petrophysical data and its relative logs has significant importance in precise schematization of how to prevent from mud loss and from reservoir rock damages. The authors completed a survey and determination was done using neutron logs and density. Then S _wirr rate and permeability were measured using experimental methods. In these processes, the gained results from permeability are qualitative and cannot show the exact rate and the only application of these methods is for estimating the permeability. For exact measurement, the processes such as well testing or coring should be exploited. For studying on fractures, the image logs were used and because of oil-based mud in this field, for assessing the fractures, the oil-based microimager tool was used. The studied reservoir layer is Asmari formation, which is one of the most important reservoir rocks in Southwest Iran. The lithology of this formation is carbonate and sandstone, which has medial and good porosity. For permeability estimating, some zones were chosen that are relatively sandstones and clean. The permeability range of them is between 80 and 400 md, and has good and medial permeability development. The observed cracks are between 2,820 and 3,000 m depth, which have different slopes and have low-level aggregation in lower zones, based on fracture assessing.     

The Effect of DC Electrical Potential on Enhancing Sandstone Reservoir Permeability and Oil Recovery

Abstract

The merits of using electrokinetic phenomena to improve reservoir permeability on sandstone reservoir core plugs are investigated with detail clay mineralogy studies. Normal and reverse DC configuration is applied along with waterflood and studies are conducted on single-phase and two-phase fluid saturation conditions. The produced brines are acid digested and analyzed by inductively coupled plasma mass spectroscopy (ICP-MS). In single-phase flow experiments, permeability enhanced 180% with the normal electrode configuration but negligible change is observed in reverse configuration. In two-phase flow 59% and 10% permeability enhancement is observed in normal and reverse configurations, respectively. In addition, 11.6% additional oil is recovered from normal configuration. The results are examined in terms of electrolyte movement and resulting changes within the clay microstructure. In normal electrode configuration, formation of colloidal clay suspension and flowing out along with produced brine is evident. This has resulted in increased pore passage and core permeability, whereas in the reverse configuration, clay structures remained unchanged. The given explanations are supported by ICP-MS and X-ray diffraction results.     

Experimental Studies of the Effects of Permeability Variations on Immiscible Flow

Abstract

The properties of hydrocarbon reservoirs are generally derived from core experiments and use theories of fluid flow that normally assume homogeneous core properties. Reservoirs, however, are generally heterogeneous, and interpretations of the results of these experiments are likely to be unreliable if the core from which the data are derived is heterogeneous. This article examines experimentally immiscible displacement through well-defined permeability heterogeneities, modeled using 2-D visual models packed with clear beads of different permeabilities.

The results indicated that the displacement patterns were dominated by capillary pressure effects and that they were different from those found in miscible systems. This understanding is needed, since in reservoir simulators, the simulator codes must contain the correct physics, and in core analysis, the effluent profiles must be correctly interpreted for sensible predictions.     

确定油田渗透率分布规律的解析法

提出了一种确定油田渗透率分布规律的解析方法，从而克服了以往用图版拟合确定渗透率分布的缺点。其方法是：首先用概率统计方法统计出油田渗透率分布的均值Ｅ（ｋ）（或Ｅ（ｌｎｋ））和Ｅ（ｋ＾２）（或Ｅ［（ｌｎｋ）＾２］），并且利用这二个均值计算出常用的４种理论渗透率分布类型（Γ（√ｘ）型、Γ（ｘ）型、Γ（ｘ＾２）型和对数正态分布型）的分布参数；然后计算出４种理论分布与实际分布的方差值Σ［ｆＮ（ｋｉ）－ｆ（ｋ