Change of Support in Spatial Variance-Based Sensitivity Analysis

Variance-based global sensitivity analysis (GSA) is used to study how the variance of the output of a model can be apportioned to different sources of uncertainty in its inputs. GSA is an essential component of model building as it helps to identify model inputs that account for most of the model output variance. However, this approach is seldom applied to spatial models because it cannot describe how uncertainty propagation interacts with another key issue in spatial modeling: the issue of model upscaling, that is, a change of spatial support of model output. In many environmental models, the end user is interested in the spatial average or the sum of the model output over a given spatial unit (for example, the average porosity of a geological block). Under a change of spatial support, the relative contribution of uncertain model inputs to the variance of aggregated model output may change. We propose a simple formalism to discuss this issue within a GSA framework by defining point and block sensitivity indices. We show that the relative contribution of an uncertain spatially distributed model input increases with its correlation length and decreases with the size of the spatial unit considered for model output aggregation. The results are briefly illustrated by a simple example.     

Global sensitivity analysis in an ocean general circulation model: a sparse spectral projection approach

Polynomial chaos (PC) expansions are used to propagate parametric uncertainties in ocean global circulation model. The computations focus on short-time, high-resolution simulations of the Gulf of Mexico, using the hybrid coordinate ocean model, with wind stresses corresponding to hurricane Ivan. A sparse quadrature approach is used to determine the PC coefficients which provides a detailed representation of the stochastic model response. The quality of the PC representation is first examined through a systematic refinement of the number of resolution levels. The PC representation of the stochastic model response is then utilized to compute distributions of quantities of interest (QoIs) and to analyze the local and global sensitivity of these QoIs to uncertain parameters. Conclusions are finally drawn regarding limitations of local perturbations and variance-based assessment and concerning potential application of the present methodology to inverse problems and to uncertainty management.     

基于多目标区域地球化学调查的中国土壤碳储量计算方法研究

土壤碳储量问题在碳循环和全球变化领域具有重要意义,长期以来这一基本参数的计算受到数据来源的制约。全国多目标区域地球化学调查采用双层网格化采样和分析,取得了大量高密度和高精度土壤地球化学数据,为土壤碳库的高精度计算提供了数据基础。文中重点探讨利用这些数据计算土壤碳储量的方法。首先提出针对多目标区域地球化学调查数据的"单位土壤碳量(USCA)"概念,用以代表调查数据基本面积单元(4km2)的碳储量,并作为区域和全国尺度土壤碳储量计算的基本单位。在收集分析14个省市414条的土壤剖面数据的基础上,发现土壤有机碳(TOC)的垂直分布与无机碳和其他元素不同,存在指数分布规律,运用面积积分运算方法发现利用直线模型计算土壤有机碳库的误差(+20%～+100%)远大于指数模型的误差(-10%～+20%)。因此,文中建议"有机碳单位土壤碳量(USCATOC)"需使用指数模型拟合后积分求算,而"无机碳单位土壤碳量(USCATIC)"则使用直线模型,"全碳单位土壤碳量(USCATC)"采用两者加和计算。文中还分析了其他元素的垂直分布特征,并提出氮储量计算需采用与有机碳类似的方法,其他51种元素(氧化物)储量采用与无机碳类似的方案,按照直线模型计算单位土壤元素量和单位土壤氧化物量(USEA)。     

基于改进稀疏网格替代模拟的地下水DNAPLs运移不确定性分析

由于实际的水文地质条件具有复杂性和变异性,地下水DNAPLs运移数值模拟的不确定性不可避免。为解决不确定性分析中因多次调用DNAPLs运移模型导致的计算耗时问题,本次研究在传统稀疏网格（SG）替代模型的基础上,提出了一种将局部自适应（LA）和维数自适应（DA）耦合的改进替代模型DA-LA-SG。通过两个解析案例和一个PCE运移室内实验,验证了DA-LA-SG的替代效率和精度,并将其用于室内砂箱PCE运移模拟不确定性分析。研究结果表明:在替代模型构建初期,LA-SG的替代效率优于或接近于DA-SG和DA-LA-SG,随着插值节点数量的增多,DA-SG和DA-LA-SG的替代效率逐渐优于LA-SG,DA-LA-SG具有最高的替代效率。DA-LA-SG能够高效、高精度地建立PCE运移模型的似然函数替代模型,且被用于PCE运移模拟参数不确定性分析。结果表明:背景介质渗透率k1、拟合系数n1和透镜体渗透率k2的可识别性较强,背景介质孔隙度μ1、透镜体孔隙度μ2和拟合系数n2的识别效果较差,这些参数对饱和度观测数据不敏感。     

