Rate/Pressure Transient Analysis of a Variable Bottom Hole Pressure Multi-Well Horizontal Pad with Well Interference

2021 ◽  
Author(s):  
Hongyang Chu ◽  
Xinwei Liao ◽  
Cao Wei ◽  
John Lee
Keyword(s):  
Radial Flow ◽  
Transient Flow ◽  
Material Balance ◽  
Flow Characteristics ◽  
Transitional Flow ◽  
Rate Performance ◽  
Transition Flow ◽  
Pressure Derivative ◽  
Laplace Domain ◽  
Well Spacing

Abstract Multi-well horizontal pads are common in unconventional reservoirs. With addition of infill wells and hydraulic fracturing, interference between multiple multi-fractured-horizontal wells (MFHWs) has become a serious issue. Current RTA workflows assume a single MFHW in the unconventional formation. This paper presents a new multi-MFHW solution and related analysis methodology to analyze targeted well rate performance in a multi-MFHW system. In this work, a semi-analytical equation describing multi-well pad in the Laplace domain with well interference is proposed. The proposed semi-analytical model can simulate the rate performance of a multi-well horizontal pad with variable BHP for a targeted well in the pad and different initial production durations for the offset well. From the constant BHP condition and Laplace transforms, we obtained multi-MFHW solutions for transient flow. We used superposition of various constant BHP solutions to study interference among various fractures and MFHWs. The variable BHP of the targeted well is achieved by a variable dimensionless BHP function in the Laplace domain without any convolution or deconvolution calculations. A systematic validation for the proposed method is conducted using a commercial numerical simulator for cases of different initial production times for offset MFHWs, multi-MFHWs with variable BHP. Through the total material balance of the multi-MFHW system, we can analyze a target well in the pad with this multi-MFHW analysis. Interference by offset wells often appears after pseudo-radial flow in the target well's hydraulic fracture. It causes the pressure derivative curve during elliptical and infinite-acting radial flow (IARF) to rise, as does the RNP derivative. The inverse semi-log derivative has the opposite trend. Well interference also makes the rate/pressure drop functions to deviate from initial straight lines in later stages. Sensitivity analysis of well spacing shows that "transition flow" will change from elliptical to formation linear flow between wells as well spacing increases and it can show the transitional flow characteristics in more common cases.

A Well-Testing Approach for Diagnostics of Fracture Complexity with Well Interference

2021 ◽  
Author(s):  
Zhiming Chen ◽  
Xinwei Liao ◽  
Pengfei Zhao ◽  
Biao Zhou ◽  
Duo Chen ◽  
...  
Keyword(s):  
Radial Flow ◽  
Flow Regimes ◽  
Well Testing ◽  
Pressure Derivative ◽  
Complex Fracture ◽  
Well Spacing ◽  
Fracture Complexity ◽  
Pressure Depletion ◽  
Testing Approach ◽  
The Impact

Abstract Owing to well interference, the fracture geometries of child wells are sometimes more complex than initially expected. Some approaches or methodologies have been developed to evaluate the complex fracture geometries, however, the fracture geometries are still poorly understood. This work uses the boundary element method to propose a new well testing approach to determine the complex fracture geometries of child wells with inter-well interference. It is found that the well interferences from Parent well on Child well mainly happen on the late stage, which can be physically expected. The flow regimes of Child well can be divided into: wellbore storage & skin effects, fracture bilinear flow, "fluid supply", formation linear flow, pseudo-boundary dominated flow, "well interferences", pseudo-radial flow, and boundary-dominated flow. The stage of "well interferences" occurs later with the increase in well spacing. The boundary-dominated flow is affected by the reservoir size and shape. When the reservoir size is fixed, the pressure curves in final stage of different-shape reservoirs overlap, which provides a tool to diagnose the reservoir size. While the reservoir size are variable, the occurrences of boundary-dominated flow are quite different. The smaller the reservoir, the quicker the boundary-dominated flow, which is in line with actual situations. It is also found that Parent-well rate mainly affects the flow regimes after pseudo-boundary dominated flow. That to say, after that flow regime, the performance of Child well is interfered by Parent well. The impact is more obvious with the increase in Parent-well rate, especially in pseudo-radial flow. In that flow stage, the horizontal value of pressure derivative also satisfies 0.5(qchd,D+qpar,D). In addition, when the Parent-well rate is negative, namely an injection well, the pressure derivatives of Child well decrease sharply, which means that the pressure depletion of Child well decreases and it is helpful to production of Child well. When the Parent-well rate is a positive and large value, the pressure depletion of Child well increase sharply and its production is harmed by the Parent well. Thus, there should be an optimized production strategies between Parent well and Child well. Finally, the model application on diagnostics of fracture complexity of an actual well is performed. This study provides a new way to identify the fracture geometries of child wells in unconventional plays.

