Optimization Of Geometric Parameters And Treatment Parameters For Compound Acid Fracturing In Carbonate Reservoir

Carbonate oil and gas fields play an important role in the distribution of oil and gas fields in the world.However,most of these oil and gas resources are buried deeper,which is characterized by low permeability,heterogeneity and difficult development.Compound acid fracturing,as a new oil and gas well stimulation technology rising at the end of last century,plays a great role in carbonate reservoir reconstruction.Its main technical idea is to combine different acid fracturing technologies or acid fracturing and other stimulation methods,so as to realize the complementary advantages of the stimulation technology.In this paper,the compound acid fracturing process with proppant is studied.The main process flow is as follows: pad fluid + main acid + sand-laden fluid + displacement fluid.The basic idea of this paper is to optimize fracture geometric parameters and treatment parameters in order to maximize the dimensionless productivity index given the injected proppant volume.Firstly,the optimal fracture geometry parameters are calculated according to the Unified Fracture Design(UFD)theory,and the optimal treatment parameters are solved by the numerical model of fracture propagation,aiming at the optimal fracture geometry parameters.At the same time,using the characteristics of reservoir,the conductivity test of acid etching fracture,the distribution equation of acid etching fracture concentration field and temperature field,the optimal effective distance of acid etching is calculated.In the UFD theory,given the proppant number,the relationship between the maximum dimensionless productivity index,the corresponding optimal dimensionless fracture conductivity and the proppant number can be obtained.Through the optimal dimensionless fracture conductivity,the optimal propped fracture length and width can be calculated.However,in the optimization of fracture geometric parameters based on the UFD theory,the fracture permeability and fracture volume are not constant and known in the equation of calculating fracture length and width.Considering the variety of proppant permeability and propped fracture volume,this paper proposes an optimization iteration method to obtain the fracture geometric size given the expected sand concentration in the fracture.This content is stated in the Chapter 2 of this paper.From the above research,it is found that following problems exist in the UFD theory:(1)The UFD method only gives the fitting solution of the maximum dimensionless productivity index corresponding to the optimal dimensionless fracture conductivity,and cannot solve the value of the dimensionless productivity index under arbitrary dimensionless fracture conductivities and proppant numbers.(2)If the value of the aspect ratio of the drainage area is not in the given related table,the UFD method will produce interpolation or extrapolation errors.(3)In the optimization of fractured horizontal wells,the skin factor induced by the radial flow is taken as a constant.Therefore,there will be errors in the optimization of fractured horizontal wells using the UFD method.In order to solve the above problems,a new analytical model for calculating the pseudosteady state dimensionless productivity index of fractured wells is proposed in Chapter 3.For the case of proppant number less than 0.1,this paper improves the fitting formula of dimensionless productivity index in rectangular drainage areas by introducing the analytical formula of the equivalent proppant number and shape factor.For the case of proppant number greater than 0.1,a new asymptotic solution is derived based on the trilinear flow model.Firstly,the related dimensionless variables are defined.Then,starting with the analytical solution of the dimensionless wellbore pressure in the Laplace space and using some approximate relations,the asymptotic solution of the dimensionless wellbore pressure after a long time is obtained(i.e.,the Laplace parameter with respect to the dimensionless time is very small).Next,the expression of the dimensionless wellbore pressure in the time domain is obtained by using the analytical solution of the Laplace inverse transformation.According to the definition of the dimensionless productivity index,its analytical solution in the pseudosteady state can be obtained.With this analytical solution,the optimal dimensionless fracture conductivity,maximum dimensionless productivity index,optimal propped fracture length and width can be directly solved without plotting a chart for fitting,and the optimal results for fractured horizontal wells are more accurate than those obtained by the UFD method.In order to quickly solve the optimal treatment parameters,a fast semi-analytical fracture propagation model is proposed in Chapter 4.The fracture propagation model and the steady-state convection-diffusion equation of the concentration field and temperature field distribution of acid-etched fracture are coupled.The fracturing optimization design software is developed,and the optimization results of fracturing treatment parameters can be obtained quickly by combining the interval search method.In Chapter 5,the physical characteristics of carbonate reservoir cores as well as the in-situ stress state in Daniudi gas field are analyzed.The design of the staged compound acid fracturing for one horizontal well is described.In Chapter 6,seven wells are selected from the field to optimize fracture geometry parameters.The results show that the dimensionless productivity index of existing fractured wells can be effectively improved after optimization.Finally,a well is selected to optimize the treatment parameters.Combining with the actual treatment conditions,the optimization method and process of treatment parameters are introduced in detail.The innovative achievements of this paper mainly include the following three points:(1)the iterative method for optimizing the geometric size of the propped fracture;(2)the analytical solution of pseudosteady state dimensionless productivity index of fractured wells;(3)a fast semi-analytical fracture propagation model.Because there are many factors affecting the fracturing process and post-fracturing production,and they are complex,in order to quickly solve the optimal treatment parameters,the fast semi-analytical fracture propagation model proposed in this paper has been simplified to a certain extent,and its application has proved that the model has certain accuracy.If the method of obtaining relevant parameters used in the theoretical model is more perfect and the results obtained are more accurate,then the optimized results will be more accurate and reliable accordingly.In a word,the theory and method proposed in this paper can relatively reduce the treatment cost in the field,and to a certain extent improve the production of fracturing wells.They can provide a basis for future fracturing engineering designs and treatments.