Impacts of proppant distribution on development of tight oil reservoirs with threshold pressure gradient

Field evidence indicates that proppant distribution and threshold pressure gradient have great impacts on well productivity.Aiming at the development of unconventional oil reservoirs in Triassic Chang-7 Unit,Ordos Basin of China,we presented an integrated workflow to investigate how(1)proppant placement in induced fracture and(2)non-linear flow in reservoir matrix would affect well productivity and fluid flow in the reservoir.Compared with our research before(Yue et al.,2020),here we extended this study into the development of multi-stage fractured horizontal wells(MFHWs)with large-scale complicated fracture geometry.The integrated workflow is based on the finite element method and consists of simulation models for proppant-laden fluid flow,fracture flow,and non-linear seepage flow,respectively.Simulation results indicate that the distribution of proppant inside the induced cracks significantly affects the productivity of the MFHW.When we assign an idealized proppant distribution instead of the real distribution,there will be an overestimation of 44.98%in daily oil rate and 30.63%in cumulative oil production after continuous development of 1000 days.Besides,threshold pressure gradient(TPG)also significantly affects the well performance in tight oil reservoirs.If we simply apply linear Darcy’s law to the reservoir matrix,the overall cumulative oil production can be overrated by 77%after 1000 days of development.In general,this research provides new insights into the development of tight oil reservoirs with TPG and meanwhile reveals the significance of proppant distribution and non-linear fluid flow in the production scenario design.

Characteristics of unsteady flow in porous media while considering threshold pressure gradient with Green＇s function

The flow behavior in porous media with threshold pressure gradient(TPG) is more complex than Darcy flow and the equations of motion, and outer boundary and inner boundary with TPG are also different from Darcy flow for unsteady flow of a producing well in a reservoir. An analytic method to solve this kind of problem is in a need of reestablishment. The classical method of Green's function and Newman product principle in a new way are used to solve the unsteady state flow problems of various shapes of well and reservoir while considering the TPG. Four Green's functions of point, line, band and circle while considering the TPG are achieved. Then, two well models of vertical well and horizontal well are built and simultaneously the function to calculate the moving boundary of each well model is provided. The results show that when considering TPG the pressure field is much different, which has a sudden pressure change, with a moving boundary in it. And the moving boundary of each well model increases with time but slows down rapidly, especially when the TGP is large.

Numerical investigation of a coupled moving boundary model of radial flow in low-permeable stress-sensitive reservoir with threshold pressure gradient

The threshold pressure gradient and formation stress-sensitive effect as the two prominent physical phenomena in the development of a low-permeable reservoir are both considered here for building a new coupled moving boundary model of radial flow in porous medium. Moreover, the wellbore storage and skin effect are both incorporated into the inner boundary conditions in the model. It is known that the new coupled moving boundary model has strong nonlinearity. A coordinate transformation based fully implicit finite difference method is adopted to obtain its numerical solutions. The involved coordinate transformation can equivalently transform the dynamic flow region for the moving boundary model into a fixed region as a unit circle, which is very convenient for the model computation by the finite difference method on fixed spatial grids. By comparing the numerical solution obtained from other different numerical method in the existing literature, its validity can be verified. Eventually, the effects of permeability modulus, threshold pressure gradient, wellbore storage coefficient, and skin factor on the transient wellbore pressure, the derivative, and the formation pressure distribution are analyzed respectively.

TRANSIENT PRESSURE OF PERCOLATION THROUGH ONE DIMENSION POROUS MEDIA WITH THRESHOLD PRESSURE GRADIENT

This paper studies the transient pressure of percolation during one production and one shutting in one dimension porous media with threshold pressure gradient, the differential equations are derived and solved with numerical computation. Basing on numerical solution, it is analyzed that: 1. the relation between the steady pressure at well bore (or at endpoint) and threshold pressure gradient, shut-in time, and the corresponding formulae are derived; 2, the regulation of transient pressure peak. The result is very useful and will help experiments and applications in the development of low permeability reservoirs with threshold pressure gradient.