Transient Flow Characteristics of Low Permeability Gas Reservoirs and Improvement of Deliverability by Nuclear Explosion

1968 ◽  
Vol 8 (03) ◽  
pp. 209-223
Author(s):  
C. Kenneth Eilerts ◽  
Eudora F. Sumner
Keyword(s):  
Natural Gas ◽  
Radial Flow ◽  
Transient Flow ◽  
Nuclear Explosion ◽  
Flow Characteristics ◽  
Economic Feasibility ◽  
Low Permeability ◽  
Significant Variable ◽  
Reservoir Properties ◽  
Economic Significance

Abstract A program for computing the transient radial flow of natural gas, taking into account significant variable properties of the fluid and of the porous medium was used in an investigation of flow characteristics of formations for which the permeability-thickness product kh is 1 to 100 md-ft. A graphic summary of the results obtained may be used with well flow-test data to estimate kh for the formation in which the well is completed. Assuming that a nuclear explosion in a gas-containing formation would create a rubble-filled chimney with a diameter of 170 ft and fissures radiating from the chimney wall out to a distance of 255 ft, formation pressure gradients were computed for the recovery of gas with a well drilled into the chimney. These computations for 640-and 160-acre spacing indicate that diminution of the radius segment re - rf over which flow occurs in unaltered formation provides for markedly greater ultimate recovery of gas in place than is possible with conventional well completions. A formation drilled with conventional wells 1.0 mile apart must have a productivity product of kh = 197 md-ft to deliver for 20 years 1.0 MMscf/D of gas into a pipeline operated at 300 psi. Aided by nuclear stimulation, one well can meet the same performance requirements with a kh of only 49 md-ft for the native formation. With a spacing of 160 acres and nuclear stimulation, kh need be only 9 md-ft. Introduction Project Gasbuggy of the El Paso Natural Gas Co. and government agencies is concerned with the creation by nuclear explosion of a chimney and radiating fissures in a low-permeability formation containing natural gas. A well is to be drilled and completed in this chimney and tests will be made on this well and other wells in the vicinity to determine the economic feasibility of nuclear stimulation for recovery of the gas. Engineering studies of the Bureau of Mines pertaining to parts of this project have been in progress since 1963. Because of the complexity of the experiment, its cost, and possible economic significance, it is desirable to define the reservoir flow problem, determine by computing the relative importance of the parameters involved, and obtain a measure of the benefits that may be expected. The results should be generalized for application to other projects. Two parts of this problem have been investigated:determination of average properties of the native formation from flow tests of wells, andevaluation of the transient flow performance of a low-permeability formation in which a relatively high-permeability area has been created to receive a recovery well. Matthews and Russell have reviewed the difficulties of testing gas wells in low-permeability formations that stabilize slowly if at all, in this investigation a means was sought for using transient flow information obtained on such wells to determine reservoir properties, including the product kh. The investigation of nuclear stimulation was conducted with emphasis on determining what transient flow performance may be expected over the 20-year period of significance to gas producers. BASIC EQUATIONS The partial differential equation for transient radial flow of a gas phase, (1) was integrated in the range rd r re. With rd/re = 0.005 and 640-acre spacing rd = 14.9 ft, so that flow over most of the radius is computed by means of Eq. 1. A program previously described by the authors was used for this purpose. SPEJ P. 209ˆ

A Semianalytical Forecasting Method for Unconventional Gas and Light Oil Wells: A Hybrid Approach for Addressing the Limitations of Existing Empirical and Analytical Methods

2015 ◽  
Vol 18 (01) ◽  
pp. 94-110 ◽  
Author(s):  
C.R.. R. Clarkson ◽  
F.. Qanbari
Keyword(s):  
Theoretical Basis ◽  
Transient Flow ◽  
Hybrid Approach ◽  
Material Balance ◽  
Analytical Models ◽  
Transitional Flow ◽  
Empirical Methods ◽  
New Production ◽  
Unconventional Gas ◽  
Light Oil

