CN104727811A - Productivity prediction method of fishbone horizontal well segmented coupling - Google Patents

Abstract

The invention provides a productivity prediction method of fishbone horizontal well segmented coupling. The method includes the steps of firstly, using a segmenting method to segment a complex structure; secondly, building a shaft flow model; thirdly, using an iteration method to solve an equation set of fluid flow in an oil reservoir and flow coupling in a shaft; fourthly, solving the model after space transformation; fifthly, using an s-K* method to process stratum anisotropic conditions. The method has the advantages that the complex well body structure can be described precisely, the complex shaft flow features can be reflected reasonably, the reservoir anisotropy is considered, and the method conforms to actual oil reservoir conditions and is high in calculation precision and applicable to oil fields.

Description

The PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples

Technical field

The present invention relates to oil-gas field development and improve oil recovery field, particularly relate to a kind of PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples.

Background technology

Compare with horizontal well with conventional straight well, multi-branched horizontal well has and increases drainage area further, increase oil well output, improve rate of oil production, improve reserves controlling extent, increase recoverable reserves, improve recovery ratio and save the advantages such as drilling cost, becoming the focus of 21st century domestic and international oil development technical development and research.Practice shows, fishbone horizontal well, as a type of multi-branched horizontal well, along with the continuous progress of its drilling and production technology, is implemented probing and exploitation at dissimilar oil reservoir, obtained higher initial productivity and good economic benefit.

But compared with drilling and production technology, the reservoir engineering research adapted with fishbone horizontal well is not yet ripe.One is that to have the flowing of comparing Special complex dynamic, is still not clear at present to the understanding of its seepage flow mechanism.Be embodied in four aspects: (1), along horizontal wellbore toe-end to heel end, liquid mass flow increases gradually (Variable Mass Flow), in oil reservoir, in seepage flow and horizontal wellbore, pipe stream intercouples; (2) because the existence of pit shaft endometamorphism amount stream makes constantly to increase along journey flow velocity, an additional acceleration pressure drop will inevitably be produced; (3) be subject to the interference of oil reservoir radial fluid around pit shaft in horizontal wellbore along the fluid of pit shaft direction PARALLEL FLOW, fluid occur and turns to, thus cause main flow section to be out of shape; (4) existence of Multilateral Wells, in Fen Zhuzhi intersection, two kinds of various flows to fluid junction can there is mutual interference.Therefore, announcement fishbone horizontal well pit shaft and nearly well stream move behavioral characteristics, are of great significance for improving fishbone horizontal well seepage theory tool.Two is lack to be suitable for reliable fishbone horizontal well capability forecasting analytical method.About the productivity prediction model research Chinese scholars common concern that branch horizontal well well shape is optimized, establish corresponding analytic modell analytical model respectively by diverse ways.But early stage forecast model mainly for be radial multi-bottom branch horizontal well, be not suitable for the calculating of fishbone horizontal well.There is following shortcoming in (partly) analytic modell analytical model being suitable for fishbone horizontal well capability forecasting representative at present: (1) model is suitable only for single-phase in description branch horizontal well form and flow performance; (2) most model does not consider the impact of wellbore pressure loss; (3) model is mostly only suitable for infinitely great stratum steady seepage condition; (4) most model cannot consider the impact of heterogeneous reservoir; (5) method simplifies, and computational accuracy is low.

Therefore, foundation accurately can describe the casing programme of its complexity, can the Wellbore Flow feature of its complexity of reasonable reaction, meet filed application research precision and requirement and adaptable Productivity, for fishbone horizontal well capability forecasting, well shape optimal design, there is very real theory value.

Summary of the invention

The object of this invention is to provide a kind of reservoir engineering application level improving fishbone horizontal well, improve capability forecasting precision, the reservoir engineering application for such well shape provides the PRODUCTION FORECASTING METHODS of the fishbone horizontal well segmented couples of more accurate technical support.