Geochemical characterization and modelling of the Toarcian/Domerian porewater at the Tournemire underground research laboratory

For safety evaluation of hazardous waste repositories in clay-rocks, a thorough assessment of porewater chemistry and water–rock interactions is required. However, this objective is a challenging task due to the low hydraulic conductivity and water content of such rocks, which subsequently renders porewater sampling difficult (without inducing perturbations). For this reason, an indirect approach was developed to determine porewater composition of clay-rocks, by a geochemical model of water–rock interaction using some properties of the rock and the solution. The goal of this paper is to obtain the porewater composition of the Toarcian/Domerian argillaceous formation at Tournemire (South of France), for which a reliable model is still lacking. The following work presents a comprehensive characterization of the geochemical system of the Tournemire clay-rock, including mineralogy, petrology, mobile anions, cation exchange properties, accessible porosity and CO₂ partial pressure. Perturbation corrections from fracture water sampling were also computed. These water were found in sealed fractures (Beaucaire et al., 2008) and their radiocarbon apparent age is estimated at 20 ka. Their age together with their equilibrium situation allow considering these fracture waters as representative of the formation porewater. The model developed to calculate the Tournemire porewater composition is essentially based on cation exchange by a multi-site approach, but equilibrium with some mineral phases (calcite, quartz and pyrite) is also considered. Different exchange sites of different affinities towards cations are used, which proportions are given by the mineralogy. Exchange on illite is performed with a three-sites model, while one site is considered for smectite phases. Multi-site model results are compared with corrected fracture water data and two other models: a model only based on mineral equilibrium and a model using cation exchange on one global site. The best results were obtained with the models that take into account cation exchange and particularly with the multi-site model. The interest in considering a model with exchange sites of different affinities is particularly obvious for a satisfactory representation of the K⁺ content in solution. A dependence of K⁺ content to the amount of high affinity sites was observed, leading to an improvement of its simulation when uncertainty on mineralogical data is considered. Once validated, the multi-site model was applied at different levels of the Tournemire argillaceous formation to obtain a profile of the porewater composition.     

Uncertainty quantification of overpressure buildup through inverse modeling of compaction processes in sedimentary basins

This study illustrates a procedure conducive to a preliminary risk analysis of overpressure development in sedimentary basins characterized by alternating depositional events of sandstone and shale layers. The approach rests on two key elements: (1) forward modeling of fluid flow and compaction, and (2) application of a model-complexity reduction technique based on a generalized polynomial chaos expansion (gPCE). The forward model considers a one-dimensional vertical compaction processes. The gPCE model is then used in an inverse modeling context to obtain efficient model parameter estimation and uncertainty quantification. The methodology is applied to two field settings considered in previous literature works, i.e. the Venture Field (Scotian Shelf, Canada) and the Navarin Basin (Bering Sea, Alaska, USA), relying on available porosity and pressure information for model calibration. It is found that the best result is obtained when porosity and pressure data are considered jointly in the model calibration procedure. Uncertainty propagation from unknown input parameters to model outputs, such as pore pressure vertical distribution, is investigated and quantified. This modeling strategy enables one to quantify the relative importance of key phenomena governing the feedback between sediment compaction and fluid flow processes and driving the buildup of fluid overpressure in stratified sedimentary basins characterized by the presence of low-permeability layers. The results here illustrated (1) allow for diagnosis of the critical role played by the parameters of quantitative formulations linking porosity and permeability in compacted shales and (2) provide an explicit and detailed quantification of the effects of their uncertainty in field settings.     

Inversion of dynamical indicators in quantitative basin analysis models. II. Synthetic tests and a case history using dynamical indicator tomography

The dynamical evolution of sediments in basins, and their compaction, is the underpinning keystone on which rests the ability to model thermal history of the basin and hydrocarbon generation, migration, and accumulation histories. A presentation is given of the dynamical tomography method, which inverts dynamical indicators to evaluate the parameters in a 1-D fluid-flow/compaction model, including values dealing with geological events as well as values dealing with intrinsic, or assumed, lithologic equations of state. Synthetic tests illustrate the operation of the system. Using observed downhole quantities: total depth, formation thicknesses, variation of porosity, permeability, and total fluid pressure with depth from the Navarin Basin COST No. 1 well, Bering Sea, Alaska, the numerical algorithm was tested and found to be effective in a nonlinear inverse sense to determine and/or constrain the parameters entering quantitative models of dynamical sedimentary evolution. The predictions of present day total depth, formation thicknesses, porosity, permeability, and fluid pressure with depth are close to the measured data. The minimization provides the uncertainty in each parameter and so the geohistory of a well can be defined better.     