Summary The rapid pace of exploitation of unconventional gas and light oil plays in North America has necessitated the development of new production-forecasting methodologies to aid in reserves assessment, capital planning, and field optimization. The generation of defendable forecasts is challenged not only by reservoir complexities but also by the use of multifractured horizontal wells (MFHWs) for development. In this work, a semianalytical method (SAM) is developed to provide a solid theoretical basis for forecasting. The technique is analytical in that it uses the methods of Agarwal (2010) to calculate contacted oil in place and contacted gas in place (COIP/CGIP) from production rates, flowing pressures, and fluid properties. The rate-normalized pressure (RNP) derivative (RNP′) is a key component of the calculation; pseudopressure is used for gas cases. The technique is also empirical in that an empirical function is fitted to the resulting COIP/CGIP curve vs. time. Although the method is flexible enough that any equation can be used to represent the COIP/CGIP curve, and hence, the sequence of flow regimes exhibited by MFHWs, the equation must be capable of being integrated to allow the extraction of RNP. The stabilized COIP/CGIP during boundary-dominated flow (BDF) must be specified for forecasting—thereafter, the method uses a material-balance simulator to model BDF. Hence, if the well is still in transient flow, a range in forecasts may be generated, depending on the assumed stabilized COIP/CGIP. The new SAM addresses some of the current limitations of empirical and fully analytical (modeling) approaches. Empirical methods, which have been adapted to account for long transient and transitional flow periods associated with ultralow-permeability reservoirs, lack a theoretical basis, and therefore input parameters may be difficult to constrain. However, empirical methods are simple to apply and require a minimum amount of data for forecasting. Analytical models, while representing the physics better, nonetheless require additional reservoir and hydraulic-fracture data that may not be available on every well in the field. The SAM proposed herein is intended to bridge the gap between empirical and modeling-based approaches—it is more rigorous than purely empirical methods, while requiring a lesser amount of data than fully analytical techniques. The new method is tested against simulated and field cases (tight oil and shale gas). Although a simple power-law function is used in the current work to represent the COIP/OGIP curve, which appears adequate for the cases studied, one should note that wells exhibiting long transitional flow periods (e.g., elliptical/radial) will likely require a different functional form.

Numerical Simulation of Transient Flow Inside Nozzle on Gasoline Direct Injection Engine

2012 ◽  
Vol 466-467 ◽  
pp. 1237-1241
Author(s):  
Yan Hua Wang ◽  
Shi Chun Yang ◽  
Yun Qing Li
Keyword(s):  
Kinetic Energy ◽  
Transient Flow ◽  
Direct Injection ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Turbulence Kinetic Energy ◽  
Gasoline Direct Injection ◽  
Injection Hole ◽  
Gasoline Direct Injection Engine ◽  
Nozzle Configuration

To achieve transient flow characteristics at exit of nozzle orifice on gasoline direct injection engine, two phase Euler-Euler schemes was used to simulate the internal flow of the swirl nozzle. Different flow characteristics were calculated in the simulation. Different kinds of nozzle configuration were studied. Cavitaion and swirl flow occured in the nozzles. Injection hole configuration matters more than area variation of swirl tangential slot to discharge coefficient of the studied nozzle. Discharge coefficient changes a little along the injection hole length. The area of the swirl tangrntial slot plays an important throttling action in nozzle internal flow. Smaller area of swirl tangential slot generates larger degree cavitation but smaller mean injection velocity. Turbulence kinetic energy changes with the time of cavitation and swirl field occurring and the nozzle configuration. Before the appearance of cavitation, smaller inclination angle of orifice can generate more turbulence kinetic energy. After that moment, turbulence kinetic energy varies with different configuration. Along injection hole length, turbulence kinetic energy obviously varies. These flow characteristics affect primary atomization and will be as input for next spray simulation. They are also applied to design reference for injection nozzle.

