Productivity Prediction Model of Perforated Horizontal Well Based on Permeability Calculation in Near-Well High Permeability Reservoir Area

To improve the productivity of oil wells,perforation technology is usually used to improve the productivity of horizontal wells in oilfield exploitation.After the perforation operation,the perforation channel around the wellbore will form a near-well high-permeability reservoir area with the penetration depth as the radius,that is,the formation has different permeability characteristics with the perforation depth as the dividing line.Generally,the permeability is measured by the permeability tester,but this approach has a high workload and limited application.In this paper,according to the reservoir characteristics of perforated horizontal wells,the reservoir is divided into two areas:the original reservoir area and the near-well high permeability reservoir area.Based on the theory of seepage mechanics and the formula of open hole productivity,the permeability calculation formula of near-well high permeability reservoir area with perforation parameters is deduced.According to the principle of seepage continuity,the seepage is regarded as the synthesis of two directions:the horizontal plane elliptic seepage field and the vertical plane radial seepage field,and the oil well productivity prediction model of the perforated horizontal well is established by partition.The model comparison demonstrates that the model is reasonable and feasible.To calculate and analyze the effect of oil well production and the law of influencing factors,actual production data of the oilfield are substituted into the oil well productivity formula.It can effectively guide the technical process design and effect prediction of perforated horizontal wells.

Productivity analysis of horizontal wells intercepted by multiple finite-conductivity fractures

Horizontal wells in the anisotropic reservoirs can be stimulated by hydraulic fracturing in order to create multiple finite-conductivity vertical fractures. Several methods for evaluating the productivity of the horizontal wells have been presented in the literature. With such methods, however, it is still difficult to obtain an accurate result. This paper firstly presents the dimensionless conductivity theory of vertical fractures. Then models for calculating the equivalent wellbore radius and the skin factor due to flow convergence to the well bore are proposed after analyzing the steady-state flow in porous reservoirs. By applying the superposition principle to the pressure drop, a new method for evaluating the productivity of horizontal wells intercepted by multiple finite-conductivity fractures is developed. The influence of fracture conductivity and fracture half length on the horizontal well productivity is quantitatively analyzed with a synthetic case. Optimum fracture number and fracture space are further discussed in this study. The results prove that the method outlined here should be useful to design optimum fracturing of horizontal wells.

A novel steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs

It is known that there is a discrepancy between field data and the results predicted from the previous equations derived by simplifying three-dimensional（3-D） flow into two-dimensions（2-D）.This paper presents a new steady-state productivity equation for horizontal wells in bottom water drive gas reservoirs.Firstly,the fundamental solution to the 3-D steady-state Laplace equation is derived with the philosophy of source and the Green function for a horizontal well located at the center of the laterally infinite gas reservoir.Then,using the fundamental solution and the Simpson integral formula,the average pseudo-pressure equation and the steady-state productivity equation are achieved for the horizontal section.Two case-studies are given in the paper,the results calculated from the newly-derived formula are very close to the numerical simulation performed with the Canadian software CMG and the real production data,indicating that the new formula can be used to predict the steady-state productivity of such horizontal gas wells.

A Well Productivity Model for Multi-Layered Marine and Continental Transitional Reservoirs with Complex Fracture Networks

Using the typical characteristics of multi-layered marine and continental transitional gas reservoirs as a basis,a model is developed to predict the related well production rate.This model relies on the fractal theory of tortuous capillary bundles and can take into account multiple gas flow mechanisms at the micrometer and nanometer scales,as well as the flow characteristics in different types of thin layers(tight sandstone gas,shale gas,and coalbed gas).Moreover,a source-sink function concept and a pressure drop superposition principle are utilized to introduce a coupled flow model in the reservoir.A semi-analytical solution for the production rate is obtained using a matrix iteration method.A specific well is selected for fitting dynamic production data,and the calculation results show that the tight sandstone has the highest gas production per unit thickness compared with the other types of reservoirs.Moreover,desorption and diffusion of coalbed gas and shale gas can significantly contribute to gas production,and the daily production of these two gases decreases rapidly with decreasing reservoir pressure.Interestingly,the gas production from fractures exhibits an approximately U-shaped distribution,indicating the need to optimize the spacing between clusters during hydraulic fracturing to reduce the area of overlapping fracture control.The coal matrix water saturation significantly affects the coalbed gas production,with higher water saturation leading to lower production.