Combining meta-modeling and categorical indicators for global sensitivity analysis of long-running flow simulators with spatially dependent inputs

Variance-based global sensitivity analysis (GSA) is a powerful procedure for importance ranking of the uncertain input parameters of a given flow model. The application of GSA is made possible for long-running flow simulators (computation (CPU) time more than several hours) by relying on meta-modeling techniques. However, such flow models can involve one or several spatial inputs, for instance, the permeability field of a reservoir and of a caprock formation in the context of CO₂ geological storage. Studying the sensitivity to each of these spatial inputs motivated the present work. In this view, we propose a strategy which combines (1) a categorical indicator (i.e., a pointer variable taking discrete values) assigned to the set of stochastic realizations associated with each spatial input (spatial maps) and (2) meta-modeling techniques, which jointly handle continuous and categorical inputs. In a first application case, a costless-to-evaluate numerical multiphase flow model was used to estimate the sensitivity indices. Comparisons with results obtained using the meta-model showed good agreement using a two-to-three ratio of the number of learning samples to the number of spatial maps. On this basis, the strategy can be recommended for cases where the number of maps remains tractable (i.e., a few hundred), for example, for moderately complex geological settings, or where a set of such maps can be selected in a preliminary stage using ranking procedures. Finally, the strategy was applied to a more complex multiphase flow model (CPU time of a few hours) to analyze the sensitivity of CO₂ saturation and injection-induced pressure build-up to seven homogeneous rock properties and two spatial inputs.     

基于统计理论方法的水文模型参数敏感性分析

参数敏感性分析是模型不确定性量化的重要环节,有助于有效识别关键参数,减少参数的不确定性影响,进而提高参数优化效率。利用Morris筛选方法定性识别相对重要参数,耦合方差分解的Sobol方法和统计理论的响应曲面模型构建一种新的定量敏感性分析方法——RSMSobol方法。以长江支流沿渡河流域的日降雨径流过程模拟为例,系统分析4种不同目标函数响应条件下新安江模型的参数敏感性。结果表明Morris方法和RSMSobol方法的集成应用极大地提高了全局敏感性分析的效率,Morris定性筛选结果为定量评估减少了模型参数维数,采用代理模型技术的RSMSobol方法减少了模型的计算消耗。     

An adaptive grid technique for minimizing heterogeneity of cells or elements

Geostatistical techniques allow simulation of properties such as porosity or conductivity on a fine scale. Typically, porous media flow modeling is performed at a coarser scale. Upscaling properties from the fine scale to the coarser scale introduces potential errors which are constrained by the degree of homogeneity of the cell or element. Adaptive grid techniques can be used to minimize the heterogeneity in the individual cells or elements, thus minimizing potential upscaling errors. A geostatistical adaptive grid (GAG) algorithm based on local minimization of heterogeneity is introduced. Local minimization allows greater control over the type of distortion permitted. Comparisons are made with a general elastic grid adjustment (GEGA) algorithm based on global minimization of heterogeneity. Several sample problems are used to test and demonstrate the two approaches.     

Decoding earth's plate tectonic history using sparse geochemical data

Accurately mapping plate boundary types and locations through time is essential for understanding the evolution of the plate-mantle system and the exchange of material between the solid Earth and surface environments.However,the complexity of the Earth system and the cryptic nature of the geological record make it difficult to discriminate tectonic environments through deep time.Here we present a new method for identifying tectonic paleo-environments on Earth through a data mining approach using global geochemical data.We first fingerprint a variety of present-day tectonic environments utilising up to 136 geochemical data attributes in any available combination.A total of 38301 geochemical analyses from basalts aged from 5-0 Ma together with a well-established plate reconstruction model are used to construct a suite of discriminatory models for the first order tectonic environments of subduction and mid-ocean ridge as distinct from intraplate hotspot oceanic environments,identifying 41,35,and 39 key discriminatory geochemical attributes,respectively.After training and validation,our model is applied to a global geochemical database of 1547 basalt samples of unknown tectonic origin aged between 1000-410 Ma,a relatively ill-constrained period of Earth’s evolution following the breakup of the Rodinia supercontinent,producing 56 unique global tectonic environment predictions throughout the Neoproterozoic and Early Paleozoic.Predictions are used to discriminate between three alternative published Rodinia configuration models,identifying the model demonstrating the closest spatio-temporal consistency with the basalt record,and emphasizing the importance of integrating geochemical data into plate reconstructions.Our approach offers an extensible framework for constructing full-plate,deeptime reconstructions capable of assimilating a broad range of geochemical and geological observations,enabling next generation Earth system models.     

