Well interference evaluation considering complex fracture networks through pressure and rate transient analysis in unconventional reservoirs

Severe well interference through complex fracture networks(CFNs)can be observed among multi-well pads in low permeability reservoirs.The well interference analysis between multi-fractured horizontal wells(MFHWs)is vitally important for reservoir effective development.Well interference has been historically investigated by pressure transient analysis,while it has shown that rate transient analysis has great potential in well interference diagnosis.However,the impact of complex fracture networks(CFNs)on rate transient behavior of parent well and child well in unconventional reservoirs is still not clear.To further investigate,this paper develops an integrated approach combining pressure and rate transient analysis for well interference diagnosis considering CFNs.To perform multi-well simulation considering CFNs,non-intrusive embedded discrete fracture model approach was applied for coupling fracture with reservoir models.The impact of CFN including natural fractures and frac-hits on pressure and rate transient behavior in multi-well system was investigated.On a logelog plot,interference flow and compound linear flow are two new flow regimes caused by nearby producers.When both NFs and frac-hits are present in the reservoir,frac-hits have a greater impact on well#1 which contains frac-hits,and NFs have greater impact on well#3 which does not have frac-hits.For all well producing circumstances,it might be challenging to see divergence during pseudosteady state flow brought on by frac-hits on the logelog plot.Besides,when NFs occur,reservoir depletion becomes noticeable in comparison to frac-hits in pressure distribution.Application of this integrated approach demonstrates that it works well to characterize the well interference among different multi-fractured horizontal wells in a well pad.Better reservoir evaluation can be acquired based on the new features observed in the novel model,demonstrating the practicability of the proposed approach.The findings of this study can help for better evaluating well interference degree in multi-well systems combing PTA and RTA,which can reduce the uncertainty and improve the accuracy of the well interference analysis based on both field pressure and rate data.

Maximizing the Benefit of Rate Transient Analysis for Gas Condensate Reservoirs

In recent years,many trials have been made to use the Rate Transient Analysis(RTA)techniques as a method to describe the gas condensate reservoirs.The problem with using these techniques is the multi-phase behavior of the gas condensate reservoirs.Therefore,the Pressure Transient Analysis(PTA)is commonly used in this case to analyze the reservoir parameters.In this paper,we are going to compare the results of both PTA and RTA of three wells in gas condensate reservoirs.The comparison showed a great match between the results of the two mentioned techniques for the first time using a reference GOR of 75,000 SCF/STB.Therefore,we concluded that we could depend on RTA instead of PTA to spare the cost associated with the PTA in the gas condensate reservoirs.

PIPBQ Effect Aware SER Analysis for Combinational Logic Circuits

Technology scaling results in the propagation-induced pulse broadening and quenching（PIPBQ） effect become more noticeable.In order to effectively evaluate the soft error rate for combinational logic circuits,a soft error rate analysis approach considering the PIPBQ effect is proposed.As different original pulse propagating through logic gate cells,pulse broadening and quenching are measured by HSPICE.After that,electrical effect look-up tables（EELUTs） for logic gate cells are created to evaluate the PIPBQ effect.Sensitized paths are accurately retrieved by the proposed re-convergence aware sensitized path search algorithm.Further,by propagating pulses on these paths to simulate fault injection,the PIPBQ effect on these paths can be quantified by EELUTs.As a result,the soft error rate of circuits can be effectively computed by the proposed technique.Simulation results verify the soft error rate improvement comparing with the PIPBQ-not-aware method.

EFFECT OF A MOVING BOUNDARY ON THE FLUID TRANSIENT FLOW IN LOW PERMEABILITY RESERVOIRS

In a low permeability reservoir, the existence of a moving boundary is considered in the study of the transient porous flow with threshold pressure gradient. The transmission of the moving boundary directly indicates the size of the drainage area as well as the apparent influences on the pressure behavior. The nonlinear transient flow mathematical model in which the threshold pressure gradient and the moving boundary are incorporated is solved by advanced mathematical methods. This paper presents some new analytical solutions describing the pressure distribution at a constant rate and the production decline in a constant pressure production with the boundary propagation. It is shown that the greater the threshold pressure gradient, the slower the transmission of the moving boundary, the larger the pressure loss will be, and there is no radial flow in the middle and later phases of the wellface pressure for a well at a constant rate. We have the the maximum moving boundary at a specific drawdown pressure for a low permeability reservoir The greater the threshold pressure gradient, the smaller the maximum moving boundary distance, the quicker the production decline for a well in a constant pressure production will be. The type curve charts for the modern well test analysis and the rate transient analysis with a moving boundary are obtained and the field test and the production data are interpreted as examples to illustrate how to use our new results.

Experimental research on transient radiation effects in microprocessors based on SPARC-V8 architecture

An experimental system is developed for the transient radiation effects testing of an anti-radiation hardened processor. Based on this system, the transient radiation effects in a microprocessor based on SPARC-V8 architecture was investigated. The dose-rate-soft-error index parameters of the processor were determined according to the test results, as were the influences on the function and timing parameters of the processor. The power supply balance is affected, which caused the system to reset and be the main source of soft errors. The results showed the circuit recovery time is primarily determined by the internal PLL, while the core power and the output-low-IO ports are more sensitive to the transient dose rate effect. The power-integrity-hardened design is proposed to mitigate the transient radiation effect.

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.