Effect of perforation density distribution on production of perforated horizontal wellbore

To address the issue of horizontal well production affected by the distribution of perforation density in the wellbore,a numerical model for simulating two-phase flow in a horizontal well is established under two perforation density distribution conditions(i.e.increasing the perforation density at inlet and outlet sections respectively).The simulation results are compared with experimental results to verify the reliability of the numerical simulation method.The behaviors of the total pressure drop,superficial velocity of air-water two-phase flow,void fraction,liquid film thickness,air production and liquid production that occur with various flow patterns are investigated under two perforation density distribution conditions based on the numerical model.The total pressure drop,superficial velocity of the mixture and void fraction increase with the air flow rate when the water flow rate is constant.The liquid film thickness decreases when the air flow rate increases.The liquid and air productions increase when the perforation density increases at the inlet section compared with increasing the perforation density at the outlet section of the perforated horizontal wellbore.It is noted that the air production increases with the air flow rate.Liquid production increases with the bubble flow and begins to decrease at the transition point of the slug-stratified flow,then increases through the stratified wave flow.The normalized liquid flux is higher when the perforation density increases at the inlet section,and increases with the radial air flow rate.

The productivity evaluation model and its application for finite conductivity horizontal wells in fault block reservoirs

It is very difficult to evaluate the productivity of horizontal wells in fault block reservoirs due to the influence of fault sealing.On the basis of the method of images and source-sink theory,a semianalytical model coupling reservoir and finite conductivity horizontal wellbore flow dynamics was built,in which the influence of fault sealing was taken into account.The distribution of wellbore flow and radial inflow profiles along the horizontal interval were also obtained.The impact of the distance between the horizontal well and the fault on the well productivity was quantitatively analyzed.Based on this analysis,the optimal distance between the horizontal well and the fault in banded fault block reservoirs could be determined.According to the field application,the relative error calculated by the model proposed in this paper is within ±15%.It is an effective evaluation method for the productivity of horizontal wells in fault block reservoirs.The productivity of the horizontal well increases logarithmically as the distance between the horizontal well and the fault increases.The optimal distance between the horizontal well and the fault is 0.25-0.3 times the horizontal well length.

Fully coupled fluid-solid productivity numerical simulation of multistage fractured horizontal well in tight oil reservoirs

A mathematical model, fully coupling multiple porous media deformation and fluid flow, was established based on the elastic theory of porous media and fluid-solid coupling mechanism in tight oil reservoirs. The finite element method was used to determine the numerical solution and the accuracy of the model was verified. On this basis, the model was used to simulate productivity of multistage fractured horizontal wells in tight oil reservoirs. The results show that during the production of tight oil wells, the reservoir region close to artificial fractures deteriorated in physical properties significantly, e.g. the aperture and conductivity of artificial fractures dropped by 52.12% and 89.02% respectively. The simulations of 3000-day production of a horizontal well in tight oil reservoir showed that the predicted productivity by the uncoupled model had an error of 38.30% from that by the fully-coupled model. Apparently, ignoring the influence of fluid-solid interaction effect led to serious deviations of the productivity prediction results. The productivity of horizontal well in tight oil reservoir was most sensitive to the start-up pressure gradient, and second most sensitive to the opening of artificial fractures. Enhancing the initial conductivity of artificial fractures was helpful to improve the productivity of tight oil wells. The influence of conductivity, spacing, number and length of artificial fractures should be considered comprehensively in fracturing design. Increasing the number of artificial fractures unilaterally could not achieve the expected increase in production.

The Productivity Model of Horizontal Well Considering Acidification Effect in Anisotropic Reservoirs

When the horizontal well was acidized, in order to predict the productivity, through coordinate transformation method, based on the formation seepage model of horizontal well after acidification,?wededuced the formula of horizontal well local skin factor,?established the coupling model of reservoir and horizontal wellbore flow,?and?deduced the semi-analytical productivity model of horizontal well considering the change of local skin factor. Based on the example, the effect of horizontal well length, reservoir anisotropy coefficient, mud damage depth and damage degree on the production-increasing ratio after acidification were studied. The results showed reservoir with greater anisotropy, serious wellbore pollution and deeper mud invasion near wellbore,?and?that the stimulation effect of horizontal well after acidification was better.