Object of the present invention realizes by following technical measures: the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples, and the PRODUCTION FORECASTING METHODS of this fishbone horizontal well segmented couples comprises: step 1, adopts split plot design to carry out segment processing to complex structural well; Step 2, sets up wellbore flow model; Step 3, adopts alternative manner to solve the equation group of Coupled with Flow in the flowing of oil reservoir inner fluid and pit shaft; Step 4, carries out solving of model after carrying out spatial alternation; And step 5, adopt the heterogeneous situation of s-K* method formation to process.

Object of the present invention also realizes by following technical measures:

In step 1, according to this segment processing method, to obtain in producing well section certain a bit of gesture that any point produces in oil reservoir, then derive the gesture of gesture that this well section produces in reservoir boundary and the generation of pit shaft inner boundary according to mirror image and gesture principle of superposition.

In step 1, along well track, pit shaft is divided into some one dimension segments, the control volume that each section is simulated as Wellbore Flow, be made up of the flow path of section node and section, its parameter comprises length, internal diameter, friction factor and inclination angle, Fluid Control Equation in all about horizontal well pit shaft and parameter are all defined in these sections, and the coupling of flow through oil reservoir and Wellbore Flow is carried out for each section, namely by the segment processing of pit shaft, consider that each section along the flowing of pit shaft direction and the impact that becomes a mandarin of oil reservoir radial direction, description pit shaft mass variable flow.

In step 2, this wellbore flow model comprising three parts such as friction pressure pressure drop, gravitational pressure pressure drop and the pressure drop of acceleration pressure is set up according to the equation of momentum.

In step 2, consider that borehole wall stratum becomes a mandarin the impact of interference on the pressure drop of pit shaft acceleration and friction pressure drop, realizes the Wellbore Flow feature interpretation under stratum filtration and wellbore tubular stream coupling condition.

In step 3, flow through oil reservoir and the wellbore flow model of simultaneous coupling carry out numerical solution, try to achieve pressure and the influx distribution of each well section, thus obtain pressure and the flow of whole pit shaft.

In step 4, in order to consider the anisotropy factor of reservoir permeability, theoretical according to Seepage In An Anisotropic Reservoir, introduce transition matrix D and carry out spatial alternation, be isotropic space of equal value by anisotropic permeability space transforming, and then carry out solving of model.

In steps of 5, calculate epidermis s and overall permeability K*, to permeability, the impact of each The Small Well section is added in each well section with the form of skin factor by each, thus embody formation heterogeneity to the impact of well capacity.

The PRODUCTION FORECASTING METHODS of the fishbone horizontal well segmented couples in the present invention, it is one fishbone horizontal well segmented couples PRODUCTION FORECASTING METHODS more accurately, the mainly analytic method of the branch horizontal well capability forecasting that comprehensive study is current, utilize the research idea that it is basic, for the problem of current method applicability difference, the composite factors such as oil reservoir heterogeneous body, the comprehensive pressure drop of pit shaft, pit shaft Variable Mass Flow, oil reservoir anisotropy are considered, sets up heterogeneous reservoir fishbone horizontal well segmented couples model.The PRODUCTION FORECASTING METHODS of the fishbone horizontal well segmented couples in the present invention accurately can describe the casing programme of its complexity, the Wellbore Flow feature of its complexity of reasonable reaction, meets filed application research precision and requirement.The method that the present invention proposes has the features such as more accurate, the workable and compliance of mechanism description is more extensive, thus has good application value.

Accompanying drawing explanation

Fig. 1 is the flow chart of a specific embodiment of the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples of the present invention;

Fig. 2 is The Small Well fragment position schematic diagram in space in a specific embodiment of the present invention;

Fig. 3 is horizontal wellbore infinitesimal section schematic diagram in a specific embodiment of the present invention;

Fig. 4 be in a specific embodiment of the present invention anisotropy to fishbone horizontal well pressure distribution effect diagram.