The establishment of a new deliverability equation considering threshold pressure gradient

The flowing mechanism of a low permeability gas reservoir is different from a conventional gas reservoir,especially for that with higher irreducible water saturation the threshold pressure gradient exists. At present,in all the deliverability equation,the additional pressure drop caused by the threshold pressure gradient is viewed as constant,but this method has big error in the practical application. Based on the non-Darcy steady flow equation,the limited integral of the additional pressure drop is solved in this paper and it is realized that the additional pressure drop is not a constant but has something to do with production data,and a new deliverability equation is derived,with the relevant processing method for modified isochronal test data. The new deliverability equation turns out to be practical through onsite application.

Study on Productivity Model of Herringbone-Like Laterals Wells and Optimization of Morphological Parameters Considering Threshold Pressure Gradient in Heavy Oil Reservoirs

Compared with conventional well, herringbone-like laterals wells can increase the area of oil release, and can reduce the number of wellhead slots of platforms,?and?also can greatly improve the development efficiency. Based on threshold pressure gradient in heavy oil reservoir,?and?the applied principle of mirror reflection and superposition, the pressure distribution equation of herringbone-like laterals wells is obtained in heavy oil reservoir. Productivity model of herringbone-like laterals wells is proposed by reservoir-wellbore steady seepage. The example shows that the productivity model is great accuracy?to?predict the productivity of herringbone-like laterals wells. The model is used to analyze the branching length, branching angle, branching symmetry, branching position and spacing and their effects on productivity of herringbone-like laterals wells. The principle of optimizing the well shape of herringbone-like laterals wells is proposed.

Tight gas production model considering TPG as a function of pore pressure,permeability and water saturation

Threshold pressure gradient has great importance in efficient tight gas field development as well as for research and laboratory experiments.This experimental study is carried out to investigate the threshold pressure gradient in detail.Experiments are carried out with and without back pressure so that the effect of pore pressure on threshold pressure gradient may be observed.The trend of increasing or decreasing the threshold pressure gradient is totally opposite in the cases of considering and not considering the pore pressure.The results demonstrate that the pore pressure of tight gas reservoirs has great influence on threshold pressure gradient.The effects of other parameters like permeability and water saturation,in the presence of pore pressure,on threshold pressure gradient are also examined which show that the threshold pressure gradient increases with either a decrease in permeability or an increase in water saturation.Two new correlations of threshold pressure gradient on the basis of pore pressure and permeability,and pore pressure and water saturation,are also introduced.Based on these equations,new models for tight gas production are proposed.The gas slip correction factor is also considered during derivation of this proposed tight gas production models.Inflow performance relationship curves based on these proposed models show that production rates and absolute open flow potential are always be overestimated while ignoring the threshold pressure gradients.

考虑启动压力梯度的致密油藏水平井裂缝干扰渗流特征

针对致密油开发中体积压裂水平井裂缝干扰的问题,在三线性流模型的基础上,通过引入半渗透边界条件和井间干扰系数α,建立了考虑未改造区启动压力梯度的致密油藏水平井裂缝干扰渗流模型,对不同干扰情况下水平井井底压力动态及产量递减特征进行了研究。研究结果表明:(1)α越大,裂缝干扰条数越多,压力动态曲线改造区线性流持续的时间越长,改造区窜流、拟稳定流动发生得越晚;未改造区启动压力梯度越大,拟稳定流发生的时间就越早。(2)裂缝导流能力越大,主裂缝线性流出现时间越早,两井裂缝导流能力越接近,α对压力动态的影响较明显。(3)α越大,井底压力相对较低的水平井初期产量越高,至晚期后,产量下降越明显,无因次启动压力梯度越大,后期产量递减越快。(4)裂缝导流能力越小,前期阶段产量曲线越靠下,两井裂缝导流能力相近时,α对产量的干扰相对较大。

