Perforation completion in oil and gas wells is the most important way of completion engineering, the optimization of perforation completion’s designing is influenced by a variety of factors. In order to get the ideal effect of perforation operation, in this paper, a Perforation plan-decision based on Grey Cluster Relation is putted forward. It aims to provide a scientific guidance for the Perforation. The simulation experimental results show that new models are effective, which offer one kind of science decision-making foundation for petroleum Perforation.

Perforated well completion As the most extensive and major method of the well’s completion, the reasonable selection of parameters for the program has great meaning of improving efficiency and reducing costs[

Due to the mutual restriction of different parameters, the current subjective decision-making for perforation program can’t make all the factors to achieve the best at the same time. In order to solve the above problems and reduce the subjective influence of the decision maker, maximize the productivity ratio[

Perforation optimization needs to confirm a solution to maximize the production capacity. This solution depends on many factors and the main influencing factors are hole depth, pore size, pore density, phase angle, formation heterogeneity, drilling pollution degree and depth, perforation compaction thickness and degree. All these factors are acting on the decision-making of the solution on the same time.

Perforation Plan-decision based on Grey Cluster has made the model of perforation parameters and the oil well productivity. Gray parameters are clustered in the parameters of the perforation scheme, and the evaluation function is established to design the optimal scheme [

First simulating and calculating the productivity ratio of oil and gas, then making a non-linear regression analysis, According to whether perforation penetration penetrate the drilling zone or not, an equation can be established, it indicates the relationship between perforating parameters and capacity.

The quantitative relationships between parameters (perforation penetration KS, perforation aperture Kj, perforation phase Xw, perforation compaction degree Yc, perforation compaction thickness Yh, drilling damage thickness Wh, drilling pollution degree Wc, shot density Km, borehole radius rw, formation permeability Kzr) and the oil production ratio PR is the basis for the optimization of perforating parameters.

The main factors in the decision-making of the perforation plan are six factors: perforation ratio, perforation phase angle, shot density, perforation penetration, perforation diameter and casing strength decreasing coefficient, which are expressed by attributes _{1}, _{2}, _{3}, _{4}, _{5}, _{6} respectively. Initial feature object matrix D is made like this:

In the formula, _{ij}_{1j} represents the productivity ratio, _{2j} is the phase angle, _{3j} is the perforation diameter, _{4j} is the hole depth, _{5j} is the aperture, and _{6j} is the casing strength reduction coefficient. There are

As the different dimensions will have an impact on decision-making, so the formula (

The normalization of attribute data based on the different effects caused by different attributes, the formula (

In the formula, 2 ≤ _{ij}_{6 × n}.

The Grey Clustering analysis is used to classify the attributes and the similar factors can be classified and simplified.

_{ik}

The critical value r ∈ (0, 1), in pursuit of accuracy the value of r is higher than 0.5, the higher the r value, the more accurate the classification is, and the accurate value of r is determined by actual data, the Ri and Rk classified as similar attributes; when _{ij}

A new feature matrix D’ and new normalization matrix _{ij}_{m × n} is established according to the Grey Clustering analysis, where m is the number of attributes and n is the number of schemes.

_{i}

In particular, when

And 0 ≤ _{i}_{1} + _{2} + … _{m} = 1, 1 ≤

Establish an evaluation function Z_{k}:

When the evaluation function value Z(Rk) is larger, the corresponding scheme is better. The program has the largest value of Z(k) is chosen as the final construction program.

White XX well in Chang-qing Oilfield, the reservoir depth of middle layer is 1 884.5m, the total thickness is 9.5 m, the thickness of the perforated zone is 3.0 m, the porosity is 13.41%, reservoir drainage radius is 200m, well-bore radius is 0.111 m, the pressure of formation is 13.073 MPa, the crude oil saturation pressure is 9.86 MPa, drilling pollution depth is 69.5mm, the drilling pollution degree is 0.6. The casing strength is 47.8MPa, reservoir heterogeneity is 0.7 (vertical permeability / horizontal permeability), the water saturation is 30.21%, rock Poisson’s ratio is 0.5, the inclination is 5º, the oil viscosity is 1.03 MPa.S, the perforation optimization scheme is shown as Table

PERFORATION TABLE OF WHITE XX

The initial feature matrix _{ij}_{6 × 24} can be constructed from the data in Table

ESTABLISH THE INITIAL FEATURE MATRIX D

The feature object matrix _{ij}_{6 × 24} is established by the above equation (

ESTABLISHMENT OF FEATURE OBJECT MATRIX R

According to the correlation degree matrix, take the critical value _{ij})4 ×24, shown as table

DEALS WITH THE FEATURE MATRIX BY GREY CLUSTER RELATION R’

The attribute weight vectors

Then the evaluation function Z is established according to (

In this paper, a Perforation plan-decision based on Grey Cluster Relation is putted forward. This method can be widely used to predict the productivity of wells under different perforation conditions, determine the perforating efficiency of perforated bombs, and study how different factors (the perforation elasticity, perforation penetration, shot density, perforation diameter, perforation phase angle) impose influence to productivity ratio, and casing strength decreasing coefficient. According to the pending reservoir, it also let the oil production capacity to achieve the higher perforation operating parameters and process of excellent combination. It also saves a lot of manpower, materials and time cost, and provide the theoretical basis for the design of completion perforation construction.