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p_{u,\rm 11}(t \rightarrow \infty) \rightarrow \frac{t}{c_t V_{\phi, 1}}

p_{u,\rm 01}(t \rightarrow \infty) \rightarrow \frac{t}{c_t V_{\phi,20}}

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1. Start with true UTRs 

   LaTeX Math Inline
   body \displaystyle p_{u, ik}(t)

   with the same LTR asymptotic

   LaTeX Math Inline
   body \displaystyle p_{u, ik}(t) \rightarrow \frac{t}{RS}

   .
2. Select injector W₀ 
   1. Select producer W₁
      1. Perform two convolution tests to account for the impact from {W₂ .. W_N} production on to DTR_11

         LaTeX Math Inline
         body p_{u, 11}(t)

          and CTR_01

         LaTeX Math Inline
         body p_{u, 01}(t)

         :
         • Test #1 – DTR_11
           
           • Calculate historically-averaged average rate for each producer: 

             LaTeX Math Inline
             body \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m)

           • Calculate interfering DTR_11: 

             LaTeX Math Inline
             body \displaystyle p^*_{u, 11}(t) = p_{u, 11}(t) + \sum_{k \neq 1} p_{u, k1}(t) \cdot q^*_k

             , meaning that injector W₀ is shut-down and all producers are working with constant rates 

             LaTeX Math Inline
             body q^*_k

             , except producer W₁ which is working with unit-rate
         •  Test #2 – CTR_01
           • Calculate historically-averaged average rate for each producer: 

             LaTeX Math Inline
             body \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m)

           • Calculate interfering CTR_01: 

             LaTeX Math Inline
             body \displaystyle p^*_{u, 01}(t) = p_{u, 01}(t) + \sum_{k} p_{u, k1}(t) \cdot q^*_k

             , meaning that injector W₀ is working with unit-rate and all producers are working with constant rates 

             LaTeX Math Inline
             body q^*_k

      2. Calculate injection share constant: 

         LaTeX Math Inline
         body \displaystyle f_{01} = \frac{\dot p^*_{01}(t)}{\dot p^*_{11}(t)} \Bigg|_{t \rightarrow \infty}

          as LLS over equation: 

         LaTeX Math Inline
         body \displaystyle \dot p^*_{01}(t) = f_{01} \cdot \dot p^*_{11}(t)

   2. Repeat the same for other producers (starting from point 2a onwards)
3. Repeat the same for other injectors (starting from point 2 onwards)

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