稠油油藏体相流体非线性渗流理论模型

根据稠油油藏体相流体渗流特点,建立基于稠油吸附边界层和屈服特性影响下的稠油体相流体非线性渗流理论模型及启动压力梯度理论公式,并利用岩心渗流与启动压力梯度试验结果对理论模型计算结果进行验证。结果表明:理论计算结果与试验结果拟合较好,启动压力梯度理论公式计算结果平均偏差为7.77%,稠油油藏体相流体非线性渗流理论模型计算结果平均偏差为7.50%,均在可接受偏差范围内,并且该模型针对不同流变类型的流体渗流都具有较好的普适性。

多层砂岩油藏油井层间干扰机理解析及讨论

多层砂岩油藏开发过程中普遍存在层间干扰现象,众多学者从不同角度开展了层间干扰机理、规律及应对策略研究,但层间干扰机理的认识程度多数停留在层间干扰系数宏观规律统计及对矿场应用的经验指导层面,有必要开展深入的定量化解析及讨论。本文首先从矿场油井层间干扰测试资料分析入手,确定了层间干扰研究的突破点,然后采用油藏数值模拟方法模拟了考虑启动压力梯度影响的油井产能测试过程,厘清了油井层间干扰规律,并综合诸多因素分析揭示了多层砂岩油藏层间干扰机理;最后深化了储层纵向非均质性认识,并探讨了油藏非均质性表征研究思路,为提高多层砂岩油藏油井产能预测精度、制定更加精细的开发对策提供理论、技术指导。

页岩油藏逆向渗吸的最大渗吸动用距离计算方法

渗吸是页岩油藏压裂开发的重要机理,最大渗吸动用距离是渗吸动用范围评价的直接指标,对页岩油藏开发具有重要意义。为确定页岩油藏最大渗吸动用距离,在表征页岩油藏毛细管力曲线基础上,运用渗流理论、数值计算方法,建立了页岩油藏逆向渗吸最大渗吸动用距离计算方法,通过与室内实验结果进行对比,验证了计算方法的可靠性,同时开展了最大渗吸动用距离影响因素分析。研究表明:随着渗透率增加,最大渗吸动用距离呈线性增加,但达到最大渗吸动用距离所用时间呈指数降低;油水黏度比对最大渗吸动用距离无影响,但原油黏度越大,达到最大渗吸动用距离所需时间越长;当储层渗透率为0.05 mD、接触角为45°、界面张力为50 mN/m时,最大渗吸动用距离为2.2 m,所需时间为170 d,用时较长。该研究可为页岩油藏渗吸动用范围评价提供借鉴。

启动压力梯度对稠油油藏开发指标的影响

稠油启动压力梯度的存在加剧了稠油渗流的阻力,为稠油开发造成了一定困难。针对该问题,利用NRSNL非线性渗流模拟软件建立机理模型,研究稠油油藏在不同韵律、渗透率级差和原油黏度条件下启动压力梯度存在与否对剩余油分布、含水率、采出程度等开发指标的影响。结果表明:启动压力梯度的存在会降低油藏采出程度,油井含水率上升较快,开采20年,采出程度降低1.72%~3.09%,含水上升1.31%~2.78%;相同启动压力梯度条件下,反韵律储层采出程度低于正韵律与复合韵律;原油黏度越大、渗透率级差越大,启动压力梯度对采出程度的影响越大。

Evaluation of Well Spacing for Primary Development of Fractured Horizontal Wells in Tight Sandstone Gas Reservoirs

Methods for horizontal well spacing calculation in tight gas reservoirs are still adversely affected by the complexity of related control factors,such as strong reservoir heterogeneity and seepage mechanisms.In this study,the stress sensitivity and threshold pressure gradient of various types of reservoirs are quantitatively evaluated through reservoir seepage experiments.On the basis of these experiments,a numerical simulation model(based on the special seepage mechanism)and an inverse dynamic reserve algorithm(with different equivalent drainage areas)were developed.The well spacing ranges of Classes I,II,and III wells in the Q gas field are determined to be 802–1,000,600–662,and 285–400 m,respectively,with their average ranges as 901,631,and 342.5 m,respectively.By considering both the pairs of parallel well groups and series well groups as examples,the reliability of the calculation results is verified.It is shown that the combination of the two models can reduce errors and provide accurate results.