Study on productivity of horizontal wells with segmental perforation based on pseudo steady-state flow

Segmental perforation is widely used for horizontal wells. However,the flow of fluid in porous media is a complex problem. Using the Fourier transform,principle of potential superposition,trigonometric function transform,asymptotic analyses,a pressure solution of a pseudo steady-state flow model in 3D circular-boxed media has been established. Comparing with the productivity of vertical wells,an equivalence radius model can be obtained. Based on the model,a method of evaluating the productivity of segmental perforation horizontal well is presented by means of principle of superposition. It shows that the equivalence radius is different for various positions of horizontal wells; the output of both ends of horizontal wells is greater than the others under the same length of perforation interval; it is more important to obtain high productivity by increasing the length of perforation interval than enlarging the spacing between perforation intervals. The result of this research can be used to ascertain the yield of each perforated interval.

Blasingame production decline type curves for analysing a multi-fractured horizontal well in tight gas reservoirs

Production decline analysis has been considered as an important method to obtain the flow parameters, reservoir properties and original gas in place. Although advanced Blasingame production decline analysis methods for vertical wells, fractured wells and horizontal wells are widely used, limited study has conducted on Blasingame production decline type curves for multi-fractured horizontal well(MFHW). Based on the perpendicular bisection(PEBI) grids, a numerical model was developed and the solution was obtained using control volume finite element method and the fully implicit method. Blasingame production decline-type curves of the infinitely conductive MFHW were plotted through computer programming. A field case was presented to analyse and verify the model developed. Five flow regimes, including early formation linear flow, early radial flow, compound linear flow, transient flow and pseudo-radial flow, are recognized. Fracture spacing is the main factor that affects early radial flow, compound linear flow and transient flow, the distance from the well to the circular boundary affects the pseudo-radial flow, and the type curves are also significantly affected by the formation permeability, fracture number and fracture half-length. The validation of field case suggests that the Blasingame production decline type curves proposed in this work can be applied to the production decline analysis for MFHW in tight gas reservoirs.

Production Capacity Evaluation of Horizontal Shale Gas Wells in Fuling District

One of the important indicators of shale gas reservoir excavation is capacity evaluation,which directly affects whether large-scale shale gas reservoirs can be excavated.Capacity evaluation is the basis of system analysis and dynamic prediction.Therefore,it is particularly important to conduct capacity evaluation studies on shale gas horizontal wells.In order to accurately evaluate the horizontal well productivity of shale gas staged fracturing,this paper uses a new method to evaluate the productivity of Fuling shale gas.The new method is aimed at the dynamic difference of horizontal wells and effectively analyzes the massive data,which are factors affecting the productivity of shale gas horizontal wells.According to the pressure system,production dynamic characteristics,well trajectory position,fracturing transformation mode and penetration depth,32 wells were divided into four types.Then,based on the classification,the principal component analysis methods can be used to evaluate the horizontal well productivity of shale gas.The new method of capacity evaluation has improved the accuracy by 10.25%compared with the traditional method,which provides a theoretical basis for guiding the efficient development of the horizontal wells of Fuling shale gas.

Steam Flooding after Steam Soak in Heavy Oil Reservoirs through Extended-reach Horizontal Wells

This paper presents a new development scheme of simultaneous injection and production in a single horizontal well drilled for developing small block reservoirs or offshore reservoirs. It is possible to set special packers within the long completion horizontal interval to establish an injection zone and a production zone. This method can also be used in steam flooding after steam soak through a horizontal well. Simulation results showed that it was desirable to start steam flooding after six steam soaking cycles and at this time the oil/steam ratio was 0.25 and oil recovery efficiency was 23.48%. Steam flooding performance was affected by separation interval and steam injection rate. Reservoir numerical simulation indicated that maximum oil recovery would be achieved at a separation section of 40-50 m at steam injection rate of 100-180 t/d; and the larger the steam injection rate, the greater the water cut and pressure difference between injection zone and production zone. A steam injection rate of 120 t/d was suitable for steam flooding under practical injection-production conditions. All the results could be useful for the guidance of steam flooding projects.