Detailed description of the invention

For making above and other object of the present invention, feature and advantage can become apparent, cited below particularly go out preferred embodiment, and coordinate institute's accompanying drawings, be described in detail below.

As shown in Figure 1, Fig. 1 is the flow chart of the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples of the present invention.Because the production Length Ratio straight well/horizontal well of fishbone horizontal well in reservoir is much longer, therefore the flow condition of pit shaft inside can produce certain impact to the Production development of fishbone horizontal well.Fishbone horizontal well is when producing, and fluid flows to fishbone horizontal well master, branch well cylinder in Three-dimensional Flow in oil reservoir, and then fluid converges along branch well cylinder to main branch wellbore again, the last heel end flowing to well along a main horizontal wellbore.Therefore, the seepage flow of fishbone horizontal well is except fluid seepage flow in the earth formation, and also have the flowing in pit shaft, these two flow process not only connect each other but also influence each other.In order to correctly reflect the Production development of fishbone horizontal well, the Model coupling describing these two flow process being got up, integrally studies.

In step 101, split plot design is adopted to carry out segment processing to complex structural well.So-called split plot design is exactly that producing well section is divided into some segments according to certain mode, because the well segment length after segmentation is shorter, it is equally distributed along this well segment length direction for can supposing that fluid flows into often a bit of flow from oil reservoir, but it is not identical to flow into often a bit of flow.According to this segmentation method, first to obtain in producing well section certain a bit of gesture that any point produces in oil reservoir, then derive the gesture of gesture that this well section produces in reservoir boundary and the generation of pit shaft inner boundary according to mirror image and gesture principle of superposition.

In this step, along well track, pit shaft is divided into some one dimension segments, the control volume that each section is simulated as Wellbore Flow, be made up of the flow path of section node and section, its typical parameter comprises length, internal diameter, friction factor and inclination angle, and the Fluid Control Equation in all about horizontal well pit shaft and parameter are all defined in these sections.Carry out the coupling of flow through oil reservoir and Wellbore Flow for each section, namely by the segment processing of pit shaft, consider that each section along the flowing of pit shaft direction and the impact that becomes a mandarin of oil reservoir radial direction, description pit shaft mass variable flow.Flow process enters into step 102.

In step 102, set up wellbore flow model.The wellbore flow model comprising three parts such as friction pressure pressure drop, gravitational pressure pressure drop and the pressure drop of acceleration pressure is set up according to the equation of momentum.The wellbore flow model of Erecting and improving here, considers that borehole wall stratum becomes a mandarin the impact of interference on the pressure drop of pit shaft acceleration and friction pressure drop, realizes the Wellbore Flow feature interpretation under stratum filtration and wellbore tubular stream coupling condition.Flow process enters into step 103.

In step 103, alternative manner is adopted to solve the equation group of Coupled with Flow in the flowing of oil reservoir inner fluid and pit shaft.Flow through oil reservoir and the wellbore flow model of simultaneous coupling carry out numerical solution, try to achieve pressure and the influx distribution of each well section, thus obtain pressure and the flow of whole pit shaft.Flow process enters into step 104.

In step 104, introduce after transition matrix D carries out spatial alternation and carry out solving of model.Anisotropy is the key factor affecting horizontal well effect, also obvious impact can be produced for fishbone horizontal well, in order to consider the anisotropy factor of reservoir permeability, theoretical according to Seepage In An Anisotropic Reservoir, introduce transition matrix D and carry out spatial alternation, be isotropic space of equal value by anisotropic permeability space transforming, and then carry out solving of model.Flow process enters step 105.

In step 105, the heterogeneous situation of s-K* method formation is adopted to process.The contact surface on fishbone horizontal well and stratum increases greatly, the impact of non-homogeneity on well inflow profile of in-place permeability is more much larger than conventional well, in order to make the reservoir condition of fishbone horizontal well flow model in porous media closing to reality more, the heterogeneous situation of s-K* method formation is adopted to process, the committed step of the method calculates epidermis s and overall permeability K*, to permeability, the impact of each The Small Well section is added in each well section with the form of skin factor by each, thus embodies formation heterogeneity to the impact of well capacity.Flow process terminates.