A simultaneous perturbation stochastic approximation algorithm for coupled well placement and control optimization under geologic uncertainty

Development of subsurface energy and environmental resources can be improved by tuning important decision variables such as well locations and operating rates to optimize a desired performance metric. Optimal well locations in a discretized reservoir model are typically identified by solving an integer programming problem while identification of optimal well settings (controls) is formulated as a continuous optimization problem. In general, however, the decision variables in field development optimization can include many design parameters such as the number, type, location, short-term and long-term operational settings (controls), and drilling schedule of the wells. In addition to the large number of decision variables, field optimization problems are further complicated by the existing technical and physical constraints as well as the uncertainty in describing heterogeneous properties of geologic formations. In this paper, we consider simultaneous optimization of well locations and dynamic rate allocations under geologic uncertainty using a variant of the simultaneous perturbation and stochastic approximation (SPSA). In addition, by taking advantage of the robustness of SPSA against errors in calculating the cost function, we develop an efficient field development optimization under geologic uncertainty, where an ensemble of models are used to describe important flow and transport reservoir properties (e.g., permeability and porosity). We use several numerical experiments, including a channel layer of the SPE10 model and the three-dimensional PUNQ-S3 reservoir, to illustrate the performance improvement that can be achieved by solving a combined well placement and control optimization using the SPSA algorithm under known and uncertain reservoir model assumptions.     

Geophysiology of mineral deposits - a model for a biological driving force of global changes through Earth history

The upper mantle, crust, hydrosphere and atmosphere of Earth are kept in a geophysical, geochemical and thermodynamical state far from astrophysical and planetary equilibrium. The system oscillates around a quasi-stable centre following laws governing dissipative or dynamic systems. The energy and materials necessary for such global pseudo-equilibria are fed in, stored and released on a geological time-scale by (a) the energy and electron channelling processes of photosynthesis, respiration and fermentation, (b) biologically controlled accumulation of energy and matter into crustal reservoirs and much later (c) release of the latter from crust and upper mantle into surface-related geotectonical and geochemical cycles. Phototrophic and chemorganotrophic bacterial microorganisms of microbial mats, potential stromatolites or microbialites are capable of anoxygenic and oxygenic photosynthesis, of aerobic and anaerobic respiration and of organic and inorganic fermentation, i.e. disproportioning of energy-rich molecules. In this way large amounts of photosynthate are transformed on a global scale into hydrocarbons and sulphides (sulphate serving as electron acceptor for anaerobic respiration or fermentation). Inorganic reduced compounds produced by the same processes of photosynthesis followed by respiration and fermentation are stored as sulphides of iron, lead, zinc, silver, gold etc. All the aforementioned microbial processes can transfer energies and matter at a global scale. Thus disparities of the Earth's crust and mantle from the geochemical equilibrium may not be caused solely by internal temperature, radioactivity and gravity gradients, but increasingly by life processes. The biogenic formation of energy-rich compounds on a global scale delivers huge amounts of energy and electrons to the crust, which are recycled through geological time. The quantities of energy involved appear in themselves to be sufficient to provide the driving force for geotectonic processes. Thus, a model of geophysiological equilibration of geochemical cycles and geotectonics is proposed in which the biota play the role of energy and matter transmitters for geodynamic processes. Living matter controls and transfers more than 10% of the Earth's mass in this system with turnover times of up to 500 million years. The transfer speed of each individual atom according to the model must have gradually decreased since the Precambrian, while the amounts of energy and matter stored and cycled have in turn increased, as also witnessed by the increase in the thickness of the crust. Earth as a bioplanet has come of age.     