海上低流度储层启动压力梯度测试新方法

目前业内主要用数值计算方法和岩心实验法获取启动压力梯度,但在勘探阶段岩心资料较少,且缺少利用现有测试资料确定启动压力梯度的方法。基于地层测试资料,利用渗流力学理论和试井分析方法刻画了低渗储层中流体流动过程,建立了一种基于测试资料的启动压力梯度计算新方法,并针对性完善了现场测试工艺制度,形成了一套低流度储层测试及评价方法。该方法在南海西部WSX-1井中进行了实践,顺利完成了地层测试及储层评价,计算得到了储层启动压力梯度1.55 MPa/100 m,说明了该技术方法的可行性。研究结果对海上低流度储层勘探开发具有一定借鉴意义。

WELL TESTING ANALYSIS FOR HORIZONTAL WELL WITH CONSIDERATION OF THRESHOLD PRESSURE GRADIENT IN TIGHT GAS RESERVOIRS

A fundamental solution for homogeneous reservoir in infinite space is derived by using the point source function with the consideration of the threshold pressure gradient. The fundamental solution of the continuous point source function is then derived based on the Green function. Various boundary conditions of the reservoirs are considered for this case and the corresponding solutions are obtained through the mirror image reflection and the principle of superimposition. The line source solution is obtained by integration. Subsequently, the horizontal-well bottom hole pressure response function for a non-linear gas flow in the homogeneous gas reservoir is obtained, and the response curve of the dimensionless bottom hole pressure and the derivative for a horizontal well in the homogeneous gas reservoir are obtained. In the end, the sensitivities of the relevant parameters are analyzed, The well test model presented in this paper can be used as the basis of the horizontal well test analysis for tight gas reservoirs.

Threshold pressure gradient of fluid flow through multi-porous media in low and extra-low permeability reservoirs

After analyzing many studies of fluid flow theory of multi-porous media in low and extra-low permeability reservoirs and the numerical simulation of non-Darcy flow, we found that a negative flow rate occurs in the existing non-Darcy flow equation, which is unreasonable. We believe that the existing equation can only be considered as a discriminant to judging Darcy flow or non-Darcy flow, and cannot be taken as a fluid flow governing equation of multi-porous media. Our analysis of the experimental results shows that the threshold pressure gradient(TPG) of low and extra-low permeability reservoirs is excessively high, and does not conform to fluid flow through multi-porous media in the actual reservoir situation. Therefore, we present a reasonable TPG ranging from 0.006 to 0.04 MPa/m at the well depth of 1500 m and oil drainage distance of 500 m. The results of our study also indicate that the non-Darcy flow phenomenon will disappear when the TPG reaches a certain value. In addition, the TPG or non-Darcy flow in low and extra-low permeability reservoirs does not need to be considered in the productivity prediction and reservoir numerical simulation. At present, the black oil model or dual-porous media is suitable for simulating low and extra-low permeability reservoirs.

Dual-porosity model of rate transient analysis for horizontal well in tight gas reservoirs with consideration of threshold pressure gradient

Most researches of the threshold pressure gradient in tight gas reservoirs are experimental and mainly focus on the transient pressure response, without paying much attention to the transient rate decline. This paper establishes a dual-porosity rate transient decline model for the horizontal well with consideration of the threshold pressure gradient, which represents the non-Darcy flow in a fracture system. The solution is obtained by employing the Laplace transform and the orthogonal transform. The bi-logarithmic type curves of the dimensionless production rate and derivative are plotted by the Stehfest numerical inversion method. Seven different flow regimes are identified and the effects of the influence factors such as the threshold pressure gradient, the elastic storativity ratio, and the cross flow coefficient are discussed. The presented research could interpret the production behavior more accurately and effectively for tight gas reservoirs.