In a specific embodiment of the present invention, be L for length, diameter is D, one end is positioned at (X _w, Y _w, Z _w) space The Small Well section, because D is much smaller than L, therefore this The Small Well section can be regarded as the congruence in a space, as shown in Figure 2.

According to the definition of gesture, micro-section at space any point M(x, y, z) gesture that produces is

$\mathrm{d\φ}=\frac{-\mathrm{dq}}{4\mathrm{\πr}}+C$

For bottom water reservoir, at constant pressure boundary place, have:

When complex structural well is produced, fluid flows to each well from oil reservoir, supposes that full well has N _b, according to split plot design, each can be divided into some segments, if i-th is divided into N _pisection, then certain a bit of gesture that produces in oil reservoir obtained according to deriving and gesture principle of superposition can obtain the full well gesture that any point produces in oil reservoir:

The pressure of any point is:

Formula can calculate the pressure P at kth Zhi Jing l segment point midway place thus _k1:

Wherein k=1,2 ..., N _b

l=1，2，…，N _pk

The pit shaft internal drop model set up as shown in Figure 3, suppose that the fluid in pit shaft is monophasic fluid, and do the One-Dimensional flows of isothermal, stable state, net horizontal section is made up of multiple infinitesimal section, infinitesimal segment length is, infinitesimal section inner fluid is subject to the effect of three kinds of power, i.e. the effect of upstream extremity pressure, downstream pressure and shear stress.The energy loss aspect of fluid is except causing fluid energy losses due to resistance fricative between fluid, and the additional drag that the mixing interference of fluid flowing produces also causes segment fluid flow energy loss.Be assumed to be unit mass fluid chemical field and disturb the energy loss caused, so the equation of momentum of this infinitesimal section, continuity equation and energy equation are respectively:

The equation of momentum: p ₁a-p ₂a-τ π D Δ x=ρ Q ₂v ₂-ρ Q ₁v ₁

Continuity equation: Av ₁+ q=Av ₂

Energy equation: $\frac{p_1}{\mathrm{\ρg}}+\frac{{v_1}^2}{2g}=\frac{p_2}{\mathrm{\ρg}}+\frac{{v_2}^2}{2g}+\frac{f{\stackrel{\‾}{v}}^2}{2\mathrm{Dg}}\mathrm{\Δx}+h_{12}$

In formula: A-pit shaft cross sectional area, m2; D-mineshaft diameter, m; ρ-fluid density, kg/m3; The flow of this wellbore section of q-flow into from oil reservoir, m3/d; Q-wellbore section main flow, m3/d; the mean flow rate of-infinitesimal section inner fluid, $\stackrel{\‾}{v}=\frac{v_1+v_2}{2},v_1=\frac{Q_1}{A},v_2=\frac{Q_2}{A};\mathrm{\τ}=\frac{1}{8}\mathrm{f\ρ}{\stackrel{\‾}{v}}^2;$ Wall friction coefficient when f-tube wall has fluid to flow into, during laminar flow f=f during turbulent flow ₀(1-0.0153R _ew ^0.3978); f ₀-without wall flow into wall skin friction coefficient, r _ew-borehole wall Reynolds number, is defined as re-Reynolds number; ε-relative roughness; q _sthe volume flow that-unit length tube wall surface current enters, m ³/ (dm); μ-viscosity of crude, mPas.