青海木里三露天水合物微生物地球化学勘查研究

以青海省天峻县木里地区天然气水合物发现区为研究对象,以天然气水合物发现井作为正演模型,采用250 m×500 m、100 m×100 m两种调查尺度,对陆地冻土区天然气水合物微生物地球化学烃检测技术的适用性进行了研究。结果显示：研究区有显著的微生物异常,指示下伏地层存在烃类富集;稀网格微生物调查查明烃类富集的有利区 ,而密网格调查很好地识别了天然气水合物分布的非均质性,与水合物钻探井所揭示的横向上天然气水合物分布不连续的特征一致。土壤吸附气的地球化学检测和分析,揭示研究区天然气水 合物的气源十分复杂,主要为热成因的煤层气和油型气。研究结果为探索天然气水合物富集规律和勘探方向提供依据和参考。微生物地球化学勘查结果精细地刻画了冻土区天然气水合物分布 规律及气源特征,结合地质学、地球物理、地球化学进行综合分析,为陆地天然气水合物的识别提供新的研究方法,同时降低天然气水合物的勘探风险,提高勘探的成功率。     

Reservoir Porosity Measurement Uncertainty and its Influence on Shale Gas Resource Assessment

Reservoir porosity is a critical parameter for the process of unconventional oil and gas resources assessment. It is difficult to determine the porosity of a gas shale reservoir, and any large deviation will directly reduce the credibility of any shale gas resources evaluation. However, there is no quantitative explanation for the accuracy of porosity measurement. In this paper, measurement uncertainty, an internationally recognized index, was used to evaluate the results of porosity measurement of gas shale plugs, and its impact on the credibility of shale gas resources assessment was determined. The following conclusions are drawn:(1) the measurement uncertainty of porosity of a shale plug is 1.76%–3.12% using current measurement methods, the upper end of which is too large to be acceptable. It is suggested that the measurement uncertainty should be factored into the standard helium gas injection porosity determination experiment, and the uncertainty should be less than 2.00% when using a high-precision pressure gauge;(2) in order to reduce the risk for exploration and decision-making, attention should be paid to the large uncertainty(30% at least) of shale gas resource assessment results, sometimes with corrections being made based on the practical considerations;(3) a pressure gauge with an accuracy of 0.25% of the full scal cannot meet the requirements of porosity measurement, and a high-precision plug cutting method or high-precision bulk volume measurement method such as one using 3 D scanning, is recommended to effectively reduce porosity uncertainty;(4) the method and process for evaluating the measurement uncertainty of gas shale porosity could also be referred for assessment of experimental quality by other laboratories.     

Probabilistic analysis of groundwater and radionuclide transport model from near surface disposal facilities

As per the regulatory requirements controlling the disposal of radioactive waste, the performance of waste disposal facilities needs to be assessed quantitatively using predictive models. This estimates the potential impact of disposal on the environment and public health. Near Surface Disposal Facilities (NSDFs), constructed to contain the low level radioactive waste are considered to model the radionuclide migration from the system to the geo-sphere. The radiation dose experienced by an individual through drinking water pathway is the endpoint of assessment of the model. A three dimensional groundwater contaminant transport model with a decaying source is modelled numerically to determine the radiation dose for short-lived and long-lived radionuclides. The consideration of uncertainties constitutes an intrinsic part of modelling. The uncertain input parameters include porosity, longitudinal dispersivity, transverse dispersivity, diffusion coefficient and distribution coefficient. The uncertainty propagation and quantification is carried out using collocation based stochastic response surface method (CSRSM). To run the simulations for the huge set of input, a code is developed using built-in python interface in the numerical model. The results are processed further to obtain the sensitive parameters affecting the output concentrations. Further, the probability of radiation dose exceeding permissible value is estimated by subset simulation.     

