Unit test async methods C#

I've a problem)

I try to reproduсe something like several sp (stored procedure) calls in my c# code, but i want to do it in async way.

TSQL example: ( Execute sp @key = 15072000173475; Execute sp @key = 15072000173571; ... Execute sp @key = n;)

[TestClass]
public class UnitTestNomenclature {
    [TestMethod]
    public void ParallelSQLMethod() {
        Task scropeTasks = null;
        //real amount is more then 1500
        long[] keys = new long[] {15072000173475,15072000173571 ... n };

        try {
            var tasks = keys.Select( i =>  Task.Run(async () => { await RunStoredProc(i); }));
            scropeTasks =  Task.WhenAll(tasks);

            scropeTasks.Wait();
        } catch (Exception ex) {
            Debug.WriteLine("Exception: " + ex.Message);

            Debug.WriteLine("IsFaulted: " + scropeTasks.IsFaulted);
            foreach (var inx in scropeTasks.Exception.InnerExceptions) {
                Debug.WriteLine("Details: " + inx.Message);
            }
        }

        Assert.AreEqual(1, 1);
    }

    public async Task RunStoredProc(long scollNumbParam) {
        const string strStoredProcName = @"[dbo].[sp]";
        using (SqlConnection conn = new SqlConnection(@"data source=SERVER;initial catalog=Db;integrated security=True;Trusted_Connection=Yes;")) {
            await conn.OpenAsync();
            Debug.WriteLine("============================================ Connection is open: ==============================================");

            // info
            Debug.WriteLine(String.Format("Connection: {0}", conn.ClientConnectionId));
            Debug.WriteLine(String.Format("State: {0}", conn.State.ToString()));

            using (SqlCommand cmd = new SqlCommand(strStoredProcName, conn) { CommandTimeout = 120, CommandType = CommandType.StoredProcedure }) {

                SqlParameter scrParam = new SqlParameter() {
                    ParameterName = "@KEYKRT",
                    Value = scollNumbParam,
                    SqlDbType = SqlDbType.BigInt
                };
                cmd.Parameters.Add(scrParam);

                Debug.WriteLine("Start of Proccesing: " + scollNumbParam);
                await cmd.ExecuteNonQueryAsync().ConfigureAwait(false);
                Debug.WriteLine("End of Proccesing: " + scollNumbParam);

            }
        }

        Debug.WriteLine("============================================ Connection is closed: ==============================================");
    }
}

This's what i get in output window:

========== Connection is open: ========
Connection: 5be9c681-6eb5-422f-a22c-b49689a2d912
State: Open
Start of Proccesing: 15072000173475
========== Connection is open: ==========
Connection: cfb66041-6646-4b56-be1c-2afb26a18cb8
State: Open
Start of Proccesing: 15072000173571
.....
End of Proccesing: 15072000173475
=========== Connection is closed: =========
End of Proccesing: 15072000173571
=========== Connection is closed: =========

....

A timeout occurred while waiting for memory resources to execute the query in resource pool 'default' (2). Rerun the query.
Actual error number: 8645
Actual line number: 98

Also debug says that connection pool is overflowed I think main reason that connection doesn't appropriatly dispose, but how i can achive that with async?

If i try just open one connection before the async tasks are declared and pass this to my RunStoredProc method then i get connection doesn't support MultipleActiveResultSets

using (SqlConnection conn = new SqlConnection(@"data source=SERVER;initial catalog=Db;integrated security=True;Trusted_Connection=Yes;)) {

                    conn.OpenAsync();
                    var tasks = keys.Select(i => Task.Run(async () => { await RunStoredProc(i, conn); }));
                    scropeTasks = Task.WhenAll(tasks);

                    scropeTasks.Wait();
                }

                Debug.WriteLine("========== Connection is closed: ==========");

This's what i get in output window:

Connection: 5be9c681-6eb5-422f-a22c-b49689a2d912
State: Open
Start of Proccesing: 15072000173475
======= Connection is open: =============
Connection: cfb66041-6646-4b56-be1c-2afb26a18cb8
State: Open
Start of Proccesing: 15072000173571
========= Connection is open: =========