Arrange the pressure drop correlations obtaining this infinitesimal section in horizontal wellbore:

$\mathrm{\Δ}{p}_w=\mathrm{\ρg}{h}_{12}+\frac{\mathrm{f\ρ}{(2v_{1}A+q)}^2}{8D{A}^2}\mathrm{\Δx}+\frac{\mathrm{\ρ}{q}^2}{2A^2}+\frac{\mathrm{\ρ}{v}_{1}q}{A}$

If pit shaft has been divided into N section altogether, pit shaft heel end place pressure p _wfknown, then the pressure distribution in pit shaft is expressed as:

$\left\{\begin{array}{c}\mathrm{\Δ}{p}_{w0}=0\\ p_{w0}=p_{\mathrm{wf}}\\ p_{\mathrm{wj}}=p_{w,j-1}+0.5(\mathrm{\Δ}{p}_{w,j-1}+\mathrm{\Δ}{p}_{\mathrm{wj}})(j=\mathrm{1,2},\mathrm{\Λ},N)\end{array}\right.$

Being write as functional form is:

p _w=F(q)

In formula: p _w=[p _w1, p _w2, Λ p _wN] ^t, q=[q ₁, q ₂, Λ q _n] ^t.

The coupling of pit shaft and oil reservoir needs two preconditions: one is the fluid flow balance in the fluid flow and horizontal wellbore of oil reservoir inflow horizontal well; Two is that pressure drop in pit shaft internal drop and oil reservoir is equal at borehole wall place, and utilize this condition, obtain the coupling model of pit shaft-oil reservoir in conjunction with pit shaft model equation and reservoir model equation, solve coupling model by iterative method, Iteration is as follows:

$\left\{\begin{array}{c}{q}^{n+1}=A^{-1}B\left(p^n\right)\\ p^{n+1}=F\left(q^{n+1}\right)\end{array}\right.$

By initial value start, using iterative form successively iteration produces new pressure vector and radial inflow vector, until the knots modification of p, q is less than certain error amount.

In order to consider the anisotropy factor of reservoir permeability, introducing transition matrix D and carrying out spatial alternation, being isotropic space of equal value by anisotropic permeability space transforming, and then carrying out solving of model.Transition matrix D form is as follows:

$D=\left[\begin{array}{ccc}a& 0& 0\\ 0& b& 0\\ 0& 0& c\end{array}\right]$

Wherein:

$a=\sqrt{K_y{K}_z}/\sqrt[3]{K_x{K}_y{K}_z}$

$b=\sqrt{K_x{K}_z}/\sqrt[3]{K_x{K}_y{K}_z}$

$c=\sqrt{K_x{K}_y}/\sqrt[3]{K_x{K}_y{K}_z}$

All directions permeability K=(Kx, Ky, Kz) in isotropism oil reservoir after conversion ^1/3, there is following change in the geometric parameter before and after conversion in space:

x'=a·x

y'=b·y

z'=c·z

h'=c·h

In formula, the hole angle of θ-complex structural well well section; The azimuth of φ-complex structural well well section; Complex structural well well segment length in l ', l-isotropism oil reservoir, anisotropic reservoir; The radius of complex structural well well section in rw ', rw-isotropism oil reservoir, anisotropic reservoir; The reservoir thickness of h '-isotropism oil reservoir.

Oil reservoir after space transforming process and Multilateral Wells morphological parameters are inputted productivity prediction model, the pressure distribution after considering anisotropy factor and production capacity can be obtained.Fig. 4 is the pressure distribution field in eight kinds of different permeability anisotropy's situations, wherein, Kx=20 in a ~ d scheme, 40,60,80 × 10-3 μm 2, Ky=30 × 10-3 μm 2; Ky=20 in e ~ h scheme, 40,60,80 × 10-3 μm 2, Kx=30 × 10-3 μm 2.Can find out in figure, oil reservoir anisotropy can produce obvious impact to pressure field distribution, and along with X-direction permeability increases gradually, fishbone horizontal well pressure field deflects to the left, along with Y-direction permeability increases gradually, fishbone horizontal well pressure field deflects to the right.

For the process of reservoir heterogeneity, s-K* method is adopted to calculate epidermis s and overall permeability K*, to permeability, the impact of each The Small Well section is added in each well section with the form of skin factor by each, thus embodies formation heterogeneity to the impact of well capacity.K* is assumed to be a diagonal tensor, shown in being expressed as follows, and can by changing average power exponent to describe different geological conditionss.