Numerical Simulation Study on the Effect of Horizontal Well Reservoir Stimulation for Gas Hydrate Production

A new gas hydrate reservoir stimulation method of in-situ fracturing with transient heating is proposed, in line with analysis of the technological bottlenecks faced by marine gas hydrate production. This method injects the developed chemical reagents into a hydrate reservoir through hydraulic fracturing, releasing heat during the chemical reaction to increase the hydrate decomposition rate. The chemical reaction product furthermore has a honeycomb structure to support fractures and increase reservoir permeability. Based on the geological model of natural gas hydrate in the South China Sea, three development methods are simulated to evaluate hydrate production capacity, consisting of horizontal well, fractured horizontal well and in-situ fracturing with transient heating well. Compared with the horizontal well, the simulation results show that the cumulative gas production of the fractured horizontal well in one year is 7 times that of the horizontal well, while the cumulative gas production of in-situ fracturing with transient heating well is 12 times that of the horizontal well, which significantly improves daily efficiency and cumulative gas production. In addition, the variation patterns of hydrate saturation and temperature-pressure fields with production time for the three exploitation plans are presented, it being found that three sensitive parameters of fracture conductivity, fracture half-length and fracture number are positively correlated with hydrate production enhancement. Through the simulations, basic data and theoretical support for the optimization of gas hydrate reservoir stimulation scheme has been provided.

Simulation logging experiment and interpretation model of array production logging measurements in a horizontal well

The distributions of local velocity and local phase holdup along the radial direction of pipes are complicated because of gravity differentiation,and the distribution of fluid velocity fi eld changes along the gravity direction in horizontal wells.Therefore,measuring the mixture flow and water holdup is difficult,resulting in poor interpretation accuracy of the production logging output profile.In this paper,oil–water two-phase flow dynamic simulation logging experiments in horizontal oil–water two-phase fl ow simulation wells were conducted using the Multiple Array Production Suite,which comprises a capacitance array tool(CAT)and a spinner array tool(SAT),and then the response characteristics of SAT and CAT in diff erent fl ow rates and water cut production conditions were studied.According to the response characteristics of CAT in diff erent water holdup ranges,interpolation imaging along the wellbore section determines the water holdup distribution,and then,the oil–water two-phase velocity fi eld in the fl ow section was reconstructed on the basis of the fl ow section water holdup distribution and the logging value of SAT and combined with the rheological equation of viscous fl uid,and the calculation method of the oil–water partial phase fl ow rate in the fl ow section was proposed.This new approach was applied in the experiment data calculations,and the results are basically consistent with the experimental data.The total fl ow rate and water holdup from the calculation are in agreement with the set values in the experiment,suggesting that the method has high accuracy.

Revolutionizing Tight Reservoir Production: A Novel Dual-Medium Unsteady Seepage Model for Optimizing Volumetrically Fractured Horizontal Wells

This study presents an avant-garde approach for predicting and optimizing production in tight reservoirs,employing a dual-medium unsteady seepage model specifically fashioned for volumetrically fractured horizontal wells.Traditional models often fail to fully capture the complex dynamics associated with these unconventional reservoirs.In a significant departure from these models,our approach incorporates an initiation pressure gradient and a discrete fracture seepage network,providing a more realistic representation of the seepage process.The model also integrates an enhanced fluid-solid interaction,which allows for a more comprehensive understanding of the fluid-structure interactions in the reservoir.This is achieved through the incorporation of improved permeability and stress coupling,leading to more precise predictions of reservoir behavior.The numerical solutions derived from the model are obtained through the sophisticated finite element method,ensuring high accuracy and computational efficiency.To ensure the model’s reliability and accuracy,the outcomes were tested against a real-world case,with results demonstrating strong alignment.A key revelation from the study is the significant difference between uncoupled and fully coupled volumetrically fractured horizontal wells,challenging conventional wisdom in the field.Additionally,the study delves into the effects of stress,fracture length,and fracture number on reservoir production,contributing valuable insights for the design and optimization of tight reservoirs.The findings from this study have the potential to revolutionize the field of tight reservoir prediction and management,offering significant advancements in petroleum engineering.The proposed approach brings forth a more nuanced understanding of tight reservoir systems and opens up new avenues for optimizing reservoir management and production.