Investigations on Flow Characteristics in Diffuser-Discharge-Channel of Volute Casing

2018 ◽  
Author(s):  
Yandong Gu ◽  
Ji Pei ◽  
Shouqi Yuan ◽  
Jinfeng Zhang ◽  
Ernst Nikolajew ◽  
...  
Keyword(s):  
Cross Sections ◽  
Discharge Channel ◽  
Transient Flow ◽  
Pressure Fluctuations ◽  
Flow Characteristics ◽  
Centrifugal Pumps ◽  
Discharge Pipe ◽  
Hydraulic Design ◽  
Flow Loss ◽  
Two Sides

The volute casing used in centrifugal pumps is efficient for the transformation of kinetic energy into pressure energy, however, its asymmetric hydraulic design makes the flow in diffuser-discharge-channel (DDC) inhomogeneous, resulting in unsatisfactory flow patterns. In this study, the unsteady numerical simulations are carried out to investigate the transient flow characteristics in DDC. The accuracy of numerical results is found to agree well with experimental performance and pressure fluctuations. It is observed that the flow in DDC is significantly uneven. At the elbow of DDC, the static pressure on the volute left side (VL) is larger than the volute right side (VR) due to the flow impact and flow separation respectively. Thereby, this high-pressure gradient induces the secondary flow on the cross sections of DDC. Further, there is an obvious dependency of pressure fluctuations in the discharge pipe on the strong interaction between the impeller and tongue, in which four small peaks and four large peaks can be observed. At each moment, the pressure on VL gradually decreases from the inlet of discharge pipe to the pump outlet, while it increases on VR, finally, two sides tend to be the same. The pressure fluctuation intensity gradually becomes equivalent-distributed. In particular, it should be noticed that the energy loss in the diffuser part is larger than the discharge pipe, which requires a redesign concerning hydraulic performance. This study can help to better understand the transient flow characteristics and provide guidance for reducing flow loss in the volute casing.

scholarly journals Bayesian Optimization Design of Inlet Volute for Supercritical Carbon Dioxide Radial-Flow Turbine

Machines ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 218
Author(s):  
Chao Bian ◽  
Shaojie Zhang ◽  
Jinguang Yang ◽  
Haitao Liu ◽  
Feng Zhao ◽  
...  
Keyword(s):  
Optimization Design ◽  
Radial Flow ◽  
Flow Characteristics ◽  
Bayesian Optimization ◽  
Working Fluid ◽  
Cross Sectional ◽  
Pressure Loss Coefficient ◽  
Flow Capacity ◽  
Cycle Efficiency ◽  
Total Pressure Loss Coefficient

The radial-flow turbine, a key component of the supercritical CO2 (S-CO2) Brayton cycle, has a significant impact on the cycle efficiency. The inlet volute is an important flow component that introduces working fluid into the centripetal turbine. In-depth research on it will help improve the performance of the turbine and the entire cycle. This article aims to improve the volute flow capacity by optimizing the cross-sectional geometry of the volute, thereby improving the volute performance, both at design and non-design points. The Gaussian process surrogate model based parameter sensitivity analysis is first conducted, and then the optimization process is implemented by Bayesian optimization (BO) wherein the acquisition function is used to query optimal design. The results show that the optimized volute has better and more uniform flow characteristics at design and non-design points. It has a smoother off-design conditions performance curve. The total pressure loss coefficient at the design point of the optimized volute is reduced by 33.26%, and the flow deformation is reduced by 54.55%.

Laminar and transitional flow of drilling muds and various suspensions in circular tubes

1967 ◽  
Vol 30 (3) ◽  
pp. 449-464 ◽  
Author(s):  
Bernard Le Fur ◽  
Madeleine Martin
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Rheological Behaviour ◽  
Simple Expression ◽  
Transitional Flow ◽  
Transition Flow ◽  
Flow Rates ◽  
Circular Tubes ◽  
Head Losses ◽  
Drilling Muds

Most suspensions exhibit a rheological behaviour which cannot be represented by either Bingham's or Ostwald–De Waele's law. In studying such cases a very simple expression with only three parameters may be used. Starting with an intermediate law of this sort, this paper gives velocity profiles and head losses in laminar flow, which have been computed and plotted on diagrams in non-dimensional co-ordinates.It has been found that transition flow rates in circular tubes for data taken from the literature and from experiments conducted on drilling muds at the Institut Français du Pétrole, are efficiently predicted by an empirical criterion (Ryan & Johnson 1959) which establishes a relation between a generalized Reynolds number and a generalized Hedström number.

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