$K_{\mathrm{dd}}^{*}={\left(\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{K_{\mathrm{dd}}}^{{\mathrm{\ω}}_{\mathrm{dd}}}\left(x_i\right)\right)}^{1/{\mathrm{\ω}}_{\mathrm{dd}}}$

Wherein the power exponent ω of all directions can difference (-1≤ω≤1).

The zero dimension expression formula of epidermis is:

$s=(\frac{K}{K_a}-1)\ln \frac{r_a}{r_w}$

Wherein K _afor contaminated zone permeability, K is oil reservoir mean permeability, r _afor contaminated zone radius.

According to actual geology, the development parameters (table 1) of well in a specific embodiment, calculate respectively according to different Productivity Formulae, contrast the computational accuracy (table 2) of existing equivalent flow resistance method and proposed PRODUCTION FORECASTING METHODS, can find out, equivalent flow resistance method error of calculation is comparatively large, and segmented couples model accuracy is higher.

Table 1 calculating parameter table

Table 2 result of calculation contrast table

Claims (8)

1. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples, is characterized in that, the PRODUCTION FORECASTING METHODS of this fishbone horizontal well segmented couples comprises:

Step 1, adopts split plot design to carry out segment processing to complex structural well;

Step 2, sets up wellbore flow model;

Step 3, adopts alternative manner to solve the equation group of Coupled with Flow in the flowing of oil reservoir inner fluid and pit shaft;

Step 4, carries out solving of model after carrying out spatial alternation; And

Step 5, adopts the heterogeneous situation of s-K* method formation to process.

2. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 1, it is characterized in that, in step 1, according to this segment processing method, to obtain in producing well section certain a bit of gesture that any point produces in oil reservoir, then derive the gesture of gesture that this well section produces in reservoir boundary and the generation of pit shaft inner boundary according to mirror image and gesture principle of superposition.

3. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 1, it is characterized in that, in step 1, along well track, pit shaft is divided into some one dimension segments, the control volume that each section is simulated as Wellbore Flow, be made up of the flow path of section node and section, its parameter comprises length, internal diameter, friction factor and inclination angle, Fluid Control Equation in all about horizontal well pit shaft and parameter are all defined in these sections, and the coupling of flow through oil reservoir and Wellbore Flow is carried out for each section, namely by the segment processing of pit shaft, consider that each section along the flowing of pit shaft direction and the impact that becomes a mandarin of oil reservoir radial direction, pit shaft mass variable flow is described.

4. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 1, it is characterized in that, in step 2, this wellbore flow model comprising three parts such as friction pressure pressure drop, gravitational pressure pressure drop and the pressure drop of acceleration pressure is set up according to the equation of momentum.

5. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 4, it is characterized in that, in step 2, consider that borehole wall stratum becomes a mandarin the impact of interference on the pressure drop of pit shaft acceleration and friction pressure drop, realizes the Wellbore Flow feature interpretation under stratum filtration and wellbore tubular stream coupling condition.

6. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 1, it is characterized in that, in step 3, flow through oil reservoir and the wellbore flow model of simultaneous coupling carry out numerical solution, try to achieve pressure and the influx distribution of each well section, thus obtain pressure and the flow of whole pit shaft.

7. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 1, it is characterized in that, in step 4, in order to consider the anisotropy factor of reservoir permeability, theoretical according to Seepage In An Anisotropic Reservoir, introduce transition matrix D and carry out spatial alternation, be isotropic space of equal value by anisotropic permeability space transforming, and then carry out solving of model.

8. the PRODUCTION FORECASTING METHODS of fishbone horizontal well segmented couples according to claim 1, it is characterized in that, in steps of 5, calculate epidermis s and overall permeability K*, to permeability, the impact of each The Small Well section is added in each well section with the form of skin factor by each, thus embodies formation heterogeneity to the impact of well capacity.