Discussion of liquid threshold pressure gradient

Some authors believe that a minimum pressure gradient(called threshold pressure gradient(TPG))is required before a liquid starts to flow in a porous medium.In a tight or shale oil formation,this TPG phenomenon becomes more important,as it is more difficult for a fluid to flow.In this paper,experimental data on TPG published in the literature are carefully reviewed.What we found is that a very low flow velocity corresponding to a very low pressure gradient cannot be measured in the experiments.Experiments can only be done above some measurable flow velocities.If these flow velocities and their corresponding pressure gradients are plotted in an XY plot and extrapolated to zero velocity,a non-zero pressure gradient corresponds to this zero velocity.This non-zero pressure gradient is called threshold pressure gradient in the literature.However,in the regime of very low velocity and very low pressure gradient,the data gradually approach to the origin of the plot,demonstrating a non-linear relationship between the pressure gradient and the velocity.But the data do not approach to a point of zero velocity and a threshold pressure gradient.Therefore,the concept of threshold pressure gradient is a result of data misinterpretation of available experimental data.The correct interpretation is that there are two flow regimes:nonlinear flow regime(non-Darcy flow regime)when the pressure gradients are low,and linear flow regime(Darcy flow regime)when the pressure gradient is intermediate or high.The nonlinear flow regime starts from the origin point.As the pressure gradient is increased,the curve becomes a straight line demonstrating the linear flow regime.We have verified our views by first analyzing the causes of non-Darcy flow,and then systematically analyzed typical experimental data and correlations in the literature.We conclude that TPG does not exist.We also use several counter examples to support our conclusion.

Exact analytical solutions for moving boundary problems of one-dimensional flow in semi-infinite porous media with consideration of threshold pressure gradient

By defining new dimensionless variables, nonlinear mathematical models for one-dimensional flow with unknown moving boundaries in semi-infinite porous media are modified to be solved analytically. The exact analytical solutions for both constant-rate and constant-pressure inner boundary constraint problems are obtained by applying the Green＇s function. Two transcendental equations for moving boundary problems are obtained and solved using the Newton-Raphson iteration. The exact analytical solutions are then compared with the approximate solutions. The Pascal＇s approximate formula in reference is fairly accurate for the moving boundary development under the constant-rate condition. But another Pascal＇s approximate formula given in reference is not very robust for constant-pressure condition problems during the early production period, and could lead to false results at the maximum moving boundary distance. Our results also show that, in presence of larger TPG, more pressure drop is required to maintain a constant-rate production. Under the constant-pressure producing condition, the flow rate may decline dramatically due to a large TPG. What＇s more, there exists a maximum distance for a given TPG, beyond which the porous media is not disturbed.

低渗致密储层微纳米孔喉分布及其对渗流的影响

低渗-致密储层微观孔喉分布有较大差异,导致其渗流特征亦有明显不同。将室内实验与油藏工程计算相结合,定量研究了低渗-致密储层微纳米孔喉分布特征及其对渗流的影响。结果表明:1)孔喉半径小于1μm的孔喉体积占总孔喉体积的主体;2)岩心渗流特征曲线呈非线性渗流规律,渗透率降低,启动压力梯度显著增大,附加渗流阻力占总渗流阻力的比例也增大,研究物性范围内,附加渗流阻力占比均大于50%,渗透率为0.4 mD时,附加渗流阻力占比可达84.8%;3)微纳米孔喉的存在使得油井泄油半径降低,渗透率为0.4 mD时,极限泄油半径仅28.5 m,制约了井间及压裂水平井段间原油的动用。该研究成果可为认识低渗-致密油藏流体渗流规律和制定合理开发方案提供指导。