Partial phase flow rate measurements for stratified oil-water flow in horizontal wells

To accurately measure and evaluate the oil-water production profile of horizontal wells, a dynamic measurement experiment of oil-water two-phase flow in horizontal wells and numerical simulation were combined to establish a method for measuring the partial phase flow rate of oil-water two-phase stratified flow in horizontal wells. An experimental work was performed in horizontal oil-water two-phase flow simulation well using combination production logging tool including mini-capacitance sensor and mini-spinner. The combination tool provides a recording of holdup and velocity profiles at five different heights of the borehole cross-section. The effect of total flow rate and water-cut on the response of spinner and capacitive sensor at five measured positions were investigated. The capacitance water holdup interpolation imaging algorithm was used to determine the local fluid property and oil-water interface height, and the measured local fluid speed was combined with the numerical simulation result to establish an optimal calculation model for obtaining the partial phase flow rate of the oil-water two-phase stratified flow in the horizontal well. The calculated flow rates of five measured points are basically consistent with the experimental data, the total flow rate and water holdup from calculation are in agreement with the set values in the experiment too, suggesting that the method has high accuracy.

Analysis of Gas and Liquid Two-Phase Slug Flow Production Logging Interpretation Model in near Horizontal Shale Gas Wells

The development of shale gas reservoir is mainly based on horizontal well production.Slug flow of gas-liquid two-phase is invariably encountered in inclined wells and horizontal wells of a producing environment.Due to gravitational differentiation,oil-water two-phase flow pattern,the local velocity and local phase holdup along the radial direction of pipe in near horizontal wells will perform complicatedly.This paper presented the results of an experimental study and a theoretical analysis of two-phase gas/water flow in horizontal and highly inclined systems.Extensive experiments were conducted using a test loop made of 124 mm diameter acrylic pipe with inclination angles from the horizontal of 0°,5°,15°,45°,°2°,°5°and°10°,and with the total flow rate ranging from 50 to 800 m3/day.Based on the research on the law of slug flow dynamics model for gas-water two-phase flow in near horizontal pipeline,the theoretical analysis and experimental researches were done to propose the expressions of stable and exact production logging interpretation model for two-phase flow in near horizontal pipeline.The performance of the proposed method for estimating water holdup and water superficial velocity is in good agreement with our measurements.As a result,the slug flow dynamics model of gas-water two-phase flow in near horizontal wellbore was developed.The application effect of production logging in near horizontal wells had been improved.

Optimization of horizontal well staggered patterns

Staggered line-drive patterns are widely used in oilfields. In this paper, to optimize a staggered pattern of horizontal wells, a 3D problem was divided into two 2D （x-y plane andy-z plane） problems with the pseudo-3D method, conformal transformation and superposition principle. A productivity equation for a horizontal well was deduced, which can be used to optimize the well pattern. A relationship between the length of horizontal wells and the shape factor of well patterns was established. The result shows that optimized well patterns can improve oil production from horizontal wells. This provides a theoretical basis for horizontal well applications to the development of oilfields, especially for overall development of oilfields by horizontal wells.

A Model for the Connectivity of Horizontal Wells in Water-Flooding Oil Reservoirs

As current calculation models for inter-well connectivity in oilfields can only account for vertical wells,an updated model is elaborated here that can predict the future production performance and evaluate the connectivity of horizontal wells(or horizontal and vertical wells).In this model,the injection-production system of the considered reservoir is simplified and represented with many connected units.Moreover,the horizontal well is modeled with multiple connected wells without considering the pressure loss in the horizontal direction.With this approach,the production performance for both injection and production wells can be obtained by calculating the bottom-hole flowing pressure and oil/water saturation according to the material balance equation and a saturation front-tracking equation.Some effort is also provided to optimize(to fit known historical production performances)the two characteristic problem parameters,namely,the interwell conductivity and connected volume by means of a SPSA gradient-free algorithm.In order to verify the validity of the model,considering a heterogenous reservoir,three conceptual examples are constructed,where the number ratio between injection and production wells are 1/4,4/1 and 4/5,respectively.It is shown that there is a high consistency between simulation results and field data.

Analysis of Wellbore Flow in Shale Gas Horizontal Wells

Theflow behavior of shale gas horizontal wells is relatively complex,and this should be regarded as the main reason for which conventional pipeflow models are not suitable to describe the related dynamics.In this study,numerical simulations have been conducted to determine the gas-liquid distribution in these wells.In particular,using the measuredflow pressure data related to 97 groups of shale gas wells as a basis,9 distinct pipeflow models have been assessed,and the models displaying a high calculation accuracy for different water-gas ratio(WGR)ranges have been identified.The results show that:(1)The variation law of WGR in gas well satisfies a power function relation.(2)The well structure is the main factor affecting the gas-liquid distribution in the wellbore.(3)The Beggs&Brill,Hagedorn&Brown and Gray models exhibit a high calculation accuracy.