Transient simulation of regression rate on thrust regulation process in hybrid rocket motor

The main goal of this paper is to study the characteristics of regression rate of solid grain during thrust regulation process. For this purpose, an unsteady numerical model of regression rate is established. Gas–solid coupling is considered between the solid grain surface and combustion gas.Dynamic mesh is used to simulate the regression process of the solid fuel surface. Based on this model, numerical simulations on a H2O2/HTPB（hydroxyl-terminated polybutadiene） hybrid motor have been performed in the flow control process. The simulation results show that under the step change of the oxidizer mass flow rate condition, the regression rate cannot reach a stable value instantly because the flow field requires a short time period to adjust. The regression rate increases with the linear gain of oxidizer mass flow rate, and has a higher slope than the relative inlet function of oxidizer flow rate. A shorter regulation time can cause a higher regression rate during regulation process. The results also show that transient calculation can better simulate the instantaneous regression rate in the operation process.

Detailing Losses in the M/M/1/1 Transient Loss System

This paper is aimed at investigating the transient losses in the M/M/1/1 Erlang loss system. We evaluate the explicit form of the probability distribution of the number of losses in the time interval [0, t） and provide two alternative representations： one based on the iterated derivatives of hyperbolic sinus and cosine and the other on the spherical modified Bessel function of the second kind. The mathematical structures of the transient loss rate and of the transient probability of losing all customers are described and several analytical properties are derived.

Estimating the Properties of Naturally Fractured Reservoirs Using Rate Transient Decline Curve Analysis

Transient rate decline curve analysis for constant pressure production is presented in this pa- per for a naturally fractured reservoir. This approach is based on exponential and constant bottom-hole pressure solution. Based on this method, when In （flow rate） is plotted versus time, two straight lines are ob- tained which can be used for estimating different parameters of a naturally fractured reservoir. Parameters such as storage capacity ratio （co）, reservoir drainage area （A）, reservoir shape factor （CA）, fracture per- meability （ky）, interporosity flow parameter （,~） and the other parameters can be determined by this ap- proach. The equations are based on a model originally presented by Warren and Root and extended by Da Prat et al. and Mavor and Cinco-Ley. The proposed method has been developed to be used for naturally fractured reservoirs with different geometries. This method does not involve the use of any chart and by us- ing the pseudo steady state flow regime, the influence of wellbore storage on the value of the parameters ob- tained from this technique is negligible. In this technique, all the parameters can be obtained directly while in conventional approaches like type curve matching method, parameters such as co and g should be ob- tained by other methods like build-up test analysis and this is one of the most important advantages of this method that could save time during reservoir analyses. Different simulated and field examples were used for testing the proposed technique. Comparison between the obtained results by this approach and the results of type curve matching method shows a high performance of decline curves in well testing.

Pressure-rate convolution and deconvolution response for fractured conventional and unconventional reservoirs using new decline rate model

This paper introduces new approach for pressure-rate convolution and deconvolution analysis of multi-stages hydraulically fractured conventional and unconventional reservoirs.This approach demonstrates the impact of variable Sand face flow rate on reservoir performance.A new model for P/R deconvolution is used to convert pressure pulse from variable flow rate to single and constant rate response.The target of this study is fractal reservoirs with and without stimulated and unstimulated reservoir volume.Multi-linear flow regimes approach is used to describe pressure behavior in the reservoirs while decline flow rate behavior is described by newly proposed model in this study.This model depicts,instead of van Everdingen model,indirectly the declining rate with time by using pressure responses with production time.Decline flow rate behavior simulated by linear and bi-linear flow models are also studied and compared with the one obtained by the new model.Several analytical models are used in this study by applying P/R convolution and deconvolution technique and solved for constant and variable flow rate considering different reservoir configurations and operating conditions.The results are interpreted and analyzed for better understanding pressure behaviors,flow regime types,and productivity index trends for continuously changing flow rate especially at early production time.Estimating stimulated reservoir volume(Vsrv)is considered one of the applications of convolved pressure since it is calculated from pseudo-steady state flow when late time boundary dominated flow regime is reached.The outcomes of this study can be summarized as:1)Introducing new approach for pressure-rate convolution and deconvolution technique for multi-stages hydraulically fractured reservoirs by applying new decline flow rate model that indirectly simulates variable flow rate with time.2)Generating analytical models for dimensionless pressure and flow rate for constant and variable flow rate using the concept of P/R convolution and deconvolution.3)Comparing the result of newly proposed models with the results obtained by applying van Everdingen model for decline rate behavior.4)Studying the applicability of linear and bi-linear flow models in converting variable flow rate pressure response to single and constant flow rate pressure response.5)Applying the deconvolution technique to simulate pressure response at late production time to estimate stimulated reservoir volume.The most interesting points are:1)The main difference in wellbore pressure behavior between variable and constant flow rate can be seen at early production time,however intermediate production time could also show very limited changes for the case of variable rate wellbore pressure.2)A unit slope line flow regime could be developed for varied flow rate pressure response at very early production time similar to the wellbore storage dominated flow regime.3)Productivity index calculated by the proposed models for variable flow rate is greater than the index for constant flow rate.4)The impact of petrophysical properties of porous media and hydraulic fracture characteristics on pressure response are similar in the two cases of variable and constant flow rate.5)The decline rate models for linear and bi-linear flow are not applicable in pressure deconvolution technique.