Multiscale mixed/mimetic methods on corner-point grids

Multiscale simulation is a promising approach to facilitate direct simulation of large and complex grid models for highly heterogeneous petroleum reservoirs. Unlike traditional simulation, approaches based on upscaling/downscaling, multiscale methods seek to solve the full flow problem by incorporating subscale heterogeneities into local discrete approximation spaces. We consider a multiscale formulation based on a hierarchical grid approach, where basis functions with subgrid resolution are computed numerically to correctly and accurately account for subscale variations from an underlying (fine-scale) geomodel when solving the global flow equations on a coarse grid. By using multiscale basis functions to discretise the global flow equations on a (moderately sized) coarse grid, one can retain the efficiency of an upscaling method and, at the same time, produce detailed and conservative velocity fields on the underlying fine grid. For pressure equations, the multiscale mixed finite-element method (MsMFEM) has been shown to be a particularly versatile approach. In this paper, we extend the method to corner-point grids, which is the industry standard for modelling complex reservoir geology. To implement MsMFEM, one needs a discretisation method for solving local flow problems on the underlying fine grids. In principle, any stable and conservative method can be used. Here, we use a mimetic discretisation, which is a generalisation of mixed finite elements that gives a discrete inner product, allows for polyhedral elements, and can (easily) be extended to curved grid faces. The coarse grid can, in principle, be any partition of the subgrid, where each coarse block is a connected collection of subgrid cells. However, we argue that, when generating coarse grids, one should follow certain simple guidelines to achieve improved accuracy. We discuss partitioning in both index space and physical space and suggest simple processing techniques. The versatility and accuracy of the new multiscale mixed methodology is demonstrated on two corner-point models: a small Y-shaped sector model and a complex model of a layered sedimentary bed. A variety of coarse grids, both violating and obeying the above mentioned guidelines, are employed. The MsMFEM solutions are compared with a reference solution obtained by direct simulation on the subgrid.     

A Monte Carlo-based framework for risk-return analysis in mineral prospectivity mapping

Quantification of a mineral prospectivity mapping (MPM) heavily relies on geological, geophysical and geochemical analysis, which combines various evidence layers into a single map. However, MPM is subject to considerable uncertainty due to lack of understanding of the metallogenesis and limited spatial data samples. In this paper, we provide a framework that addresses how uncertainty in the evidence layers can be quantified and how such uncertainty is propagated to the prediction of mineral potential. More specifically, we use Monte Carlo simulation to jointly quantify uncertainties on all uncertain evidence variables, categorized into geological, geochemical and geophysical. On stochastically simulated sets of the multiple input layers, logistic regression is employed to produce different quantifications of the mineral potential in terms of probability. Uncertainties we address lie in the downscaling of magnetic data to a scale that makes such data comparable with known mineral deposits. Additionally, we deal with the limited spatial sampling of geochemistry that leads to spatial uncertainty. Next, we deal with the conceptual geological uncertainty related to how the spatial extent of the influence of evidential geological features such as faults, granite intrusions and sedimentary formations. Finally, we provide a novel way to interpret the established uncertainty in a risk-return analysis to decide areas with high potential but at the same time low uncertainty on that potential. Our methods are illustrated and compared with traditional deterministic MPM on a real case study of prospecting skarn Fe deposition in southwestern Fujian, China.     

Fluid–rock interactions during continuous diagenesis of sandstone reservoirs and their effects on reservoir porosity

The Cretaceous sandstone reservoir in the Kuche Depression, Tarim Basin, western China, was investigated with reference to its reservoir property evolution during diagenesis. Six general diagenetic stages were recognized through petrographic, mineralogical and geochemical analyses. Fluid–rock interaction experiments were conducted under these six continuous diagenetic conditions, that is with a simulation sequence of compaction → early diagenesis → organic acid incursion I → elevated temperature/pressure → organic acid incursion II → late diagenesis. Corresponding to these six experimental stages, a total of six models were constructed. Finally, an extended model of fluid–rock interaction during diagenesis at a geological timescale (from 30 Ma to present) was constructed after various parameters had been validated. Results demonstrate that the diagenetic stages from both the experimental and numerical simulations generally matched findings obtained from the petrographic and geochemical analyses: (i) With compaction becoming weakened, cementation by various minerals was gradually increased. (ii) Quartz overgrowth occurred because the contemporaneous sedimentary water was alkaline. (iii) Most minerals (for example, calcite and feldspar minerals) displayed dissolution owing to the first organic acid incursion, resulting in the visual porosity increasing to 29·26%. (iv) Increases in temperature and pressure caused a minor fluctuation of the porosity change. (v) The cement that formed during earlier stages largely dissolved with the second organic acid incursion. (vi) During the last stage, the reservoir fluid was diluted by sedimentary alkaline water and most minerals precipitated under an alkalic environment. The present porosity simulated is about 11·4%, comparable with the actually measured data. This study demonstrates that the combination of petrographic observations, laboratory experiments and numerical simulations can not only reconstruct the diagenetic process, but also provide a quantitative evaluation and prediction of reservoir petrophysical properties.