The Stress Analyses Of Oil Well Structures Based On Cement Solidification Process

In petroleum engineering, a correct calculation procedure of stress distributionin oil well structures is very important to predict the service life of an oil well. Inrecent years, lots of researchers calculated the stresses of the oil well by usingdifferent theoretical and numerical methods. However, these methods proposed bythe researchers are usually adopted by the so called direct algorithm method, inwhich the models are established based on the well-logging data and the pre-stresseffects of cement solidification process are not considered at all. Solutions obtainedby the direct algorithm method are not perfectly conformed to the practicalengineering and significant errors will therefore be generated. To overcome theshortcomings of the direct algorithm, a new algorithm, called as interference fitalgorithm, based on the cement solidification process is proposed in this work andapplied to a Daqing oil well field successfully.In practical engineering, the stratum deformation due to the ground stressesexist before drilling, and all the processes of drilling and cementing are allconducted under the condition of ground stresses, i.e., ground stresses exist first andthen drilling. It should be noted that the direct algorithm is always used to establishthe stratum-cement sheath-casing model first and then the ground stresses areloaded to the whole model, i.e., drilling first and then loading the ground stresses.So, it is obviously different from practical engineering situations. The maindifferences between the direct algorithm and the practical engineering are as follow:At first, the data used to establish the model are based on the well logging, andall the well loggings are under the loading of ground stresses, so all the data isunder the action of ground stresses, but not the original data under no loading.Secondly, the cement sheath of the oil well is poured with liquid, and duringthe solidification progress, the volume and the mechanical parameters will bechanged and some kinds of chemical solidification stresses will be produced aftersolidification. In application of the direct algorithm method, the cementsolidification process is completely ignored and the cement sheath is regarded as asolid object. Nowadays, the expansive cement is often utilized to cement the oilwell and the expansion ratio is sometimes more than0.001, so a considerable errorwill be generated due to the neglect of solidification process.In order to overcome the shortcomings of the direct algorithm, the interferencefit algorithm method based on the cement solidification process is proposed in thiswork and a step-by-step solution procedure is given as follows:First, the original shape of the well bore under no loading is calculated. In this paper, an optimization method and a self-design program are used to compute theoriginal shape of the well bore under no loading based on the measurement data inthe practical engineering. Under the condition of uniform ground stresses, theoriginal shape of the well bore is a circle, and under the condition of non-uniformground stresses, the original shape is an ellipse. By the way, the result of themeasurement in the practical engineering under the condition of non-uniformground stresses is still a circle，that is the result of ellipse well bore deformationunder the non-uniform ground stresses.Then, computation of the stresses generated during the cement solidificationprocess is conducted. A theoretical solution of cement sheath solidification stressesis carried out in this work and verified by experiments. The results of experimentare in good agreement to the theoretical solution.At last, the cement sheath with an original shape with no loading calculatedbased on the stress distribution is assembled into an annular gap between thestratum and casing and the contact boundary condition is applied. The stressdistribution is computed under the consideration of compatible deformations of thethree parts of the oil well.Compared to the direct algorithm, the interference fit algorithm proposed inthis work takes the actual construction process of the oil well into consideration andits advantages are as follows:At first, the interference fit algorithm is concerned with the original data of theobject and it is obviously coincided with the mechanical analysis principle. Theoriginal data are calculated based on the measurement or the experiment withtheoretical and numerical methods.Secondly, the interference fit algorithm takes the solidification progress of thecement sheath into consideration, including the hydrostatic effects by loadingduring the cement pouring progress, the hydrostatic pressure lead by the gravity ofthe cement itself, the thermal stress and the chemical solidification stress during thecement solidification progress and so on. All the factors above-mentioned will affectthe stress distribution of the oil well structure at last.At last, the interference fit algorithm takes the variations of the ground stressesinto consideration, and the direct algorithm just takes the up-to-date ground stressesinto account.The results obtained by the interference fit algorithm show that, the early shorttime stress distribution of the oil well is related to the hydrostatic pressure and thesolidification stresses significantly. At the soft stratum layer, the result obtained bythe interference fit algorithm show that the radial stress of the cement sheath issmaller than the stresses on the adjacent hard layer, rather than the results obtainedby the direct algorithm method. Concerned with the long time stress analysis of the oil well, the results obtained by the interference fit algorithm show that the stressdistribution is not only related with the ground stresses at this time, but alsodetermined by the variation history of the ground stresses. Especially, the stressdistribution of the oil well will not be a state of axial symmetry when the groundstresses become uniform even if the oil well drilled under a non-uniform groundstress condition.